The numbers set within the text of this edition refer to the corresponding lines of the Greek text in the great modern
edition of Aristotle’s work published between 1831 and 1870 by the Berlin Academy. The pagination of the Berlin edition
has become the customary means by which to locate a passage of Aristotle. A reference to, say, Metaphysics xii. 10.
1075a25 would place the passage in question in Chapter 10 of Book 12 of the Metaphysics, on line 25 of the first column,
i. e., column a, of page 1075 of the Berlin edition.
Copyright © 1941 by Random House, Inc.
Biographical note copyright © 1947 by Random House, Inc.
Introduction copyright © 2001 by C.D.C. Reeve
All rights reserved under International and Pan-American Copyright Conventions. Published in the United States by
Modern Library, an imprint of The Random House Publishing Group, a division of Random House, Inc., New York, and
simultaneously in Canada by Random House of Canada Limited, Toronto.
MODERN LIBRARY and the TORCHBEARER Design are registered trademarks of Random House, Inc.
LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA
Aristotle.
[Selections. English. 2001]
The basic works of Aristotle / edited by Richard McKeon; introduction by C.D.C. Reeve
p.
cm.—(Modern Library classics)
Originally published: New York: Random House, © 1941. With new intro.
eISBN: 978-0-307-41752-7
1. Philosophy.
I. McKeon, Richard Peter, 1900— II. Title. III. Series.
B407 .A2713 2001
185—dc21
2001030607
Modern Library website address: www.modernlibrary.com
v3.1_r1
ARISTOTLE
Aristotle was born in 384/3 B.C. in the little town of Stagira on the
eastern coast of the peninsula of Chalcidice in Thrace. His father,
Nicomachus, was court physician and, according to tradition, friend of
Amyntas II, king of Macedon and father of Philip the Great. Nicomachus
died while Aristotle was still a child, and he was raised by Proxenus of
Atarneus, whose son Nicanor was later adopted, in turn, by Aristotle and
was married to Aristotle’s daughter. In 368/7, at the age of eighteen,
Aristotle was sent to Athens, where he remained in close association
with the Academy of Plato for twenty years, until the death of Plato in
348/7. After Plato’s death he left Athens and, together with Xenocrates,
visited the court of Hermias, a former member of the Academy who had
become tyrant of Assos and Atarneus in Mysia in Asia Minor. Aristotle
married Hermias’ niece Pythias, and he probably taught at a kind of
Academic center in Assos. Somewhat later he went to Mitylene in
Lesbos, where he doubtless engaged in biological research. In 343/2, on
the invitation of Philip of Macedon, he became tutor to Alexander. The
instruction probably extended only to 340, when Alexander was
appointed regent for his father, but his tutor did not return to Athens
until 335/4, a year after the death of Philip.
The next twelve years Aristotle devoted with extraordinary industry to
the establishment of a school, the Lyceum, to the institution and pursuit
of a program of investigation, speculation, and teaching in almost every
branch of knowledge, and to the composition of all, or most, or at least
the more scientific portions, of those of his writings which are now
extant. When Alexander died in 323, Aristotle’s Macedonian connections
brought him under suspicion and he fled Athens lest, as he is said to
have remarked, the Athenians sin twice against philosophy. An
accusation of impiety was brought against him, not unlike those which
had been brought against Anaxagoras and Protagoras or that on which
Socrates had been condemned. The specific charge was that he had
instituted a private cult in the memory of his friend Hermias, since he
had erected a statue to him at Delphi and had composed a poem, in
what was alleged to be the manner of a paean, in his honor. He took
refuge under the protection of Antipater, viceroy to Alexander, in
Chalcis in Euboea, where he died in 322 a short time before the death of
Demosthenes.
Most of the scant information that has come to us concerning the life
of Aristotle is suggestive, but there is little positive evidence, in his
works or in external sources, to support inferences concerning the
formative forces that influenced his work. Since his father was a
physician, he was a hereditary member of the guild of Asclepiads, and it
is tempting to speculate on the youthful beginnings of his interest in
biological investigations and his possible training in dissection,
pharmacology, and medicine; but his father died when he was young,
and there is no evidence in his works of an early training in medicine.
He spent twenty years in the Academy; that period has been used as
evidence of a close association with Plato which resulted in a deep
impress on his thought, but it has also been argued, by scholars like
Burnet and Taylor, that Plato was not in the Academy at the time of
Aristotle’s arrival, that he was away for repeated and lengthy periods
during Aristotle’s stay, and that Aristotle’s knowledge of Platonism was
acquired at secondhand and was never accurate. We do not know how
he spent his time at the Academy: there is an ancient tradition that he
undertook the teaching of rhetoric in opposition to the flourishing school
of Isocrates; it seems probable that he participated in the biological
research which was flourishing at the Academy; the fragments of his
early dialogues suggest that he wrote works intended to popularize
Platonism. His reasons for leaving Athens on the death of Plato can only
be conjectured: he may have been dissatisfied with the prospects of the
Academy under Plato’s nephew and successor Speusippus, who seemed
to Aristotle to have reduced metaphysics to mathematics, or Speusippus
may have charged Aristotle and Xenocrates to open a branch of the
Academy in Asia Minor. He probably taught in Assos; there is evidence
in his biological writings that he collected specimens of animals and fish
in Lesbos and in the waters adjacent to the island; he doubtless began
the composition of some of the works that have survived during his
travels.
In spite of the fact that the relation between Aristotle and Alexander
has been a tempting subject for speculation since Plutarch and that the
ambition to influence kings through philosophy was deeply implanted in
the Academy, there is no evidence that Aristotle had any influence on
the moral ideals or political ambitions of his royal pupil, and Aristotle in
turn seems to have taken no account of the effects of the ideal of world
empire on the forms of political association and on the possible survival
of the Greek city-state. There is good reason to doubt the accuracy of the
legend that Alexander sent records of astronomical observations and
biological specimens to his former master from the East. His writings
contain interesting sidelights on the methods and adjuncts of teaching in
the Lyceum, but the relation of his writings to the work of the Lyceum,
and even the order of their composition, are far from clear. Since they
are obviously not “published” works, it has been supposed that they are
“lecture-notes,” notes of students, or records of research and thought,
brought periodically up to date, for consultation by advanced students.
Since the structure of his doctrines is complex, and since he was long
associated with the Academy and later a persistent critic of the doctrines
of the Academy, his works have been chopped into pieces by critics
seeking an evolution in them from Platonic idealism to scientific
empiricism.
The period of Aristotle’s manhood coincided with the reduction of the
Greek city-states to the hegemony of Macedonia and the twelve or
thirteen years of his work in the Lyceum with the campaigns of
Alexander the Great. Hermias was doubtless a kind of advance-guard of
Philip’s projects against the Persians; Philip’s choice of Aristotle as tutor
to Alexander associated him closely with the political fortunes of
Macedonia; and Alexander doubtless suspected him of complicity in the
plot against his life for which Aristotle’s nephew Callisthenes was
executed; it is highly probable that the Lyceum received support and
endowments from Callisthenes, Antipater, or even Alexander. In an
important sense an epoch of Greek history was brought to a close when
Alexander, Aristotle, and Demosthenes all died within somewhat more
than a year.
The life of Aristotle was thus spent in a period which has seemed
confused and dim to historians who have learned from Demosthenes to
see it as the time of the loss of Greek liberties and the decline of Greek
ideals; it has seemed a period of stirring action which came close to the
fulfillment of an ambitious hope to those who see in the growth of
panhellenism preached by Isocrates the beginnings of more stable
political organizations and in the exploits of Alexander the spread of
Greek ideals. Aristotle spent a large part of his life as an alien in Athens,
and he seems to have been unsympathetic with, if not unmindful of, the
ambitions of Alexander. Contemporary political events and social
changes left few marks on his political and moral philosophy, and the
search for effects of social conditions in his metaphysics and in his
contributions to science has led only to speculative generalizations
concerning the influence of environment on thought: to the conclusion
that the existence of classes in society suggested hierarchies in his
conception of the universe, that slave labor led him to neglect the
mechanical arts and prefer the theoretic to the practical sciences, that
his theories were therefore verbal rather than based on the resources of
experience, and that his physical principles reflected his conception of
political rule. Apart from such speculations, it is clear that the peace
which was forced on Athens by Macedonian domination permitted
Aristotle to organize a course of studies and to initiate a vast scheme of
research into the history of political organizations, of science, and
philosophy—the study of constitutions of Greek states, of the history of
mathematics and medicine, and of the opinions of philosophers—as well
as into the natural history of minerals, plants, and animals, and to lay
the foundations thereby for one of the first attempts at an encyclopedic
organization of human knowledge.
Richard McKeon
CONTENTS
Cover
Title Page
Copyright
BIOGRAPHICAL NOTE
How to Use Chapter and Footnote Links
PREFACE by Richard McKeon
INTRODUCTION by C.D.C. Reeve
ORGANON (The collection of Aristotle’s logical treatises)
CATEGORIAE (Categories) (complete)
DE INTERPRETATIONE (On Interpretation) (complete)
ANALYTICA PRIORA (Prior Analytics) (Book I, Chapters 1–7, 13, 23–31; Book II, Chapters
16–27)
ANALYTICA POSTERIORA (Posterior Analytics) (complete)
TOPICA (Topics) (Book I; Books II–VIII omitted)
DE SOPHISTICIS ELENCHIS (On Sophistical Refutations) (Chapters 1–3 and 34; [Chapters 4–
33 omitted])
PHYSICA (Physics) (complete)
DE CAELO (On the Heavens) (Books I, II [Chapters 13 and 14], III and
IV; [Chapters 1–12 of Book II omitted])
DE GENERATIONE ET CORRUPTIONE (On Generation and Corruption)
(complete)
DE ANIMA (On the Soul) (complete)
PARVA NATURALIA (The Short Physical Treatises)
DE MEMORIA ET REMINISCENTIA (On Memory and Reminiscence) (complete)
DE SOMNIIS (On Dreams) (complete)
DE DIVINATIONE PER SOMNUM (On Prophesying by Dreams) (complete)
HISTORIA ANIMALIUM (The History of Animals) (Book V, Chapter 1;
Book VIII, Chapter 1; Book IX, Chapter 1)
DE PARTIBUS ANIMALIUM (On the Parts of Animals) (Book I, Chapters
1–5; Book II, Chapter 1)
DE GENERATIONE ANIMALIUM (On the Generation of Animals) (Book
I, Chapters 1, 17–18, 20–23)
METAPHYSICA (Metaphysics) (complete)
ETHICA NICOMACHEA (Nicomachean Ethics) (complete)
POLITICA (Politics) (complete)
RHETORICA (Rhetoric) (Books I and II complete; Book III, Chapters 1,
13–19 [Chapters 2–12 omitted])
DE POETICA (Poetics) (complete)
Kunsthistorisches Museum, Vienna
ARISTOTLE
How to Use Chapter and Footnote Links
This eBook edition allows you to click to specific sections via the chapter
and footnote links included throughout the text.
At the beginning of each work, you can click on the individual chapter
numbers in the Contents listing to go to a specific section of that work.
Click the number at the start of that section to go back to the Contents
listing.
Within the works, you can click on footnotes to access explanatory notes
or references to other works. Click the number at the beginning of a
footnote to return to your place within the text.
PREFACE
The study of an ancient writer might appropriately envisage one or
more of three objectives: the re-discovery and appreciation of past
accomplishments and thoughts, the assemblage for present employment
of odd, edifying, or useful items of information or knowledge, or the
inquiry into truths whose specifications do not change with time.
Although these three ends sometimes coincide in the reading of a
philosopher who has been studied for centuries, the usual fate of
philosophers, notwithstanding the concern for truth evinced in their
writings, is to suffer doctrinal dismemberment by later philosophers and
to undergo at the hands of historians and philologists reconstructions in
which doctrine is barely discernible. As a result of the possible
diversification of these ends, the influences that have been attributed to
the thoughts of philosophers are not always easily calculable from
examination of their own statements, yet the paradoxes, no less than the
cumulative lines of progress, in intellectual history suggest the three
ideals relevant to an introduction to the philosophy of Aristotle and
selections from his works.
An introduction to the works of a philosopher should, first, since it is
intended to supply aids to understanding the man and his thought, be
specific and clear in its authentication of the information it conveys. The
words of the philosopher himself are the best means by which to achieve
such authenticity, and therefore the works of Aristotle have been
reproduced intact and unabridged so far as the generous limits of space
in this large volume have made such reproduction practicable and,
where omissions have been unavoidable, the fact of the omission and the
character of the omitted portions have been indicated as explicitly as
possible. To select and rearrange small fragments of a philosopher’s
works is to recompose them and often to alter the doctrines they express.
Therefore instead of parcels and snatches selected and pieced together
with an eye to what seems more likely to catch the interest of the reader,
the entire texts of seven of the most important books are included, and
even when omissions have been made from the other seven works of
which parts are published in this edition, entire books or entire chapters
have been retained.
The vast labors which have been expended on the text of Aristotle
during the last century have greatly facilitated the study of his
philosophy. The monumental Oxford translation of his works into
English, completed in 1931, was made possible by antecedent scholarly
efforts, in which philologists have engaged at least since the publication
of the great modern edition of Aristotle’s works by the Berlin Academy
between 1831 and 1870, to determine and to clarify what Aristotle says.
That translation is readable and makes Aristotle’s philosophy available
to readers untrained in Greek as no previous English translation had. The
eleven volumes of the Oxford translation can be reduced to a single
volume, once the clearly inauthentic works have been excluded from
consideration, without too serious loss of portions that bear on problems
of general philosophic interest. The texts of seven works are complete:
the Physics, On generation and corruption, On the soul, the Metaphysics, the
Nicomachean ethics, the Politics, and the Poetics. For the most part
omissions are from the four biological works; several of the Short natural
treatises are omitted; of the physical works only the Meteorology and a
portion of one of the four books of On the heavens are omitted; similarly
three of the six books of the Organon and one of the three books of the
Rhetoric are in part omitted; the Constitution of Athens is not included. Of
the works which are commonly held to be authentic only three are not
reproduced even in partial selection—the Meteorology, On the progression
of animals, and the Constitution of Athens; or, if the tendency to accept On
the motion of animals and the Eudemian ethics as genuine is justified, the
number omitted is five, although it might be held, since three books of
the Nicomachean ethics appear without alteration in the Eudemian ethics,
that selections from the latter work may be found in the text of the
former.
Explanatory notes and cross references by which difficult passages and
interrelations have been elucidated by the translators have for the most
part been retained. Purely philological notes, on the other hand, have
been omitted, although major problems which have led to emendations,
interpolations, and transpositions are indicated. The pagination of the
Bekker edition of the Greek text of Aristotle, which is published in the
first two of the five volumes of the Berlin edition, has become the
customary means to locate a passage in Aristotle, and it has therefore
been reproduced within the text of the present edition. Thus, a reference
to, say, Metaphysics xiii. 4. 1078b27, would place the passage in question
in Chapter 4 of Book 13 (or Book M) of the Metaphysics, on line 27 of the
second column, i. e. column b, of page 1078 of the Berlin edition. Since
the two volumes are paged continuously, no special designation of the
volumes is needed; since the line references are to lines in the Greek
text, they are of course only approximate in the English translation.
To make a difficult writer like Aristotle available in translation
without, in the second place, supplying the dubious reader with more
specific and urgent motivation for study than the recommendation that
Aristotle is of the select group of timelessly great philosophers would
scarcely constitute adequate introduction to his philosophy. For good or
evil our interests and our erudition are grounded in the age in which we
live, and the justice of our view of the past is moderated by the
contemporary angle which can never be wholly removed from the
perspective in which we see it. The words, the aphorisms, the
distinctions, and even the ideas of Aristotle have in many instances
become commonplaces in our culture and in other instances have been
made the familiar whipping horses by which we castigate old errors and
so boast of our own advances. It is wise to profit by our limitations and
to make the familiar vestiges of a philosopher’s thoughts in present-day
inquiries and interests the beginning point of the study of his
philosophy. The ordered presentation of Aristotle’s doctrines in the
Introduction finds its emphases precisely in such vestigial remains
selected as points of interest for the reader who comes to Aristotle for
renewed acquaintance or for the first time.
An introduction to a philosopher which did no more than confirm the
student in established opinions, or an edition whose apparatus did no
more than supply the reader with instruments by which to find what he
had conceived to be useful prior to his reading of the philosopher and
prior to philosophic analysis of his standards of utility, would aid the
reader to find what he was looking for but at the expense of its subject,
for the philosophy would almost certainly not be understood, and
misconceived philosophic doctrines, however ingeniously contrived, are
of doubtful ultimate utility. The third objective of an introduction to the
works of a philosopher, to which the preceding two must be subordinate
since there is no adequate reason for reading the works of a philosopher
other than the philosophy they express, is more easily obscured than
achieved by aids to reading or to philosophy. Some aid is needed,
however, and therefore a method of reading Aristotle’s works is
suggested in the Introduction by a brief statement of the interrelations
and continuity of his doctrines. The reader is advised to treat this
interpretation skeptically until and unless he can find it confirmed in his
own reading of the text, for it is useful only as a device by which to
permit Aristotle to speak for himself. The achievement of Aristotle can
be discovered only by reading and rereading his works, and the
appreciation of that achievement depends quite as much on the
deepened sense of value and the precision of criteria which he inculcates
as on the materials he treats. The Middle Ages may seem to have
exaggerated in calling him the Philosopher, but the understanding of
what he said is still an unparalleled introduction to philosophy.
It is as difficult to reconstruct some notion of the appearance of
Aristotle as to determine the lineaments and characteristics of his
thought. The representation of him which was most familiar a
generation ago, the statue in the Palazzo Spada in Rome, is almost
certainly not a portrait of Aristotle. It was long supposed to be Aristotle
because of its fragmentary inscription which should in all probability be
restored more correctly as “Aristippos,” and in any case the head does
not belong to the statue. The portrait reproduced as the frontispiece, a
bust in the Kunsthistorisches Museum in Vienna, has rather better claim
to rank as a genuine portrait of Aristotle, although the identification
rests on a tortuous argument. As proposed by Studniczka (Das Bildnis des
Aristoteles; Leipzig, 1908), the identification goes back to a bust which
was found in Rome about 1590 and which was bought by the learned
antiquary Fulvio Orsini. It was identified by an inscription on its base.
This bust is lost, but two drawings, one of them by Rubens, have
survived. A family of twelve busts, varying in quality, preservation, and
probable date, has been assembled, which seem, from their close
correspondence, not only to represent one man but to imitate one
original portrait, and which further, from their similarity to two
drawings of the lost bust, may be portraits of Aristotle. The identification
is plausible, though by no means certain. The style places the original
portrait approximately in the time of Aristotle, and of the twelve extant
busts the Vienna head probably gives the best idea of the original. The
nose is almost entirely modern, but there is little other restoration.
Several features ascribed to Aristotle by ancient tradition may be seen in
these portraits: small eyes, short beard, and thinning hair.
Grateful acknowledgment is hereby extended to the Oxford University
Press for permission to reprint the translation of the works of Aristotle
prepared under the editorship of W. D. Ross. The arduous task of reading
proof, checking quotations, and preparing the enormous materials of this
volume for publication was rendered manageable by the assistance of
Dr. Herbert Lamm and Dr. Meyer W. Isenberg, while the actual
consummation of the task was not only facilitated by the co-operation of
the staff of Random House, but is largely due to the jogging
encouragement and reproaches of Mr. Bennett A. Cerf and Mr. Saxe
Commins.
RICHARD MCKEON
INTRODUCTION
C.D.C. Reeve
Aristotle’s Writings
A list of Aristotle’s papers, probably made in the third century B.C.,
seems to describe most of his extant writings, as well as a number of
works—some in dialogue form—that are now lost. When Sulla captured
Athens in 87 B.C., these papers were brought to Rome, where they were
edited, organized into different treatises, and arranged in a logical
sequence by Andronicus of Rhodes in around 30 B.C. Most of the writings
he thought to be genuinely Aristotelian have been transmitted to us via
manuscript copies produced between the ninth and the sixteenth
centuries.
These writings, of which the present volume include a rich selection,
may be classified as follows: logic, dialectic, metaphysics: Categories, On
Interpretation, Prior Analytics, Topics, On Sophistical Refutations,
Metaphysics; science and philosophy of science: Posterior Analytics,
Physics, On the Heavens, On Generation and Corruption, Meteorology,
History of Animals, On the Parts of Animals, On the Motion of Animals, On
the Progression of Animals, On the Generation of Animals; psychology and
philosophy of mind: On the Soul, Sense and Sensibilia, On Memory and
Reminiscence, On Sleep, On Dreams, On Prophesying by Dreams, On Length
and Shortness of Life, On Youth, Old Age, Life and Death, Respiration; ethics
and politics: Nicomachean Ethics, Magna Moralia, Eudemian Ethics, Politics,
Rhetoric, Constitution of Athens; aesthetics: Poetics.
The most credible view of these writings is that they are lecture notes
written or dictated by Aristotle himself and not intended for publication.
Their organization into treatises and the internal organization of the
treatises into books and chapters may, however, not be his. No doubt
this accounts for some, though not all, of their legendary and manifest
difficulty.
The Aristotelian World
Of the various things that exist in the world described in Aristotle’s
writings, “some exist by nature, some from other causes” (Physics 192b8–
9). Those that exist by nature have a nature of their own, an internal
source of movement, growth, and alteration (192b13–15). Thus, for
example, a feline embryo has within it a source that explains why it
grows into a cat, why that cat moves and alters in the ways it does, and
why it eventually decays and dies. A house or any other artifact, by
contrast, has no such source within it; instead, the source is “in
something else external to the thing,” namely, the craftsman who
manufactures it (Physics 192b30–31; also Metaphysics 1032a32–b10).
A thing’s nature is the same as its essence or function, which is the
same as its end, or that for the sake of which it exists. For its end just is
to actualize its nature by performing its function (Nicomachean Ethics
1168a6–9), and something that cannot perform its function ceases to be
what it is except in name (On the Parts of Animals 640b33–641a6, Politics
1253a23–25). Aristotle’s view of natural beings is therefore teleological:
He sees them as being defined by an end (telos) for which they are
striving, and as needing to have their behavior explained by reference to
it. It is this end, essence, or function that fixes what the good for that
being consists in, and what its virtues or excellences are (Nicomachean
Ethics 1098a7–20, Physics 195a23–25).
Most natural things, as well as the products of art or craft, are
hylomorphic compounds, compounds of matter (hulě) and form
(morphě). Statues are examples: Their matter is the stone or metal from
which they are made; their form is their shape. Human beings are also
examples: Their matter is (roughly speaking) their body; their soul is
their form. Thus a person’s soul is not something separable from his
body, but is more like the structural organization responsible for his
body’s being alive and functioning appropriately.
While the natures of such compounds owe something to their matter
and something to their form, what they owe to form is more important
(Metaphysics 1025b26–1026a6, Physics 193b6–7). For example, a human
being can survive through change in his matter (we are constantly
metabolizing), but if his form is changed, he ceases to exist (Politics
1276b1–13). That is why the sort of investigation into human beings we
find in De Anima and in ethical and political treatises focuses on souls
rather than bodies.
These souls consist of distinct, hierarchically organized constituents
(Nicomachean Ethics, bk. I, ch. 13). The lowest rung in the hierarchy is
the vegetative soul, which is responsible for nutrition and growth, and
which is also found in plants and other animals. At the next rung up, we
find appetitive soul, which is responsible for perception, imagination,
and movement, and so is present in other animals too, but not in plants.
This sort of soul lacks reason but, unlike the vegetative, can be
influenced by it. The third element in the human soul is reason. It is
divided into the scientific element, which enables us to contemplate or
engage in theoretical activity, and the calculative or deliberative
element, which enables us to engage in practical and political activity
(Nicomachean Ethics 1097b33–1098a8, 1139a3–b5).
Because the human soul contains these different elements, the human
good might be defined by properties exemplified by all three of them or
by properties exemplified by only some of them. In the famous function
argument from the Nicomachean Ethics, bk. I, ch. 7, Aristotle argues for
the latter alternative: The human good is happiness, which is “an active
life of the element that has a rational principle” (1098a3–4). The
problem is that the scientific and the deliberative element both fit this
description. Human happiness might, therefore, consist in practical
political activity, or in contemplative theorizing, or in a mixture of both.
Even a brief glance at Nicomachean Ethics, bk. X, chs. 6–8 will reveal
how hard it is to determine which of these Aristotle has in mind.
Aristotelian Sciences
The Aristotelian sciences provide us with knowledge of the world, how
to live successfully in it, and how to produce what we need to do so.
Hence they fall into three distinct types:
I.
II.
Theoretical sciences: theology, philosophy, mathematics, natural sciences.
Practical sciences: ethics, household management, statesmanship, which is divided into
legislation and politics, with politics being further divided into deliberative science and
judicial science (Nicomachean Ethics 1141b29–32).
III.
Productive sciences (crafts, arts): medicine, building, etc.
Of these, the theoretical ones are the Aristotelian paradigm, since they
provide us with knowledge of universal necessary truths. The extent to
which ethics or statesmanship fit the paradigm, however, is less clear.
One reason for this is that a huge part of these sciences has to do not
with universal principles of the sort one finds in physics, but with
particular cases, whose near infinite variety cannot easily be summed up
in a formula (Nicomachean Ethics 1109b21, Rhetoric 1374a18–b23). The
knowledge of what justice is may well be scientific knowledge, but to
know what justice requires in a particular case one also needs equity,
which is a combination of virtue and a trained eye (Nicomachean Ethics,
bk. V, ch. 10). Perhaps, then, we should think of practical sciences as
having something like a theoretically scientific core, but as not being
reducible to it.
Theoretical Science
Each Aristotelian theoretical science deals with a genus—a natural
class of beings that have forms or essences (Posterior Analytics 87a38–39,
Metaphysics 1003b19–21). When appropriately regimented, it may be set
out as a structure of demonstrations, the indemonstrable first principles
of which are definitions of those essences. More precisely, the first
principles special to biology, or to some other science that applies to
only a part of reality, are like this. Others that are common to all
sciences—such as the principle of non-contradiction and other logical
principles—have a somewhat different character. Since all these first
principles are necessary truths, and demonstration is a type of deductive
inference, scientific theorems are also necessary.
Though we cannot grasp a first principle by demonstrating it from yet
more primitive principles, it must—if we are to have any unqualified
scientific knowledge at all—be “better known” to us than any of the
science’s theorems (Nicomachean Ethics 1139b33–34). This better
knowledge is provided by intuition (nous), and the process by which
principles come within intuition’s ken is induction (1139b28–29,
1141a7–8).
Induction begins with perception of particulars, which gives rise to
retention of perceptual contents, or memories (Posterior Analytics 100a1–
3). From a unified set of such memories experience arises (100a3–6),
“when, from many notions gained by experience, one universal
supposition about similar objects is produced” (Metaphysics 981a1–7).
Getting from particulars to universals, therefore, is a largely
noninferential process. If we simply attend to particular cases—perhaps
to all, perhaps to just one—and have some acumen, we will get there
(Prior Analytics 68b15–29, Posterior Analytics 88a12–17, 89b10–13).
When these universals are appropriately analyzed into their “elements
(stoicheia) and first principles,” they become intrinsically clear and
unqualifiedly known (Physics 184a16–21).
A universal essence is something out there in the world. Its analogue
in a scientific theory, however, is a definition similar in structure to it
(Metaphysics 1034b20–22). That is why the first principles of the sciences
are not essences, but definitions of them.
The inductive path to first principles and scientific knowledge begins
with perception of particulars and of perceptually accessible, unanalyzed
universals, and leads eventually to analyzed universal essences (first
principles) and definitions of them. At this point, induction gives way to
deduction, as we descend from these essences to other principles.
Perception alone cannot reach the end of this journey, but without
perception it cannot so much as begin. Perception, elaborated in theory,
is the soul’s window on the Aristotelian world (Prior Analytics 46a17–18,
On the Soul 432a7–9).
Dialectic
The first principles proper to a science cannot be demonstrated within
that science. If they could, they would not be genuine first principles.
They can, however, be defended by dialectic. For, since it “examines,”
and does so by appeal not to scientific principles but to common or
generally accepted opinions (endoxa), “dialectic is a process of criticism
wherein lies the path to the [first] principles of all inquiries” (Topics
101a36–b4).
Now opinions are endoxa when they are accepted without demurral
“by every one or by the majority or by the wise, either by all of them, or
by most or by the most notable and illustrious of them” (Topics 100b21–
23), so that the majority do not disagree with the wise about them, nor
do either group disagree among themselves (104a8–11). Generally
accepted opinions, therefore, are beliefs to which there is simply no
worthwhile opposition. Apparent endoxa, by contrast, are beliefs that
mistakenly appear to have this uncontested status (100b23–25, 104a15–
33).
Defending first principles on the basis of endoxa is a matter of going
through the difficulties (aporiai) “on both sides of a subject” until they
are solved (Topics 101a35). Suppose, then, that the topic to be
dialectically investigated is this: Is being a single unchanging thing, or
not? A competent dialectician will, first, follow out the consequences of
each alternative to see what difficulties they face. Second, he will go
through the difficulties he has uncovered to determine which can be
solved and which cannot. As a result, he will be well placed to attack or
defend either alternative in the strongest possible way.
Aporematic, which is the part of philosophy that deals with such
difficulties, is like dialectic in its methods, but differs from it in
important respects. In a dialectical argument, for example, the opponent
may refuse to accept a proposition that a philosopher would accept:
“The premises of the philosopher’s deductions or those of the one
investigating by himself, though true and familiar, may be refused
by … [an opponent] because they lie too near to the original
proposition, and so he sees what will happen if he grants them. But the
philosopher is unconcerned about this. Indeed, he will presumably be
eager that his axioms should be as familiar and as near to the question at
hand as possible, since it is from premises of this sort that scientific
deductions proceed” (Topics 155b10–16). Since the truth may well hinge
on propositions whose status is just like these premises, there is no
guarantee that what a dialectician considers most defensible will be true.
Drawing on this new class of endoxa, then, the philosopher examines
both the claim that being is a single unchanging thing, and the claim
that it is not, in just the way that the dialectician does. As a result, he
determines, let us suppose, that the most defensible, or least
problematic, conclusion is that in some senses of the terms, being is one
and unchanging, in others, not. To reach this conclusion, however, he
will have to disambiguate and reformulate endoxa on both sides, partly
accepting and partly rejecting them. Others, he may well have to reject
outright, so that beliefs that initially seemed to be endoxa—that seemed
to be unproblematic—will have emerged as only apparently such (Topics
100b23–25). These he will have to explain away: “We should state not
only the truth, but also the cause of error—for this contributes towards
producing conviction, since when a reasonable explanation is given of
why the false view appears true, this tends to produce belief in the true
view” (Nicomachean Ethics 1154a22–25). If, at the end of this process,
the difficulties are solved and most of the most-authoritative endoxa are
left, that, Aristotle claims, will be a sufficient proof of the philosopher’s
conclusion (1145b6–7).
But in that claim lies a problem. For while dialectic treats things “only
with an eye to general opinion,” philosophy must treat them “according
to their truth” (Topics 105b30–31). Endoxa, however, are just generally
accepted and unobjectionable opinions. Since even such unopposed
opinions may nevertheless be false, how can an argument that relies on
them be guaranteed to reach the truth? The answer lies in aporematic
philosophy’s dialectical capacity to criticize or examine (101b3).
Because he is a generally educated person, an aporematic philosopher
knows what it takes to be a genuine science of whatever sort (On the
Parts of Animals 639a1–8). Hence he will know, for example, what level
of exactness a science should have, given its subject matter, and what we
should and should not seek to have demonstrated (Nicomachean Ethics
1094b23–27, Metaphysics 1006a5–11). Using his dialectical capacity to
examine, therefore, a philosopher can, for example, determine whether a
person, A, has any sort of mathematical knowledge, or is simply a
charlatan. If A passes the examination, the philosopher can use his own
knowledge of what a mathematical science must be like to determine
whether A’s mathematical knowledge is genuinely scientific. If he finds
that it is, he knows that the undemonstrated mathematical first
principles A accepts are true. If, in particular, A accepts that magnitudes
are divisible without limit, the philosopher knows that this is true.
When he uses his dialectical skill to draw out the consequences of this
principle and of its negation, however, he sees difficulties and
supporting arguments based on endoxa on both sides. Since he knows
the principle is true, however, his goal will be to resolve the difficulties
it faces and undo the arguments that seem to support its negation. If he
is successful, he will have refuted all the objections to it, and so will
have provided a negative demonstration, or demonstration by refutation,
of it (Metaphysics 1006a12). Such a demonstration is aporematic
philosophy’s way to a scientific first principle, and constitutes the
sufficient proof of it to which Aristotle refers.
In many texts, Aristotle characterizes problems as knots in our
understanding that dialectic enables us to untie, in others, he
characterizes dialectic itself as enabling us to make first principles clear.
What aporematic philosophy offers us in regard to the first principles of
the sciences, then, is no knots—no impediments to clear and exact
intuitive grasp. And with such clarity comes scientific knowledge of the
most excellent and unqualified sort—knowledge that manifests the
virtue of theoretical wisdom (Nicomachean Ethics 1141a16–17).
The marginal numbers accompanying the text correspond to the page
number, column (represented by the letters a and b), and line of the
edition of Aristotle’s works published in Berlin by Immanuel Bekker in
1831. Line numbers given in citations are those of the Greek text and
correspond only approximately to lines in translations.
Organon
CATEGORIAE
Translated by E. M. Edghill
CONTENTS
CHAPTER
1. Homonyms, synonyms, and derivatives.
2. (1) Simple and composite expressions.
(2) Things (a) predicable of a subject, (b) present in a subject, (c) both predicable of,
and present in, a subject, (d) neither predicable of, nor present in, a subject.
3. (1) That which is predicable of the predicate is predicable of the subject.
(2) The differentiae of species in one genus are not the same as those in another, unless
one genus is included in the other.
4. The eight categories of the objects of thought.
5. Substance.
(1) Primary and secondary substance.
(2) Difference in the relation subsisting between essential and accidental attributes and
their subject.
(3) All that which is not primary substance is either an essential or an accidental
attribute of primary substance.
(4) Of secondary substances, species are more truly substance than genera.
(5) All species, which are not genera, are substance in the same degree, and all
primary substances are substance in the same degree.
(6) Nothing except species and genera is secondary substance.
(7) The relation of primary substance to secondary substance and to all other
predicates is the same as that of secondary substance to all other predicates.
(8) Substance is never an accidental attribute.
(9) The differentiae of species are not accidental attributes.
(10) Species, genus, and differentiae, as predicates, are ‘univocal’ with their subject.
(11) Primary substance is individual; secondary substance is the qualification of that
which is individual.
(12) No substance has a contrary.
(13) No substance can be what it is in varying degrees.
(14) The particular mark of substance is that contrary qualities can be predicated of it.
(15) Contrary qualities cannot be predicated of anything other than substances, not
even of propositions and judgements.
6. Quantity.
(1) Discrete and continuous quantity.
(2) Division of quantities, i. e. number, the spoken word, the line, the surface, the
solid, time, place, into these two classes.
(3) The parts of some quantities have a relative position, those of others have not.
Division of quantities into these two classes.
(4) Quantitative terms are applied to things other than quantity, in view of their
relation to one of the aforesaid quantities.
(5) Quantities have no contraries.
(6) Terms such as ‘great’ and ‘small’ are relative, not quantitative, and moreover
cannot be contrary to each other.
(7) That which is most reasonably supposed to contain a contrary is space.
(8) No quantity can be what it is in varying degrees.
(9) The peculiar mark of quantity is that equality and inequality can be predicated of
it.
7. Relation.
(1) First definition of relatives.
(2) Some relatives have contraries.
(3) Some relatives are what they are in varying degrees.
(4) A relative term has always its correlative, and the two are interdependent.
(5) The correlative is only clear when the relative is given its proper name, and in
some cases words must be coined for this purpose.
(6) Most relatives come into existence simultaneously; but the objects of knowledge
and perception are prior to knowledge and perception.
(7) No primary substance or part of a primary substance is relative.
(8) Revised definition of relatives, excluding secondary substances.
(9) It is impossible to know that a thing is relative, unless we know that to which it is
relative.
8. Quality.
(1) Definition of qualities.
(2) Different kinds of quality:
(a) habits and dispositions;
(b) capacities;
(c) affective qualities [Distinction between affective qualities and affections.]
(d) shape, &c. [Rarity, density, &c., are not qualities.]
(3) Adjectives are generally formed derivatively from the names of the corresponding
qualities.
(4) Most qualities have contraries.
(5) If of two contraries one is a quality, the other is also a quality.
(6) A quality can in most cases be what it is in varying degrees, and subjects can
possess most qualities in varying degrees. Qualities of shape are an exception to
this rule.
(7) The peculiar mark of quality is that likeness and unlikeness is predicable of things
in respect of it.
(8) Habits and dispositions as genera are relative; as individual, qualitative.
9. Action and affection and the other categories described.
10. Four classes of ‘opposites’.
(a) Correlatives.
(b) Contraries. [Some contraries have an intermediate, and some have not.]
(c) Positives and privatives.
The terms expressing possession and privation are not the positive and
privative, though the former are opposed each to each in the same sense as the
latter.
Similarly the facts which form the basis of an affirmation or a denial are
opposed each to each in the same sense as the affirmation and denial themselves.
Positives and privatives are not opposed in the sense in which correlatives are
opposed.
Positives and privatives are not opposed in the same sense in which contraries
are opposed.
For (i) they are not of the class which has no intermediate, nor of the class
which has intermediates.
(ii) There can be no change from one state (privation) to its opposite.
(d) Affirmation and negation. These are distinguished from other contraries by the
fact that one is always false and the other true. [Opposite affirmations seem to
possess this mark, but they do not.]
11. Contraries further discussed.
Evil is generally the contrary of good, but sometimes two evils are contrary.
When one contrary exists, the other need not exist.
Contrary attributes are applicable within the same species or genus.
Contraries must themselves be within the same genus, or within opposite genera, or be
themselves genera.
12. The word ‘prior’ is applicable:
(a) to that which is previous in time;
(b) to that on which something else depends, but which is not itself dependent on
it;
(c) to that which is prior in arrangement;
(d) to that which is better or more honourable;
(e) to that one of two interdependent things which is the cause of the other.
13. The word ‘simultaneous’ is used:
(a) of those things which come into being at the same time;
(b) of those things which are interdependent, but neither of which is the cause of
the other.
(c) of the different species of the same genus.
14. Motion is of six kinds.
Alteration is distinct from other kinds of motion.
Definition of the contrary of motion and of the various kinds of motion.
15. The meanings of the term ‘to have’.
CATEGORIAE
(Categories)
1
[1a] Things are said to be named ‘equivocally’ when, though they
have a common name, the definition corresponding with the name
differs for each. Thus, a real man and a figure in a picture can both lay
claim to the name ‘animal’; yet these are equivocally so named, for,
though they have a common name, the definition corresponding with
the name differs for each. For should any one define in what sense each
is an animal, his definition in the one case will be appropriate to that
case only. (5)
On the other hand, things are said to be named ‘univocally’ which
have both the name and the definition answering to the name in
common. A man and an ox are both ‘animal’, and these are univocally so
named, inasmuch as not only the name, but also the definition, is the
same in both cases: for if a man should state in what sense each is an
animal, (10) the statement in the one case would be identical with that in
the other.
Things are said to be named ‘derivatively’, which derive their name
from some other name, but differ from it in termination. Thus the
grammarian derives his name from the word ‘grammar’, (15) and the
courageous man from the word ‘courage’.
2
Forms of speech are either simple or composite. Examples of the
latter are such expressions as ‘the man runs’, ‘the man wins’; of the
former ‘man’, ‘ox’, ‘runs’, ‘wins’.
Of things themselves some are predicable of a subject, (20) and are
never present in a subject. Thus ‘man’ is predicable of the individual
man, and is never present in a subject.
By being ‘present in a subject’ I do not mean present as parts are
present in a whole, but being incapable of existence apart from the said
subject.
Some things, again, are present in a subject, but are never predicable
of a subject. For instance, a certain point of grammatical knowledge is
present in the mind, (25) but is not predicable of any subject; or again, a
certain whiteness may be present in the body (for colour requires a
material basis), yet it is never predicable of anything.
Other things, again, are both predicable of a subject and present in a
subject. [1b] Thus while knowledge is present in the human mind, it is
predicable of grammar.
There is, lastly, a class of things which are neither present in a subject
nor predicable of a subject, such as the individual man or the individual
horse. (5) But, to speak more generally, that which is individual and has
the character of a unit is never predicable of a subject. Yet in some cases
there is nothing to prevent such being present in a subject. Thus a
certain point of grammatical knowledge is present in a subject.
3
When one thing is predicated of another, (10) all that which is
predicable of the predicate will be predicable also of the subject. Thus,
‘man’ is predicated of the individual man; but ‘animal’ is predicated of
‘man’; it will, therefore, be predicable of the individual man also: for the
individual man is both ‘man’ and ‘animal’. (15)
If genera are different and co-ordinate, their differentiae are
themselves different in kind. Take as an instance the genus ‘animal’ and
the genus ‘knowledge’. ‘With feet’, ‘two-footed’, ‘winged’, ‘aquatic’, are
differentiae of ‘animal’; the species of knowledge are not distinguished
by the same differentiae. One species of knowledge does not differ from
another in being ‘two-footed’.
But where one genus is subordinate to another, (20) there is nothing to
prevent their having the same differentiae: for the greater class is
predicated of the lesser, so that all the differentiae of the predicate will
be differentiae also of the subject.
4
Expressions which are in no way composite signify substance, (25)
quantity, quality, relation, place, time, position, state, action, or
affection. To sketch my meaning roughly, examples of substance are
‘man’ or ‘the horse’, of quantity, such terms as ‘two cubits long’ or ‘three
cubits long’, of quality, such attributes as ‘white’, ‘grammatical’.
‘Double’, ‘half’, ‘greater’, fall under the category of relation; ‘in the
market place’, ‘in the Lyceum’, under that of place; ‘yesterday’, ‘last
year’, under that of time. [2a] ‘Lying’, ‘sitting’, are terms indicating
position; ‘shod’, ‘armed’, state; ‘to lance’, ‘to cauterize’, action; ‘to be
lanced’, ‘to be cauterized’, affection.
No one of these terms, in and by itself, involves an affirmation; it is by
the combination of such terms that positive or negative statements arise.
(5) For every assertion must, as is admitted, be either true or false,
whereas expressions which are not in any way composite, such as ‘man’,
(10) ‘white’, ‘runs’, ‘wins’, cannot be either true or false.
5
Substance, in the truest and primary and most definite sense of the
word, is that which is neither predicable of a subject nor present in a
subject; for instance, the individual man or horse. But in a secondary
sense those things are called substances within which, (15) as species, the
primary substances are included; also those which, as genera, include
the species. For instance, the individual man is included in the species
‘man’, and the genus to which the species belongs is ‘animal’; these,
therefore—that is to say, the species ‘man’ and the genus ‘animal’—are
termed secondary substances.
It is plain from what has been said that both the name and the
definition of the predicate must be predicable of the subject.(20) For
instance, ‘man’ is predicated of the individual man. Now in this case the
name of the species ‘man’ is applied to the individual, for we use the
term ‘man’ in describing the individual; and the definition of ‘man’ will
also be predicated of the individual man, for the individual man is both
man and animal. Thus, both the name and the definition of the species
are predicable of the individual. (25)
With regard, on the other hand, to those things which are present in a
subject, it is generally the case that neither their name nor their
definition is predicable of that in which they are present. Though,
however, the definition is never predicable, (30) there is nothing in
certain cases to prevent the name being used. For instance, ‘white’ being
present in a body is predicated of that in which it is present, for a body
is called white: the definition, however, of the color ‘white’ is never
predicable of the body.
Everything except primary substances is either predicable of a primary
substance or present in a primary substance. This becomes evident by
reference to particular instances which occur. (35) ‘Animal’ is predicated
of the species ‘man’, therefore of the individual man, for if there were no
individual man of whom it could be predicated, it could not be
predicated of the species ‘man’ at all. [2b] Again, colour is present in
body, therefore in individual bodies, for if there were no individual body
in which it was present, it could not be present in body at all. Thus
everything except primary substances is either predicated of primary
substances, or is present in them, (5) and if these last did not exist, it
would be impossible for anything else to exist.
Of secondary substances, the species is more truly substance than the
genus, being more nearly related to primary substance. For if any one
should render an account of what a primary substance is, he would
render a more instructive account, and one more proper to the subject,
by stating the species than by stating the genus. (10) Thus, he would give
a more instructive account of an individual man by stating that he was
man than by stating that he was animal, for the former description is
peculiar to the individual in a greater degree, while the latter is too
general. Again, the man who gives an account of the nature of an
individual tree will give a more instructive account by mentioning the
species ‘tree’ than by mentioning the genus ‘plant’.
Moreover, primary substances are most properly called substances in
virtue of the fact that they are the entities which underlie everything
else, (15) and that everything else is either predicated of them or present
in them. Now the same relation which subsists between primary
substance and everything else subsists also between the species and the
genus: for the species is to the genus as subject is to predicate, (20) since
the genus is predicated of the species, whereas the species cannot be
predicated of the genus. Thus we have a second ground for asserting that
the species is more truly substance than the genus.
Of species themselves, except in the case of such as are genera, no one
is more truly substance than another. We should not give a more
appropriate account of the individual man by stating the species to
which he belonged, (25) than we should of an individual horse by
adopting the same method of definition. In the same way, of primary
substances, no one is more truly substance than another; an individual
man is not more truly substance than an individual ox.
It is, then, with good reason that of all that remains, when we exclude
primary substances, we concede to species and genera alone the name
‘secondary substance’, (30) for these alone of all the predicates convey a
knowledge of primary substance. For it is by stating the species or the
genus that we appropriately define any individual man; and we shall
make our definition more exact by stating the former than by stating the
latter. All other things that we state, such as that he is white, (35) that he
runs, and so on, are irrelevant to the definition. Thus it is just that these
alone, apart from primary substances, should be called substances.
Further, primary substances are most properly so called, because they
underlie and are the subjects of everything else. [3a] Now the same
relation that subsists between primary substance and everything else
subsists also between the species and the genus to which the primary
substance belongs, on the one hand, and every attribute which is not
included within these, on the other. For these are the subjects of all
such. If we call an individual man ‘skilled in grammar’, the predicate is
applicable also to the species and to the genus to which he belongs. (5)
This law holds good in all cases.
It is a common characteristic of all substance that it is never present in
a subject. For primary substance is neither present in a subject nor
predicated of a subject; while, with regard to secondary substances, it is
clear from the following arguments (apart from others) that they are not
present in a subject. For ‘man’ is predicated of the individual man, but is
not present in any subject: (10) for manhood is not present in the
individual man. In the same way, ‘animal’ is also predicated of the
individual man, but is not present in him. Again, when a thing is present
in a subject, though the name may quite well be applied to that in which
it is present, (15) the definition cannot be applied. Yet of secondary
substances, not only the name, but also the definition, applies to the
subject: we should use both the definition of the species and that of the
genus with reference to the individual man. (20) Thus substance cannot be
present in a subject.
Yet this is not peculiar to substance, for it is also the case that
differentiae cannot be present in subjects. The characteristics ‘terrestrial’
and ‘two-footed’ are predicated of the species ‘man’, but not present in
it. For they are not in man. Moreover, (25) the definition of the differentia
may be predicated of that of which the differentia itself is predicated.
For instance, if the characteristic ‘terrestrial’ is predicated of the species
‘man’, the definition also of that characteristic may be used to form the
predicate of the species ‘man’: for ‘man’ is terrestrial.
The fact that the parts of substances appear to be present in the whole,
as in a subject, should not make us apprehensive lest we should have to
admit that such parts are not substances: (30) for in explaining the phrase
‘being present in a subject’, we stated that we meant ‘otherwise than as
parts in a whole’.1
It is the mark of substances and of differentiae that, in all propositions
of which they form the predicate, they are predicated univocally. For all
such propositions have for their subject either the individual or the
species. It is true that, inasmuch as primary substance is not predicable
of anything, (35) it can never form the predicate of any proposition. But of
secondary substances, the species is predicated of the individual, the
genus both of the species and of the individual. Similarly the differentiae
are predicated of the species and of the individuals. [3b] Moreover, the
definition of the species and that of the genus are applicable to the
primary substance, and that of the genus to the species. For all that is
predicated of the predicate will be predicated also of the subject.
Similarly, (5) the definition of the differentiae will be applicable to the
species and to the individuals. But it was stated above that the word
‘univocal’ was applied to those things which had both name and
definition in common.2 It is, therefore, established that in every
proposition, of which either substance or a differentia forms the
predicate, these are predicated univocally.
All substance appears to signify that which is individual. (10) In the
case of primary substance this is indisputably true, for the thing is a unit.
In the case of secondary substances, when we speak, for instance, of
‘man’ or ‘animal’, our form of speech gives the impression that we are
here also indicating that which is individual, but the impression is not
strictly true; (15) for a secondary substance is not an individual, but a
class with a certain qualification; for it is not one and single as a primary
substance is; the words ‘man’, ‘animal’, are predicable of more than one
subject.
Yet species and genus do not merely indicate quality, like the term
‘white’; ‘white’ indicates quality and nothing further, but species and
genus determine the quality with reference to a substance: they signify
substance qualitatively differentiated. (20) The determinate qualification
covers a larger field in the case of the genus than in that of the species:
he who uses the word ‘animal’ is herein using a word of wider extension
than he who uses the word ‘man’.
Another mark of substance is that it has no contrary. What could be
the contrary of any primary substance, (25) such as the individual man or
animal? It has none. Nor can the species or the genus have a contrary.
Yet this characteristic is not peculiar to substance, but is true of many
other things, such as quantity. There is nothing that forms the contrary
of ‘two cubits long’ or of ‘three cubits long’, or of ‘ten’, or of any such
term. (30) A man may contend that ‘much’ is the contrary of ‘little’, or
‘great’ of ‘small’, but of definite quantitative terms no contrary exists.
Substance, again, does not appear to admit of variation of degree. I do
not mean by this that one substance cannot be more or less truly
substance than another, for it has already been stated3 that this is the
case; (35) but that no single substance admits of varying degrees within
itself. For instance, one particular substance, ‘man’, cannot be more or
less man either than himself at some other time or than some other man.
One man cannot be more man than another, as that which is white may
be more or less white than some other white object, or as that which is
beautiful may be more or less beautiful than some other beautiful object.
[4a] The same quality, moreover, is said to subsist in a thing in varying
degrees at different times. A body, being white, is said to be whiter at
one time than it was before, or, being warm, is said to be warmer or less
warm than at some other time. But substance is not said to be more or
less that which it is: (5) a man is not more truly a man at one time than
he was before, nor is anything, if it is substance, more or less what it is.
Substance, then, does not admit of variation of degree.
The most distinctive mark of substance appears to be that, (10) while
remaining numerically one and the same, it is capable of admitting
contrary qualities. From among things other than substance, we should
find ourselves unable to bring forward any which possessed this mark.
Thus, one and the same colour cannot be white and black. (15) Nor can
the same one action be good and bad: this law holds good with
everything that is not substance. But one and the self-same substance,
while retaining its identity, is yet capable of admitting contrary
qualities. The same individual person is at one time white, at another
black, at one time warm, at another cold, at one time good, (20) at
another bad. This capacity is found nowhere else, though it might be
maintained that a statement or opinion was an exception to the rule. The
same statement, it is agreed, can be both true and false. For if the
statement ‘he is sitting’ is true, yet, (25) when the person in question has
risen, the same statement will be false. The same applies to opinions. For
if any one thinks truly that a person is sitting, yet, when that person has
risen, this same opinion, if still held, will be false. Yet although this
exception may be allowed, there is, nevertheless, a difference in the
manner in which the thing takes place. It is by themselves changing that
substances admit contrary qualities. (30) It is thus that that which was hot
becomes cold, for it has entered into a different state. Similarly that
which was white becomes black, and that which was bad good, by a
process of change; and in the same way in all other cases it is by
changing that substances are capable of admitting contrary qualities. But
statements and opinions themselves remain unaltered in all respects: it is
by the alteration in the facts of the case that the contrary quality comes
to be theirs. (35) The statement ‘he is sitting’ remains unaltered, but it is
at one time true, at another false, according to circumstances. [4b]
What has been said of statements applies also to opinions. Thus, in
respect of the manner in which the thing takes place, it is the peculiar
mark of substance that it should be capable of admitting contrary
qualities; for it is by itself changing that it does so.
If, then, a man should make this exception and contend that
statements and opinions are capable of admitting contrary qualities, his
contention is unsound. For statements and opinions are said (5) to have
this capacity, not because they themselves undergo modification, but
because this modification occurs in the case of something else. The truth
or falsity of a statement depends on facts, and not on any power on the
part of the statement itself of admitting contrary qualities. (10) In short,
there is nothing which can alter the nature of statements and opinions.
As, then, no change takes place in themselves, these cannot be said to be
capable of admitting contrary qualities.
But it is by reason of the modification which takes place within the
substance itself that a substance is said to be capable of admitting
contrary qualities; for a substance admits within itself either disease or
health, (15) whiteness or blackness. It is in this sense that it is said to be
capable of admitting contrary qualities.
To sum up, it is a distinctive mark of substance, that, while remaining
numerically one and the same, it is capable of admitting contrary
qualities, the modification taking place through a change in the
substance itself.
Let these remarks suffice on the subject of substance.
6
Quantity is either discrete or continuous. (20) Moreover, some
quantities are such that each part of the whole has a relative position to
the other parts: others have within them no such relation of part to part.
Instances of discrete quantities are number and speech; of continuous,
lines, surfaces, solids, and, besides these, time and place.
In the case of the parts of a number, (25) there is no common boundary
at which they join. For example: two fives make ten, but the two fives
have no common boundary, but are separate; the parts three and seven
also do not join at any boundary. Nor, to generalize, would it ever be
possible in the case of number that there should be a common boundary
among the parts; (30) they are always separate. Number, therefore, is a
discrete quantity.
The same is true of speech. That speech is a quantity is evident: for it
is measured in long and short syllables. I mean here that speech which is
vocal. Moreover, it is a discrete quantity, for its parts have no common
boundary. (35) There is no common boundary at which the syllables join,
but each is separate and distinct from the rest.
[5a] A line, on the other hand, is a continuous quantity, for it is
possible to find a common boundary at which its parts join. In the case
of the line, this common boundary is the point; in the case of the plane,
it is the line: for the parts of the plane have also a common boundary.
Similarly you can find a common boundary in the case of the parts of a
solid, (5) namely either a line or a plane.
Space and time also belong to this class of quantities. Time, past,
present, and future, forms a continuous whole. Space, likewise, is a
continuous quantity: for the parts of a solid occupy a certain space, and
these have a common boundary; it follows that the parts of space also,
which are occupied by the parts of the solid, (10) have the same common
boundary as the parts of the solid. Thus, not only time, but space also, is
a continuous quantity, for its parts have a common boundary.
Quantities consist either of parts which bear a relative position each to
each, (15) or of parts which do not. The parts of a line bear a relative
position to each other, for each lies somewhere, and it would be possible
to distinguish each, and to state the position of each on the plane and to
explain to what sort of part among the rest each was contiguous.
Similarly the parts of a plane have position, (20) for it could similarly be
stated what was the position of each and what sort of parts were
contiguous. The same is true with regard to the solid and to space. But it
would be impossible to show that the parts of a number had a relative
position each to each, or a particular position, (25) or to state what parts
were contiguous. Nor could this be done in the case of time, for none of
the parts of time has an abiding existence, and that which does not abide
can hardly have position. It would be better to say that such parts had a
relative order, in virtue of one being prior to another. Similarly with
number: in counting, ‘one’ is prior to ‘two’, and ‘two’ to ‘three’, (30) and
thus the parts of number may be said to possess a relative order, though
it would be impossible to discover any distinct position for each. This
holds good also in the case of speech. None of its parts has an abiding
existence: when once a syllable is pronounced, it is not possible to retain
it, so that, naturally, as the parts do not abide, (35) they cannot have
position. Thus, some quantities consist of parts which have position, and
some of those which have not.
Strictly speaking, only the things which I have mentioned belong to
the category of quantity: everything else that is called quantitative is a
quantity in a secondary sense. It is because we have in mind some one of
these quantities, properly so called, that we apply quantitative terms to
other things. [5b] We speak of what is white as large, because the
surface over which the white extends is large; we speak of an action or a
process as lengthy, because the time covered is long; these things cannot
in their own right claim the quantitative epithet. For instance, should
any one explain how long an action was, his statement would be made
in terms of the time taken, (5) to the effect that it lasted a year, or
something of that sort. In the same way, he would explain the size of a
white object in terms of surface, for he would state the area which it
covered. Thus the things already mentioned, and these alone, are in their
intrinsic nature quantities; nothing else can claim the name in its own
right, (10) but, if at all, only in a secondary sense.
Quantities have no contraries. In the case of definite quantities this is
obvious; thus, there is nothing that is the contrary of ‘two cubits long’ or
of ‘three cubits long’, or of a surface, or of any such quantities. A man
might, indeed, argue that ‘much’ was the contrary of ‘little’, (15) and
‘great’ of ‘small’. But these are not quantitative, but relative; things are
not great or small absolutely, they are so called rather as the result of an
act of comparison. For instance, a mountain is called small, a grain large,
in virtue of the fact that the latter is greater than others of its kind, the
former less. (20) Thus there is a reference here to an external standard, for
if the terms ‘great’ and ‘small’ were used absolutely, a mountain would
never be called small or a grain large. Again, we say that there are many
people in a village, and few in Athens, although those in the city are
many times as numerous as those in the village: or we say that a house
has many in it, (25) and a theatre few, though those in the theatre far
outnumber those in the house. The terms ‘two cubits long’, ‘three cubits
long’, and so on indicate quantity, the terms ‘great’ and ‘small’ indicate
relation, for they have reference to an external standard. It is, therefore,
plain that these are to be classed as relative.
Again, (30) whether we define them as quantitative or not, they have
no contraries: for how can there be a contrary of an attribute which is
not to be apprehended in or by itself, but only by reference to something
external? Again, if ‘great’ and ‘small’ are contraries, it will come about
that the same subject can admit contrary qualities at one and the same
time, and that things will themselves be contrary to themselves. (35) For
it happens at times that the same thing is both small and great. For the
same thing may be small in comparison with one thing, and great in
comparison with another, so that the same thing comes to be both small
and great at one and the same time, and is of such a nature as to admit
contrary qualities at one and the same moment. Yet it was agreed, when
substance was being discussed, that nothing admits contrary qualities at
one and the same moment. [6a] For though substance is capable of
admitting contrary qualities, yet no one is at the same time both sick and
healthy, nothing is at the same time both white and black. Nor is there
anything which is qualified in contrary ways at one and the same time.
Moreover, if these were contraries, they would themselves be contrary
to themselves. For if ‘great’ is the contrary of ‘small’, (5) and the same
thing is both great and small at the same time, then ‘small’ or ‘great’ is
the contrary of itself. But this is impossible. The term ‘great’, therefore,
is not the contrary of the term ‘small’, nor ‘much’ of ‘little’. And even
though a man should call these terms not relative, but quantitative, they
would not have contraries. (10)
It is in the case of space that quantity most plausibly appears to admit
of a contrary. For men define the term ‘above’ as the contrary of ‘below’,
when it is the region at the centre they mean by ‘below’; and this is so,
because nothing is farther from the extremities of the universe than the
region at the centre. Indeed, (15) it seems that in defining contraries of
every kind men have recourse to a spatial metaphor, for they say that
those things are contraries which, within the same class, are separated
by the greatest possible distance.
Quantity does not, it appears, admit of variation of degree. One thing
cannot be two cubits long in a greater degree than another. (20) Similarly
with regard to number: what is ‘three’ is not more truly three than what
is ‘five’ is five; nor is one set of three more truly three than another set.
Again, one period of time is not said to be more truly time than another.
Nor is there any other kind of quantity, of all that have been mentioned,
with regard to which variation of degree can be predicated. The category
of quantity, therefore, (25) does not admit of variation of degree.
The most distinctive mark of quantity is that equality and inequality
are predicated of it. Each of the aforesaid quantities is said to be equal
or unequal. For instance, one solid is said to be equal or unequal to
another; number, too, and time can have these terms applied to them, as
indeed can all those kinds of quantity that have been mentioned. (30)
That which is not a quantity can by no means, it would seem, be
termed equal or unequal to anything else. One particular disposition or
one particular quality, such as whiteness, is by no means compared with
another in terms of equality and inequality but rather in terms of
similarity. Thus it is the distinctive mark of quantity that it can be called
equal and unequal. (35)
7
Those things are called relative, which, being either said to be of
something else or related to something else, are explained by reference to
that other thing. For instance, the word ‘superior’ is explained by
reference to something else, for it is superiority over something else that is
meant. Similarly, the expression ‘double’ has this external reference, for
it is the double of something else that is meant. [6b] So it is with
everything else of this kind. There are, moreover, other relatives, e. g.
habit, disposition, perception, knowledge, and attitude. The significance
of all these is explained by a reference to something else and in no other
way. Thus, a habit is a habit of something, (5) knowledge is knowledge of
something, attitude is the attitude of something. So it is with all other
relatives that have been mentioned. Those terms, then, are called
relative, the nature of which is explained by reference to something else,
the preposition ‘of’ or some other preposition being used to indicate the
relation. Thus, one mountain is called great in comparison with another;
for the mountain claims this attribute by comparison with something. (10)
Again, that which is called similar must be similar to something else, and
all other such attributes have this external reference. It is to be noted
that lying and standing and sitting are particular attitudes, but attitude is
itself a relative term. To lie, to stand, to be seated, are not themselves
attitudes, but take their name from the aforesaid attitudes.
It is possible for relatives to have contraries. (15) Thus virtue has a
contrary, vice, these both being relatives; knowledge, too, has a
contrary, ignorance. But this is not the mark of all relatives; ‘double’ and
‘triple’ have no contrary, nor indeed has any such term.
It also appears that relatives can admit of variation of degree. (20) For
‘like’ and ‘unlike’, ‘equal’ and ‘unequal’, have the modifications ‘more’
and ‘less’ applied to them, and each of these is relative in character: for
the terms ‘like’ and ‘unequal’ bear a reference to something external.
Yet, again, it is not every relative term that admits of variation of
degree. (25) No term such as ‘double’ admits of this modification. All
relatives have correlatives: by the term ‘slave’ we mean the slave of a
master; by the term ‘master’, the master of a slave; by ‘double’, (30) the
double of its half; by ‘half’, the half of its double; by ‘greater’, greater than
that which is less; by ‘less’, less than that which is greater.
So it is with every other relative term; but the case we use to express
the correlation differs in some instances. Thus, by knowledge we mean
knowledge of the knowable; by the knowable, that which is to be
apprehended by knowledge; by perception, (35) perception of the
perceptible; by the perceptible, that which is apprehended by perception.
Sometimes, however, reciprocity of correlation does not appear to
exist. This comes about when a blunder is made, and that to which the
relative is related is not accurately stated. If a man states that a wing is
necessarily relative to a bird, the connexion between these two will not
be reciprocal, for it will not be possible to say that a bird is a bird by
reason of its wings. The reason is that the original statement was
inaccurate, for the wing is not said to be relative to the bird qua bird,
since many creatures besides birds have wings, but qua winged creature.
[7a] If, then, the statement is made accurate, the connexion will be
reciprocal, for we can speak of a wing having reference necessarily to a
winged creature, and of a winged creature as being such because of its
wings.
Occasionally, perhaps, it is necessary to coin words, (5) if no word
exists by which a correlation can adequately be explained. If we define a
rudder as necessarily having reference to a boat, our definition will not
be appropriate, for the rudder does not have this reference to a boat qua
boat, as there are boats which have no rudders. (10) Thus we cannot use
the terms reciprocally, for the word ‘boat’ cannot be said to find its
explanation in the word ‘rudder’. As there is no existing word, our
definition would perhaps be more accurate if we coined some word like
‘ruddered’ as the correlative of ‘rudder’. If we express ourselves thus
accurately, at any rate the terms are reciprocally connected, for the
‘ruddered’ thing is ‘ruddered’ in virtue of its rudder. So it is in all other
cases. A head will be more accurately defined as the correlative of that
which is ‘headed’, (15) than as that of an animal, for the animal does not
have a head qua animal, since many animals have no head.
Thus we may perhaps most easily comprehend that to which a thing is
related; when a name does not exist, if, from that which has a name, we
derive a new name, and apply it to that with which the first is
reciprocally connected, as in the aforesaid instances, (20) when we
derived the word ‘winged’ from ‘wing’ and ‘ruddered’ from ‘rudder’.
All relatives, then, if properly defined, have a correlative. I add this
condition because, if that to which they are related is stated at
haphazard and not accurately, the two are not found to be
interdependent. Let me state what I mean more clearly. (25) Even in the
case of acknowledged correlatives, and where names exist for each, there
will be no interdependence if one of the two is denoted, not by that
name which expresses the correlative notion, but by one of irrelevant
significance. The term ‘slave’, if defined as related, not to a master, but
to a man, or a biped, or anything of that sort, is not reciprocally
connected with that in relation to which it is defined, (30) for the
statement is not exact. Further, if one thing is said to be correlative with
another, and the terminology used is correct, then, though all irrelevant
attributes should be removed, and only that one attribute left in virtue of
which it was correctly stated to be correlative with that other, the stated
correlation will still exist. If the correlative of ‘the slave’ is said to be ‘the
master’, (35) then, though all irrelevant attributes of the said ‘master’,
such as ‘biped’, ‘receptive of knowledge’, ‘human’, should be removed,
and the attribute ‘master’ alone left, the stated correlation existing
between him and the slave will remain the same, for it is of a master that
a slave is said to be the slave. [7b] On the other hand, if, of two
correlatives, one is not correctly termed, then, when all other attributes
are removed and that alone is left in virtue of which it was stated to be
correlative, the stated correlation will be found to have disappeared.
For suppose the correlative of ‘the slave’ should be said to be ‘the
man’, or the correlative of ‘the wing’ ‘the bird’; if the attribute ‘master’
be withdrawn from ‘the man’, (5) the correlation between ‘the man’ and
‘the slave’ will cease to exist, for if the man is not a master, the slave is
not a slave. Similarly, if the attribute ‘winged’ be withdrawn from ‘the
bird’, ‘the wing’ will no longer be relative; for if the so-called correlative
is not winged, it follows that ‘the wing’ has no correlative.
Thus it is essential that the correlated terms should be exactly
designated; if there is a name existing, (10) the statement will be easy; if
not, it is doubtless our duty to construct names. When the terminology is
thus correct, it is evident that all correlatives are interdependent.
Correlatives are thought to come into existence simultaneously. (15)
This is for the most part true, as in the case of the double and the half.
The existence of the half necessitates the existence of that of which it is a
half. Similarly the existence of a master necessitates the existence of a
slave, and that of a slave implies that of a master; these are merely
instances of a general rule. Moreover, (20) they cancel one another; for if
there is no double it follows that there is no half, and vice versa; this
rule also applies to all such correlatives. Yet it does not appear to be true
in all cases that correlatives come into existence simultaneously. The
object of knowledge would appear to exist before knowledge itself, for it
is usually the case that we acquire knowledge of objects already existing;
it would be difficult, (25) if not impossible, to find a branch of knowledge
the beginning of the existence of which was contemporaneous with that
of its object.
Again, while the object of knowledge, if it ceases to exist, cancels at
the same time the knowledge which was its correlative, the converse of
this is not true. It is true that if the object of knowledge does not exist
there can be no knowledge: for there will no longer be anything to
know. Yet it is equally true that, (30) if the knowledge of a certain object
does not exist, the object may nevertheless quite well exist. Thus, in the
case of the squaring of the circle, if indeed that process is an object of
knowledge, though it itself exists as an object of knowledge, yet the
knowledge of it has not yet come into existence. Again, if all animals
ceased to exist, there would be no knowledge, but there might yet be
many objects of knowledge.
This is likewise the case with regard to perception: for the object of
perception is, (35) it appears, prior to the act of perception. If the
perceptible is annihilated, perception also will cease to exist; but the
annihilation of perception does not cancel the existence of the
perceptible. For perception implies a body perceived and a body in
which perception takes place. Now if that which is perceptible is
annihilated, it follows that the body is annihilated, for the body is a
perceptible thing; and if the body does not exist, it follows that
perception also ceases to exist. [8a] Thus the annihilation of the
perceptible involves that of perception.
But the annihilation of perception does not involve that of the
perceptible. For if the animal is annihilated, it follows that perception
also is annihilated, but perceptibles such as body, heat, sweetness, (5)
bitterness, and so on, will remain.
Again, perception is generated at the same time as the perceiving
subject, for it comes into existence at the same time as the animal. But
the perceptible surely exists before perception; for fire and water and
such elements, out of which the animal is itself composed, (10) exist
before the animal is an animal at all, and before perception. Thus it
would seem that the perceptible exists before perception.
It may be questioned whether it is true that no substance is relative, as
seems to be the case, or whether exception is to be made in the case of
certain secondary substances. With regard to primary substances, it is
quite true that there is no such possibility, (15) for neither wholes nor
parts of primary substances are relative. The individual man or ox is not
defined with reference to something external. Similarly with the parts: a
particular hand or head is not defined as a particular hand or head of a
particular person, (20) but as the hand or head of a particular person. It is
true also, for the most part at least, in the case of secondary substances;
the species ‘man’ and the species ‘ox’ are not defined with reference to
anything outside themselves. Wood, again, is only relative in so far as it
is some one’s property, not in so far as it is wood. It is plain, then, (25)
that in the cases mentioned substance is not relative. But with regard to
some secondary substances there is a difference of opinion; thus, such
terms as ‘head’ and ‘hand’ are defined with reference to that of which
the things indicated are a part, and so it comes about that these appear
to have a relative character. (30) Indeed, if our definition of that which is
relative was complete, it is very difficult, if not impossible, to prove that
no substance is relative. If, however, our definition was not complete, if
those things only are properly called relative in the case of which
relation to an external object is a necessary condition of existence,
perhaps some explanation of the dilemma may be found.
The former definition does indeed apply to all relatives, but the fact
that a thing is explained with reference to something else does not make
it essentially relative.
From this it is plain that, (35) if a man definitely apprehends a relative
thing, he will also definitely apprehend that to which it is relative.
Indeed this is self-evident: for if a man knows that some particular thing
is relative, assuming that we call that a relative in the case of which
relation to something is a necessary condition of existence, he knows
that also to which it is related. [8b] For if he does not know at all that
to which it is related, he will not know whether or not it is relative. This
is clear, moreover, in particular instances. (5) If a man knows definitely
that such and such a thing is ‘double’, he will also forthwith know
definitely that of which it is the double. For if there is nothing definite of
which he knows it to be the double, he does not know at all that it is
double. Again, if he knows that a thing is more beautiful, it follows
necessarily that he will forthwith definitely know that also than which it
is more beautiful. He will not merely know indefinitely that it is more
beautiful than something which is less beautiful, (10) for this would be
supposition, not knowledge. For if he does not know definitely that than
which it is more beautiful, he can no longer claim to know definitely
that it is more beautiful than something else which is less beautiful: for
it might be that nothing was less beautiful. It is, therefore, evident that if
a man apprehends some relative thing definitely, he necessarily knows
that also definitely to which it is related.
Now the head, (15) the hand, and such things are substances, and it is
possible to know their essential character definitely, but it does not
necessarily follow that we should know that to which they are related. It
is not possible to know forthwith whose head or hand is meant. Thus
these are not relatives, and, this being the case, (20) it would be true to
say that no substance is relative in character. It is perhaps a difficult
matter, in such cases, to make a positive statement without more
exhaustive examination, but to have raised questions with regard to
details is not without advantage.
8 By ‘quality’ I mean that in virtue of which people are said to be such
and such. (25)
Quality is a term that is used in many senses. One sort of quality let us
call ‘habit’ or ‘disposition’. Habit differs from disposition in being more
lasting and more firmly established. The various kinds of knowledge and
of virtue are habits, for knowledge, even when acquired only in a
moderate degree, is, it is agreed, (30) abiding in its character and difficult
to displace, unless some great mental upheaval takes place, through
disease or any such cause. The virtues, also, such as justice, self-restraint,
and so on, are not easily dislodged or dismissed, so as to give place to
vice.
By a disposition, on the other hand, we mean a condition that is easily
changed and quickly gives place to its opposite. (35) Thus, heat, cold,
disease, health, and so on are dispositions. For a man is disposed in one
way or another with reference to these, but quickly changes, becoming
cold instead of warm, ill instead of well. [9a] So it is with all other
dispositions also, unless through lapse of time a disposition has itself
become inveterate and almost impossible to dislodge: in which case we
should perhaps go so far as to call it a habit.
It is evident that men incline to call those conditions habits which are
of a more or less permanent type and difficult to displace; for those who
are not retentive of knowledge, but volatile, (5) are not said to have such
and such a ‘habit’ as regards knowledge, yet they are disposed, we may
say, either better or worse, towards knowledge. Thus habit differs from
disposition in this, that while the latter is ephemeral, the former is
permanent and difficult to alter.
Habits are at the same time dispositions, but dispositions are not
necessarily habits. (10) For those who have some specific habit may be
said also, in virtue of that habit, to be thus or thus disposed; but those
who are disposed in some specific way have not in all cases the
corresponding habit.
Another sort of quality is that in virtue of which, for example, we call
men good boxers or runners, or healthy or sickly: in fact it includes all
those terms which refer to inborn capacity or incapacity. (15) Such things
are not predicated of a person in virtue of his disposition, but in virtue of
his inborn capacity or incapacity to do something with ease or to avoid
defeat of any kind. Persons are called good boxers or good runners, not
in virtue of such and such a disposition, (20) but in virtue of an inborn
capacity to accomplish something with ease. Men are called healthy in
virtue of the inborn capacity of easy resistance to those unhealthy
influences that may ordinarily arise; unhealthy, in virtue of the lack of
this capacity. (25) Similarly with regard to softness and hardness.
Hardness is predicated of a thing because it has that capacity of
resistance which enables it to withstand disintegration; softness, again, is
predicated of a thing by reason of the lack of that capacity.
A third class within this category is that of affective qualities and
affections. Sweetness, bitterness, sourness, are examples of this sort of
quality, (30) together with all that is akin to these; heat, moreover, and
cold, whiteness, and blackness are affective qualities. It is evident that
these are qualities, for those things that possess them are themselves said
to be such and such by reason of their presence. Honey is called sweet
because it contains sweetness; the body is called white because it
contains whiteness; and so in all other cases.
The term ‘affective quality’ is not used as indicating that those things
which admit these qualities are affected in any way. (35) Honey is not
called sweet because it is affected in a specific way, nor is this what is
meant in any other instance. [9b] Similarly heat and cold are called
affective qualities, not because those things which admit them are
affected. (5) What is meant is that these said qualities are capable of
producing an ‘affection’ in the way of perception. For sweetness has the
power of affecting the sense of taste; heat, that of touch; and so it is with
the rest of these qualities.
Whiteness and blackness, however, and the other colours, (10) are not
said to be affective qualities in this sense, but because they themselves
are the results of an affection. It is plain that many changes of colour
take place because of affections. When a man is ashamed, he blushes;
when he is afraid, he becomes pale, and so on. So true is this, (15) that
when a man is by nature liable to such affections, arising from some
concomitance of elements in his constitution, it is a probable inference
that he has the corresponding complexion of skin. For the same
disposition of bodily elements, which in the former instance was
momentarily present in the case of an access of shame, might be a result
of a man’s natural temperament, so as to produce the corresponding
colouring also as a natural characteristic. All conditions, therefore, of
this kind, if caused by certain permanent and lasting affections, (20) are
called affective qualities. For pallor and duskiness of complexion are
called qualities, inasmuch as we are said to be such and such in virtue of
them, not only if they originate in natural constitution, but also if they
come about through long disease or sunburn, (25) and are difficult to
remove, or indeed remain throughout life. For in the same way we are
said to be such and such because of these.
Those conditions, however, which arise from causes which may easily
be rendered ineffective or speedily removed, are called, not qualities, but
affections: for we are not said to be such and such in virtue of them. The
man who blushes through shame is not said to be a constitutional
blusher, (30) nor is the man who becomes pale through fear said to be
constitutionally pale. He is said rather to have been affected. Thus such
conditions are called affections, not qualities.
In like manner there are affective qualities and affections of the soul.
(35) That temper with which a man is born and which has its origin in
certain deep-seated affections is called a quality. [10a] I mean such
conditions as insanity, irascibility, and so on: for people are said to be
mad or irascible in virtue of these. Similarly those abnormal psychic
states which are not inborn, but arise from the concomitance of certain
other elements, and are difficult to remove, or altogether permanent, are
called qualities, for in virtue of them men are said to be such and such.
(5)
Those, however, which arise from causes easily rendered ineffective
are called affections, not qualities. Suppose that a man is irritable when
vexed: he is not even spoken of as a bad-tempered man, when in such
circumstances he loses his temper somewhat, but rather is said to be
affected. Such conditions are therefore termed, not qualities, but
affections. (10)
The fourth sort of quality is figure and the shape that belongs to a
thing; and besides this, straightness and curvedness and any other
qualities of this type; each of these defines a thing as being such and
such. Because it is triangular or quadrangular a thing is said to have a
specific character, (15) or again because it is straight or curved; in fact a
thing’s shape in every case gives rise to a qualification of it.
Rarity and density, roughness and smoothness, seem to be terms
indicating quality: yet these, it would appear, really belong to a class
different from that of quality. For it is rather a certain relative position
of the parts composing the thing thus qualified which, it appears, is
indicated by each of these terms. A thing is dense, (20) owing to the fact
that its parts are closely combined with one another; rare, because there
are interstices between the parts; smooth, because its parts lie, so to
speak, evenly; rough, because some parts project beyond others.
There may be other sorts of quality, (25) but those that are most
properly so called have, we may safely say, been enumerated.
These, then, are qualities, and the things that take their name from
them as derivatives, or are in some other way dependent on them, are
said to be qualified in some specific way. In most, indeed in almost all
cases, the name of that which is qualified is derived from that of the
quality. (30) Thus the terms ‘whiteness’, ‘grammar’, ‘justice’, give us the
adjectives ‘white’, ‘grammatical’, ‘just’, and so on.
There are some cases, however, in which, as the quality under
consideration has no name, it is impossible that those possessed of it
should have a name that is derivative. For instance, (35) the name given
to the runner or boxer, who is so called in virtue of an inborn capacity,
is not derived from that of any quality; for those capacities have no
name assigned to them. [10b] In this, the inborn capacity is distinct
from the science, with reference to which men are called, e. g., boxers or
wrestlers. Such a science is classed as a disposition; it has a name, and is
called ‘boxing’ or ‘wrestling’ as the case may be, and the name given to
those disposed in this way is derived from that of the science.
Sometimes, (5) even though a name exists for the quality, that which
takes its character from the quality has a name that is not a derivative.
For instance, the upright man takes his character from the possession of
the quality of integrity, but the name given him is not derived from the
word ‘integrity’. Yet this does not occur often.
We may therefore state that those things are said to be possessed of
some specific quality which have a name derived from that of the
aforesaid quality, (10) or which are in some other way dependent on it.
One quality may be the contrary of another; thus justice is the
contrary of injustice, whiteness of blackness, and so on. The things, also,
which are said to be such and such in virtue of these qualities, may be
contrary the one to the other; for that which is unjust is contrary to that
which is just, (15) that which is white to that which is black. This,
however, is not always the case. Red, yellow, and such colours, though
qualities, have no contraries.
If one of two contraries is a quality, the other will also be a quality.
This will be evident from particular instances, if we apply the names
used to denote the other categories; for instance, (20) granted that justice
is the contrary of injustice and justice is a quality, injustice will also be a
quality: neither quantity, nor relation, nor place, nor indeed any other
category but that of quality, will be applicable properly to injustice. So it
is with all other contraries falling under the category of quality. (25)
Qualities admit of variation of degree. Whiteness is predicated of one
thing in a greater or less degree than of another. This is also the case
with reference to justice. Moreover, one and the same thing may exhibit
a quality in a greater degree than it did before: if a thing is white, it may
become whiter.
Though this is generally the case, there are exceptions. For if we
should say that justice admitted of variation of degree, (30) difficulties
might ensue, and this is true with regard to all those qualities which are
dispositions. There are some, indeed, who dispute the possibility of
variation here. They maintain that justice and health cannot very well
admit of variation of degree themselves, (35) but that people vary in the
degree in which they possess these qualities, and that this is the case
with grammatical learning and all those qualities which are classed as
dispositions. [11a] However that may be, it is an incontrovertible fact
that the things which in virtue of these qualities are said to be what they
are vary in the degree in which they possess them; for one man is said to
be better versed in grammar, or more healthy or just, than another, and
so on.
The qualities expressed by the terms ‘triangular’ and ‘quadrangular’ do
not appear to admit of variation of degree, (5) nor indeed do any that
have to do with figure. For those things to which the definition of the
triangle or circle is applicable are all equally triangular or circular.
Those, on the other hand, to which the same definition is not applicable,
cannot be said to differ from one another in degree; the square is no
more a circle than the rectangle, (10) for to neither is the definition of the
circle appropriate. In short, if the definition of the term proposed is not
applicable to both objects, they cannot be compared. Thus it is not all
qualities which admit of variation of degree.
Whereas none of the characteristics I have mentioned are peculiar to
quality, (15) the fact that likeness and unlikeness can be predicated with
reference to quality only, gives to that category its distinctive feature.
One thing is like another only with reference to that in virtue of which it
is such and such; thus this forms the peculiar mark of quality.
We must not be disturbed because it may be argued that, (20) though
proposing to discuss the category of quality, we have included in it many
relative terms. We did say that habits and dispositions were relative. In
practically all such cases the genus is relative, the individual not. Thus
knowledge, as a genus, is explained by reference to something else, (25)
for we mean a knowledge of something. But particular branches of
knowledge are not thus explained. The knowledge of grammar is not
relative to anything external, nor is the knowledge of music, but these, if
relative at all, (30) are relative only in virtue of their genera; thus
grammar is said to be the knowledge of something, not the grammar of
something; similarly music is the knowledge of something, not the music
of something.
Thus individual branches of knowledge are not relative. And it is
because we possess these individual branches of knowledge that we are
said to be such and such. It is these that we actually possess: we are
called experts because we possess knowledge in some particular branch.
(35) Those particular branches, therefore, of knowledge, in virtue of
which we are sometimes said to be such and such, are themselves
qualities, and are not relative. Further, if anything should happen to fall
within both the category of quality and that of relation, there would be
nothing extraordinary in classing it under both these heads.
9
[11b] Action and affection both admit of contraries and also of
variation of degree. Heating is the contrary of cooling, being heated of
being cooled, being glad of being vexed. Thus they admit of contraries.
(5) They also admit of variation of degree: for it is possible to heat in a
greater or less degree; also to be heated in a greater or less degree. Thus
action and affection also admit of variation of degree. So much, then, is
stated with regard to these categories.
We spoke, moreover, of the category of position when we were
dealing with that of relation, and stated that such terms derived their
names from those of the corresponding attitudes.
As for the rest, (10) time, place, state, since they are easily intelligible, I
say no more about them than was said at the beginning, that in the
category of state are included such states as ‘shod’, ‘armed’, in that of
place ‘in the Lyceum’ and so on, as was explained before.
10
The proposed categories have, (15) then, been adequately dealt
with.
We must next explain the various senses in which the term ‘opposite’
is used. Things are said to be opposed in four senses: (i) as correlatives
to one another, (ii) as contraries to one another, (iii) as privatives to
positives, (iv) as affirmatives to negatives.
Let me sketch my meaning in outline. An instance of the use of the
word ‘opposite’ with reference to correlatives is afforded by the
expressions ‘double’ and ‘half’; with reference to contraries by ‘bad’ and
‘good’. (20) Opposites in the sense of ‘privatives’ and ‘positives’ are
‘blindness’ and ‘sight’; in the sense of affirmatives and negatives, the
propositions ‘he sits’, ‘he does not sit’.
(i) Pairs of opposites which fall under the category of relation are
explained by a reference of the one to the other, the reference being
indicated by the preposition ‘of’ or by some other preposition. (25) Thus,
double is a relative term, for that which is double is explained as the
double of something. Knowledge, again, is the opposite of the thing
known, in the same sense; and the thing known also is explained by its
relation to its opposite, (30) knowledge. For the thing known is explained
as that which is known by something; that is, by knowledge. Such things,
then, as are opposite the one to the other in the sense of being
correlatives are explained by a reference of the one to the other.
(ii) Pairs of opposites which are contraries are not in any way
interdependent, but are contrary the one to the other. The good is not
spoken of as the good of the bad, but as the contrary of the bad, (35) nor is
white spoken of as the white of the black, but as the contrary of the black.
These two types of opposition are therefore distinct. [12a] Those
contraries which are such that the subjects in which they are naturally
present, or of which they are predicated, must necessarily contain either
the one or the other of them, have no intermediate, but those in the case
of which no such necessity obtains, always have an intermediate. Thus
disease and health are naturally present in the body of an animal, and it
is necessary that either the one or the other should be present in the
body of an animal. (5) Odd and even, again, are predicated of number,
and it is necessary that the one or the other should be present in
numbers. Now there is no intermediate between the terms of either of
these two pairs. On the other hand, in those contraries with regard to
which no such necessity obtains, we find an intermediate. (10) Blackness
and whiteness are naturally present in the body, but it is not necessary
that either the one or the other should be present in the body, inasmuch
as it is not true to say that everybody must be white or black. Badness
and goodness, again, are predicated of man, and of many other things,
(15) but it is not necessary that either the one quality or the other should
be present in that of which they are predicated: it is not true to say that
everything that may be good or bad must be either good or bad. These
pairs of contraries have intermediates: the intermediates between white
and black are grey, sallow, and all the other colours that come between;
the intermediate between good and bad is that which is neither the one
nor the other.
Some intermediate qualities have names, (20) such as grey and sallow
and all the other colours that come between white and black; in other
cases, however, it is not easy to name the intermediate, but we must
define it as that which is not either extreme, (25) as in the case of that
which is neither good nor bad, neither just nor unjust.
(iii) ‘Privatives’ and ‘positives’ have reference to the same subject.
Thus, sight and blindness have reference to the eye. It is a universal rule
that each of a pair of opposites of this type has reference to that to
which the particular ‘positive’ is natural. We say that that which is
capable of some particular faculty or possession has suffered privation
when the faculty or possession in question is in no way present in that in
which, (30) and at the time at which, it should naturally be present. We
do not call that toothless which has not teeth, or that blind which has
not sight, but rather that which has not teeth or sight at the time when
by nature it should. For there are some creatures which from birth are
without sight, or without teeth, but these are not called toothless or
blind.
To be without some faculty or to possess it is not the same as the
corresponding ‘privative’ or ‘positive’. (35) ‘Sight’ is a ‘positive’,
‘blindness’ a ‘privative’, but ‘to possess sight’ is not equivalent to ‘sight’,
‘to be blind’ is not equivalent to ‘blindness’. Blindness is a ‘privative’, to
be blind is to be in a state of privation, but is not a ‘privative’. Moreover,
if ‘blindness’ were equivalent to ‘being blind’, (40) both would be
predicated of the same subject; but though a man is said to be blind, he
is by no means said to be blindness.
[12b] To be in a state of ‘possession’ is, it appears, the opposite of
being in a state of ‘privation’, just as ‘positives’ and ‘privatives’
themselves are opposite. There is the same type of antithesis in both
cases; for just as blindness is opposed to sight, (5) so is being blind
opposed to having sight.
That which is affirmed or denied is not itself affirmation or denial. By
‘affirmation’ we mean an affirmative proposition, by ‘denial’ a negative.
Now, those facts which form the matter of the affirmation or denial are
not propositions; yet these two are said to be opposed in the same sense
as the affirmation and denial, (10) for in this case also the type of
antithesis is the same. For as the affirmation is opposed to the denial, as
in the two propositions ‘he sits’, ‘he does not sit’, so also the fact which
constitutes the matter of the proposition in one case is opposed to that in
the other, his sitting, that is to say, (15) to his not sitting.
It is evident that ‘positives’ and ‘privatives’ are not opposed each to
each in the same sense as relatives. The one is not explained by
reference to the other; sight is not sight of blindness, nor is any other
preposition used to indicate the relation. Similarly blindness is not said
to be blindness of sight, but rather, privation of sight. (20) Relatives,
moreover, reciprocate; if blindness, therefore, were a relative, there
would be a reciprocity of relation between it and that with which it was
correlative. But this is not the case. Sight is not called the sight of
blindness. (25)
That those terms which fall under the heads of ‘positives’ and
‘privatives’ are not opposed each to each as contraries, either, is plain
from the following facts: Of a pair of contraries such that they have no
intermediate, one or the other must needs be present in the subject in
which they naturally subsist, or of which they are predicated; for it is
those, (30) as we proved, in the case of which this necessity obtains, that
have no intermediate. Moreover, we cited health and disease, odd and
even, as instances. But those contraries which have an intermediate are
not subject to any such necessity. It is not necessary that every
substance, receptive of such qualities, should be either black or white,
cold or hot, for something intermediate between these contraries may
very well be present in the subject. (35) We proved, moreover, that those
contraries have an intermediate in the case of which the said necessity
does not obtain. Yet when one of the two contraries is a constitutive
property of the subject, as it is a constitutive property of fire to be hot,
of snow to be white, it is necessary determinately that one of the two
contraries, not one or the other, should be present in the subject; for fire
cannot be cold, (40) or snow black. Thus, it is not the case here that one
of the two must needs be present in every subject receptive of these
qualities, but only in that subject of which the one forms a constitutive
property. [13a] Moreover, in such cases it is one member of the pair
determinately, and not either the one or the other, which must be
present.
In the case of ‘positives’ and ‘privatives’, on the other hand, neither of
the aforesaid statements holds good. For it is not necessary that a subject
receptive of the qualities should always have either the one or the other;
that which has not yet advanced to the state when sight is natural is not
said either to be blind or to see. (5) Thus ‘positives’ and ‘privatives’ do
not belong to that class of contraries which consists of those which have
no intermediate. On the other hand, they do not belong either to that
class which consists of contraries which have an intermediate. For under
certain conditions it is necessary that either the one or the other should
form part of the constitution of every appropriate subject. For when a
thing has reached the stage when it is by nature capable of sight, (10) it
will be said either to see or to be blind, and that in an indeterminate
sense, signifying that the capacity may be either present or absent; for it
is not necessary either that it should see or that it should be blind, but
that it should be either in the one state or in the other. Yet in the case of
those contraries which have an intermediate we found that it was never
necessary that either the one or the other should be present in every
appropriate subject, but only that in certain subjects one of the pair
should be present, (15) and that in a determinate sense. It is, therefore,
plain that ‘positives’ and ‘privatives’ are not opposed each to each in
either of the senses in which contraries are opposed.
Again, in the case of contraries, it is possible that there should be
changes from either into the other, while the subject retains its identity,
unless indeed one of the contraries is a constitutive property of that
subject, (20) as heat is of fire. For it is possible that that which is healthy
should become diseased, that which is white, black, that which is cold,
hot, that which is good, bad, that which is bad, good. The bad man, if he
is being brought into a better way of life and thought, may make some
advance, however slight, and if he should once improve, (25) even ever so
little, it is plain that he might change completely, or at any rate make
very great progress; for a man becomes more and more easily moved to
virtue, however small the improvement was at first. It is, therefore,
natural to suppose that he will make yet greater progress than he has
made in the past; and as this process goes on, it will change him
completely and establish him in the contrary state, (30) provided he is not
hindered by lack of time. In the case of ‘positives’ and ‘privatives’,
however, change in both directions is impossible. There may be a change
from possession to privation, but not from privation to possession. (35)
The man who has become blind does not regain his sight; the man who
has become bald does not regain his hair; the man who has lost his teeth
does not grow a new set.
[13b] (iv) Statements opposed as affirmation and negation belong
manifestly to a class which is distinct, for in this case, and in this case
only, it is necessary for the one opposite to be true and the other false.
Neither in the case of contraries, nor in the case of correlatives, nor in
the case of ‘positives’ and ‘privatives’, is it necessary for one to be true
and the other false. Health and disease are contraries: neither of them is
true or false. ‘Double’ and ‘half’ are opposed to each other as
correlatives: neither of them is true or false. The case is the same, of
course, with regard to ‘positives’ and ‘privatives’ such as ‘sight’ and
‘blindness’. In short, where there is no sort of combination of words, (10)
truth and falsity have no place, and all the opposites we have mentioned
so far consist of simple words.
At the same time, when the words which enter into opposed
statements are contraries, these, more than any other set of opposites,
would seem to claim this characteristic. ‘Socrates is ill’ is the contrary of
‘Socrates is well’, but not even of such composite expressions is it true to
say that one of the pair must always be true and the other false. (15) For if
Socrates exists, one will be true and the other false, but if he does not
exist, both will be false; for neither ‘Socrates is ill’ nor ‘Socrates is well’
is true, if Socrates does not exist at all.
In the case of ‘positives’ and ‘privatives’, if the subject does not exist at
all, (20) neither proposition is true, but even if the subject exists, it is not
always the fact that one is true and the other false. For ‘Socrates has
sight’ is the opposite of ‘Socrates is blind’ in the sense of the word
‘opposite’ which applies to possession and privation. Now if Socrates
exists, it is not necessary that one should be true and the other false, for
when he is not yet able to acquire the power of vision, both are false, as
also if Socrates is altogether non-existent. (25)
But in the case of affirmation and negation, whether the subject exists
or not, one is always false and the other true. For manifestly, if Socrates
exists, one of the two propositions ‘Socrates is ill’, ‘Socrates is not ill’, is
true, and the other false. (30) This is likewise the case if he does not exist;
for if he does not exist, to say that he is ill is false, to say that he is not
ill is true. Thus it is in the case of those opposites only, which are
opposite in the sense in which the term is used with reference to
affirmation and negation, that the rule holds good, that one of the pair
must be true and the other false. (35)
11
That the contrary of a good is an evil is shown by induction: the
contrary of health is disease, of courage, cowardice, and so on. But the
contrary of an evil is sometimes a good, sometimes an evil. [14a] For
defect, which is an evil, has excess for its contrary, this also being an
evil, and the mean, which is a good, is equally the contrary of the one
and of the other. It is only in a few cases, however, that we see instances
of this: in most, the contrary of an evil is a good. (5)
In the case of contraries, it is not always necessary that if one exists
the other should also exist: for if all become healthy there will be health
and no disease, and again, if everything turns white, (10) there will be
white, but no black. Again, since the fact that Socrates is ill is the
contrary of the fact that Socrates is well, and two contrary conditions
cannot both obtain in one and the same individual at the same time,
both these contraries could not exist at once: for if that Socrates was well
was a fact, then that Socrates was ill could not possibly be one.
It is plain that contrary attributes must needs be present in subjects
which belong to the same species or genus. (15) Disease and health
require as their subject the body of an animal; white and black require a
body, without further qualification; justice and injustice require as their
subject the human soul.
Moreover, it is necessary that pairs of contraries should in all cases
either belong to the same genus or belong to contrary genera or be
themselves genera. (20) White and black belong to the same genus,
colour; justice and injustice, to contrary genera, virtue and vice; while
good and evil do not belong to genera, but are themselves actual genera,
(25) with terms under them.
12
There are four senses in which one thing can be said to be ‘prior’
to another. Primarily and most properly the term has reference to time:
in this sense the word is used to indicate that one thing is older or more
ancient than another, for the expressions ‘older’ and ‘more ancient’
imply greater length of time.
Secondly, one thing is said to be ‘prior’ to another when the sequence
of their being cannot be reversed. (30) In this sense ‘one’ is ‘prior’ to ‘two’.
For if ‘two’ exists, it follows directly that ‘one’ must exist, but if ‘one’
exists, it does not follow necessarily that ‘two’ exists: thus the sequence
subsisting cannot be reversed. It is agreed, then, that when the sequence
of two things cannot be reversed, (35) then that one on which the other
depends is called ‘prior’ to that other.
In the third place, the term ‘prior’ is used with reference to any order,
as in the case of science and of oratory. For in sciences which use
demonstration there is that which is prior and that which is posterior in
order; in geometry, the elements are prior to the propositions; in reading
and writing, the letters of the alphabet are prior to the syllables. [14b]
Similarly, in the case of speeches, the exordium is prior in order to the
narrative.
Besides these senses of the word, there is a fourth. That which is better
and more honourable is said to have a natural priority. (5) In common
parlance men speak of those whom they honour and love as ‘coming
first’ with them. This sense of the word is perhaps the most far-fetched.
Such, then, are the different senses in which the term ‘prior’ is used.
Yet it would seem that besides those mentioned there is yet another.
(10) For in those things, the being of each of which implies that of the
other, that which is in any way the cause may reasonably be said to be
by nature ‘prior’ to the effect. It is plain that there are instances of this.
The fact of the being of a man carries with it the truth of the proposition
that he is, and the implication is reciprocal: for if a man is, (15) the
proposition wherein we allege that he is is true, and conversely, if the
proposition wherein we allege that he is is true, then he is. The true
proposition, however, is in no way the cause of the being of the man, but
the fact of the man’s being does seem somehow to be the cause of the
truth of the proposition, (20) for the truth or falsity of the proposition
depends on the fact of the man’s being or not being.
Thus the word ‘prior’ may be used in five senses.
13
The term ‘simultaneous’ is primarily and most appropriately
applied to those things the genesis of the one of which is simultaneous
with that of the other; for in such cases neither is prior or posterior to
the other. (25) Such things are said to be simultaneous in point of time.
Those things, again, are ‘simultaneous’ in point of nature, the being of
each of which involves that of the other, while at the same time neither
is the cause of the other’s being. This is the case with regard to the
double and the half, for these are reciprocally dependent, since, if there
is a double, there is also a half, (30) and if there is a half, there is also a
double, while at the same time neither is the cause of the being of the
other.
Again, those species which are distinguished one from another and
opposed one to another within the same genus are said to be
‘simultaneous’ in nature. I mean those species which are distinguished
each from each by one and the same method of division. (35) Thus the
‘winged’ species is simultaneous with the ‘terrestrial’ and the ‘water’
species. These are distinguished within the same genus, and are opposed
each to each, for the genus ‘animal’ has the ‘winged’, the ‘terrestrial’,
and the ‘water’ species, and no one of these is prior or posterior to
another; on the contrary, all such things appear to be ‘simultaneous’ in
nature. [15a] Each of these also, the terrestrial, the winged, and the
water species, can be divided again into sub-species. Those species, then,
also will be ‘simultaneous’ in point of nature, which, belonging to the
same genus, are distinguished each from each by one and the same
method of differentiation.
But genera are prior to species, (5) for the sequence of their being
cannot be reversed. If there is the species ‘water-animal’, there will be
the genus ‘animal’, but granted the being of the genus ‘animal’, it does
not follow necessarily that there will be the species ‘water-animal’.
Those things, therefore, are said to be ‘simultaneous’ in nature, the
being of each of which involves that of the other, while at the same time
neither is in any way the cause of the other’s being; those species, (10)
also, which are distinguished each from each and opposed within the
same genus. Those things, moreover, are ‘simultaneous’ in the
unqualified sense of the word which come into being at the same time.
14
There are six sorts of movement: generation, destruction, increase,
diminution, alteration, and change of place.
It is evident in all but one case that all these sorts of movement are
distinct each from each. (15) Generation is distinct from destruction,
increase and change of place from diminution, and so on. But in the case
of alteration it may be argued that the process necessarily implies one or
other of the other five sorts of motion. (20) This is not true, for we may
say that all affections, or nearly all, produce in us an alteration which is
distinct from all other sorts of motion, for that which is affected need not
suffer either increase or diminution or any of the other sorts of motion.
Thus alteration is a distinct sort of motion; for, (25) if it were not, the
thing altered would not only be altered, but would forthwith necessarily
suffer increase or diminution or some one of the other sorts of motion in
addition; which as a matter of fact is not the case. Similarly that which
was undergoing the process of increase or was subject to some other sort
of motion would, if alteration were not a distinct form of motion,
necessarily be subject to alteration also. But there are some things which
undergo increase but yet not alteration. The square, (30) for instance, if a
gnomon is applied to it, undergoes increase but not alteration, and so it
is with all other figures of this sort. Alteration and increase, therefore,
are distinct.
[15b] Speaking generally, rest is the contrary of motion. But the
different forms of motion have their own contraries in other forms; thus
destruction is the contrary of generation, diminution of increase, rest in
a place, of change of place. As for this last, change in the reverse
direction would seem to be most truly its contrary; thus motion upwards
is the contrary of motion downwards and vice versa. (5)
In the case of that sort of motion which yet remains, of those that
have been enumerated, it is not easy to state what is its contrary. It
appears to have no contrary, unless one should define the contrary here
also either as ‘rest in its quality’ or as ‘change in the direction of the
contrary quality’, (10) just as we defined the contrary of change of place
either as rest in a place or as change in the reverse direction. For a thing
is altered when change of quality takes place; therefore either rest in its
quality or change in the direction of the contrary quality may be called
the contrary of this qualitative form of motion. In this way becoming
white is the contrary of becoming black; there is alteration in the
contrary direction, (15) since a change of a qualitative nature takes place.
15
The term ‘to have’ is used in various senses. In the first place it is
used with reference to habit or disposition or any other quality, for we
are said to ‘have’ a piece of knowledge or a virtue. Then, again, it has
reference to quantity, as, for instance, (20) in the case of a man’s height;
for he is said to ‘have’ a height of three cubits or four cubits. It is used,
moreover, with regard to apparel, a man being said to ‘have’ a coat or
tunic; or in respect of something which we have on a part of ourselves,
as a ring on the hand: or in respect of something which is a part of us, as
hand or foot. The term refers also to content, as in the case of a vessel
and wheat, or of a jar and wine; a jar is said to ‘have’ wine, and a cornmeasure wheat. (25) The expression in such cases has reference to
content. Or it refers to that which has been acquired; we are said to
‘have’ a house or a field. A man is also said to ‘have’ a wife, and a wife a
husband, and this appears to be the most remote meaning of the term,
for by the use of it we mean simply that the husband lives with the wife.
(30)
Other senses of the word might perhaps be found, but the most
ordinary ones have all been enumerated.
1
1a 24.
2
1a 6.
3
2a 11—b 22.
DE INTERPRETATIONE
Translated by E. M. Edghill
CONTENTS
CHAPTER
1. (1) The spoken word is a symbol of thought.
(2) Isolated thoughts or expressions are neither true nor false.
(3) Truth and falsehood are only attributable to certain combinations of thoughts or of
words.
2. (1) Definition of a noun.
(2) Simple and composite nouns.
(3) Indefinite nouns.
(4) Cases of a noun.
3. (1) Definition of a verb.
(2) Indefinite verbs.
(3) Tenses of a verb.
(4) Verbal nouns and adjectives.
4. Definition of a sentence.
5. Simple and compound propositions.
6. Contradictory propositions.
7. (1) Universal, indefinite, and particular affirmations and denials.
(2) Contrary as opposed to contradictory propositions.
(3) In contrary propositions, of which the subject is universal or particular, the truth of
the one proposition implies the falsity of the other, but this is not the case in
indefinite propositions.
8. Definition of single propositions.
9. Propositions which refer to present or past time must be either true or false:
propositions which refer to future time must be either true or false, but it is not
determined which must be true and which false.
10. (1) Diagrammatic arrangement of pairs of affirmations and denials, (a) without the
complement of the verb ‘to be’, (b) with the complement of the verb ‘to be’, (c)
with an indefinite noun for subject.
(2) The right position of the negative.
(3) Contraries can never both be true, but subcontraries may both be true.
(4) In particular propositions, if the affirmative is false, the contrary is true; in
universal propositions, if the affirmative is false, the contradictory is true.
(5) Propositions consisting of an indefinite noun and an indefinite verb are not denials.
(6) The relation to other propositions of those which have an indefinite noun as
subject.
(7) The transposition of nouns and verbs makes no difference to the sense of the
proposition.
11. (1) Some seemingly simple propositions are really compound.
(2) Similarly some dialectical questions are really compound.
(3) The nature of a dialectical question.
(4) When two simple propositions having the same subject are true, it is not
necessarily the case that the proposition resulting from the combination of the
predicates is true.
(5) A plurality of predicates which individually belong to the same subject can only be
combined to form a simple proposition when they are essentially predicable of the
subject, and when one is not implicit in another.
(6) A compound predicate cannot be resolved into simple predicates when the
compound predicate has within it a contradiction in terms, or when one of the
predicates is used in a secondary sense.
12. (1) Propositions concerning possibility, impossibility, contingency, and necessity.
(2) Determination of the proper contradictories of such propositions.
13. (1) Scheme to show the relation subsisting between such propositions.
(2) Illogical character of this scheme proved.
(3) Revised scheme.
(4) That which is said to be possible may be (a) always actual, (b) sometimes actual
and sometimes not, (c) never actual.
14. Discussion as to whether a contrary affirmation or a denial is the proper contrary of an
affirmation, either universal or particular.
DE INTERPRETATIONE
(On Interpretation)
1
[16a] First we must define the terms ‘noun’ and ‘verb’, then the
terms ‘denial’ and ‘affirmation’, then ‘proposition’ and ‘sentence’.
Spoken words are the symbols of mental experience and written words
are the symbols of spoken words. Just as all men have not the same
writing, (5) so all men have not the same speech sounds, but the mental
experiences, which these directly symbolize, are the same for all, as also
are those things of which our experiences are the images. This matter
has, however, been discussed in my treatise about the soul, for it belongs
to an investigation distinct from that which lies before us.
As there are in the mind thoughts which do not involve truth or
falsity, (10) and also those which must be either true or false, so it is in
speech. For truth and falsity imply combination and separation. Nouns
and verbs, provided nothing is added, are like thoughts without
combination or separation; ‘man’ and ‘white’, (15) as isolated terms, are
not yet either true or false. In proof of this, consider the word ‘goat-stag’.
It has significance, but there is no truth or falsity about it, unless ‘is’ or
‘is not’ is added, either in the present or in some other tense.
2 By a noun we mean a sound significant by convention, (20) which has
no reference to time, and of which no part is significant apart from the
rest. In the noun ‘Fairsteed’, the part ‘steed’ has no significance in and by
itself, as in the phrase ‘fair steed’. Yet there is a difference between
simple and composite nouns; for in the former the part is in no way
significant, (25) in the latter it contributes to the meaning of the whole,
although it has not an independent meaning. Thus in the word ‘pirateboat’ the word ‘boat’ has no meaning except as part of the whole word.
The limitation ‘by convention’ was introduced because nothing is by
nature a noun or name—it is only so when it becomes a symbol;
inarticulate sounds, such as those which brutes produce, are significant,
yet none of these constitutes a noun.
The expression ‘not-man’ is not a noun. (30) There is indeed no
recognized term by which we may denote such an expression, for it is
not a sentence or a denial. Let it then be called an indefinite noun.
The expressions ‘of Philo’, ‘to Philo’, and so on, constitute not nouns,
but cases of a noun. [16b] The definition of these cases of a noun is in
other respects the same as that of the noun proper, but, when coupled
with ‘is’, ‘was’, or ‘will be’, they do not, as they are, form a proposition
either true or false, and this the noun proper always does, under these
conditions. Take the words ‘of Philo is’ or ‘of Philo is not’; these words
do not, as they stand, form either a true or a false proposition. (5)
3
A verb is that which, in addition to its proper meaning, carries with
it the notion of time. No part of it has any independent meaning, and it
is a sign of something said of something else.
I will explain what I mean by saying that it carries with it the notion
of time. ‘Health’ is a noun, but ‘is healthy’ is a verb; for besides its
proper meaning it indicates the present existence of the state in question.
Moreover, a verb is always a sign of something said of something else,
(10) i. e. of something either predicable of or present in some other thing.
Such expressions as ‘is not-healthy’, ‘is not-ill’, I do not describe as
verbs; for though they carry the additional note of time, and always
form a predicate, there is no specified name for this variety; but let them
be called indefinite verbs, (15) since they apply equally well to that which
exists and to that which does not.
Similarly ‘he was healthy’, ‘he will be healthy’, are not verbs, but
tenses of a verb; the difference lies in the fact that the verb indicates
present time, while the tenses of the verb indicate those times which lie
outside the present.
Verbs in and by themselves are substantial and have significance, for
he who uses such expressions arrests the hearer’s mind, (20) and fixes his
attention; but they do not, as they stand, express any judgement, either
positive or negative. For neither are ‘to be’ and ‘not to be’ and the
participle ‘being’ significant of any fact, unless something is added; for
they do not themselves indicate anything, but imply a copulation, of
which we cannot form a conception apart from the things coupled. (25)
4
A sentence is a significant portion of speech, some parts of which
have an independent meaning, that is to say, as an utterance, though not
as the expression of any positive judgement. Let me explain. The word
‘human’ has meaning, but does not constitute a proposition, either
positive or negative. It is only when other words are added that the
whole will form an affirmation or denial. (30) But if we separate one
syllable of the word ‘human’ from the other, it has no meaning; similarly
in the word ‘mouse’, the part ‘-ouse’ has no meaning in itself, but is
merely a sound. In composite words, indeed, the parts contribute to the
meaning of the whole; yet, as has been pointed out,1 they have not an
independent meaning.
[17a] Every sentence has meaning, not as being the natural means
by which a physical faculty is realized, but, as we have said, by
convention. Yet every sentence is not a proposition; only such are
propositions as have in them either truth or falsity. Thus a prayer is a
sentence, but is neither true nor false.
Let us therefore dismiss all other types of sentence but the proposition,
(5) for this last concerns our present inquiry, whereas the investigation of
the others belongs rather to the study of rhetoric or of poetry.2
5
The first class of simple propositions is the simple affirmation, the
next, the simple denial; all others are only one by conjunction.
Every proposition must contain a verb or the tense of a verb. (10) The
phrase which defines the species ‘man’, if no verb in present, past, or
future time be added, is not a proposition. It may be asked how the
expression ‘a footed animal with two feet’ can be called single; for it is
not the circumstance that the words follow in unbroken succession that
effects the unity. This inquiry, however, finds its place in an
investigation foreign to that before us.
We call those propositions single which indicate a single fact, (15) or
the conjunction of the parts of which results in unity: those propositions,
on the other hand, are separate and many in number, which indicate
many facts, or whose parts have no conjunction.
Let us, moreover, consent to call a noun or a verb an expression only,
and not a proposition, since it is not possible for a man to speak in this
way when he is expressing something, in such a way as to make a
statement, whether his utterance is an answer to a question or an act of
his own initiation.
To return: of propositions one kind is simple, (20) i. e. that which
asserts or denies something of something, the other composite, i. e. that
which is compounded of simple propositions. A simple proposition is a
statement, with meaning, as to the presence of something in a subject or
its absence, in the present, past, or future, according to the divisions of
time.
6
An affirmation is a positive assertion of something about something,
(25) a denial a negative assertion.
Now it is possible both to affirm and to deny the presence of
something which is present or of something which is not, and since these
same affirmations and denials are possible with reference to those times
which lie outside the present, it would be possible to contradict any
affirmation or denial. (30) Thus it is plain that every affirmation has an
opposite denial, and similarly every denial an opposite affirmation.
We will call such a pair of propositions a pair of contradictories. Those
positive and negative propositions are said to be contradictory which
have the same subject and predicate. (35) The identity of subject and of
predicate must not be ‘equivocal’. Indeed there are definitive
qualifications besides this, which we make to meet the casuistries of
sophists.
7
Some things are universal, others individual. By the term ‘universal’
I mean that which is of such a nature as to be predicated of many
subjects, by ‘individual’ that which is not thus predicated. Thus ‘man’ is
a universal, ‘Callias’ an individual. (40)
Our propositions necessarily sometimes concern a universal subject,
sometimes an individual. [17b]
If, then, a man states a positive and a negative proposition of universal
character with regard to a universal, these two propositions are
‘contrary’. By the expression ‘a proposition of universal character with
regard to a universal’, (5) such propositions as ‘every man is white’, ‘no
man is white’ are meant. When, on the other hand, the positive and
negative propositions, though they have regard to a universal, are yet
not of universal character, they will not be contrary, albeit the meaning
intended is sometimes contrary. As instances of propositions made with
regard to a universal, but not of universal character, we may take the
propositions ‘man is white’, ‘man is not white’. (10) ‘Man’ is a universal,
but the proposition is not made as of universal character; for the word
‘every’ does not make the subject a universal, but rather gives the
proposition a universal character. If, however, both predicate and
subject are distributed, the proposition thus constituted is contrary to
truth; no affirmation will, under such circumstances, be true. The
proposition ‘every man is every animal’ is an example of this type. (15)
An affirmation is opposed to a denial in the sense which I denote by
the term ‘contradictory’, when, while the subject remains the same, the
affirmation is of universal character and the denial is not. The
affirmation ‘every man is white’ is the contradictory of the denial ‘not
every man is white’, or again, the proposition ‘no man is white’ is the
contradictory of the proposition ‘some men are white’. (20) But
propositions are opposed as contraries when both the affirmation and the
denial are universal, as in the sentences ‘every man is white’, ‘no man is
white’, ‘every man is just’, ‘no man is just’.
We see that in a pair of this sort both propositions cannot be true, but
the contradictories of a pair of contraries can sometimes both be true
with reference to the same subject; for instance ‘not every man is white’
and ‘some men are white’ are both true. (25) Of such corresponding
positive and negative propositions as refer to universals and have a
universal character, one must be true and the other false. This is the case
also when the reference is to individuals, as in the propositions ‘Socrates
is white’, ‘Socrates is not white’.
When, on the other hand, the reference is to universals, but the
propositions are not universal, it is not always the case that one is true
and the other false, (30) for it is possible to state truly that man is white
and that man is not white and that man is beautiful and that man is not
beautiful; for if a man is deformed he is the reverse of beautiful, also if
he is progressing towards beauty he is not yet beautiful.
This statement might seem at first sight to carry with it a
contradiction, (35) owing to the fact that the proposition ‘man is not
white’ appears to be equivalent to the proposition ‘no man is white’.
This, however, is not the case, nor are they necessarily at the same time
true or false.
It is evident also that the denial corresponding to a single affirmation
is itself single; for the denial must deny just that which the affirmation
affirms concerning the same subject, and must correspond with the
affirmation both in the universal or particular character of the subject
and in the distributed or undistributed sense in which it is understood.
[18a]
For instance, the affirmation ‘Socrates is white’ has its proper denial in
the proposition ‘Socrates is not white’. If anything else be negatively
predicated of the subject or if anything else be the subject though the
predicate remain the same, the denial will not be the denial proper to
that affirmation, but one that is distinct.
The denial proper to the affirmation ‘every man is white’ is ‘not every
man is white’; that proper to the affirmation ‘some men are white’ is ‘no
man is white’, (5) while that proper to the affirmation ‘man is white’ is
‘man is not white’.
We have shown further that a single denial is contradictorily opposite
to a single affirmation and we have explained which these are; we have
also stated that contrary are distinct from contradictory propositions and
which the contrary are; also that with regard to a pair of opposite
propositions it is not always the case that one is true and the other false.
(10) We have pointed out, moreover, what the reason of this is and under
what circumstances the truth of the one involves the falsity of the other.
8
An affirmation or denial is single, if it indicates some one fact about
some one subject; it matters not whether the subject is universal and
whether the statement has a universal character, or whether this is not
so. Such single propositions are: ‘every man is white’, ‘not every man is
white’; ‘man is white’, ‘man is not white’; ‘no man is white’, (15) ‘some
men are white’; provided the word ‘white’ has one meaning. If, on the
other hand, one word has two meanings which do not combine to form
one, the affirmation is not single. For instance, if a man should establish
the symbol ‘garment’ as significant both of a horse and of a man, (20) the
proposition ‘garment is white’ would not be a single affirmation, nor its
opposite a single denial. For it is equivalent to the proposition ‘horse and
man are white’, which, again, is equivalent to the two propositions
‘horse is white’, ‘man is white’. If, then, these two propositions have
more than a single significance, and do not form a single proposition, it
is plain that the first proposition either has more than one significance
or else has none; for a particular man is not a horse. (25)
This, then, is another instance of those propositions of which both the
positive and the negative forms may be true or false simultaneously.
9
In the case of that which is or which has taken place, propositions,
whether positive or negative, must be true or false. Again, in the case of
a pair of contradictories, either when the subject is universal and the
propositions are of a universal character, or when it is individual, (30) as
has been said,3 one of the two must be true and the other false; whereas
when the subject is universal, but the propositions are not of a universal
character, there is no such necessity. We have discussed this type also in
a previous chapter.4
When the subject, however, is individual, and that which is predicated
of it relates to the future, the case is altered. For if all propositions
whether positive or negative are either true or false, (35) then any given
predicate must either belong to the subject or not, so that if one man
affirms that an event of a given character will take place and another
denies it, it is plain that the statement of the one will correspond with
reality and that of the other will not. For the predicate cannot both
belong and not belong to the subject at one and the same time with
regard to the future.
[18b] Thus, if it is true to say that a thing is white, it must
necessarily be white; if the reverse proposition is true, it will of necessity
not be white. Again, if it is white, the proposition stating that it is white
was true; if it is not white, the proposition to the opposite effect was
true. And if it is not white, the man who states that it is is making a false
statement; and if the man who states that it is white is making a false
statement, it follows that it is not white. It may therefore be argued that
it is necessary that affirmations or denials must be either true or false.
Now if this be so, (5) nothing is or takes place fortuitously, either in the
present or in the future, and there are no real alternatives; everything
takes place of necessity and is fixed. For either he that affirms that it will
take place or he that denies this is in correspondence with fact, whereas
if things did not take place of necessity, an event might just as easily not
happen as happen; for the meaning of the word ‘fortuitous’ with regard
to present or future events is that reality is so constituted that it may
issue in either of two opposite directions.
Again, (10) if a thing is white now, it was true before to say that it
would be white, so that of anything that has taken place it was always
true to say ‘it is’ or ‘it will be’. But if it was always true to say that a
thing is or will be, it is not possible that it should not be or not be about
to be, and when a thing cannot not come to be, it is impossible that it
should not come to be, and when it is impossible that it should not come
to be, it must come to be. (15) All, then, that is about to be must of
necessity take place. It results from this that nothing is uncertain or
fortuitous, for if it were fortuitous it would not be necessary.
Again, to say that neither the affirmation nor the denial is true,
maintaining, let us say, that an event neither will take place nor will not
take place, is to take up a position impossible to defend. In the first
place, though facts should prove the one proposition false, (20) the
opposite would still be untrue. Secondly, if it was true to say that a thing
was both white and large, both these qualities must necessarily belong to
it; and if they will belong to it the next day, they must necessarily belong
to it the next day. But if an event is neither to take place nor not to take
place the next day, the element of chance will be eliminated. For
example, it would be necessary that a sea-fight should neither take place
nor fail to take place on the next day. (25)
These awkward results and others of the same kind follow, if it is an
irrefragable law that of every pair of contradictory propositions, whether
they have regard to universals and are stated as universally applicable,
or whether they have regard to individuals, one must be true and the
other false, and that there are no real alternatives, (30) but that all that is
or takes place is the outcome of necessity. There would be no need to
deliberate or to take trouble, on the supposition that if we should adopt
a certain course, a certain result would follow, while, if we did not, the
result would not follow. For a man may predict an event ten thousand
years before-hand, and another may predict the reverse; that which was
truly predicted at the moment in the past will of necessity take place in
the fullness of time. (35)
Further, it makes no difference whether people have or have not
actually made the contradictory statements. For it is manifest that the
circumstances are not influenced by the fact of an affirmation or denial
on the part of anyone. For events will not take place or fail to take place
because it was stated that they would or would not take place, nor is this
any more the case if the prediction dates back ten thousand years or any
other space of time. [19a] Wherefore, if through all time the nature of
things was so constituted that a prediction about an event was true, then
through all time it was necessary that that prediction should find
fulfilment; and with regard to all events, circumstances have always
been such that their occurrence is a matter of necessity. For that of
which someone has said truly that it will be, cannot fail to take place;
and of that which takes place, (5) it was always true to say that it would
be.
Yet this view leads to an impossible conclusion; for we see that both
deliberation and action are causative with regard to the future, and that,
to speak more generally, in those things which are not continuously
actual there is a potentiality in either direction. Such things may either
be or not be; events also therefore may either take place or not take
place. (10) There are many obvious instances of this. It is possible that this
coat may be cut in half, and yet it may not be cut in half, but wear out
first. In the same way, it is possible that it should not be cut in half;
unless this were so, (15) it would not be possible that it should wear out
first. So it is therefore with all other events which possess this kind of
potentiality. It is therefore plain that it is not of necessity that everything
is or takes place; but in some instances there are real alternatives, in
which case the affirmation is no more true and no more false than the
denial; while some exhibit a predisposition and general tendency in one
direction or the other, (20) and yet can issue in the opposite direction by
exception.
Now that which is must needs be when it is, and that which is not
must needs not be when it is not. Yet it cannot be said without
qualification that all existence and non-existence is the outcome of
necessity. (25) For there is a difference between saying that that which is,
when it is, must needs be, and simply saying that all that is must needs
be, and similarly in the case of that which is not. In the case, also, of two
contradictory propositions this holds good. Everything must either be or
not be, whether in the present or in the future, but it is not always
possible to distinguish and state determinately which of these
alternatives must necessarily come about.
Let me illustrate. (30) A sea-fight must either take place to-morrow or
not, but it is not necessary that it should take place to-morrow, neither is
it necessary that it should not take place, yet it is necessary that it either
should or should not take place to-morrow. Since propositions
correspond with facts, it is evident that when in future events there is a
real alternative, and a potentiality in contrary directions, the
corresponding affirmation and denial have the same character.
This is the case with regard to that which is not always existent or not
always non-existent. (35) One of the two propositions in such instances
must be true and the other false, but we cannot say determinately that
this or that is false, but must leave the alternative undecided. One may
indeed be more likely to be true than the other, but it cannot be either
actually true or actually false. [19b] It is therefore plain that it is not
necessary that of an affirmation and a denial one should be true and the
other false. For in the case of that which exists potentially, but not
actually, the rule which applies to that which exists actually does not
hold good. The case is rather as we have indicated.
10
An affirmation is the statement of a fact with regard to a subject,
(5) and this subject is either a noun or that which has no name; the
subject and predicate in an affirmation must each denote a single thing. I
have already explained5 what is meant by a noun and by that which has
no name; for I stated that the expression ‘not-man’ was not a noun, in
the proper sense of the word, but an indefinite noun, denoting as it does
in a sense a single thing. Similarly the expression ‘does not enjoy health’
is not a verb proper, but an indefinite verb. Every affirmation, then, and
every denial, (10) will consist of a noun and a verb, either definite or
indefinite.
There can be no affirmation or denial without a verb; for the
expressions ‘is’, ‘will be’, ‘was’, ‘is coming to be’, and the like are verbs
according to our definition, since besides their specific meaning they
convey the notion of time.
Thus the primary affirmation and denial are as follows: ‘man is’, ‘man
is not’. Next to these, there are the propositions: ‘not-man is’, (15) ‘notman is not’. Again we have the propositions: ‘every man is’, ‘every man
is not’, ‘all that is not-man is’, ‘all that is not-man is not’. The same
classification holds good with regard to such periods of time as lie
outside the present.
When the verb ‘is’ is used as a third element in the sentence, there can
be positive and negative propositions of two sorts. Thus in the sentence
‘man is just’ the verb ‘is’ is used as a third element, (20) call it verb or
noun, which you will. Four propositions, therefore, instead of two can be
formed with these materials. Two of the four, as regards their
affirmation and denial, correspond in their logical sequence with the
propositions which deal with a condition of privation; the other two do
not correspond with these.
I mean that the verb ‘is’ is added either to the term ‘just’ or to the term
“not-just’, and two negative propositions are formed in the same way. (25)
Thus we have the four propositions. Reference to the sub-joined table
will make matters clear:
Here ‘is’ and ‘is not’ are added either to ‘just’ or to ‘not-just’. This then is
the proper scheme for these propositions, (30) as has been said in the
Analytics.6 The same rule holds good, if the subject is distributed. Thus
we have the table:
Yet here it is not possible, (35) in the same way as in the former case, that
the propositions joined in the table by a diagonal line should both be
true; though under certain circumstances this is the case.
We have thus set out two pairs of opposite propositions; there are
moreover two other pairs, if a term be conjoined with ‘not-man’, the
latter forming a kind of subject. Thus:
[20a] This is an exhaustive enumeration of all the pairs of opposite
propositions that can possibly be framed. This last group should remain
distinct from those which preceded it, since it employs as its subject the
expression ‘not-man’.
When the verb ‘is’ does not fit the structure of the sentence (for
instance, when the verbs ‘walks’, ‘enjoys health’ are used), that scheme
applies, which applied when the word ‘is’ was added.
Thus we have the propositions: ‘every man enjoys health’, (5) ‘every
man does-not-enjoy-health’, ‘all that is not-man enjoys health’, ‘all that is
not-man does-not-enjoy-health’.
We must not in these propositions use the expression ‘not every man’.
The negative must be attached to the word ‘man’, for the word ‘every’
does not give to the subject a universal significance, (10) but implies that,
as a subject, it is distributed. This is plain from the following pairs: ‘man
enjoys health’, ‘man does not enjoy health’; ‘not-man enjoys health’, ‘notman does not enjoy health’. These propositions differ from the former in
being indefinite and not universal in character. Thus the adjectives
‘every’ and ‘no’ have no additional significance except that the subject,
whether in a positive or in a negative sentence, is distributed. The rest of
the sentence, therefore, will in each case be the same. (15)
Since the contrary of the proposition ‘every animal is just’ is ‘no
animal is just’, it is plain that these two propositions will never both be
true at the same time or with reference to the same subject. Sometimes,
however, the contradictories of these contraries will both be true, as in
the instance before us: the propositions ‘not every animal is just’ and
‘some animals are just’ are both true.
Further, the proposition ‘no man is just’ follows from the proposition
‘every man is not-just’ and the proposition ‘not every man is not-just’, (20)
which is the opposite of ‘every man is not-just’, follows from the
proposition ‘some men are just’; for if this be true, there must be some
just men.
It is evident, also, that when the subject is individual, if a question is
asked and the negative answer is the true one, a certain positive
proposition is also true. Thus, if the question were asked ‘Is Socrates
wise?’ and the negative answer were the true one, (25) the positive
inference ‘Then Socrates is unwise’ is correct. But no such inference is
correct in the case of universals, but rather a negative proposition. For
instance, if to the question ‘Is every man wise?’ the answer is ‘no’, the
inference ‘Then every man is unwise’ is false. But under these
circumstances the inference ‘Not every man is wise’ is correct. (30) This
last is the contradictory, the former the contrary. Negative expressions,
which consist of an indefinite noun or predicate, such as ‘not-man’ or
‘not-just’, may seem to be denials containing neither noun nor verb in
the proper sense of the words. But they are not. For a denial must always
be either true or false, (35) and he that uses the expression ‘not-man’, if
nothing more be added, is not nearer but rather further from making a
true or a false statement than he who uses the expression ‘man’.
The propositions ‘everything that is not man is just’, and the
contradictory of this, are not equivalent to any of the other propositions;
on the other hand, the proposition ‘everything that is not man is not just’
is equivalent to the proposition ‘nothing that is not man is just’. (40)
The conversion of the position of subject and predicate in a sentence
involves no difference in its meaning. [20b] Thus we say ‘man is white’
and ‘white is man’. If these were not equivalent, there would be more
than one contradictory to the same proposition, whereas it has been
demonstrated7 that each proposition has one proper contradictory and
one only. For of the proposition ‘man is white’ the appropriate
contradictory is ‘man is not white’, (5) and of the proposition ‘white is
man’, if its meaning be different, the contradictory will either be ‘white
is not not-man’ or ‘white is not man’. Now the former of these is the
contradictory of the proposition ‘white is not-man’, and the latter of
these is the contradictory of the proposition ‘man is white’; thus there
will be two contradictories to one proposition.
It is evident, (10) therefore, that the inversion of the relative position of
subject and predicate does not affect the sense of affirmations and
denials.
11
There is no unity about an affirmation or denial which, either
positively or negatively, predicates one thing of many subjects, or many
things of the same subject, unless that which is indicated by the many is
really some one thing.
I do not apply this word ‘one’ to those things which, (15) though they
have a single recognized name, yet do not combine to form a unity.
Thus, man may be an animal, and biped, and domesticated, but these
three predicates combine to form a unity. On the other hand, the
predicates ‘white’, ‘man’, and ‘walking’ do not thus combine. Neither,
therefore, if these three form the subject of an affirmation, (20) nor if they
form its predicate, is there any unity about that affirmation. In both
cases the unity is linguistic, but not real.
If therefore the dialectical question is a request for an answer, i. e.
either for the admission of a premiss or for the admission of one of two
contradictories—and the premiss is itself always one of two
contradictories—the answer to such a question as contains the above
predicates cannot be a single proposition. (25) For as I have explained in
the Topics,8 the question is not a single one, even if the answer asked for
is true.
At the same time it is plain that a question of the form ‘what is it?’ is
not a dialectical question, for a dialectical questioner must by the form
of his question give his opponent the chance of announcing one of two
alternatives, whichever he wishes. (30) He must therefore put the question
into a more definite form, and inquire, e. g. whether man has such and
such a characteristic or not.
Some combinations of predicates are such that the separate predicates
unite to form a single predicate. Let us consider under what conditions
this is and is not possible. We may either state in two separate
propositions that man is an animal and that man is a biped, or we may
combine the two, and state that man is an animal with two feet.
Similarly we may use ‘man’ and ‘white’ as separate predicates, or unite
them into one. Yet if a man is a shoemaker and is also good, (35) we
cannot construct a composite proposition and say that he is a good
shoemaker. For if, whenever two separate predicates truly belong to a
subject, it follows that the predicate resulting from their combination
also truly belongs to the subject, many absurd results ensue. For
instance, a man is man and white. Therefore, if predicates may always
be combined, he is a white man. Again, if the predicate ‘white’ belongs
to him, then the combination of that predicate with the former
composite predicate will be permissible. Thus it will be right to say that
he is a white white man and so on indefinitely. (40) Or, again, we may
combine the predicates ‘musical’, ‘white’, and ‘walking’, and these may
be combined many times. [21a] Similarly we may say that Socrates is
Socrates and a man, and that therefore he is the man Socrates, or that
Socrates is a man and a biped, and that therefore he is a two-footed man.
Thus it is manifest that if a man states unconditionally that predicates
can always be combined, (5) many absurd consequences ensue.
We will now explain what ought to be laid down.
Those predicates, and terms forming the subject of predication, which
are accidental either to the same subject or to one another, do not
combine to form a unity. Take the proposition ‘man is white of
complexion and musical’. (10) Whiteness and being musical do not
coalesce to form a unity, for they belong only accidentally to the same
subject. Nor yet, if it were true to say that that which is white is musical,
would the terms ‘musical’ and ‘white’ form a unity, for it is only
incidentally that that which is musical is white; the combination of the
two will, therefore, not form a unity.
Thus, again, whereas, if a man is both good and a shoemaker, we
cannot combine the two propositions and say simply that he is a good
shoemaker, we are, at the same time, able to combine the predicates
‘animal’ and ‘biped’ and say that a man is an animal with two feet, (15)
for these predicates are not accidental.
Those predicates, again, cannot form a unity, of which the one is
implicit in the other: thus we cannot combine the predicate ‘white’ again
and again with that which already contains the notion ‘white’, nor is it
right to call a man an animal-man or a two-footed man; for the notions
‘animal’ and ‘biped’ are implicit in the word ‘man’. On the other hand, it
is possible to predicate a term simply of any one instance, and to say
that some one particular man is a man or that some one white man is a
white man. (20)
Yet this is not always possible: indeed, when in the adjunct there is
some opposite which involves a contradiction, the predication of the
simple term is impossible. Thus it is not right to call a dead man a man.
When, however, this is not the case, it is not impossible.
Yet the facts of the case might rather be stated thus: when some such
opposite elements are present, resolution is never possible, (25) but when
they are not present, resolution is nevertheless not always possible. Take
the proposition ‘Homer is so-and-so’, say ‘a poet’; does it follow that
Homer is, or does it not? The verb ‘is’ is here used of Homer only
incidentally, the proposition being that Homer is a poet, not that he is,
in the independent sense of the word.
Thus, in the case of those predications which have within them no
contradiction when the nouns are expanded into definitions, (30) and
wherein the predicates belong to the subject in their own proper sense
and not in any indirect way, the individual may be the subject of the
simple propositions as well as of the composite. But in the case of that
which is not, it is not true to say that because it is the object of opinion,
it is; for the opinion held about it is that it is not, not that it is.
12
As these distinctions have been made, (35) we must consider the
mutual relation of those affirmations and denials which assert or deny
possibility or contingency, impossibility or necessity: for the subject is
not without difficulty.
We admit that of composite expressions those are contradictory each
to each which have the verb ‘to be’ in its positive and negative form
respectively. Thus the contradictory of the proposition ‘man is’ is ‘man is
not’, not ‘not-man is’, and the contradictory of ‘man is white’ is ‘man is
not white’, not ‘man is not-white’. [21b] For otherwise, since either the
positive or the negative proposition is true of any subject, it will turn out
true to say that a piece of wood is a man that is not white.
Now if this is the case, (5) in those propositions which do not contain
the verb ‘to be’ the verb which takes its place will exercise the same
function. Thus the contradictory of ‘man walks’ is ‘man does not walk’,
not ‘not-man walks’; for to say ‘man walks’ is merely equivalent to
saying ‘man is walking’.
If then this rule is universal, (10) the contradictory of ‘it may be’ is ‘it
may not be’, not ‘it cannot be’.
Now it appears that the same thing both may and may not be; for
instance, everything that may be cut or may walk may also escape
cutting and refrain from walking; and the reason is that those things that
have potentiality in this sense are not always actual. In such cases, both
the positive and the negative propositions will be true; for that which is
capable of walking or of being seen has also a potentiality in the
opposite direction. (15)
But since it is impossible that contradictory propositions should both
be true of the same subject, it follows that ‘it may not be’ is not the
contradictory of ‘it may be’. For it is a logical consequence of what we
have said, either that the same predicate can be both applicable and
inapplicable to one and the same subject at the same time, (20) or that it
is not by the addition of the verbs ‘be’ and ‘not be’, respectively, that
positive and negative propositions are formed. If the former of these
alternatives must be rejected, we must choose the latter.
The contradictory, then, of ‘it may be’ is ‘it cannot be’. The same rule
applies to the proposition ‘it is contingent that it should be’; the
contradictory of this is ‘it is not contingent that it should be’. The similar
propositions, (25) such as ‘it is necessary’ and ‘it is impossible’, may be
dealt with in the same manner. For it comes about that just as in the
former instances the verbs ‘is’ and ‘is not’ were added to the subjectmatter of the sentence ‘white’ and ‘man’, so here ‘that it should be’ and
‘that it should not be’ are the subject-matter and ‘is possible’, ‘is
contingent’, are added. These indicate that a certain thing is or is not
possible, (30) just as in the former instances ‘is’ and ‘is not’ indicated that
certain things were or were not the case.
The contradictory, then, of ‘it may not be’ is not ‘it cannot be’, but ‘it
cannot not be’, and the contradictory of ‘it may be’ is not ‘it may not be’,
but ‘it cannot be’. Thus the propositions ‘it may be’ and ‘it may not be’
appear each to imply the other: for, (35) since these two propositions are
not contradictory, the same thing both may and may not be. But the
propositions ‘it may be’ and ‘it cannot be’ can never be true of the same
subject at the same time, for they are contradictory. Nor can the
propositions ‘it may not be’ and ‘it cannot not be’ be at once true of the
same subject. [22a]
The propositions which have to do with necessity are governed by the
same principle. The contradictory of ‘it is necessary that it should be’ is
not ‘it is necessary that it should not be’, but ‘it is not necessary that it
should be’, and the contradictory of ‘it is necessary that it should not be’
is ‘it is not necessary that it should not be’. (5)
Again, the contradictory of ‘it is impossible that it should be’ is not ‘it
is impossible that it should not be’ but ‘it is not impossible that it should
be’, and the contradictory of ‘it is impossible that it should not be’ is ‘it is
not impossible that it should not be’.
To generalize, we must, as has been stated, define the clauses ‘that it
should be’ and ‘that it should not be’ as the subject-matter of the
propositions, and in making these terms into affirmations and denials we
must combine them with ‘that it should be’ and ‘that it should not be’
respectively. (10)
We must consider the following pairs as contradictory propositions:
It may be.
It cannot be.
It is contingent.
It is not contingent.
It is impossible.
It is not impossible.
It is necessary.
It is not necessary.
It is true.
It is not true.
13
Logical sequences follow in due course when we have arranged the
propositions thus. (15) From the proposition ‘it may be’ it follows that it is
contingent, and the relation is reciprocal. It follows also that it is not
impossible and not necessary.
From the proposition ‘it may not be’ or ‘it is contingent that it should
not be’ it follows that it is not necessary that it should not be and that it
is not impossible that it should not be. From the proposition ‘it cannot
be’ or ‘it is not contingent’ it follows that it is necessary that it should
not be and that it is impossible that it should be. (20) From the
proposition ‘it cannot not be’ or ‘it is not contingent that it should not
be’ it follows that it is necessary that it should be and that it is
impossible that it should not be.
Let us consider these statements by the help of a table: (25)
A. It may be.
B. It cannot be.
It is contingent.
It is not contingent.
It is not impossible that it should be.
It is impossible that it should be.
It is not necessary that it should be.
It is necessary that it should not be.
C. It may not be.
D. It cannot not be.
It is contingent that it should not be.
It is not contingent that it should not be.
It is not impossible that it should not be.
It is impossible that it should not be.
It is not necessary that it should not be.
It is necessary that it should be.
Now the propositions ‘it is impossible that it should be’ and ‘it is not
impossible that it should be’ are consequent upon the propositions ‘it
may be’, (30) ‘it is contingent’, and ‘it cannot be’, ‘it is not contingent’, the
contradictories upon the contradictories. But there is inversion. The
negative of the proposition ‘it is impossible’ is consequent upon the
proposition ‘it may be’ and the corresponding positive in the first case
upon the negative in the second. (35) For ‘it is impossible’ is a positive
proposition and ‘it is not impossible’ is negative.
We must investigate the relation subsisting between these propositions
and those which predicate necessity. That there is a distinction is clear.
In this case, contrary propositions follow respectively from contradictory
propositions, and the contradictory propositions belong to separate
sequences. For the proposition ‘it is not necessary that it should be’ is not
the negative of ‘it is necessary that it should not be’, for both these
propositions may be true of the same subject; for when it is necessary
that a thing should not be, it is not necessary that it should be. [22b]
The reason why the propositions predicating necessity do not follow in
the same kind of sequence as the rest, lies in the fact that the proposition
‘it is impossible’ is equivalent, when used with a contrary subject, to the
proposition ‘it is necessary’. For when it is impossible that a thing should
be, it is necessary, not that it should be, (5) but that it should not be, and
when it is impossible that a thing should not be, it is necessary that it
should be. Thus, if the propositions predicating impossibility or nonimpossibility follow without change of subject from those predicating
possibility or non-possibility, those predicating necessity must follow
with the contrary subject; for the propositions ‘it is impossible’ and ‘it is
necessary’ are not equivalent, but, as has been said, inversely connected.
Yet perhaps it is impossible that the contradictory propositions
predicating necessity should be thus arranged. (10) For when it is
necessary that a thing should be, it is possible that it should be. (For if
not, the opposite follows, since one or the other must follow; so, if it is
not possible, it is impossible, and it is thus impossible that a thing should
be, which must necessarily be; which is absurd.)
Yet from the proposition ‘it may be’ it follows that it is not impossible,
and from that it follows that it is not necessary; it comes about therefore
that the thing which must necessarily be need not be; which is absurd.
(15) But again, the proposition ‘it is necessary that it should be’ does not
follow from the proposition ‘it may be’, nor does the proposition ‘it is
necessary that it should not be’. For the proposition ‘it may be’ implies a
twofold possibility, while, if either of the two former propositions is
true, the twofold possibility vanishes. For if a thing may be, it may also
not be, but if it is necessary that it should be or that it should not be, (20)
one of the two alternatives will be excluded. It remains, therefore, that
the proposition ‘it is not necessary that it should not be’ follows from the
proposition ‘it may be’. For this is true also of that which must
necessarily be.
Moreover the proposition ‘it is not necessary that it should not be’ is
the contradictory of that which follows from the proposition ‘it cannot
be’; for ‘it cannot be’ is followed by ‘it is impossible that it should be’
and by ‘it is necessary that it should not be’, (25) and the contradictory of
this is the proposition ‘it is not necessary that it should not be’. Thus in
this case also contradictory propositions follow contradictory in the way
indicated, and no logical impossibilities occur when they are thus
arranged.
It may be questioned whether the proposition ‘it may be’ follows from
the proposition ‘it is necessary that it should be’. If not, (30) the
contradictory must follow, namely that it cannot be, or, if a man should
maintain that this is not the contradictory, then the proposition ‘it may
not be’.
Now both of these are false of that which necessarily is. At the same
time, it is thought that if a thing may be cut it may also not be cut, if a
thing may be it may also not be, and thus it would follow that a thing
which must necessarily be may possibly not be; which is false. (35) It is
evident, then, that it is not always the case that that which may be or
may walk possesses also a potentiality in the other direction. There are
exceptions. In the first place we must except those things which possess
a potentiality not in accordance with a rational principle, as fire
possesses the potentiality of giving out heat, that is, an irrational
capacity. Those potentialities which involve a rational principle are
potentialities of more than one result, that is, of contrary results; those
that are irrational are not always thus constituted. [23a] As I have said,
fire cannot both heat and not heat, neither has anything that is always
actual any twofold potentiality. Yet some even of those potentialities
which are irrational admit of opposite results. (5) However, thus much
has been said to emphasize the truth that it is not every potentiality
which admits of opposite results, even where the word is used always in
the same sense.
But in some cases the word is used equivocally. For the term ‘possible’
is ambiguous, being used in the one case with reference to facts, to that
which is actualized, as when a man is said to find walking possible
because he is actually walking, and generally when a capacity is
predicated because it is actually realized; in the other case, (10) with
reference to a state in which realization is conditionally practicable, as
when a man is said to find walking possible because under certain
conditions he would walk. This last sort of potentiality belongs only to
that which can be in motion, the former can exist also in the case of that
which has not this power. Both of that which is walking and is actual,
and of that which has the capacity though not necessarily realized, it is
true to say that it is not impossible that it should walk (or, in the other
case, that it should be), but while we cannot predicate this latter kind of
potentiality of that which is necessary in the unqualified sense of the
word, (15) we can predicate the former.
Our conclusion, then, is this: that since the universal is consequent
upon the particular, that which is necessary is also possible, though not
in every sense in which the word may be used.
We may perhaps state that necessity and its absence are the initial
principles of existence and non-existence, and that all else must be
regarded as posterior to these. (20)
It is plain from what has been said that that which is of necessity is
actual. Thus, if that which is eternal is prior, actuality also is prior to
potentiality. Some things are actualities without potentiality, namely,
the primary substances; a second class consists of those things which are
actual but also potential, whose actuality is in nature prior to their
potentiality, though posterior in time; a third class comprises those
things which are never actualized, (25) but are pure potentialities.
14
The question arises whether an affirmation finds its contrary in a
denial or in another affirmation; whether the proposition ‘every man is
just’ finds its contrary in the proposition ‘no man is just’, or in the
proposition ‘every man is unjust’. Take the propositions ‘Callias is just’,
‘Callias is not just’, ‘Callias is unjust’; we have to discover which of these
form contraries. (30)
Now if the spoken word corresponds with the judgement of the mind,
and if, in thought, that judgement is the contrary of another, which
pronounces a contrary fact, in the way, for instance, in which the
judgement ‘every man is just’ pronounces a contrary to that pronounced
by the judgement ‘every man is unjust’, the same must needs hold good
with regard to spoken affirmations. (35)
But if, in thought, it is not the judgement which pronounces a contrary
fact that is the contrary of another, then one affirmation will not find its
contrary in another, but rather in the corresponding denial. We must
therefore consider which true judgement is the contrary of the false, that
which forms the denial of the false judgement or that which affirms the
contrary fact.
Let me illustrate. There is a true judgement concerning that which is
good, (40) that it is good; another, a false judgement, that it is not good;
and a third, which is distinct, that it is bad. [23b] Which of these two
is contrary to the true? And if they are one and the same, which mode of
expression forms the contrary?
It is an error to suppose that judgements are to be defined as contrary
in virtue of the fact that they have contrary subjects; for the judgement
concerning a good thing, that it is good, and that concerning a bad
thing, (5) that it is bad, may be one and the same, and whether they are
so or not, they both represent the truth. Yet the subjects here are
contrary. But judgements are not contrary because they have contrary
subjects, but because they are to the contrary effect.
Now if we take the judgement that that which is good is good, and
another that it is not good, and if there are at the same time other
attributes, which do not and cannot belong to the good, we must
nevertheless refuse to treat as the contraries of the true judgement those
which opine that some other attribute subsists which does not subsist,
(10) as also those that opine that some other attribute does not subsist
which does subsist, for both these classes of judgement are of unlimited
content.
Those judgements must rather be termed contrary to the true
judgements, in which error is present. Now these judgements are those
which are concerned with the starting points of generation, and
generation is the passing from one extreme to its opposite; therefore
error is a like transition.
Now that which is good is both good and not bad. (15) The first quality
is part of its essence, the second accidental; for it is by accident that it is
not bad. But if that true judgement is most really true, which concerns
the subject’s intrinsic nature, then that false judgement likewise is most
really false, which concerns its intrinsic nature. Now the judgement that
that which is good is not good is a false judgement concerning its
intrinsic nature, the judgement that it is bad is one concerning that
which is accidental. (20) Thus the judgement which denies the truth of the
true judgement is more really false than that which positively asserts the
presence of the contrary quality. But it is the man who forms that
judgement which is contrary to the true who is most thoroughly
deceived, for contraries are among the things which differ most widely
within the same class. If then of the two judgements one is contrary to
the true judgement, but that which is contradictory is the more truly
contrary, then the latter, it seems, (25) is the real contrary. The judgement
that that which is good is bad is composite. For presumably the man
who forms that judgement must at the same time understand that that
which is good is not good.
Further, the contradictory is either always the contrary or never;
therefore, if it must necessarily be so in all other cases, our conclusion in
the case just dealt with would seem to be correct. (30) Now where terms
have no contrary, that judgement is false, which forms the negative of
the true; for instance, he who thinks a man is not a man forms a false
judgement. If then in these cases the negative is the contrary, then the
principle is universal in its application.
Again, the judgement that that which is not good is not good is
parallel with the judgement that that which is good is good. Besides
these there is the judgement that that which is good is not good, parallel
with the judgement that that which is not good is good. Let us consider,
(35) therefore, what would form the contrary of the true judgement that
that which is not good is not good. The judgement that it is bad would,
of course, fail to meet the case, since two true judgements are never
contrary and this judgement might be true at the same time as that with
which it is connected. For since some things which are not good are bad,
both judgements may be true. Nor is the judgement that it is not bad the
contrary, for this too might be true, since both qualities might be
predicated of the same subject. It remains, therefore, that of the
judgement concerning that which is not good, (40) that it is not good, the
contrary judgement is that it is good; for this is false. [24a] In the same
way, moreover, the judgement concerning that which is good, that it is
not good, is the contrary of the judgement that it is good.
It is evident that it will make no difference if we universalize the
positive judgement, for the universal negative judgement will form the
contrary. For instance, the contrary of the judgement that everything
that is good is good is that nothing that is good is good. (5) For the
judgement that that which is good is good, if the subject be understood
in a universal sense, is equivalent to the judgement that whatever is
good is good, and this is identical with the judgement that everything
that is good is good. We may deal similarly with judgements concerning
that which is not good.
If therefore this is the rule with judgements, and if spoken affirmations
and denials are judgements expressed in words, it is plain that the
universal denial is the contrary of the affirmation about the same
subject. [24b] Thus the propositions ‘everything good is good’, ‘every
man is good’, have for their contraries the propositions ‘nothing good is
good’, ‘no man is good’. The contradictory propositions, (5) on the other
hand, are ‘not everything good is good’, ‘not every man is good’.
It is evident, also, that neither true judgements nor true propositions
can be contrary the one to the other. For whereas, when two
propositions are true, a man may state both at the same time without
inconsistency, contrary propositions are those which state contrary
conditions, and contrary conditions cannot subsist at one and the same
time in the same subject.
1
Cf. 16a 22–26.
2
Cf. Poet. 1456b 11.
3
Cf. 17b 26–9.
4
Cf. 17b 29–37.
5
Cf. 16a 19, 30.
6
Analytica Priora, 51b 36–52a 17.
7
Cf. 17b 38.
8
Topica, viii. 7.
ANALYTICA PRIORA
Translated by A. J. Jenkinson
CONTENTS
BOOK I
A. Structure of the Syllogism.
1. PRELIMINARY DISCUSSIONS.
CHAPTER
1. Subject and scope of the Analytics. Certain definitions and divisions.
2. Conversion of pure propositions.
3. Conversion of necessary and contingent propositions.
2. EXPOSITION OF THE THREE FIGURES.
4. Pure syllogisms in the first figure.
5. Pure syllogisms in the second figure.
6. Pure syllogisms in the third figure.
7. Common properties of the three figures.
[Chapters 8–12 omitted.]
13. Preliminary discussion of the contingent.
[Chapters 14–22 omitted.]
3. SUPPLEMENTARY DISCUSSIONS.
23. Every syllogism is in one of the three figures, is completed through the first figure, and
reducible to a universal mood of the first figure.
24. Quality and quantity of the premisses of the syllogism.
25. Number of the terms, propositions, and conclusions.
26. The kinds of proposition to be established or disproved in each figure.
B. Mode of discovery of arguments.
1. GENERAL.
27. Rules for categorical syllogisms, applicable to all problems.
28. Rules for categorical syllogisms, peculiar to different problems.
29. Rules for reductio ad impossibile, hypothetical syllogisms, and modal syllogisms.
30.
2. PROPER TO THE SEVERAL SCIENCES AND ARTS.
31.
3. DIVISION.
C. Analysis (1) of arguments into figures and moods of syllogism.
[Chapters 32–46 omitted.]
BOOK II
Properties and defects of syllogism; arguments akin to syllogism.
A. PROPERTIES.
[Chapters 1–15 omitted.]
B. DEFECTS.
16. Petitio principii.
17. False Cause.
18. Falsity of conclusion due to falsity in one or more premisses.
19. How to impede opposing arguments and conceal one’s own.
20. When refutation is possible.
21. Error.
C. ARGUMENTS AKIN TO SYLLOGISM.
22. Rules for conversion and for the comparison of desirable and undesirable objects.
23. Induction.
24. Example.
25. Reduction.
26. Objection.
27. Enthymeme.
ANALYTICA PRIORA
(Prior Analytics)
BOOK I
1
We must first state the subject of our inquiry and the faculty to
which it belongs: (10) its subject is demonstration and the faculty that
carries it out demonstrative science. [24a] We must next define a
premiss, a term, and a syllogism, and the nature of a perfect and of an
imperfect syllogism; and after that, the inclusion or non-inclusion of one
term in another as in a whole, and what we mean by predicating one
term of all, or none, of another. (15)
A premiss then is a sentence affirming or denying one thing of
another. This is either universal or particular or indefinite. By universal I
mean the statement that something belongs to all or none of something
else; by particular that it belongs to some or not to some or not to all; by
indefinite that it does or does not belong, without any mark to show
whether it is universal or particular, (20) e. g. ‘contraries are subjects of
the same science’, or ‘pleasure is not good’. The demonstrative premiss
differs from the dialectical, because the demonstrative premiss is the
assertion of one of two contradictory statements (the demonstrator does
not ask for his premiss, but lays it down), whereas the dialectical
premiss depends on the adversary’s choice between two contradictories.
(25) But this will make no difference to the production of a syllogism in
either case; for both the demonstrator and the dialectician argue
syllogistically after stating that something does or does not belong to
something else. Therefore a syllogistic premiss without qualification will
be an affirmation or denial of something concerning something else in
the way we have described; it will be demonstrative, if it is true and
obtained through the first principles of its science; while a dialectical
premiss is the giving of a choice between two contradictories, (30) when a
man is proceeding by question, (10) but when he is syllogizing it is the
assertion of that which is apparent and generally admitted, as has been
said in the Topics.1 [24b] The nature then of a premiss and the
difference between syllogistic, demonstrative, and dialectical premisses,
may be taken as sufficiently defined by us in relation to our present
need, (15) but will be stated accurately in the sequel.2
I call that a term into which the premiss is resolved, i. e. both the
predicate and that of which it is predicated, ‘being’ being added and ‘not
being’ removed, or vice versa.
A syllogism is discourse in which, certain things being stated,
something other than what is stated follows of necessity from their being
so. (20) I mean by the last phrase that they produce the consequence, and
by this, that no further term is required from without in order to make
the consequence necessary.
I call that a perfect syllogism which needs nothing other than what
has been stated to make plain what necessarily follows; a syllogism is
imperfect, if it needs either one or more propositions, (25) which are
indeed the necessary consequences of the terms set down, but have not
been expressly stated as premisses.
That one term should be included in another as in a whole is the same
as for the other to be predicated of all of the first. And we say that one
term is predicated of all of another, whenever no instance of the subject
can be found of which the other term cannot be asserted: ‘to be
predicated of none’ must be understood in the same way. (30)
2
[25a] Every premiss states that something either is or must be or
may be the attribute of something else; of premisses of these three kinds
some are affirmative, others negative, in respect of each of the three
modes of attribution; again some affirmative and negative premisses are
universal, (5) others particular, others indefinite. It is necessary then that
in universal attribution the terms of the negative premiss should be
convertible, e. g. if no pleasure is good, then no good will be pleasure;
the terms of the affirmative must be convertible, not however
universally, but in part, e. g. if every pleasure is good, some good must
be pleasure; the particular affirmative must convert in part (for if some
pleasure is good, (10) then some good will be pleasure); but the particular
negative need not convert, for if some animal is not man, it does not
follow that some man is not animal.
First then take a universal negative with the terms A and B. (15) If no B
is A, neither can any A be B. For if some A (say C) were B, it would not
be true that no B is A; for C is a B. But if every B is A, then some A is B.
For if no A were B, then no B could be A. (20) But we assumed that every
B is A. Similarly too, if the premiss is particular. For if some B is A, then
some of the As must be B. For if none were, then no B would be A. But if
some B is not A, there is no necessity that some of the As should not be
B; e. g. let B stand for animal and A for man. Not every animal is a man:
but every man is an animal. (25)
3
The same manner of conversion will hold good also in respect of
necessary premisses. The universal negative converts universally; each of
the affirmatives converts into a particular. If it is necessary that no B is
A, it is necessary also that no A is B. For if it is possible that some A is B,
(30) it would be possible also that some B is A. If all or some B is A of
necessity, it is necessary also that some A is B: for if there were no
necessity, neither would some of the Bs be A necessarily. But the
particular negative does not convert, (35) for the same reason which we
have already stated.3
In respect of possible premisses, since possibility is used in several
senses (for we say that what is necessary and what is not necessary and
what is potential is possible), affirmative statements will all convert in a
manner similar to those described.4 For if it is possible that all or some B
is A, (40) it will be possible that some A is B. [25b] For if that were not
possible, then no B could possibly be A. This has been already proved.5
But in negative statements the case is different. Whatever is said to be
possible, either because B necessarily is A, or because B is not necessarily
A, admits of conversion like other negative statements, (5) e. g. if one
should say, it is possible that man is not horse, or that no garment is
white. For in the former case the one term necessarily does not belong to
the other; in the latter there is no necessity that it should: and the
premiss converts like other negative statements. For if it is possible for
no man to be a horse, it is also admissible for no horse to be a man; and
if it is admissible for no garment to be white, (10) it is also admissible for
nothing white to be a garment. For if any white thing must be a
garment, then some garment will necessarily be white. This has been
already proved.6 The particular negative also must be treated like those
dealt with above.7 But if anything is said to be possible because it is the
general rule and natural (and it is in this way we define the possible), (15)
the negative premisses can no longer be converted like the simple
negative; the universal negative premiss does not convert, and the
particular does. This will be plain when we speak about the possible.8 At
present we may take this much as clear in addition to what has been
said: the statement that it is possible that no B is A or some B is not A is
affirmative in form: for the expression ‘is possible’ ranks along with ‘is’,
(20) and ‘is’ makes an affirmation always and in every case, whatever the
terms to which it is added in predication, e. g. ‘it is not-good’ or ‘it is
not-white’ or in a word ‘it is not-this’. But this also will be proved in the
sequel.9 (25) In conversion these premisses will behave like the other
affirmative propositions.
4
After these distinctions we now state by what means, when, and
how every syllogism is produced; subsequently10 we must speak of
demonstration. Syllogism should be discussed before demonstration, (30)
because syllogism is the more general: the demonstration is a sort of
syllogism, but not every syllogism is a demonstration.
Whenever three terms are so related to one another that the last is
contained in the middle as in a whole, and the middle is either contained
in, or excluded from, the first as in or from a whole, (35) the extremes
must be related by a perfect syllogism. I call that term middle which is
itself contained in another and contains another in itself: in position also
this comes in the middle. By extremes I mean both that term which is
itself contained in another and that in which another is contained. If11 A
is predicated of all B, and B of all C, (40) A must be predicated of all C: we
have already explained12 what we mean by ‘predicated of all’. [26a]
Similarly13 also, if A is predicated of no B, and B of all C, it is necessary
that no C will be A.
But14 if the first term belongs to all the middle, but the middle to none
of the last term, there will be no syllogism in respect of the extremes; for
nothing necessary follows from the terms being so related; for it is
possible that the first should belong either to all or to none of the last, (5)
so that neither a particular nor a universal conclusion is necessary. But if
there is no necessary consequence, there cannot be a syllogism by means
of these premisses. As an example of a universal affirmative relation
between the extremes we may take the terms animal, man, horse; of a
universal negative relation, the terms animal, man, stone. Nor15 again
can a syllogism be formed when neither the first term belongs to any of
the middle, (10) nor the middle to any of the last. As an example of a
positive relation between the extremes take the terms science, line,
medicine: of a negative relation science, line, unit.
If then the terms are universally related, it is clear in this figure when
a syllogism will be possible and when not, and that if a syllogism is
possible the terms must be related as described, (15) and if they are so
related there will be a syllogism.
But if one term is related universally, the other in part only, to its
subject, there must be a perfect syllogism whenever universality is
posited with reference to the major term either affirmatively or
negatively, and particularity with reference to the minor term
affirmatively: but whenever the universality is posited in relation to the
minor term, (20) or the terms are related in any other way, a syllogism is
impossible. I call that term the major in which the middle is contained
and that term the minor which comes under the middle. Let16 all B be A
and some C be B. Then if ‘predicated of all’ means what was said
above,17 it is necessary that some C is A. And18 if no B is A, (25) but some
C is B, it is necessary that some C is not A. (The meaning of ‘predicated
of none’ has also been defined.19) So there will be a perfect syllogism.
This holds good also if the premiss BC20 should be indefinite, provided
that it is affirmative: for we shall have the same syllogism whether the
premiss is indefinite or particular.
But if the universality is posited with respect to the minor term either
affirmatively or negatively, (30) a syllogism will not be possible, whether
the major premiss is positive or negative, indefinite or particular: e. g.21
if some B is or is not A, and all C is B. As an example of a positive
relation between the extremes take the terms good, state, (35) wisdom: of
a negative relation, good, state, ignorance. Again22 if no C is B, but some
B is or is not A, or not every B is A, there cannot be a syllogism. Take the
terms white, horse, swan: white, horse, raven. The same terms may be
taken also if the premiss BA is indefinite.
Nor when the major premiss is universal, whether affirmative or
negative, and the minor premiss is negative and particular, can there be
a syllogism, whether the minor premiss be indefinite or particular: e. g.23
if all B is A, and some C is not B, or if not all C is B. [26b] For the
major term may be predicable both of all and of none of the minor, to
some of which the middle term cannot be attributed. Suppose the terms
are animal, (5) man, white: next take some of the white things of which
man is not predicated—swan and snow: animal is predicated of all of the
one, but of none of the other. Consequently there cannot be a syllogism.
Again24 let no B be A, but let some C not be B. (10) Take the terms
inanimate, man, white: then take some white things of which man is not
predicated—swan and snow: the term inanimate is predicated of all of
the one, of none of the other.
Further since it is indefinite to say some C is not B, and it is true that
some C is not B, (15) whether no C is B, or not all C is B, and since if
terms are assumed such that no C is B, no syllogism follows (this has
already been stated25), it is clear that this arrangement of terms26 will
not afford a syllogism: otherwise one would have been possible with a
universal negative minor premiss. (20) A similar proof may also be given if
the universal premiss27 is negative.28
Nor can there in any way be a syllogism if both the relations of subject
and predicate are particular, either positively or negatively, or the one
negative and the other affirmative,29 or one indefinite and the other
definite, or both indefinite. Terms common to all the above are animal,
(25) white, horse: animal, white, stone.
It is clear then from what has been said that if there is a syllogism in
this figure with a particular conclusion, the terms must be related as we
have stated: if they are related otherwise, no syllogism is possible
anyhow. It is evident also that all the syllogisms in this figure are perfect
(for they are all completed by means of the premisses originally taken)
and that all conclusions are proved by this figure, (30) viz. universal and
particular, affirmative and negative. Such a figure I call the first.
5
Whenever the same thing belongs to all of one subject, (35) and to
none of another, or to all of each subject or to none of either, I call such
a figure the second; by middle term in it I mean that which is predicated
of both subjects, by extremes the terms of which this is said, by major
extreme that which lies near the middle, by minor that which is further
away from the middle. [27a] The middle term stands outside the
extremes, and is first in position. A syllogism cannot be perfect anyhow
in this figure, but it may be valid whether the terms are related
universally or not.
If then the terms are related universally a syllogism will be possible,
whenever the middle belongs to all of one subject and to none of another
(it does not matter which has the negative relation), (5) but in no other
way. Let M be predicated of no N, but of all O. Since, then, the negative
relation is convertible, N will belong to no M: but M was assumed to
belong to all O: consequently N will belong to no O.30 This has already
been proved.31 Again if M belongs to all N, but to no O, then N will
belong to no O.32 For if M belongs to no O, (10) O belongs to no M: but M
(as was said) belongs to all N: O then will belong to no N: for the first
figure has again been formed. But since the negative relation is
convertible, N will belong to no O. Thus it will be the same syllogism
that proves both conclusions.
It is possible to prove these results also by reduction ad impossibile. (15)
It is clear then that a syllogism is formed when the terms are so
related, but not a perfect syllogism; for necessity is not perfectly
established merely from the original premisses; others also are needed.
But if M is predicated of every N and O, there cannot be a syllogism.
Terms to illustrate a positive relation between the extremes are
substance, animal, man; a negative relation, substance, animal, (20)
number—substance being the middle term.
Nor is a syllogism possible when M is predicated neither of any N nor
of any O. Terms to illustrate a positive relation are line, animal, man: a
negative relation, line, animal, stone.
It is clear then that if a syllogism is formed when the terms are
universally related, the terms must be related as we stated at the
outset:33 for if they are otherwise related no necessary consequence
follows. (25)
If the middle term is related universally to one of the extremes, a
particular negative syllogism must result whenever the middle term is
related universally to the major whether positively or negatively, and
particularly to the minor and in a manner opposite to that of the
universal statement: by ‘an opposite manner’ I mean, if the universal
statement is negative, the particular is affirmative: if the universal is
affirmative, (30) the particular is negative. For if M belongs to no N, but
to some O, it is necessary that N does not belong to some O.34 For since
the negative statement is convertible, N will belong to no M: but M was
admitted to belong to some O: therefore N will not belong to some O: for
the result is reached by means of the first figure. (35) Again if M belongs
to all N, but not to some O, it is necessary that N does not belong to
some O:35 for if N belongs to all O, and M is predicated also of all N, M
must belong to all O: but we assumed that M does not belong to some O.
And if M belongs to all N but not to all O, we shall conclude that N does
not belong to all O: the proof is the same as the above. [27b] But if M
is predicated of all O, but not of all N, there will be no syllogism. Take
the terms animal, (5) substance, raven; animal, white, raven. Nor will
there be a conclusion when M is predicated of no O, but of some N.
Terms to illustrate a positive relation between the extremes are animal,
substance, unit: a negative relation, animal, substance, science.
If then the universal statement is opposed to the particular, (10) we
have stated when a syllogism will be possible and when not: but if the
premisses are similar in form, I mean both negative or both affirmative,
a syllogism will not be possible anyhow. First let them be negative, and
let the major premiss be universal, e. g. let M belong to no N, (15) and not
to some O. It is possible then for N to belong either to all O or to no O.
Terms to illustrate the negative relation are black, snow, animal. But it is
not possible to find terms of which the extremes are related positively
and universally, if M belongs to some O, and does not belong to some O.
For if N belonged to all O, but M to no N, then M would belong to no O:
but we assumed that it belongs to some O. (20) In this way then it is not
admissible to take terms: our point must be proved from the indefinite
nature of the particular statement. For since it is true that M does not
belong to some O, even if it belongs to no O, and since if it belongs to no
O a syllogism is (as we have seen36 not possible, clearly it will not be
possible now either.
Again let the premisses be affirmative, and let the major premiss as
before be universal, e. g. let M belong to all N and to some O. (25) It is
possible then for N to belong to all O or to no O. Terms to illustrate the
negative relation are white, swan, stone. But it is not possible to take
terms to illustrate the universal affirmative relation, for the reason
already stated:37 the point must be proved from the indefinite nature of
the particular statement. But if the minor premiss is universal, (30) and M
belongs to no O, and not to some N, it is possible for N to belong either
to all O or to no O. Terms for the positive relation are white, animal,
raven: for the negative relation, white, stone, raven. If the premisses are
affirmative, terms for the negative relation are white, animal, snow; for
the positive relation, white, animal, swan. Evidently then, whenever the
premisses are similar in form, (35) and one is universal, the other
particular, a syllogism cannot be formed anyhow. Nor is one possible if
the middle term belongs to some of each of the extremes, or does not
belong to some of either, or belongs to some of the one, not to some of
the other, or belongs to neither universally, or is related to them
indefinitely. Common terms for all the above are white, animal, man:
white, animal, inanimate.
[28a] It is clear then from what has been said that if the terms are
related to one another in the way stated, a syllogism results of necessity;
and if there is a syllogism, the terms must be so related. But it is evident
also that all the syllogisms in this figure are imperfect: for all are made
perfect by certain supplementary statements, (5) which either are
contained in the terms of necessity or are assumed as hypotheses, i. e.
when we prove per impossibile. And it is evident that an affirmative
conclusion is not attained by means of this figure, but all are negative,
whether universal or particular.
6
But if one term belongs to all, and another to none, of a third, (10) or
if both belong to all, or to none, of it, I call such a figure the third; by
middle term in it I mean that of which both the predicates are
predicated, by extremes I mean the predicates, by the major extreme
that which is further from the middle, by the minor that which is nearer
to it. The middle term stands outside the extremes, and is last in
position. (15) A syllogism cannot be perfect in this figure either, but it
may be valid whether the terms are related universally or not to the
middle term.
If they are universal, whenever both P and R belong to all S, it follows
that P will necessarily belong to some R.38 For, since the affirmative
statement is convertible, S will belong to some R: consequently since P
belongs to all S, and S to some R, P must belong to some R: for a
syllogism in the first figure is produced. (20) It is possible to demonstrate
this also per impossibile and by exposition. For if both P and R belong to
all S, should one of the Ss, e. g. N, be taken, both P and R will belong to
this, and thus P will belong to some R. (25)
If R belongs to all S, and P to no S, there will be a syllogism to prove
that P will necessarily not belong to some R.39 This may be
demonstrated in the same way as before by converting the premiss RS.40
It might be proved also per impossibile, as in the former cases. (30) But if R
belongs to no S, P to all S, there will be no syllogism. Terms for the
positive relation are animal, horse, man: for the negative relation
animal, inanimate, man.
Nor can there be a syllogism when both terms are asserted of no S.
Terms for the positive relation are animal, horse, inanimate; for the
negative relation man, horse, inanimate—inanimate being the middle
term. (35)
It is clear then in this figure also when a syllogism will be possible and
when not, if the terms are related universally. For whenever both the
terms are affirmative, there will be a syllogism to prove that one extreme
belongs to some of the other; but when they are negative, no syllogism
will be possible. [28b] But when one is negative, the other affirmative,
if the major is negative, the minor affirmative, there will be a syllogism
to prove that the one extreme does not belong to some of the other: but
if the relation is reversed, no syllogism will be possible.
If one term is related universally to the middle, (5) the other in part
only, when both are affirmative there must be a syllogism, no matter
which of the premisses is universal. For if R belongs to all S, P to some S,
P must belong to some R.41 For since the affirmative statement is
convertible S will belong to some P: consequently since R belongs to all
S, (10) and S to some P, R must also belong to some P: therefore P must
belong to some R.
Again if R belongs to some S, and P to all S, P must belong to some
42
R. This may be demonstrated in the same way as the preceding. And it
is possible to demonstrate it also per impossibile and by exposition, (15) as
in the former cases. But if one term is affirmative, the other negative,
and if the affirmative is universal, a syllogism will be possible whenever
the minor term is affirmative. For if R belongs to all S, but P does not
belong to some S, it is necessary that P does not belong to some R.43 For
if P belongs to all R, and R belongs to all S, then P will belong to all S:
but we assumed that it did not. (20) Proof is possible also without
reduction ad impossibile, if one of the Ss be taken to which P does not
belong.
But whenever the major is affirmative, no syllogism will be possible,
e. g. if P belongs to all S, and R does not belong to some S. Terms for the
universal affirmative relation are animate, man, animal. For the
universal negative relation it is not possible to get terms, (25) if R belongs
to some S, and does not belong to some S. For if P belongs to all S, and R
to some S, then P will belong to some R: but we assumed that it belongs
to no R. We must put the matter as before.44 Since the expression ‘it does
not belong to some’ is indefinite, it may be used truly of that also which
belongs to none. But if R belongs to no S, (30) no syllogism is possible, as
has been shown.45 Clearly then no syllogism will be possible here.
But if the negative term is universal, whenever the major is negative
and the minor affirmative there will be a syllogism. For if P belongs to
no S, and R belongs to some S, P will not belong to some R:46 for we
shall have the first figure again, (35) if the premiss RS is converted.
But when the minor is negative, there will be no syllogism. Terms for
the positive relation are animal, man, wild: for the negative relation,
animal, science, wild—the middle in both being the term wild.
Nor is a syllogism possible when both are stated in the negative, but
one is universal, the other particular. When the minor is related
universally to the middle, take the terms animal, science, wild; animal,
man, wild. [29a] When the major is related universally to the middle,
take as terms for a negative relation raven, snow, white. For a positive
relation terms cannot be found, if R belongs to some S, and does not
belong to some S. For if P belongs to all R, and R to some S, (5) then P
belongs to some S: but we assumed that it belongs to no S. Our point,
then, must be proved from the indefinite nature of the particular
statement.
Nor is a syllogism possible anyhow, if each of the extremes belongs to
some of the middle, or does not belong, or one belongs and the other
does not to some of the middle, or one belongs to some of the middle,
the other not to all, or if the premisses are indefinite. Common terms for
all are animal, man, white: animal, inanimate, (10) white.
It is clear then in this figure also when a syllogism will be possible,
and when not; and that if the terms are as stated, a syllogism results of
necessity, and if there is a syllogism, the terms must be so related. It is
clear also that all the syllogisms in this figure are imperfect (for all are
made perfect by certain supplementary assumptions), (15) and that it will
not be possible to reach a universal conclusion by means of this figure,
whether negative or affirmative.
7
It is evident also that in all the figures, whenever a proper syllogism
does not result, if both the terms are affirmative or negative nothing
necessary follows at all, (20) but if one is affirmative, the other negative,
and if the negative is stated universally, a syllogism always results
relating the minor to the major term, e. g. if A belongs to all or some B,
and B belongs to no C: for if the premisses are converted it is necessary
that C does not belong to some A.47 Similarly also in the other figures: a
syllogism always results by means of conversion. (25) It is evident also
that the substitution of an indefinite for a particular affirmative will
effect the same syllogism in all the figures.
It is clear too that all the imperfect syllogisms are made perfect by
means of the first figure. (30) For all are brought to a conclusion either
ostensively or per impossibile. In both ways the first figure is formed: if
they are made perfect ostensively, because (as we saw) all are brought to
a conclusion by means of conversion, (35) and conversion produces the
first figure: if they are proved per impossibile, because on the assumption
of the false statement the syllogism comes about by means of the first
figure, e. g. in the last figure, if A and B belong to all C, it follows that A
belongs to some B: for if A belonged to no B, and B belongs to all C, A
would belong to no C: but (as we stated) it belongs to all C. Similarly
also with the rest.
[29b] It is possible also to reduce all syllogisms to the universal
syllogisms in the first figure. Those in the second figure are clearly made
perfect by these, though not all in the same way; the universal
syllogisms are made perfect by converting the negative premiss, (5) each
of the particular syllogisms by reduction ad impossibile. In the first figure
particular syllogisms are indeed made perfect by themselves, but it is
possible also to prove them by means of the second figure, reducing
them ad impossibile, e. g. if A belongs to all B, and B to some C, it follows
that A belongs to some C. For if it belonged to no C, and belongs to all B,
then B will belong to no C: this we know by means of the second figure.
(10) Similarly also demonstration will be possible in the case of the
negative. For if A belongs to no B, and B belongs to some C, A will not
belong to some C: for if it belonged to all C, and belongs to no B, then B
will belong to no C: and this (as we saw) is the middle figure. (15)
Consequently, since all syllogisms in the middle figure can be reduced to
universal syllogisms in the first figure, and since particular syllogisms in
the first figure can be reduced to syllogisms in the middle figure, it is
clear that particular syllogisms48 can be reduced to universal syllogisms
in the first figure. Syllogisms in the third figure, if the terms are
universal, (20) are directly made perfect by means of those syllogisms;49
but, when one of the premisses is particular, by means of the particular
syllogisms in the first figure: and these (we have seen) may be reduced
to the universal syllogisms in the first figure: consequently also the
particular syllogisms in the third figure may be so reduced. It is clear
then that all syllogisms may be reduced to the universal syllogisms in
the first figure. (25)
We have stated then how syllogisms which prove that something
belongs or does not belong to something else are constituted, both how
syllogisms of the same figure are constituted in themselves, and how
syllogisms of different figures are related to one another.…
13 Perhaps enough has been said about the proof of necessity, (15) how
it comes about and how it differs from the proof of a simple statement.
[32a] We proceed to discuss that which is possible, when and how and
by what means it can be proved. I use the terms ‘to be possible’ and ‘the
possible’ of that which is not necessary but, being assumed, results in
nothing impossible. (20) We say indeed ambiguously of the necessary that
it is possible. But that my definition of the possible is correct is clear
from the phrases by which we deny or on the contrary affirm possibility.
For the expressions ‘it is not possible to belong’, ‘it is impossible to
belong’, and ‘it is necessary not to belong’ are either identical or follow
from one another; consequently their opposites also, ‘it is possible to
belong’, ‘it is not impossible to belong’, (25) and ‘it is not necessary not to
belong’, will either be identical or follow from one another. For of
everything the affirmation or the denial holds good. That which is
possible then will be not necessary and that which is not necessary will
be possible. It results that all premisses in the mode of possibility are
convertible into one another. (30) I mean not that the affirmative are
convertible into the negative, but that those which are affirmative in
form admit of conversion by opposition, e. g. ‘it is possible to belong’
may be converted into ‘it is possible not to belong’, and ‘it is possible for
A to belong to all B’ into ‘it is possible for A to belong to no B’ or ‘not to
all B’, and ‘it is possible for A to belong to some B’ into ‘it is possible for
A not to belong to some B’. (35) And similarly the other propositions in
this mode can be converted. For since that which is possible is not
necessary, and that which is not necessary may possibly not belong, it is
clear that if it is possible that A should belong to B, it is possible also
that it should not belong to B: and if it is possible that it should belong
to all, it is also possible that it should not belong to all. The same holds
good in the case of particular affirmations: (40) for the proof is identical.
[32b] And such premisses are affirmative and not negative: for ‘to be
possible’ is in the same rank as ‘to be’, as was said above.50
Having made these distinctions we next point out that the expression
‘to be possible’ is used in two ways. In one it means to happen generally
and fall short of necessity, (5) e. g. man’s turning grey or growing or
decaying, or generally what naturally belongs to a thing (for this has not
its necessity unbroken, since man’s existence is not continuous for ever,
although if a man does exist, it comes about either necessarily or
generally). In another sense the expression means the indefinite, (10)
which can be both thus and not thus, e. g. an animal’s walking or an
earthquake’s taking place while it is walking, or generally what happens
by chance: for none of these inclines by nature in the one way more than
in the opposite.
That which is possible in each of its two senses is convertible into its
opposite, (15) not however in the same way: but what is natural is
convertible because it does not necessarily belong (for in this sense it is
possible that a man should not grow grey) and what is indefinite is
convertible because it inclines this way no more than that. Science and
demonstrative syllogism are not concerned with things which are
indefinite, because the middle term is uncertain; but they are concerned
with things that are natural, (20) and as a rule arguments and inquiries
are made about things which are possible in this sense. Syllogisms
indeed can be made about the former, but it is unusual at any rate to
inquire about them.
These matters will be treated more definitely in the sequel;51 our
business at present is to state the moods and nature of the syllogism
made from possible premisses. The expression ‘it is possible for this to
belong to that’ may be understood in two senses: ‘that’ may mean either
that to which ‘that’ belongs or that to which it may belong; for the
expression ‘A is possible of the subject of B’ means that it is possible
either of that of which B is stated or of that of which B may possibly be
stated. (25) It makes no difference whether we say, A is possible of the
subject of B, (30) or all B admits of A. It is clear then that the expression
‘A may possibly belong to all B’ might be used in two senses. First then
we must state the nature and characteristics of the syllogism which
arises if B is possible of the subject of C, and A is possible of the subject
of B. For thus both premisses are assumed in the mode of possibility; but
whenever A is possible of that of which B is true, (35) one premiss is a
simple assertion, the other a problematic. Consequently we must start
from premisses which are similar in form, as in the other cases.…
23
[40b] It is clear from what has been said that the syllogisms in
these figures are made perfect by means of universal syllogisms in the
first figure and are reduced to them. (20) That every syllogism without
qualification can be so treated, will be clear presently, when it has been
proved that every syllogism is formed through one or other of these
figures.
It is necessary that every demonstration and every syllogism should
prove either that something belongs or that it does not, (25) and this
either universally or in part, and further either ostensively or
hypothetically. One sort of hypothetical proof is the reductio ad
impossibile. Let us speak first of ostensive syllogisms: for after these have
been pointed out the truth of our contention will be clear with regard to
those which are proved per impossibile, and in general hypothetically.
If then one wants to prove syllogistically A of B, (30) either as an
attribute of it or as not an attribute of it, one must assert something of
something else. If now A should be asserted of B, the proposition
originally in question will have been assumed. But if A should be
asserted of C, but C should not be asserted of anything, nor anything of
it, nor anything else of A, no syllogism will be possible. For nothing
necessarily follows from the assertion of some one thing concerning
some other single thing. (35) Thus we must take another premiss as well.
If then A be asserted of something else, or something else of A, or
something different of C, nothing prevents a syllogism being formed, but
it will not be in relation to B through the premisses taken. Nor when C
belongs to something else, (40) and that to something else and so on, no
connexion however being made with B, will a syllogism be possible
concerning A in its relation to B. [41a] For in general we stated52 that
no syllogism can establish the attribution of one thing to another, unless
some middle term is taken, which is somehow related to each by way of
predication. For the syllogism in general is made out of premisses, and a
syllogism referring to this out of premisses with the same reference, (5)
and a syllogism relating this to that proceeds through premisses which
relate this to that. But it is impossible to take a premiss in reference to B,
if we neither affirm nor deny anything of it; or again to take a premiss
relating A to B, if we take nothing common, (10) but affirm or deny
peculiar attributes of each. So we must take something midway between
the two, which will connect the predications, if we are to have a
syllogism relating this to that. If then we must take something common
in relation to both, and this is possible in three ways (either by
predicating A of C, and C of B, or C of both, or both of C), (15) and these
are the figures of which we have spoken, it is clear that every syllogism
must be made in one or other of these figures. The argument is the same
if several middle terms should be necessary to establish the relation to B;
for the figure will be the same whether there is one middle term or
many. (20)
It is clear then that the ostensive syllogisms are effected by means of
the aforesaid figures; these considerations will show that reductiones ad
impossibile also are effected in the same way. For all who effect an
argument per impossibile infer syllogistically what is false, (25) and prove
the original conclusion hypothetically when something impossible
results from the assumption of its contradictory; e. g. that the diagonal
of the square is incommensurate with the side, because odd numbers are
equal to evens if it is supposed to be commensurate. One infers
syllogistically that odd numbers come out equal to evens, and one proves
hypothetically the incommensurability of the diagonal, (30) since a
falsehood results through contradicting this. For this we found to be
reasoning per impossibile, viz. proving something impossible by means of
an hypothesis conceded at the beginning. Consequently, since the
falsehood is established in reductions ad impossibile by an ostensive
syllogism, and the original conclusion is proved hypothetically, (35) and
we have already stated that ostensive syllogisms are effected by means
of these figures, it is evident that syllogisms per impossibile also will be
made through these figures. Likewise all the other hypothetical
syllogisms: for in every case the syllogism leads up to the proposition
that is substituted for the original thesis; but the original thesis is
reached by means of a concession or some other hypothesis.53 [41b]
(40) But if this is true, every demonstration and every syllogism must be
formed by means of the three figures mentioned above. But when this
has been shown it is clear that every syllogism is perfected by means of
the first figure and is reducible to the universal syllogisms in this figure.
(5)
24
Further in every syllogism one of the premisses must be
affirmative, and universality must be present: unless one of the
premisses is universal either a syllogism will not be possible, or it will
not refer to the subject proposed, or the original position will be begged.
(10) Suppose we have to prove that pleasure in music is good. If one
should claim as a premiss that pleasure is good without adding ‘all’, no
syllogism will be possible; if one should claim that some pleasure is
good, then if it is different from pleasure in music, it is not relevant to
the subject proposed; if it is this very pleasure, one is assuming that
which was proposed at the outset to be proved. This is more obvious in
geometrical proofs, e. g. (15) that the angles at the base of an isosceles
triangle are equal. Suppose the lines A and B have been drawn to the
centre. If then one should assume that the angle AC is equal to the angle
BD, without claiming generally that angles of semicircles are equal; and
again if one should assume that the angle C is equal to the angle D,
without the additional assumption that every angle of a segment is equal
to every other angle of the same segment; and further if one should
assume that when equal angles are taken from the whole angles, which
are themselves equal, the remainders E and F are equal, he will beg the
thing to be proved, (20) unless he also states that when equals are taken
from equals the remainders are equal.54
It is clear then that in every syllogism there must be a universal
premiss, and that a universal statement is proved only when all the
premisses are universal, while a particular statement is proved both from
two universal premisses and from one only: consequently if the
conclusion is universal, the premisses also must be universal, (25) but if
the premisses are universal it is possible that the conclusion may not be
universal. And it is clear also that in every syllogism either both or one
of the premisses must be like the conclusion. I mean not only in being
affirmative or negative, but also in being necessary, pure, or
problematic. We must consider also the other forms of predication. (30)
It is clear also when a syllogism in general can be made and when it
cannot; and when a valid,55 when a perfect syllogism can be formed; and
that if a syllogism is formed the terms must be arranged in one of the
ways that have been mentioned. (35)
25
It is clear too that every demonstration will proceed through three
terms and no more, unless the same conclusion is established by
different pairs of propositions; e. g. the conclusion E may be established
through the propositions A and B, and through the propositions C and D,
or through the propositions A and B, or A and C, (40) or B and C. For
nothing prevents there being several middles for the same terms. But in
that case there is not one but several syllogisms. [42a] Or again when
each of the propositions A and B is obtained by syllogistic inference, e. g.
A by means of D and E, and again B by means of F and G. Or one may be
obtained by syllogistic, the other by inductive inference. But thus also
the syllogisms are many; for the conclusions are many, (5) e. g. A and B
and C. But if this can be called one syllogism, not many, the same
conclusion may be reached by more than three terms in this way, but it
cannot be reached as C is established by means of A and B. Suppose that
the proposition E is inferred from the premisses A, B, C, and D. It is
necessary then that of these one should be related to another as whole to
part: for it has already been proved that if a syllogism is formed some of
its terms must be related in this way.56 (10) Suppose then that A stands in
this relation to B. Some conclusion then follows from them. It must
either be E or one or other of C and D, or something other than these. (15)
(1) If it is E the syllogism will have A and B for its sole premisses. But
if C and D are so related that one is whole, the other part, some
conclusion will follow from them also; and it must be either E, or one or
other of the propositions A and B, or something other than these. And if
it is (i) E, or (ii) A or B, either (i) the syllogisms will be more than one,
or (ii) the same thing happens to be inferred by means of several terms
only in the sense which we saw to be possible.57 But if (iii) the
conclusion is other than E or A or B, (20) the syllogisms will be many, and
unconnected with one another. But if C is not so related to D as to make
a syllogism, the propositions will have been assumed to no purpose,
unless for the sake of induction or of obscuring the argument or
something of the sort.
(2) But if from the propositions A and B there follows not E but some
other conclusion, (25) and if from C and D either A or B follows or
something else, then there are several syllogisms, and they do not
establish the conclusion proposed: for we assumed that the syllogism
proved E. And if no conclusion follows from C and D, it turns out that
these propositions have been assumed to no purpose, and the syllogism
does not prove the original proposition. (30)
So it is clear that every demonstration and every syllogism will
proceed through three terms only.
This being evident, it is clear that a syllogistic conclusion follows from
two premisses and not from more than two. For the three terms make
two premisses, unless a new premiss is assumed, as was said at the
beginning,58 to perfect the syllogisms. It is clear therefore that in
whatever syllogistic argument the premisses through which the main
conclusion follows (for some of the preceding conclusions must be
premisses) are not even in number, (35) this argument either has not been
drawn syllogistically or it has assumed more than was necessary to
establish its thesis. (40)
If then syllogisms are taken with respect to their main premisses,
every syllogism will consist of an even number of premisses and an odd
number of terms (for the terms exceed the premisses by one), and the
conclusions will be half the number of the premisses. [42b] (5) But
whenever a conclusion is reached by means of prosyllogisms or by
means of several continuous middle terms, e. g. the proposition AB by
means of the middle terms C and D, the number of the terms will
similarly exceed that of the premisses by one (for the extra term must
either be added outside or inserted: but in either case it follows that the
relations of predication are one fewer than the terms related), and the
premisses will be equal in number to the relations of predication. (10) The
premisses however will not always be even, the terms odd; but they will
alternate—when the premisses are even, the terms must be odd; when
the terms are even, the premisses must be odd: for along with one term
one premiss is added, if a term is added from any quarter. Consequently
since the premisses were (as we saw) even, and the terms odd, (15) we
must make them alternately even and odd at each addition. But the
conclusions will not follow the same arrangement either in respect to the
terms or to the premisses. For if one term is added, conclusions will be
added less by one than the pre-existing terms: for the conclusion is
drawn not in relation to the single term last added, but in relation to all
the rest, (20) e. g. if to ABC the term D is added, two conclusions are
thereby added, one in relation to A, the other in relation to B. Similarly
with any further additions. And similarly too if the term is inserted in
the middle: for in relation to one term only, a syllogism will not be
constructed. (25) Consequently the conclusions will be much more
numerous than the terms or the premisses.
26
Since we understand the subjects with which syllogisms are
concerned, what sort of conclusion is established in each figure, and in
how many moods this is done, it is evident to us both what sort of
problem is difficult and what sort is easy to prove. (30) For that which is
concluded in many figures and through many moods is easier; that
which is concluded in few figures and through few moods is more
difficult to attempt. The universal affirmative is proved by means of the
first figure only and by this in only one mood; the universal negative is
proved both through the first figure and through the second, (35) through
the first in one mood, through the second in two. The particular
affirmative is proved through the first and through the last figure, in one
mood through the first, in three moods through the last. The particular
negative is proved in all the figures, (40) but once in the first, in two
moods in the second, in three moods in the third. [43a] It is clear then
that the universal affirmative is most difficult to establish, most easy to
overthrow. In general, universals are easier game for the destroyer than
particulars: for whether the predicate belongs to none or not to some,
they are destroyed: and the particular negative is proved in all the
figures, (5) the universal negative in two. Similarly with universal
negatives: the original statement is destroyed, whether the predicate
belongs to all or to some: and this we found possible in two figures. But
particular statements can be refuted in one way only—by proving that
the predicate belongs either to all or to none. But particular statements
are easier to establish: for proof is possible in more figures and through
more moods. (10) And in general we must not forget that it is possible to
refute statements by means of one another, I mean, universal statements
by means of particular, and particular statements by means of universal:
but it is not possible to establish universal statements by means of
particular, though it is possible to establish particular statements by
means of universal. At the same time it is evident that it is easier to
refute than to establish. (15)
The manner in which every syllogism is produced, the number of the
terms and premisses through which it proceeds, the relation of the
premisses to one another, the character of the problem proved in each
figure, and the number of the figures appropriate to each problem, all
these matters are clear from what has been said.
27
We must now state how we may ourselves always have a supply of
syllogisms in reference to the problem proposed and by what road we
may reach the principles relative to the problem: for perhaps we ought
not only to investigate the construction of syllogisms, (20) but also to
have the power of making them.
Of all the things which exist some are such that they cannot be
predicated of anything else truly and universally, (25) e. g. Cleon and
Callias, i. e. the individual and sensible, but other things may be
predicated of them (for each of these is both man and animal); and some
things are themselves predicated of others, (30) but nothing prior is
predicated of them; and some are predicated of others, and yet others of
them, e. g. man of Callias and animal of man. It is clear then that some
things are naturally not stated of anything: for as a rule each sensible
thing is such that it cannot be predicated of anything, save incidentally:
for we sometimes say that that white object is Socrates, or that that
which approaches is Callias. (35) We shall explain in another place59 that
there is an upward limit also to the process of predicating: for the
present we must assume this. Of these ultimate predicates it is not
possible to demonstrate another predicate, save as a matter of opinion,
but these may be predicated of other things. Neither can individuals be
predicated of other things, (40) though other things can be predicated of
them. Whatever lies between these limits can be spoken of in both ways:
they may be stated of others, and others stated of them. And as a rule
arguments and inquiries are concerned with these things.
We must select the premisses suitable to each problem in this manner:
first we must lay down the subject and the definitions and the properties
of the thing; next we must lay down those attributes which follow the
thing, and again those which the thing follows, and those which cannot
belong to it. [43b] But those to which it cannot belong need not be
selected, (5) because the negative statement implied above is convertible.
Of the attributes which follow we must distinguish those which fall
within the definition, those which are predicated as properties, and
those which are predicated as accidents, and of the latter those which
apparently and those which really belong. The larger the supply a man
has of these, the more quickly will he reach a conclusion; and in
proportion as he apprehends those which are truer, (10) the more
cogently will he demonstrate. But he must select not those which follow
some particular but those which follow the thing as a whole e. g. not
what follows a particular man but what follows every man: for the
syllogism proceeds through universal premisses. (15) If the statement is
indefinite, it is uncertain whether the premiss is universal, but if the
statement is definite, the matter is clear. Similarly one must select those
attributes which the subject follows as wholes, for the reason given. But
that which follows one must not suppose to follow as a whole, e. g. that
every animal follows man or every science music, but only that it
follows, without qualification, (20) as indeed we state it in a proposition:
for the other statement is useless and impossible, e. g. that every man is
every animal or justice is all good. But that which something follows
receives the mark ‘every’. Whenever the subject, for which we must
obtain the attributes that follow, is contained by something else, what
follows or does not follow the highest term universally must not be
selected in dealing with the subordinate term (for these attributes have
been taken in dealing with the superior term; for what follows animal
also follows man, (25) and what does not belong to animal does not
belong to man); but we must choose those attributes which are peculiar
to each subject. For some things are peculiar to the species as distinct
from the genus; for species being distinct there must be attributes
peculiar to each. Nor must we take as things which the superior term
follows, those things which the inferior term follows, (30) e. g. take as
subjects of the predicate ‘animal’ what are really subjects of the
predicate ‘man’. It is necessary indeed, if animal follows man, that it
should follow all these also. But these belong more properly to the
choice of what concerns man. One must apprehend also normal
consequents and normal antecedents; for propositions which obtain
normally are established syllogistically from premisses which obtain
normally, (35) some if not all of them having this character of normality.
For the conclusion of each syllogism resembles its principles. We must
not however choose attributes which are consequent upon all the
terms:60 for no syllogism can be made out of such premisses. The reason
why this is so will be clear in the sequel.61
28
If men wish to establish something about some whole, (40) they
must look to the subjects of that which is being established (the subjects
of which it happens to be asserted), and the attributes which follow that
of which it is to be predicated. For if any of these subjects is the same as
any of these attributes, the attribute originally in question must belong
to the subject originally in question.62 But if the purpose is to establish
not a universal but a particular proposition, they must look for the terms
of which the terms in question are predicable: for if any of these are
identical, the attribute in question must belong to some of the subject in
question.63 [44a] Whenever the one term has to belong to none of the
other, one must look to the consequents of the subject, and to those
attributes which cannot possibly be present in the predicate in
question:64 or conversely to the attributes which cannot possibly be
present in the subject, and to the consequents of the predicate.65 If any
members of these groups are identical, (5) one of the terms in question
cannot possibly belong to any of the other. For sometimes a syllogism in
the first figure results,66 sometimes a syllogism in the second. But if the
object is to establish a particular negative proposition, we must find
antecedents of the subject in question and attributes which cannot
possibly belong to the predicate in question.67 If any members of these
two groups are identical, (10) it follows that one of the terms in question
does not belong to some of the other. Perhaps each of these statements
will become clearer in the following way. Suppose the consequents of A
are designated by B, the antecedents of A by C, attributes which cannot
possibly belong to A by D. Suppose again that the attributes of E are
designated by F, (15) the antecedents of E by G, and attributes which
cannot belong to E by H. If then one of the Cs should be identical with
one of the Fs, A must belong to all E: for F belongs to all E, and A to all
C, consequently A belongs to all E. If C and G are identical, A must
belong to some of the Es: for A follows C, and E follows all G. (20) If F and
D are identical, A will belong to none of the Es by a prosyllogism: for
since the negative proposition is convertible, and F is identical with D, A
will belong to none of the Fs, but F belongs to all E. Again, if B and H are
identical, A will belong to none of the Es: for B will belong to all A, but
to no E: for it was assumed to be identical with H, (25) and H belonged to
none of the Es. If D and G are identical, A will not belong to some of the
Es: for it will not belong to G, because it does not belong to D: but G falls
under E: consequently A will not belong to some of the Es. (30) If B is
identical with G, there will be a converted syllogism: for E will belong to
all A, since B belongs to A and E to B (for B was found to be identical
with G): but that A should belong to all E is not necessary, but it must
belong to some E because it is possible to convert the universal
statement into a particular. (35)
It is clear then that in every proposition which requires proof we must
look to the aforesaid relations of the subject and predicate in question:
for all syllogisms proceed through these. But if we are seeking
consequents and antecedents we must look for those which are primary
and most universal, (40) e. g. in reference to E we must look to KF rather
than to F alone, and in reference to A we must look to KC rather than to
C alone. [44b] For if A belongs to KF, it belongs both to F and to E: but
if it does not follow KF, it may yet follow F. Similarly we must consider
the antecedents of A itself: for if a term follows the primary antecedents,
it will follow those also which are subordinate, (5) but if it does not
follow the former, it may yet follow the latter.
It is clear too that the inquiry proceeds through the three terms and
the two premisses, and that all the syllogisms proceed through the
aforesaid figures. For it is proved that A belongs to all E, whenever an
identical term is found among the Cs and Fs. (10) This will be the middle
term; A and E will be the extremes. So the first figure is formed. And A
will belong to some E, whenever C and G are apprehended to be the
same. This is the last figure: for G becomes the middle term. And A will
belong to no E, when D and F are identical. Thus we have both the first
figure and the middle figure; the first, because A belongs to no F, since
the negative statement is convertible, (15) and F belongs to all E; the
middle figure because D belongs to no A, and to all E. And A will not
belong to some E, whenever D and G are identical. This is the last figure:
for A will belong to no G, and E will belong to all G. Clearly then all
syllogisms proceed through the aforesaid figures, (20) and we must not
select consequents of all the terms,68 because no syllogism is produced
from them. For (as we saw)69 it is not possible at all to establish a
proposition from consequents, and it is not possible to refute by means
of a consequent of both the terms in question: for the middle term must
belong to the one, and not belong to the other.
It is clear too that other methods of inquiry by selection of middle
terms are useless to produce a syllogism, (25) e. g. if the consequents of
the terms in question are identical, or if the antecedents of A are
identical with those attributes which cannot possibly belong to E, or if
those attributes are identical which cannot belong to either term: for no
syllogism is produced by means of these. For if the consequents are
identical, (30) e. g. B and F, we have the middle figure with both
premisses affirmative: if the antecedents of A are identical with
attributes which cannot belong to E, e. g. C with H, we have the first
figure with its minor premiss negative. If attributes which cannot belong
to either term are identical, e. g. C and H, both premisses are negative,
(35) either in the first or in the middle figure. But no syllogism is possible
in this way.
It is evident too that we must find out which terms in this inquiry are
identical, not which are different or contrary, first because the object of
our investigation is the middle term, (40) and the middle term must be
not diverse but identical. Secondly, wherever it happens that a syllogism
results from taking contraries or terms which cannot belong to the same
thing, all arguments can be reduced to the aforesaid moods, e. g. if B and
F are contraries or cannot belong to the same thing. [45a] For if these
are taken, a syllogism will be formed to prove that A belongs to none of
the Es, (5) not however from the premisses taken but in the aforesaid
mood. For B will belong to all A and to no E. Consequently B must be
identical with one of the Hs. Again, if B and G cannot belong to the same
thing, it follows that A will not belong to some of the Es: for then too we
shall have the middle figure: for B will belong to all A and to no G. (10)
Consequently B must be identical with some of the Hs. For the fact that
B and G cannot belong to the same thing differs in no way from the fact
that B is identical with some of the Hs: for that includes everything
which cannot belong to E. (15)
It is clear then that from the inquiries taken by themselves no
syllogism results; but if B and F are contraries B must be identical with
one of the Hs, and the syllogism results through these terms. (20) It turns
out then that those who inquire in this manner are looking gratuitously
for some other way than the necessary way because they have failed to
observe the identity of the Bs with the Hs.
29
Syllogisms which lead to impossible conclusions are similar to
ostensive syllogisms; they also are formed by means of the consequents
and antecedents of the terms in question. (25) In both cases the same
inquiry is involved. For what is proved ostensively may also be
concluded syllogistically per impossibile by means of the same terms; and
what is proved per impossibile may also be proved ostensively, e. g. that
A belongs to none of the Es. For suppose A to belong to some E: then
since B belongs to all A and A to some of the Es, B will belong to some of
the Es: but it was assumed that it belongs to none. (30) Again we may
prove that A belongs to some E: for if A belonged to none of the Es, and
E belongs to all G, A will belong to none of the Gs: but it was assumed to
belong to all. Similarly with the other propositions requiring proof. The
proof per impossibile will always and in all cases be from the consequents
and antecedents of the terms in question. (35) Whatever the problem the
same inquiry is necessary whether one wishes to use an ostensive
syllogism or a reduction to impossibility. For both the demonstrations
start from the same terms, e. g. suppose it has been proved that A
belongs to no E, because it turns out that otherwise B belongs to some of
the Es and this is impossible—if now it is assumed that B belongs to no E
and to all A, (40) it is clear that A will belong to no E. [45b] Again if it
has been proved by an ostensive syllogism that A belongs to no E,
assume that A belongs to some E and it will be proved per impossibile to
belong to no E. Similarly with the rest. In all cases it is necessary to find
some common term other than the subjects of inquiry, (5) to which the
syllogism establishing the false conclusion may relate, so that if this
premiss is converted,70 and the other remains as it is, the syllogism will
be ostensive by means of the same terms. For the ostensive syllogism
differs from the reductio ad impossibile in this: in the ostensive syllogism
both premisses are laid down in accordance with the truth, (10) in the
reductio ad impossibile one of the premisses is assumed falsely.
These points will be made clearer by the sequel,71 when we discuss
the reduction to impossibility: at present this much must be clear, that
we must look to terms of the kinds mentioned whether we wish to use
an ostensive syllogism or a reduction to impossibility. (15) In the other
hypothetical syllogisms, I mean those which proceed by substitution,72
or by positing a certain quality, the inquiry will be directed to the terms
of the problem to be proved—not the terms of the original problem, but
the new terms introduced; and the method of the inquiry will be the
same as before. (20) But we must consider and determine in how many
ways hypothetical syllogisms are possible.
Each of the problems then can be proved in the manner described; but
it is possible to establish some of them syllogistically in another way,
e. g. universal problems by the inquiry which leads up to a particular
conclusion, with the addition of an hypothesis. For if the Cs and the Gs
should be identical, but E should be assumed to belong to the Gs only,
(25) then A would belong to every E: and again if the Ds and the Gs
should be identical, but E should be predicated of the Gs only, it follows
that A will belong to none of the Es. Clearly then we must consider the
matter in this way also. The method is the same whether the relation is
necessary or possible. For the inquiry will be the same, and the syllogism
will proceed through terms arranged in the same order whether a
possible or a pure proposition is proved. (30) We must find in the case of
possible relations, as well as terms that belong, terms which can belong
though they actually do not: for we have proved that the syllogism
which establishes a possible relation proceeds through these terms as
well. (35) Similarly also with the other modes of predication.
It is clear then from what has been said not only that all syllogisms
can be formed in this way, but also that they cannot be formed in any
other. For every syllogism has been proved to be formed through one of
the aforementioned figures, (40) and these cannot be composed through
other terms than the consequents and antecedents of the terms in
question: for from these we obtain the premisses and find the middle
term. [46a] Consequently a syllogism cannot be formed by means of
other terms.
30
The method is the same in all cases, in philosophy, in any art or
study. We must look for the attributes and the subjects of both our
terms, and we must supply ourselves with as many of these as possible,
(5) and consider them by means of the three terms, refuting statements in
one way, confirming them in another, in the pursuit of truth starting
from premisses in which the arrangement of the terms is in accordance
with truth, while if we look for dialectical syllogisms we must start from
probable premisses. (10) The principles of syllogisms have been stated in
general terms, both how they are characterized and how we must hunt
for them, so as not to look to everything that is said about the terms of
the problem or to the same points whether we are confirming or
refuting, or again whether we are confirming of all or of some, and
whether we are refuting of all or some; we must look to fewer points and
they must be definite. (15) We have also stated how we must select with
reference to everything that is, e. g. about good or knowledge. But in
each science the principles which are peculiar are the most numerous.
Consequently it is the business of experience to give the principles which
belong to each subject. I mean for example that astronomical experience
supplies the principles of astronomical science: for once the phenomena
were adequately apprehended, (20) the demonstrations of astronomy were
discovered. Similarly with any other art or science. Consequently, if the
attributes of the thing are apprehended, our business will then be to
exhibit readily the demonstrations. For if none of the true attributes of
things had been omitted in the historical survey, (25) we should be able to
discover the proof and demonstrate everything which admitted of proof,
and to make that clear, whose nature does not admit of proof.
In general then we have explained fairly well how we must select
premisses: we have discussed the matter accurately in the treatise
concerning dialectic.73 (30)
31
It is easy to see that division into classes74 is a small part of the
method we have described: for division is, so to speak, a weak syllogism;
for what it ought to prove, it begs, and it always establishes something
more general than the attribute in question. First, (35) this very point had
escaped all those who used the method of division; and they attempted
to persuade men that it was possible to make a demonstration of
substance and essence. Consequently they did not understand what it is
possible to prove syllogistically by division, nor did they understand that
it was possible to prove syllogistically in the manner we have
described.75 In demonstrations, (40) when there is a need to prove a
positive statement, the middle term through which the syllogism is
formed must always be inferior to and not comprehend the first of the
extremes. [46b] But division has a contrary intention: for it takes the
universal as middle. Let animal be the term signified by A, mortal by B,
and immortal by C, and let man, (5) whose definition is to be got, be
signified by D. The man who divides assumes that every animal is either
mortal or immortal: i. e. whatever is A is all either B or C. Again, always
dividing, he lays it down that man is an animal, so he assumes A of D as
belonging to it. Now the true conclusion is that every D is either B or C,
(10) consequently man must be either mortal or immortal, but it is not
necessary that man should be a mortal animal—this is begged: and this
is what ought to have been proved syllogistically. And again, taking A as
mortal animal, B as footed, C as footless, and D as man, (15) he assumes
in the same way that A inheres either in B or in C (for every mortal
animal is either footed or footless), and he assumes A of D (for he
assumed man, as we saw, to be a mortal animal); consequently it is
necessary that man should be either a footed or a footless animal; but it
is not necessary that man should be footed: this he assumes: and it is just
this again which he ought to have demonstrated. Always dividing then
in this way it turns out that these logicians assume as middle the
universal term, (20) and as extremes that which ought to have been the
subject of demonstration and the differentiae. In conclusion, they do not
make it clear, and show it to be necessary, that this is man or whatever
the subject of inquiry may be: for they pursue the other method
altogether, never even suspecting the presence of the rich supply of
evidence which might be used. (25) It is clear that it is neither possible to
refute a statement by this method of division, nor to draw a conclusion
about an accident or property of a thing, nor about its genus, nor in
cases in which it is unknown whether it is thus or thus, e. g. whether the
diagonal is incommensurate. For if he assumes that every length is either
commensurate or incommensurate, (30) and the diagonal is a length, he
has proved that the diagonal is either incommensurate or commensurate.
But if he should assume that it is incommensurate, he will have assumed
what he ought to have proved. He cannot then prove it: for this is his
method, but proof is not possible by this method. Let A stand for
‘incommensurate or commensurate’, B for ‘length’, C for ‘diagonal’. It is
clear then that this method of investigation is not suitable for every
inquiry, (35) nor is it useful in those cases in which it is thought to be
most suitable.
From what has been said it is clear from what elements
demonstrations are formed and in what manner, and to what points we
must look in each problem.…
1
100a 29, 104a 8.
2
The nature of demonstrative premisses is discussed in the Post. An.; that of dialectical premisses
in the Topics.
3
ll. 12, 22–6.
4
In ll. 7–13.
5 a20–2.
6a
14–17.
7
In a12.
8
cc. 13, 17.
9
c. 46.
10
In the Posterior Analytics.
11
Barbara, major A, minor A.
12
24b 28.
13
Celarent, major E, minor A.
14
Major A, minor E.
15
Major E, minor E.
16
Darii.
17
24b 28.
18
Ferio.
19
24b 30.
20
The Aristotelian formula for the proposition, AB, in which B represents the subject and A the
predicate (A belongs to B), has been retained throughout, because in most places this suits the
context better than the modern formula in which A represents the subject and B the predicate.
21
Major I or O, minor A.
22
Major I or O, minor E.
23
Major A, minor O.
24
Major E, minor O.
25 a
2.
26
Major A, minor O.
27
i. e. the major premiss.
28
Major E, minor O.
29
II, OO, IO, OI.
30
Cesare.
31
25b 40.
32
Camestres.
33
l. 3.
34
Festino.
35
Baroco.
36 a
21.
37
l. 18.
38
Darapti.
39
Felapton.
40
See note 20.
41
Disamis.
42
Datisi.
43
Bocardo.
44
27b 20.
45
28a 30.
46
Ferison.
47
Fesapo, Fresison.
48
sc. in the first figure.
49
viz. by reduction per impossibile to Celarent and Barbara.
50
25b 21.
51
Post An. i. 8.
52
Cf. 25b 32.
53
Aristotle is thinking of the method of establishing a proposition A is B by inducing the
opponent to agree that A is B if X is Y. All that remains then is to establish syllogistically that X is
Y. That A is B thus follows from the agreement.
54
The diagram Aristotle has in mind appears to be the following:
Here A and B are the equal sides, E and F the angles at the base of the isosceles triangle. C and D
are the angles formed by the base with the circumference. The angles formed by the equal sides
with the base are loosely called AC, BD.
55
sc. but imperfect.
56
40b 30.
57
l. 6.
58
The reference is to the new premisses produced by conversion, when a syllogism in the second
or third figure is being reduced to one in the first. Cf. 24b 24.
59
Post An. i. 19–22.
60
i. e. on the major and minor terms. Two affirmative premisses in the second figure give no
conclusion.
61
44b 20.
62
We thus get a syllogism in Barbara.
63
Darapti.
64
Cesare.
65
Camestres.
66
By converting the major premiss of the Cesare syllogism or the minor premiss of the Camestres
syllogism.
67
Felapton, by conversion.
68
i. e. the consequents of A and E.
69
27a 18–20,b 23–8.
70
i. e. if this false conclusion is replaced by its contradictory and this is treated as a premiss.
71
ii. 14.
72
Cf. 41a 39.
73
Topics, especially i. 14.
74
Aristotle is thinking of Plato’s establishment of definitions by means of division by dichotomy.
75
In cc. 1–30.
BOOK II
16
… To beg and assume the original question is a species of failure
to demonstrate the problem proposed; but this happens in many ways.
[64b] A man may not reason syllogistically at all, (30) or he may argue
from premisses which are less known or equally unknown, or he may
establish the antecedent by means of its consequents; for demonstration
proceeds from what is more certain and is prior. Now begging the
question is none of these: but since we get to know some things naturally
through themselves, and other things by means of something else (the
first principles through themselves, (35) what is subordinate to them
through something else), whenever a man tries to prove what is not selfevident by means of itself, then he begs the original question. [65a]
This may be done by assuming what is in question at once; it is also
possible to make a transition to other things which would naturally be
proved through the thesis proposed, (40) and demonstrate it through
them, e. g. if A should be proved through B, and B through C, though it
was natural that C should be proved through A: for it turns out that
those who reason thus are proving A by means of itself. This is what
those persons do who suppose that they are constructing parallel straight
lines: for they fail to see that they are assuming facts which it is
impossible to demonstrate unless the parallels exist. (5) So it turns out
that those who reason thus merely say a particular thing is, if it is: in
this way everything will be self-evident. But that is impossible. (10)
If then it is uncertain whether A belongs to C, and also whether A
belongs to B, and if one should assume that A does belong to B, it is not
yet clear whether he begs the original question, but it is evident that he
is not demonstrating: for what is as uncertain as the question to be
answered cannot be a principle of a demonstration. If however B is so
related to C that they are identical, (15) or if they are plainly convertible,
or the one belongs to the other, the original question is begged. For one
might equally well prove that A belongs to B through those terms if they
are convertible. But if they are not convertible, it is the fact that they are
not that prevents such a demonstration, not the method of
demonstrating. But if one were to make the conversion, then he would
be doing what we have described and effecting a reciprocal proof with
three propositions.
Similarly if he should assume that B belongs to C, (20) this being as
uncertain as the question whether A belongs to C, the question is not yet
begged, but no demonstration is made. If however A and B are identical
either because they are convertible or because A follows B, then the
question is begged for the same reason as before. For we have explained
the meaning of begging the question, (25) viz. proving that which is not
self-evident by means of itself.
If then begging the question is proving what is not self-evident by
means of itself, in other words failing to prove when the failure is due to
the thesis to be proved and the premiss through which it is proved being
equally uncertain, either because predicates which are identical belong
to the same subject, or because the same predicate belongs to subjects
which are identical, the question may be begged in the middle and third
figures in both ways, (30) though, if the syllogism is affirmative, only in
the third and first figures. If the syllogism is negative, the question is
begged when identical predicates are denied of the same subject; and
both premisses do not beg the question indifferently (in a similar way
the question may be begged in the middle figure), because the terms in
negative syllogisms are not convertible. In scientific demonstrations the
question is begged when the terms are really related in the manner
described, (35) in dialectical arguments when they are according to
common opinion so related.
17
The objection that ‘this is not the reason why the result is false’,
which we frequently make in argument, is made primarily in the case of
a reductio ad impossibile, to rebut the proposition which was being
proved by the reduction. [65b] (40) For unless a man has contradicted
this proposition he will not say, ‘False cause’, but urge that something
false has been assumed in the earlier parts of the argument; nor will he
use the formula in the case of an ostensive proof; for here what one
denies is not assumed as a premiss. Further when anything is refuted
ostensively by the terms ABC, it cannot be objected that the syllogism
does not depend on the assumption laid down. (5) For we use the
expression ‘false cause’, when the syllogism is concluded in spite of the
refutation of this position; but that is not possible in ostensive proofs:
since if an assumption is refuted, a syllogism can no longer be drawn in
reference to it. It is clear then that the expression ‘false cause’ can only
be used in the case of a reductio ad impossibile, (10) and when the original
hypothesis is so related to the impossible conclusion, that the conclusion
results indifferently whether the hypothesis is made or not. The most
obvious case of the irrelevance of an assumption to a conclusion which is
false is when a syllogism drawn from middle terms to an impossible
conclusion is independent of the hypothesis, as we have explained in the
Topics.1 For to put that which is not the cause as the cause, (15) is just
this: e. g. if a man, wishing to prove that the diagonal of the square is
incommensurate with the side, should try to prove Zeno’s theorem that
motion is impossible, and so establish a reductio ad impossibile: for Zeno’s
false theorem has no connexion at all with the original assumption. (20)
Another case is where the impossible conclusion is connected with the
hypothesis, but does not result from it. This may happen whether one
traces the connexion upwards or downwards, e. g. if it is laid down that
A belongs to B, B to C, and C to D, (25) and it should be false that B
belongs to D: for if we eliminated A and assumed all the same that B
belongs to C and C to D, the false conclusion would not depend on the
original hypothesis. Or again trace the connexion upwards; e. g. suppose
that A belongs to B, E to A, (30) and F to E, it being false that F belongs to
A. In this way too the impossible conclusion would result, though the
original hypothesis were eliminated. But the impossible conclusion
ought to be connected with the original terms: in this way it will depend
on the hypothesis, e. g. when one traces the connexion downwards, (35)
the impossible conclusion must be connected with that term which is
predicate in the hypothesis: for if it is impossible that A should belong to
D, the false conclusion will no longer result after A has been eliminated.
If one traces the connexion upwards, the impossible conclusion must be
connected with that term which is subject in the hypothesis: for if it is
impossible that F should belong to B, the impossible conclusion will
disappear if B is eliminated. (40) Similarly when the syllogisms are
negative.
[66a] It is clear then that when the impossibility is not related to the
original terms, the false conclusion does not result on account of the
assumption. Or perhaps even so it may sometimes be independent. For if
it were laid down that A belongs not to B but to K, (5) and that K belongs
to C and C to D, the impossible conclusion would still stand. Similarly if
one takes the terms in an ascending series. Consequently since the
impossibility results whether the first assumption is suppressed or not, it
would appear to be independent of that assumption. Or perhaps we
ought not to understand the statement that the false conclusion results
independently of the assumption, in the sense that if something else
were supposed the impossibility would result; but rather we mean that
when the first assumption is eliminated, (10) the same impossibility
results through the remaining premisses; since it is not perhaps absurd
that the same false result should follow from several hypotheses, e. g.
that parallels meet, both on the assumption that the interior angle is
greater than the exterior and on the assumption that a triangle contains
more than two right angles. (15)
18
A false argument depends on the first false statement in it. Every
syllogism is made out of two or more premisses. If then the false
conclusion is drawn from two premisses, one or both of them must be
false: for (as was proved2) a false syllogism cannot be drawn from true
premisses. (20) But if the premisses are more than two, e. g. if C is
established through A and B, and these through D, E, F, and G, one of
these higher propositions must be false, and on this the argument
depends: for A and B are inferred by means of D, E, F, and G. Therefore
the conclusion and the error results from one of them.
19
In order to avoid having a syllogism drawn against us, (25) we must
take care, whenever an opponent asks us to admit the reason without the
conclusions, not to grant him the same term twice over in his premisses,
since we know that a syllogism cannot be drawn without a middle term,
and that term which is stated more than once is the middle. How we
ought to watch the middle in reference to each conclusion, is evident
from our knowing what kind of thesis is proved in each figure. (30) This
will not escape us since we know how we are maintaining the argument.
That which we urge men to beware of in their admissions, they ought
in attack to try to conceal. This will be possible first, if, instead of
drawing the conclusions of preliminary syllogisms, (35) they take the
necessary premisses and leave the conclusions in the dark; secondly if
instead of inviting assent to propositions which are closely connected
they take as far as possible those that are not connected by middle
terms. For example suppose that A is to be inferred to be true of F; B, C,
D, and E being middle terms. One ought then to ask whether A belongs
to B, and next whether D belongs to E, instead of asking whether B
belongs to C; after that he may ask whether B belongs to C, (40) and so
on. [66b] And if the syllogism is drawn through one middle term, he
ought to begin with that: in this way he will most likely deceive his
opponent.
20
Since we know when a syllogism can be formed and how its terms
must be related, it is clear when refutation will be possible and when
impossible. (5) A refutation is possible whether everything is conceded, or
the answers alternate (one, I mean, being affirmative, the other
negative). For as has been shown a syllogism is possible whether the
terms are related in affirmative propositions or one proposition is
affirmative, the other negative: consequently, if what is laid down is
contrary to the conclusion, (10) a refutation must take place: for a
refutation is a syllogism which establishes the contradictory. But if
nothing is conceded, a refutation is impossible: for no syllogism is
possible (as we saw3) when all the terms are negative: therefore no
refutation is possible. For if a refutation were possible, a syllogism must
be possible; although if a syllogism is possible it does not follow that a
refutation is possible. (15) Similarly refutation is not possible if nothing is
conceded universally: since the fields of refutation and syllogism are
defined in the same way.
21
It sometimes happens that just as we are deceived in the
arrangement of the terms,4 (20) so error may arise in our thought about
them, e. g. if it is possible that the same predicate should belong to more
than one subject immediately, but although knowing the one, a man
may forget the other and think the opposite true. Suppose that A belongs
to B and to C in virtue of their nature, and that B and C belong to all D
in the same way. If then a man thinks that A belongs to all B, and B to D,
but A to no C, and C to all D, (25) he will both know and not know the
same thing5 in respect of the same thing.6 Again if a man were to make a
mistake about the members of a single series; e. g. suppose A belongs to
B, B to C, and C to D, but some one thinks that A belongs to all B, but to
no C: he will both know that A belongs to D, (30) and think that it does
not. Does he then maintain after this simply that what he knows, he does
not think? For he knows in a way that A belongs to C through B, since
the part is included in the whole; so that what he knows in a way, this
he maintains he does not think at all: but that is impossible.
In the former case, (35) where the middle term does not belong to the
same series, it is not possible to think both the premisses with reference
to each of the two middle terms: e. g. that A belongs to all B, but to no
C, and both B and C belong to all D. For it turns out that the first premiss
of the one syllogism is either wholly or partially contrary to the first
premiss of the other. For if he thinks that A belongs to everything to
which B belongs, (40) and he knows that B belongs to D, then he knows
that A belongs to D. [67a] Consequently if again he thinks that A
belongs to nothing to which C belongs, he thinks that A does not belong
to some of that to which B belongs; but if he thinks that A belongs to
everything to which B belongs, and again thinks that A does not belong
to some of that to which B belongs, (5) these beliefs are wholly or
partially contrary. In this way then it is not possible to think; but
nothing prevents a man thinking one premiss of each syllogism or both
premisses of one of the two syllogisms: e. g. A belongs to all B, and B to
D, and again A belongs to no C. An error of this kind is similar to the
error into which we fall concerning particulars: e. g. if A belongs to all B,
and B to all C, (10) A will belong to all C. If then a man knows that A
belongs to everything to which B belongs, he knows that A belongs to C.
But nothing prevents his being ignorant that C exists; e. g. let A stand for
two right angles, B for triangle, C for a particular diagram of a triangle.
A man might think that C did not exist, though he knew that every
triangle contains two right angles; consequently he will know and not
know the same thing at the same time. (15) For the expression ‘to know
that every triangle has its angles equal to two right angles’ is ambiguous,
meaning to have the knowledge either of the universal or of the
particulars. Thus then he knows that C contains two right angles with a
knowledge of the universal, but not with a knowledge of the particulars;
consequently his knowledge will not be contrary to his ignorance. (20)
The argument in the Meno7 that learning is recollection may be criticized
in a similar way. For it never happens that a man starts with a
foreknowledge of the particular, but along with the process of being led
to see the general principle he receives a knowledge of the particulars,
by an act (as it were) of recognition. For we know some things directly;
e. g. that the angles are equal to two right angles, if we know that the
figure is a triangle. (25) Similarly in all other cases.
By a knowledge of the universal then we see the particulars, but we do
not know them by the kind of knowledge which is proper to them;
consequently it is possible that we may make mistakes about them, but
not that we should have the knowledge and error that are contrary to
one another: rather we have the knowledge of the universal but make a
mistake in apprehending the particular. (30) Similarly in the cases stated
above.8 The error in respect of the middle term is not contrary to the
knowledge obtained through the syllogism, nor is the thought in respect
of one middle term contrary to that in respect of the other. Nothing
prevents a man who knows both that A belongs to the whole of B, and
that B again belongs to C, thinking that A does not belong to C, e. g. (35)
knowing that every mule is sterile and that this is a mule, and thinking
that this animal is with foal: for he does not know that A belongs to C,
unless he considers the two propositions together. So it is evident that if
he knows the one and does not know the other, he will fall into error.
And this is the relation of knowledge of the universal to knowledge of
the particular. For we know no sensible thing, once it has passed beyond
the range of our senses, even if we happen to have perceived it, except
by means of the universal and the possession of the knowledge which is
proper to the particular, but without the actual exercise of that
knowledge. [67b] For to know is used in three senses: it may mean
either to have knowledge of the universal or to have knowledge proper
to the matter in hand or to exercise such knowledge: consequently three
kinds of error also are possible. (5) Nothing then prevents a man both
knowing and being mistaken about the same thing, provided that his
knowledge and his error are not contrary. And this happens also to the
man whose knowledge is limited to each of the premisses and who has
not previously considered the particular question. For when he thinks
that the mule is with foal he has not the knowledge in the sense of its
actual exercise, (10) nor on the other hand has his thought caused an
error contrary to his knowledge: for the error contrary to the knowledge
of the universal would be a syllogism.
But he who thinks the essence of good is the essence of bad will think
the same thing to be the essence of good and the essence of bad. Let A
stand for the essence of good and B for the essence of bad, (15) and again
C for the essence of good. Since then he thinks B and C identical, he will
think that C is B, and similarly that B is A, consequently that C is A. For
just as we saw that if B is true of all of which C is true, and A is true of
all of which B is true, A is true of C, similarly with the word ‘think’.
Similarly also with the word ‘is’; for we saw that if C is the same as B, (20)
and B as A, C is the same as A. Similarly therefore with ‘opine’. Perhaps
then this9 is necessary if a man will grant the first point.10 But
presumably that is false, that any one could suppose the essence of good
to be the essence of bad, (25) save incidentally. For it is possible to think
this in many different ways. But we must consider this matter better.11
22
Whenever the extremes are convertible it is necessary that the
middle should be convertible with both. For if A belongs to C through B,
then if A and C are convertible and C belongs to everything to which A
belongs, (30) B is convertible with A, and B belongs to everything to
which A belongs, through C as middle, and C is convertible with B
through A as middle. Similarly if the conclusion is negative, e. g. if B
belongs to C, but A does not belong to B, neither will A belong to C. If
then B is convertible with A, C will be convertible with A. (35) Suppose B
does not belong to A; neither then will C: for ex hypothesi B belonged to
all C. And if C is convertible with B, B is convertible also with A: for C is
said of that of all of which B is said. And if C is convertible in relation to
A and to B, B also is convertible in relation to A. For C belongs to that to
which B belongs: but C does not belong to that to which A belongs.
[68a] And this alone starts from the conclusion; the preceding moods
do not do so as in the affirmative syllogism. Again if A and B are
convertible, and similarly C and D, and if A or C must belong to
anything whatever, (5) then B and D will be such that one or other
belongs to anything whatever. For since B belongs to that to which A
belongs, and D belongs to that to which C belongs, and since A or C
belongs to everything, but not together, it is clear that B or D belongs to
everything, but not together. For example if that which is uncreated is
incorruptible and that which is incorruptible is uncreated, it is necessary
that what is created should be corruptible and what is corruptible should
have been created. (10) For two syllogisms have been put together. Again
if A or B belongs to everything and if C or D belongs to everything, but
they cannot belong together, then when A and C are convertible B and D
are convertible. For if B does not belong to something to which D
belongs, it is clear that A belongs to it. But if A then C: for they are
convertible. Therefore C and D belong together. But this is impossible.
(15) When A belongs to the whole of B and to C and is affirmed of nothing
else, and B also belongs to all C, it is necessary that A and B should be
convertible: for since A is said of B and C only, and B is affirmed both of
itself and of C, it is clear that B will be said of everything of which A is
said, (20) except A itself. Again when A and B belong to the whole of C,
and C is convertible with B, it is necessary that A should belong to all B:
for since A belongs to all C, and C to B by conversion, A will belong to
all B.
When, of two opposites A and B, A is preferable to B, (25) and similarly
D is preferable to C, then if A and C together are preferable to B and D
together, A must be preferable to D. For A is an object of desire to the
same extent as B is an object of aversion, since they are opposites: and C
is similarly related to D, since they also are opposites. If then A is an
object of desire to the same extent as D, (30) B is an object of aversion to
the same extent as C (since each is to the same extent as each—the one
an object of aversion, the other an object of desire). Therefore both A
and C together, and B and D together, will be equally objects of desire or
aversion. But since A and C are preferable to B and D, A cannot be
equally desirable with D; for then B along with D would be equally
desirable with A along with C. But if D is preferable to A, then B must be
less an object of aversion than C: for the less is opposed to the less. (35)
But the greater good and lesser evil are preferable to the lesser good and
greater evil: the whole BD then is preferable to the whole AC. But ex
hypothesi this is not so. A then is preferable to D, and C consequently is
less an object of aversion than B. If then every lover in virtue of his love
would prefer A, viz. that the beloved should be such as to grant a favour,
(40) and yet should not grant it (for which C stands), to the beloved’s
granting the favour (represented by D) without being such as to grant it
(represented by B), it is clear that A (being of such a nature) is
preferable to granting the favour. [68b] To receive affection then is
preferable in love to sexual intercourse. Love then is more dependent on
friendship than on intercourse. And if it is most dependent on receiving
affection, then this is its end. (5) Intercourse then either is not an end at
all or is an end relative to the further end, the receiving of affection. And
indeed the same is true of the other desires and arts.
23
It is clear then how the terms are related in conversion, and in
respect of being in a higher degree objects of aversion or of desire. (10)
We must now state that not only dialectical and demonstrative
syllogisms are formed by means of the aforesaid figures, but also
rhetorical syllogisms and in general any form of persuasion, however it
may be presented. For every belief comes either through syllogism or
from induction.
Now induction, (15) or rather the syllogism which springs out of
induction, consists in establishing syllogistically a relation between one
extreme and the middle by means of the other extreme, e. g. if B is the
middle term between A and C, it consists in proving through C that A
belongs to B. For this is the manner in which we make inductions. For
example let A stand for long-lived, B for bileless, (20) and C for the
particular long-lived animals, e. g. man, horse, mule. A then belongs to
the whole of C: for whatever is bileless is long-lived. But B also (‘not
possessing bile’) belongs to all C. If then C is convertible with B, and the
middle term is not wider in extension, it is necessary that A should
belong to B. For it has already been proved that if two things belong to
the same thing, (25) and the extreme is convertible with one of them, then
the other predicate will belong to the predicate that is converted. But we
must apprehend C as made up of all the particulars. For induction
proceeds through an enumeration of all the cases.
Such is the syllogism which establishes the first and immediate
premiss: for where there is a middle term the syllogism proceeds through
the middle term; when there is no middle term, (30) through induction.
And in a way induction is opposed to syllogism: for the latter proves the
major term to belong to the third term by means of the middle, the
former proves the major to belong to the middle by means of the third.
(35) In the order of nature, syllogism through the middle term is prior and
better known, but syllogism through induction is clearer to us.
24
We have an ‘example’ when the major term is proved to belong to
the middle by means of a term which resembles the third. It ought to be
known both that the middle belongs to the third term, (40) and that the
first belongs to that which resembles the third. For example let A be evil,
B making war against neighbours, C Athenians against Thebans, D
Thebans against Phocians. [69a] If then we wish to prove that to fight
with the Thebans is an evil, we must assume that to fight against
neighbours is an evil. Evidence of this is obtained from similar cases,
e. g. that the war against the Phocians was an evil to the Thebans. (5)
Since then to fight against neighbours is an evil, and to fight against the
Thebans is to fight against neighbours, it is clear that to fight against the
Thebans is an evil. Now it is clear that B belongs to C and to D (for both
are cases of making war upon one’s neighbours) and that A belongs to D
(for the war against the Phocians did not turn out well for the Thebans):
but that A belongs to B will be proved through D. (10) Similarly if the
belief in the relation of the middle term to the extreme should be
produced by several similar cases. Clearly then to argue by example is
neither like reasoning from part to whole, nor like reasoning from whole
to part, but rather reasoning from part to part, when both particulars are
subordinate to the same term, (15) and one of them is known. It differs
from induction, because induction starting from all the particular cases
proves (as we saw12) that the major term belongs to the middle, and
does not apply the syllogistic conclusion to the minor term, whereas
argument by example does make this application and does not draw its
proof from all the particular cases.
25
By reduction we mean an argument in which the first term clearly
belongs to the middle, (20) but the relation of the middle to the last term
is uncertain though equally or more probable than the conclusion; or
again an argument in which the terms intermediate between the last
term and the middle are few. For in any of these cases it turns out that
we approach more nearly to knowledge. For example let A stand for
what can be taught, B for knowledge, C for justice. (25) Now it is clear
that knowledge can be taught: but it is uncertain whether virtue is
knowledge. If now the statement BC13 is equally or more probable than
AC, we have a reduction: for we are nearer to knowledge, since we have
taken a new term,14 being so far without knowledge that A belongs to C.
Or again suppose that the terms intermediate between B and C are few:
for thus too we are nearer knowledge. (30) For example let D stand for
squaring, E for rectilinear figure, F for circle. If there were only one term
intermediate between E and F (viz. that the circle is made equal to a
rectilinear figure by the help of lunules), we should be near to
knowledge. (35) But when BC is not more probable than AC, and the
intermediate terms are not few, I do not call this reduction: nor again
when the statement BC is immediate: for such a statement is knowledge.
26
An objection is a premiss contrary to a premiss. It differs from a
premiss, because it may be particular, but a premiss either cannot be
particular at all or not in universal syllogisms. [69b] An objection is
brought in two ways and through two figures; in two ways because
every objection is either universal or particular, by two figures because
objections are brought in opposition to the premiss, (5) and opposites can
be proved only in the first and third figures. If a man maintains a
universal affirmative, we reply with a universal or a particular negative;
the former is proved from the first figure, the latter from the third. For
example let A stand for there being a single science, B for contraries. If a
man premisses that contraries are subjects of a single science, (10) the
objection may be either that opposites are never subjects of a single
science, and contraries are opposites, so that we get the first figure, or
that the knowable and the unknowable are not subjects of a single
science: this proof is in the third figure: for it is true of C (the knowable
and the unknowable) that they are contraries, and it is false that they are
the subjects of a single science.
Similarly if the premiss objected to is negative. (15) For if a man
maintains that contraries are not subjects of a single science, we reply
either that all opposites or that certain contraries, e. g. what is healthy
and what is sickly, are subjects of the same science: the former argument
issues from the first, the latter from the third figure.
In general if a man urges a universal objection he must frame his
contradiction with reference to the universal of the terms taken by his
opponent, (20) e. g. if a man maintains that contraries are not subjects of
the same science, his opponent must reply that there is a single science
of all opposites. Thus we must have the first figure: for the term which
embraces the original subject becomes the middle term.
If the objection is particular, the objector must frame his contradiction
with reference to a term relatively to which the subject of his opponent’s
premiss is universal, e. g. he will point out that the knowable and the
unknowable are not subjects of the same science: ‘contraries’ is universal
relatively to these. (25) And we have the third figure: for the particular
term assumed is middle, e. g. the knowable and the unknowable.
Premisses from which it is possible to draw the contrary conclusion are
what we start from when we try to make objections. Consequently we
bring objections in these figures only: for in them only are opposite
syllogisms possible, (30) since the second figure cannot produce an
affirmative conclusion.
Besides, an objection in the middle figure would require a fuller
argument, e. g. if it should not be granted that A belongs to B, because C
does not follow B. This can be made clear only by other premisses. (35)
But an objection ought not to turn off into other things, but have its new
premiss quite clear immediately. For this reason also this is the only
figure from which proof by signs cannot be obtained.
We must consider later the other kinds of objection, namely the
objection from contraries, from similars, and from common opinion, and
inquire whether a particular objection cannot be elicited from the first
figure or a negative objection from the second. [70a]
27
A probability and a sign are not identical, but a probability is a
generally approved proposition: what men know to happen or not to
happen, to be or not to be, for the most part thus and thus, (5) is a
probability, e. g. ‘the envious hate’, ‘the beloved show affection’. A sign
means a demonstrative proposition necessary or generally approved: for
anything such that when it is another thing is, or when it has come into
being the other has come into being before or after, is a sign of the
other’s being or having come into being. Now an enthymeme is a
syllogism starting from probabilities or signs, (10) and a sign may be
taken in three ways, corresponding to the position of the middle term in
the figures. For it may be taken as in the first figure or the second or the
third. For example the proof that a woman is with child because she has
milk is in the first figure: for to have milk is the middle term. Let A
represent to be with child, B to have milk, (15) C woman. The proof that
wise men are good, since Pittacus is good, comes through the last figure.
Let A stand for good, B for wise men, C for Pittacus. It is true then to
affirm both A and B of C: only men do not say the latter, because they
know it, though they state the former. The proof that a woman is with
child because she is pale is meant to come through the middle figure: for
since paleness follows women with child and is a concomitant of this
woman, (20) people suppose it has been proved that she is with child. Let
A stand for paleness, B for being with child, C for woman. (25) Now if the
one proposition is stated, we have only a sign, but if the other is stated
as well, a syllogism, e. g. ‘Pittacus is generous, since ambitious men are
generous and Pittacus is ambitious’. Or again ‘Wise men are good, since
Pittacus is not only good but wise’. In this way then syllogisms are
formed, only that which proceeds through the first figure is irrefutable if
it is true (for it is universal), (30) that which proceeds through the last
figure is refutable even if the conclusion is true, since the syllogism is
not universal nor correlative to the matter in question: for though
Pittacus is good, it is not therefore necessary that all other wise men
should be good. But the syllogism which proceeds through the middle
figure is always refutable in any case: for a syllogism can never be
formed when the terms are related in this way: for though a woman with
child is pale, (35) and this woman also is pale, it is not necessary that she
should be with child. Truth then may be found in signs whatever their
kind, but they have the differences we have stated.
[70b] We must either divide signs in the way stated, and among
them designate the middle term as the index15 (for people call that the
index which makes us know, and the middle term above all has this
character), or else we must call the arguments derived from the extremes
signs, that derived from the middle term the index: for that which is
proved through the first figure is most generally accepted and most true.
(5)
It is possible to infer character from features, if it is granted that the
body and the soul are changed together by the natural affections: I say
‘natural’, for though perhaps by learning music a man has made some
change in his soul, (10) this is not one of those affections which are
natural to us; rather I refer to passions and desires when I speak of
natural motions. If then this were granted and also that for each change
there is a corresponding sign, and we could state the affection and sign
proper to each kind of animal, we shall be able to infer character from
features. For if there is an affection which belongs properly to an
individual kind, (15) e. g. courage to lions, it is necessary that there
should be a sign of it: for ex hypothesi body and soul are affected
together. Suppose this sign is the possession of large extremities: this
may belong to other kinds also though not universally. For the sign is
proper in the sense stated, because the affection is proper to the whole
kind, though not proper to it alone, (20) according to our usual manner of
speaking. The same thing then will be found in another kind, and man
may be brave, and some other kinds of animal as well. They will then
have the sign: for ex hypothesi there is one sign corresponding to each
affection. If then this is so, and we can collect signs of this sort in these
animals which have only one affection proper to them—but each
affection has its sign, since it is necessary that it should have a single
sign—we shall then be able to infer character from features. (25) But if
the kind as a whole has two properties, e. g. if the lion is both brave and
generous, how shall we know which of the signs which are its proper
concomitants is the sign of a particular affection? Perhaps if both belong
to some other kind though not to the whole of it, and if, in those kinds in
which each is found though not in the whole of their members, some
members possess one of the affections and not the other: e. g. if a man is
brave but not generous, but possesses, of the two signs, large extremities,
(30) it is clear that this is the sign of courage in the lion also. To judge
character from features, then, is possible in the first figure if the middle
term is convertible with the first extreme, but is wider than the third
term and not convertible with it: e. g. let A stand for courage, B for large
extremities, and C for lion. B then belongs to everything to which C
belongs, (35) but also to others. But A belongs to everything to which B
belongs, and to nothing besides, but is convertible with B: otherwise,
there would not be a single sign correlative with each affection.
1
Soph. El. 167b 21–36.
2
53b 11–25.
3
41b 6.
4
Cf. i. 32 ff.
5
i. e. subject.
6
i. e. attribute.
7
81.
8
66b 20–6, 26–30.
9
That a man should think the same thing to be the essence of good and to be the essence of bad.
10
That the essence of good is the essence of bad.
11
The reference may be to Met. iv. (Γ).
12
ch. 23.
13
See note 20.
14
viz. B, thus obtaining a certain premiss AB, and a premiss BC, on which the inquiry now turns.
15
This points to the argument in the first figure, whose middle term is a genuine middle term.
ANALYTICA POSTERIORA
Translated by G. R. G. Mure
CONTENTS
BOOK I
CHAPTER
1. The student’s need of pre-existent knowledge. Its nature.
2. The nature of scientific knowledge. The conditions of demonstration. The meaning of
Contradiction, Enunciation, Proposition, Basic truth, Thesis, Axiom, Hypothesis,
Definition.
3. Two erroneous views of scientific knowledge. The futility of circular demonstration.
4. Types of attribute: ‘True in every instance’, ‘Essential’, ‘Commensurate and universal’,
‘Accidental’.
5. Causes through which we erroneously suppose a conclusion commensurate and
universal when it is not. How to avoid this error.
6. The premisses of demonstration must be necessary and essential.
7. The premisses and conclusion of a demonstration must fall within a single genus. The
three constituent elements of demonstration.
8. Only eternal connexions can be demonstrated.
9. Demonstration must proceed from the basic premisses peculiar to each science, except
in the case of subalternate sciences.
10. The different sorts of basic truth.
11. The function of the common axioms in demonstration.
12. The scientific premiss in interrogative form. Formal fallacy. The growth of a science.
13. The difference between knowledge of the fact and knowledge of the reasoned fact.
14. The first figure is the true type of scientific syllogism.
15. Immediate negative propositions.
16. Ignorance as erroneous inference when the premisses are immediate.
17. Ignorance as erroneous inference when the premisses are mediate.
18. Ignorance as the negation of knowledge, e. g. such as must result from the lack of a
sense.
19. Can demonstration develop an indefinite regress of premisses, (1) supposing the primary
attribute fixed? (2) supposing the ultimate subject fixed? (3) supposing both
primary attribute and ultimate subject fixed?
20. If (1) and (2) are answered negatively, the answer to (3) must be in the negative.
21. If affirmative demonstration cannot develop an indefinite regress, then negative
demonstration cannot.
22. Dialectical and analytic proofs that the answer to both (1) and (2) is in the negative.
23. Corollaries.
24. The superiority of universal to particular demonstration.
25. The superiority of affirmative to negative demonstration.
26. The superiority of affirmative and negative demonstration to reductio ad impossibile.
27. The more abstract science is the prior and the more accurate science.
28. What constitutes the unity of a science.
29. How there may be several demonstrations of one connexion.
30. Chance conjunctions are not demonstrable.
31. There can be no demonstration through sense-perception.
32. Different sciences must possess different basic truths.
33. The relation of opinion to knowledge.
34. Quick wit: the faculty of instantaneously hitting upon the middle term.
BOOK II
1. The four possible forms of inquiry.
2. They all concern the middle term.
3. The difference between definition and demonstration.
4. Essential nature cannot be demonstrated.
5. Essential nature cannot be inferred by division.
6. Attempts to prove a thing’s essential nature either hypothetically or through the
definition of its contrary beg the question.
7. Definition does not touch the question of existence; demonstration proves existence.
Hence definition cannot demonstrate.
8. Yet only demonstration can reveal the essential nature of things which have a cause
other than themselves—i. e. attributes.
9. That which is self-caused—the basic premisses—is grasped immediately.
10. Types of definition.
11. The several causes as middle terms.
12. The question of time in causal inference.
13. How to obtain the definition of a substance. The use of division for this purpose.
14. How to select a connexion for demonstration.
15. One middle will often serve to prove several connexions.
16. If the effect is present, is the cause also present? Plurality of causes is impossible where
cause and effect are commensurate.
17. Different causes may produce the same effect, but not in things specifically identical.
18. The true cause of a connexion is the proximate and not the more universal cause.
19. How the individual mind comes to know the basic truths.
ANALYTICA POSTERIORA
(Posterior Analytics)
BOOK I
1
[71a] All instruction given or received by way of argument
proceeds from pre-existent knowledge. This becomes evident upon a
survey of all the species of such instruction. The mathematical sciences
and all other speculative disciplines are acquired in this way, (5) and so
are the two forms of dialectical reasoning, syllogistic and inductive: for
each of these latter makes use of old knowledge to impart new, the
syllogism assuming an audience that accepts its premisses, induction
exhibiting the universal as implicit in the clearly known particular.
Again, the persuasion exerted by rhetorical arguments is in principle the
same, since they use either example, a kind of induction, (10) or
enthymeme, a form of syllogism.
The pre-existent knowledge required is of two kinds. In some cases
admission of the fact must be assumed, in others comprehension of the
meaning of the term used, and sometimes both assumptions are
essential. Thus, we assume that every predicate can be either truly
affirmed or truly denied of any subject, and that ‘triangle’ means so and
so; as regards ‘unit’ we have to make the double assumption of the
meaning of the word and the existence of the thing. (15) The reason is
that these several objects are not equally obvious to us. Recognition of a
truth may in some cases contain as factors both previous knowledge and
also knowledge acquired simultaneously with that recognition—
knowledge, this latter, of the particulars actually falling under the
universal and therein already virtually known. For example, (20) the
student knew beforehand that the angles of every triangle are equal to
two right angles; but it was only at the actual moment at which he was
being led on to recognize this as true in the instance before him that he
came to know ‘this figure inscribed in the semicircle’ to be a triangle.
For some things (viz. the singulars finally reached which are not
predicable of anything else as subject) are only learnt in this way, i. e.
there is here no recognition through a middle of a minor term as subject
to a major. Before he was led on to recognition or before he actually
drew a conclusion, we should perhaps say that in a manner he knew, (25)
in a manner not.
If he did not in an unqualified sense of the term know the existence of
this triangle, how could he know without qualification that its angles
were equal to two right angles? No: clearly he knows not without
qualification but only in the sense that he knows universally. If this
distinction is not drawn, we are faced with the dilemma in the Meno:1
either a man will learn nothing or what he already knows; for we cannot
accept the solution which some people offer. A man is asked, (30) ‘Do
you, or do you not, know that every pair is even?’ He says he does know
it. The questioner then produces a particular pair, of the existence, and
so a fortiori of the evenness, of which he was unaware. The solution
which some people offer is to assert that they do not know that every
pair is even, but only that everything which they know to be a pair is
even: yet what they know to be even is that of which they have
demonstrated evenness, i. e. what they made the subject of their
premiss, viz. not merely every triangle or number which they know to be
such, but any and every number or triangle without reservation. [71b]
For no premiss is ever couched in the form ‘every number which you
know to be such’, or ‘every rectilinear figure which you know to be
such’: the predicate is always construed as applicable to any and every
instance of the thing. On the other hand, (5) I imagine there is nothing to
prevent a man in one sense knowing what he is learning, in another not
knowing it. The strange thing would be, not if in some sense he knew
what he was learning, but if he were to know it in that precise sense and
manner in which he was learning it.2
2
We suppose ourselves to possess unqualified scientific knowledge of
a thing, as opposed to knowing it in the accidental way in which the
sophist knows, when we think that we know the cause on which the fact
depends, (10) as the cause of that fact and of no other, and, further, that
the fact could not be other than it is. Now that scientific knowing is
something of this sort is evident—witness both those who falsely claim it
and those who actually possess it, since the former merely imagine
themselves to be, while the latter are also actually, in the condition
described. Consequently the proper object of unqualified scientific
knowledge is something which cannot be other than it is. (15)
There may be another manner of knowing as well—that will be
discussed later.3 What I now assert is that at all events we do know by
demonstration. By demonstration I mean a syllogism productive of
scientific knowledge, a syllogism, that is, the grasp of which is eo ipso
such knowledge. Assuming then that my thesis as to the nature of
scientific knowing is correct, (20) the premisses of demonstrated
knowledge must be true, primary, immediate, better known than and
prior to the conclusion, which is further related to them as effect to
cause. Unless these conditions are satisfied, the basic truths will not be
‘appropriate’ to the conclusion. Syllogism there may indeed be without
these conditions, but such syllogism, not being productive of scientific
knowledge, will not be demonstration. (25) The premisses must be true:
for that which is non-existent cannot be known—we cannot know, e. g.,
that the diagonal of a square is commensurate with its side. The
premisses must be primary and indemonstrable; otherwise they will
require demonstration in order to be known, since to have knowledge, if
it be not accidental knowledge, of things which are demonstrable, means
precisely to have a demonstration of them. The premisses must be the
causes of the conclusion, better known than it, (30) and prior to it; its
causes, since we possess scientific knowledge of a thing only when we
know its cause; prior, in order to be causes; antecedently known, this
antecedent knowledge being not our mere understanding of the
meaning, but knowledge of the fact as well. Now ‘prior’ and ‘better
known’ are ambiguous terms, for there is a difference between what is
prior and better known in the order of being and what is prior and better
known to man. [72a] I mean that objects nearer to sense are prior and
better known to man; objects without qualification prior and better
known are those further from sense. Now the most universal causes are
furthest from sense and particular causes are nearest to sense, (5) and
they are thus exactly opposed to one another. In saying that the
premisses of demonstrated knowledge must be primary, I mean that they
must be the ‘appropriate’ basic truths, for I identify primary premiss and
basic truth. A ‘basic truth’ in a demonstration is an immediate
proposition. An immediate proposition is one which has no other
proposition prior to it. A proposition is either part of an enunciation, i. e.
it predicates a single attribute of a single subject. If a proposition is
dialectical, (10) it assumes either part indifferently; if it is demonstrative,
it lays down one part to the definite exclusion of the other because that
part is true. The term ‘enunciation’ denotes either part of a contradiction
indifferently. A contradiction is an opposition which of its own nature
excludes a middle. The part of a contradiction which conjoins a
predicate with a subject is an affirmation; the part disjoining them is a
negation. (15) I call an immediate basic truth of syllogism a ‘thesis’ when,
though it is not susceptible of proof by the teacher, yet ignorance of it
does not constitute a total bar to progress on the part of the pupil: one
which the pupil must know if he is to learn anything whatever is an
axiom. I call it an axiom because there are such truths and we give them
the name of axioms par excellence. If a thesis assumes one part or the
other of an enunciation, i. e. asserts either the existence or the nonexistence of a subject, (20) it is a hypothesis; if it does not so assert, it is a
definition. Definition is a ‘thesis’ or a ‘laying something down’, since the
arithmetician lays it down that to be a unit is to be quantitatively
indivisible; but it is not a hypothesis, for to define what a unit is is not
the same as to affirm its existence.
Now since the required ground of our knowledge—i. e. of our
conviction—of a fact is the possession of such a syllogism as we call
demonstration, and the ground of the syllogism is the facts constituting
its premisses, (25) we must not only know the primary premisses—some if
not all of them—beforehand, but know them better than the conclusion:
for the cause of an attribute’s inherence in a subject always itself inheres
in the subject more firmly than that attribute; e. g. the cause of our
loving anything is dearer to us than the object of our love. So since the
primary premisses are the cause of our knowledge—i. e. of our
conviction—it follows that we know them better—that is, (30) are more
convinced of them—than their consequences, precisely because our
knowledge of the latter is the effect of our knowledge of the premisses.
Now a man cannot believe in anything more than in the things he
knows, unless he has either actual knowledge of it or something better
than actual knowledge. But we are faced with this paradox if a student
whose belief rests on demonstration has not prior knowledge; a man
must believe in some, (35) if not in all, of the basic truths more than in
the conclusion. Moreover, if a man sets out to acquire the scientific
knowledge that comes through demonstration, he must not only have a
better knowledge of the basic truths and a firmer conviction of them
than of the connexion which is being demonstrated: more than this,
nothing must be more certain or better known to him than these basic
truths in their character as contradicting the fundamental premisses
which lead to the opposed and erroneous conclusion. [72b] For indeed
the conviction of pure science must be unshakable.
3
Some hold that, owing to the necessity of knowing the primary
premisses, (5) there is no scientific knowledge. Others think there is, but
that all truths are demonstrable. Neither doctrine is either true or a
necessary deduction from the premisses. The first school, assuming that
there is no way of knowing other than by demonstration, maintain that
an infinite regress is involved, on the ground that if behind the prior
stands no primary, we could not know the posterior through the prior
(wherein they are right, (10) for one cannot traverse an infinite series): if
on the other hand—they say—the series terminates and there are
primary premisses, yet these are unknowable because incapable of
demonstration, which according to them is the only form of knowledge.
And since thus one cannot know the primary premisses, knowledge of
the conclusions which follow from them is not pure scientific knowledge
nor properly knowing at all, but rests on the mere supposition that the
premisses are true. (15) The other party agree with them as regards
knowing, holding that it is only possible by demonstration, but they see
no difficulty in holding that all truths are demonstrated, on the ground
that demonstration may be circular and reciprocal.
Our own doctrine is that not all knowledge is demonstrative: on the
contrary, knowledge of the immediate premisses is independent of
demonstration. (20) (The necessity of this is obvious; for since we must
know the prior premisses from which the demonstration is drawn, and
since the regress must end in immediate truths, those truths must be
indemonstrable.) Such, then, is our doctrine, and in addition we
maintain that besides scientific knowledge there is its originative source
which enables us to recognize the definitions.
Now demonstration must be based on premisses prior to and better
known than the conclusion; and the same things cannot simultaneously
be both prior and posterior to one another: so circular demonstration is
clearly not possible in the unqualified sense of ‘demonstration’, (25) but
only possible if ‘demonstration’ be extended to include that other
method of argument which rests on a distinction between truths prior to
us and truths without qualification prior, (30) i. e. the method by which
induction produces knowledge. But if we accept this extension of its
meaning, our definition of unqualified knowledge will prove faulty; for
there seem to be two kinds of it. Perhaps, however, the second form of
demonstration, that which proceeds from truths better known to us, is
not demonstration in the unqualified sense of the term.
The advocates of circular demonstration are not only faced with the
difficulty we have just stated: in addition their theory reduces to the
mere statement that if a thing exists, then it does exist—an easy way of
proving anything. (35) That this is so can be clearly shown by taking three
terms, for to constitute the circle it makes no difference whether many
terms or few or even only two are taken. Thus by direct proof, if A is, B
must be; if B is, C must be; therefore if A is, C must be. Since then—by
the circular proof—if A is, B must be, and if B is, A must be, A may be
substituted for C above. [73a] Then ‘if B is, A must be’ = ‘if B is, C
must be’, which above gave the conclusion ‘if A is, C must be’: but C and
A have been identified. Consequently the upholders of circular
demonstration are in the position of saying that if A is, A must be—a
simple way of proving anything. (5) Moreover, even such circular
demonstration is impossible except in the case of attributes that imply
one another, viz. ‘peculiar’ properties.
Now, it has been shown that the positing of one thing—be it one term
or one premiss—never involves a necessary consequent:4 two premisses
constitute the first and smallest foundation for drawing a conclusion at
all and therefore a fortiori for the demonstrative syllogism of science. (10)
If, then, A is implied in B and C, and B and C are reciprocally implied in
one another and in A, it is possible, as has been shown in my writings on
the syllogism,5 to prove all the assumptions on which the original
conclusion rested, by circular demonstration in the first figure. But it has
also been shown that in the other figures either no conclusion is
possible, (15) or at least none which proves both the original premisses.6
Propositions the terms of which are not convertible cannot be circularly
demonstrated at all, and since convertible terms occur rarely in actual
demonstrations, it is clearly frivolous and impossible to say that
demonstration is reciprocal and that therefore everything can be
demonstrated. (20)
4
Since the object of pure scientific knowledge cannot be other than it
is, the truth obtained by demonstrative knowledge will be necessary.
And since demonstrative knowledge is only present when we have a
demonstration, it follows that demonstration is an inference from
necessary premisses. So we must consider what are the premisses of
demonstration—i. e. what is their character: and as a preliminary, (25) let
us define what we mean by an attribute ‘true in every instance of its
subject’, an ‘essential’ attribute, and a ‘commensurate and universal’
attribute. I call ‘true in every instance’ what is truly predicable of all
instances—not of one to the exclusion of others—and at all times, not at
this or that time only; e. g. if animal is truly predicable of every instance
of man, then if it be true to say ‘this is a man’, (30) ‘this is an animal’ is
also true, and if the one be true now the other is true now. A
corresponding account holds if point is in every instance predicable as
contained in line. There is evidence for this in the fact that the objection
we raise against a proposition put to us as true in every instance is either
an instance in which, or an occasion on which, it is not true. Essential
attributes are (1) such as belong to their subject as elements in its
essential nature (e. g. line thus belongs to triangle, (35) point to line; for
the very being or ‘substance’ of triangle and line is composed of these
elements, which are contained in the formulae defining triangle and
line): (2) such that, while they belong to certain subjects, the subjects to
which they belong are contained in the attribute’s own defining formula.
Thus straight and curved belong to line, odd and even, prime and
compound, (40) square and oblong, to number; and also the formula
defining any one of these attributes contains its subject—e. g. line or
number as the case may be. [73b]
Extending this classification to all other attributes, I distinguish those
that answer the above description as belonging essentially to their
respective subjects; whereas attributes related in neither of these two
ways to their subjects I call accidents or ‘coincidents’; e. g. musical or
white is a ‘coincident’ of animal. (5)
Further (a) that is essential which is not predicated of a subject other
than itself: e. g. ‘the walking [thing]’ walks and is white in virtue of
being something else besides; whereas substance, in the sense of
whatever signifies a ‘this somewhat’, is not what it is in virtue of being
something else besides. Things, then, not predicated of a subject I call
essential; things predicated of a subject I call accidental or ‘coincidental’.
(10)
In another sense again (b) a thing consequentially connected with
anything is essential; one not so connected is ‘coincidental’. An example
of the latter is ‘While he was walking it lightened’: the lightning was not
due to his walking; it was, we should say, a coincidence. If, on the other
hand, there is a consequential connexion, the predication is essential;
e. g. if a beast dies when its throat is being cut, then its death is also
essentially connected with the cutting, (15) because the cutting was the
cause of death, not death a ‘coincident’ of the cutting.
So far then as concerns the sphere of connexions scientifically known
in the unqualified sense of that term, all attributes which (within that
sphere) are essential either in the sense that their subjects are contained
in them, or in the sense that they are contained in their subjects, are
necessary as well as consequentially connected with their subjects. For it
is impossible for them not to inhere in their subjects—either simply or in
the qualified sense that one or other of a pair of opposites must inhere in
the subject; e. g. in line must be either straightness or curvature, (20) in
number either oddness or evenness. For within a single identical genus
the contrary of a given attribute is either its privative or its
contradictory; e. g. within number what is not odd is even, inasmuch as
within this sphere even is a necessary consequent of not-odd. So, since
any given predicate must be either affirmed or denied of any subject,
essential attributes must inhere in their subjects of necessity.
Thus, then, we have established the distinction between the attribute
which is ‘true in every instance’ and the ‘essential’ attribute. (25)
I term ‘commensurately universal’ an attribute which belongs to every
instance of its subject, and to every instance essentially and as such;
from which it clearly follows that all commensurate universals inhere
necessarily in their subjects. The essential attribute, and the attribute that
belongs to its subject as such, are identical. e. g. point and straight
belong to line essentially, for they belong to line as such; and triangle as
such has two right angles, (30) for it is essentially equal to two right
angles.
An attribute belongs commensurately and universally to a subject
when it can be shown to belong to any random instance of that subject
and when the subject is the first thing to which it can be shown to
belong. Thus, e. g., (1) the equality of its angles to two right angles is
not a commensurately universal attribute of figure. For though it is
possible to show that a figure has its angles equal to two right angles, (35)
this attribute cannot be demonstrated of any figure selected at
haphazard, nor in demonstrating does one take a figure at random—a
square is a figure but its angles are not equal to two right angles. On the
other hand, any isosceles triangle has its angles equal to two right
angles, yet isosceles triangle is not the primary subject of this attribute
but triangle is prior. So whatever can be shown to have its angles equal
to two right angles, or to possess any other attribute, (40) in any random
instance of itself and primarily—that is the first subject to which the
predicate in question belongs commensurately and universally, and the
demonstration, in the essential sense, of any predicate is the proof of it
as belonging to this first subject commensurately and universally: while
the proof of it as belonging to the other subjects to which it attaches is
demonstration only in a secondary and unessential sense. [74a] Nor
again (2) is equality to two right angles a commensurately universal
attribute of isosceles; it is of wider application.
5
We must not fail to observe that we often fall into error because our
conclusion is not in fact primary and commensurately universal in the
sense in which we think we prove it so. (5) We make this mistake (1)
when the subject is an individual or individuals above which there is no
universal to be found: (2) when the subjects belong to different species
and there is a higher universal, but it has no name: (3) when the subject
which the demonstrator takes as a whole is really only a part of a larger
whole; for then the demonstration will be true of the individual
instances within the part and will hold in every instance of it, (10) yet the
demonstration will not be true of this subject primarily and
commensurately and universally. When a demonstration is true of a
subject primarily and commensurately and universally, that is to be
taken to mean that it is true of a given subject primarily and as such.
Case (3) may be thus exemplified. If a proof were given that
perpendiculars to the same line are parallel, it might be supposed that
lines thus perpendicular were the proper subject of the demonstration
because being parallel is true of every instance of them. (15) But it is not
so, for the parallelism depends not on these angles being equal to one
another because each is a right angle, but simply on their being equal to
one another. An example of (1) would be as follows: if isosceles were the
only triangle, it would be thought to have its angles equal to two right
angles qua isosceles. An instance of (2) would be the law that
proportionals alternate. Alternation used to be demonstrated separately
of numbers, lines, solids, (20) and durations, though it could have been
proved of them all by a single demonstration. Because there was no
single name to denote that in which numbers, lengths, durations, and
solids are identical, and because they differed specifically from one
another, this property was proved of each of them separately. To-day,
however, the proof is commensurately universal, for they do not possess
this attribute qua lines or qua numbers, but qua manifesting this generic
character which they are postulated as possessing universally. (25) Hence,
even if one prove of each kind of triangle that its angles are equal to two
right angles, whether by means of the same or different proofs; still, as
long as one treats separately equilateral, scalene, and isosceles, one does
not yet know, except sophistically, that triangle has its angles equal to
two right angles, nor does one yet know that triangle has this property
commensurately and universally, even if there is no other species of
triangle but these. (30) For one does not know that triangle as such has
this property, nor even that ‘all’ triangles have it—unless ‘all’ means
‘each taken singly’: if ‘all’ means ‘as a whole class’, then, though there be
none in which one does not recognize this property, one does not know
it of ‘all triangles’.
When, then, does our knowledge fail of commensurate universality,
and when is it unqualified knowledge? If triangle be identical in essence
with equilateral, i. e. with each or all equilaterals, then clearly we have
unqualified knowledge: if on the other hand it be not, and the attribute
belongs to equilateral qua triangle; then our knowledge fails of
commensurate universality. ‘But’, it will be asked, (35) ‘does this attribute
belong to the subject of which it has been demonstrated qua triangle or
qua isosceles? What is the point at which the subject to which it belongs
is primary? (i. e. to what subject can it be demonstrated as belonging
commensurately and universally?)’ Clearly this point is the first term in
which it is found to inhere as the elimination of inferior differentiae
proceeds. Thus the angles of a brazen isosceles triangle are equal to two
right angles: but eliminate brazen and isosceles and the attribute
remains. ‘But’—you may say—‘eliminate figure or limit, and the
attribute vanishes’. [74b] True, but figure and limit are not the first
differentiae whose elimination destroys the attribute. ‘Then what is the
first?’ If it is triangle, it will be in virtue of triangle that the attribute
belongs to all the other subjects of which it is predicable, and triangle is
the subject to which it can be demonstrated as belonging
commensurately and universally.
6
Demonstrative knowledge must rest on necessary basic truths; for
the object of scientific knowledge cannot be other than it is. (5) Now
attributes attaching essentially to their subjects attach necessarily to
them: for essential attributes are either elements in the essential nature
of their subjects, or contain their subjects as elements in their own
essential nature. (The pairs of opposites which the latter class includes
are necessary because one member or the other necessarily inheres.) It
follows from this that premisses of the demonstrative syllogism must be
connexions essential in the sense explained: for all attributes must inhere
essentially or else be accidental, (10) and accidental attributes are not
necessary to their subjects.
We must either state the case thus, or else premise that the conclusion
of demonstration is necessary and that a demonstrated conclusion
cannot be other than it is, and then infer that the conclusion must be
developed from necessary premisses. (15) For though you may reason
from true premisses without demonstrating, yet if your premisses are
necessary you will assuredly demonstrate—in such necessity you have at
once a distinctive character of demonstration. That demonstration
proceeds from necessary premisses is also indicated by the fact that the
objection we raise against a professed demonstration is that a premiss of
it is not a necessary truth—whether we think it altogether devoid of
necessity, (20) or at any rate so far as our opponent’s previous argument
goes. This shows how naïve it is to suppose one’s basic truths rightly
chosen if one starts with a proposition which is (1) popularly accepted
and (2) true, such as the sophists’ assumption that to know is the same
as to possess knowledge.7 For (1) popular acceptance or rejection is no
criterion of a basic truth, which can only be the primary law of the
genus constituting the subject matter of the demonstration; and (2) not
all truth is ‘appropriate’. (25)
A further proof that the conclusion must be the development of
necessary premisses is as follows. Where demonstration is possible, one
who can give no account which includes the cause has no scientific
knowledge. If, then, we suppose a syllogism in which, though A
necessarily inheres in C, yet B, the middle term of the demonstration, is
not necessarily connected with A and C, then the man who argues thus
has no reasoned knowledge of the conclusion, (30) since this conclusion
does not owe its necessity to the middle term; for though the conclusion
is necessary, the mediating link is a contingent fact. Or again, if a man is
without knowledge now, though he still retains the steps of the
argument, though there is no change in himself or in the fact and no
lapse of memory on his part; then neither had he knowledge previously.
But the mediating link, not being necessary, (35) may have perished in the
interval; and if so, though there be no change in him nor in the fact, and
though he will still retain the steps of the argument, yet he has not
knowledge, and therefore had not knowledge before. Even if the link has
not actually perished but is liable to perish, this situation is possible and
might occur. But such a condition cannot be knowledge.
[75a] When the conclusion is necessary, the middle through which it
was proved may yet quite easily be non-necessary. You can in fact infer
the necessary even from a non-necessary premiss, just as you can infer
the true from the not true. On the other hand, (5) when the middle is
necessary the conclusion must be necessary; just as true premisses
always give a true conclusion. Thus, if A is necessarily predicated of B
and B of C, then A is necessarily predicated of C. But when the
conclusion is non-necessary the middle cannot be necessary either. (10)
Thus: let A be predicated non-necessarily of C but necessarily of B, and
let B be a necessary predicate of C; then A too will be a necessary
predicate of C, which by hypothesis it is not.
To sum up, then: demonstrative knowledge must be knowledge of a
necessary nexus, and therefore must clearly be obtained through a
necessary middle term; otherwise its possessor will know neither the
cause nor the fact that his conclusion is a necessary connexion. (15) Either
he will mistake the non-necessary for the necessary and believe the
necessity of the conclusion without knowing it, or else he will not even
believe it—in which case he will be equally ignorant, whether he
actually infers the mere fact through middle terms or the reasoned fact
and from immediate premisses.
Of accidents that are not essential according to our definition of
essential there is no demonstrative knowledge; for since an accident, in
the sense in which I here speak of it, may also not inhere, (20) it is
impossible to prove its inherence as a necessary conclusion. A difficulty,
however, might be raised as to why in dialectic, if the conclusion is not a
necessary connexion, such and such determinate premisses should be
proposed in order to deal with such and such determinate problems.
Would not the result be the same if one asked any questions whatever
and then merely stated one’s conclusion? The solution is that
determinate questions have to be put, (25) not because the replies to them
affirm facts which necessitate facts affirmed by the conclusion, but
because these answers are propositions which if the answerer affirm, he
must affirm the conclusion—and affirm it with truth if they are true.
Since it is just those attributes within every genus which are essential
and possessed by their respective subjects as such that are necessary, it is
clear that both the conclusions and the premisses of demonstrations
which produce scientific knowledge are essential. (30) For accidents are
not necessary: and, further, since accidents are not necessary one does
not necessarily have reasoned knowledge of a conclusion drawn from
them (this is so even if the accidental premisses are invariable but not
essential, as in proofs through signs; for though the conclusion be
actually essential, one will not know it as essential nor know its reason);
but to have reasoned knowledge of a conclusion is to know it through its
cause. (35) We may conclude that the middle must be consequentially
connected with the minor, and the major with the middle.
7
It follows that we cannot in demonstrating pass from one genus to
another. We cannot, for instance, prove geometrical truths by arithmetic.
For there are three elements in demonstration: (1) what is proved, the
conclusion—an attribute inhering essentially in a genus; (2) the axioms,
(40) i. e. axioms which are premisses of demonstration; (3) the subjectgenus whose attributes, i. e. essential properties, are revealed by the
demonstration. [75b] The axioms which are premisses of
demonstration may be identical in two or more sciences: but in the case
of two different genera such as arithmetic and geometry you cannot
apply arithmetical demonstration to the properties of magnitudes unless
the magnitudes in question are numbers.8 (5) How in certain cases
transference is possible I will explain later.9
Arithmetical demonstration and the other sciences likewise possess,
each of them, their own genera; so that if the demonstration is to pass
from one sphere to another, the genus must be either absolutely or to
some extent the same. (10) If this is not so, transference is clearly
impossible, because the extreme and the middle terms must be drawn
from the same genus: otherwise, as predicated, they will not be essential
and will thus be accidents. That is why it cannot be proved by geometry
that opposites fall under one science, nor even that the product of two
cubes is a cube. Nor can the theorem of any one science be demonstrated
by means of another science, (15) unless these theorems are related as
subordinate to superior (e. g. as optical theorems to geometry or
harmonic theorems to arithmetic). Geometry again cannot prove of lines
any property which they do not possess qua lines, i. e. in virtue of the
fundamental truths of their peculiar genus: it cannot show, for example,
that the straight line is the most beautiful of lines or the contrary of the
circle; for these qualities do not belong to lines in virtue of their peculiar
genus, (20) but through some property which it shares with other genera.
8
It is also clear that if the premisses from which the syllogism
proceeds are commensurately universal, the conclusion of such
demonstration—demonstration, i. e., in the unqualified sense—must also
be eternal. Therefore no attribute can be demonstrated nor known by
strictly scientific knowledge to inhere in perishable things. (25) The proof
can only be accidental, because the attribute’s connexion with its
perishable subject is not commensurately universal but temporary and
special. If such a demonstration is made, one premiss must be perishable
and not commensurately universal (perishable because only if it is
perishable will the conclusion be perishable; not commensurately
universal, because the predicate will be predicable of some instances of
the subject and not of others); so that the conclusion can only be that a
fact is true at the moment—not commensurately and universally. (30) The
same is true of definitions, since a definition is either a primary premiss
or a conclusion of a demonstration, or else only differs from a
demonstration in the order of its terms. Demonstration and science of
merely frequent occurrences—e. g. of eclipse as happening to the moon
—are, as such, clearly eternal: whereas so far as they are not eternal
they are not fully commensurate. Other subjects too have properties
attaching to them in the same way as eclipse attaches to the moon. (35)
9
It is clear that if the conclusion is to show an attribute inhering as
such, nothing can be demonstrated except from its ‘appropriate’ basic
truths. Consequently a proof even from true, indemonstrable, and
immediate premisses does not constitute knowledge. (40) Such proofs are
like Bryson’s method of squaring the circle; for they operate by taking as
their middle a common character—a character, therefore, which the
subject may share with another—and consequently they apply equally to
subjects different in kind. [76a] They therefore afford knowledge of an
attribute only as inhering accidentally, not as belonging to its subject as
such: otherwise they would not have been applicable to another genus.
Our knowledge of any attribute’s connexion with a subject is
accidental unless we know that connexion through the middle term in
virtue of which it inheres, and as an inference from basic premisses
essential and ‘appropriate’ to the subject—unless we know, (5) e. g., the
property of possessing angles equal to two right angles as belonging to
that subject in which it inheres essentially, and as inferred from basic
premisses essential and ‘appropriate’ to that subject: so that if that
middle term also belongs essentially to the minor, the middle must
belong to the same kind as the major and minor terms. The only
exceptions to this rule are such cases as theorems in harmonics which
are demonstrable by arithmetic. Such theorems are proved by the same
middle terms as arithmetical properties, (10) but with a qualification—the
fact falls under a separate science (for the subject genus is separate), but
the reasoned fact concerns the superior science, to which the attributes
essentially belong. Thus, even these apparent exceptions show that no
attribute is strictly demonstrable except from its ‘appropriate’ basic
truths, which, however, in the case of these sciences have the requisite
identity of character. (15)
It is no less evident that the peculiar basic truths of each inhering
attribute are indemonstrable; for basic truths from which they might be
deduced would be basic truths of all that is, and the science to which
they belonged would possess universal sovereignty. This is so because he
knows better whose knowledge is deduced from higher causes, for his
knowledge is from prior premisses when it derives from causes
themselves uncaused: hence, (20) if he knows better than others or best of
all, his knowledge would be science in a higher or the highest degree.
But, as things are, demonstration is not transferable to another genus,
with such exceptions as we have mentioned of the application of
geometrical demonstrations to theorems in mechanics or optics, (25) or of
arithmetical demonstrations to those of harmonics.
It is hard to be sure whether one knows or not; for it is hard to be sure
whether one’s knowledge is based on the basic truths appropriate to
each attribute—the differentia of true knowledge. We think we have
scientific knowledge if we have reasoned from true and primary
premisses. But that is not so: the conclusion must be homogeneous with
the basic facts of the science. (30)
10
I call the basic truths of every genus those elements in it the
existence of which cannot be proved. As regards both these primary
truths and the attributes dependent on them the meaning of the name is
assumed. The fact of their existence as regards the primary truths must
be assumed; but it has to be proved of the remainder, the attributes.
Thus we assume the meaning alike of unity, straight, (35) and triangular;
but while as regards unity and magnitude we assume also the fact of
their existence, in the case of the remainder proof is required.
Of the basic truths used in the demonstrative sciences some are
peculiar to each science, and some are common, but common only in the
sense of analogous, being of use only in so far as they fall within the
genus constituting the province of the science in question.
Peculiar truths are, (40) e. g., the definitions of line and straight;
common truths are such as ‘take equals from equals and equals remain’.
Only so much of these common truths is required as falls within the
genus in question: for a truth of this kind will have the same force even
if not used generally but applied by the geometer only to magnitudes, or
by the arithmetician only to numbers. [76b] Also peculiar to a science
are the subjects the existence as well as the meaning of which it
assumes, and the essential attributes of which it investigates, e. g. (5) in
arithmetic units, in geometry points and lines. Both the existence and
the meaning of the subjects are assumed by these sciences; but of their
essential attributes only the meaning is assumed. For example arithmetic
assumes the meaning of odd and even, square and cube, geometry that
of incommensurable, or of deflection or verging of lines, whereas the
existence of these attributes is demonstrated by means of the axioms and
from previous conclusions as premisses. (10) Astronomy too proceeds in
the same way. For indeed every demonstrative science has three
elements: (1) that which it posits, the subject genus whose essential
attributes it examines; (2) the so-called axioms, (15) which are primary
premisses of its demonstration; (3) the attributes, the meaning of which
it assumes. Yet some sciences may very well pass over some of these
elements; e. g. we might not expressly posit the existence of the genus if
its existence were obvious (for instance, the existence of hot and cold is
more evident than that of number); or we might omit to assume
expressly the meaning of the attributes if it were well understood. In the
same way the meaning of axioms, (20) such as ‘Take equals from equals
and equals remain’, is well known and so not expressly assumed.
Nevertheless in the nature of the case the essential elements of
demonstration are three: the subject, the attributes, and the basic
premisses.
That which expresses necessary self-grounded fact, and which we must
necessarily believe,10 is distinct both from the hypotheses of a science
and from illegitimate postulate—I say ‘must believe’, because all
syllogism, and therefore a fortiori demonstration, is addressed not to the
spoken word, but to the discourse within the soul,11 and though we can
always raise objections to the spoken word, (25) to the inward discourse
we cannot always object. That which is capable of proof but assumed by
the teacher without proof is, if the pupil believes and accepts it,
hypothesis, though only in a limited sense hypothesis—that is, relatively
to the pupil; if the pupil has no opinion or a contrary opinion on the
matter, (30) the same assumption is an illegitimate postulate. Therein lies
the distinction between hypothesis and illegitimate postulate: the latter
is the contrary of the pupil’s opinion, demonstrable, but assumed and
used without demonstration.
The definitions—viz. those which are not expressed as statements that
anything is or is not—are not hypotheses: but it is in the premisses of a
science that its hypotheses are contained. (35) Definitions require only to
be understood, and this is not hypothesis—unless it be contended that
the pupil’s hearing is also an hypothesis required by the teacher.
Hypotheses, on the contrary, postulate facts on the being of which
depends the being of the fact inferred. Nor are the geometer’s
hypotheses false, as some have held, (40) urging that one must not employ
falsehood and that the geometer is uttering falsehood in stating that the
line which he draws is a foot long or straight, when it is actually neither.
The truth is that the geometer does not draw any conclusion from the
being of the particular line of which he speaks, but from what his
diagrams symbolize. [77a] A further distinction is that all hypotheses
and illegitimate postulates are either universal or particular, whereas a
definition is neither.
11
So demonstration does not necessarily imply the being of Forms
nor a One beside a Many, (5) but it does necessarily imply the possibility
of truly predicating one of many; since without this possibility we
cannot save the universal, and if the universal goes, the middle term
goes with it, and so demonstration becomes impossible. We conclude,
then, that there must be a single identical term unequivocally predicable
of a number of individuals.
The law that it is impossible to affirm and deny simultaneously the
same predicate of the same subject is not expressly posited by any
demonstration except when the conclusion also has to be expressed in
that form; in which case the proof lays down as its major premiss that
the major is truly affirmed of the middle but falsely denied. (10) It makes
no difference, however, if we add to the middle, or again to the minor
term, the corresponding negative. For grant a minor term of which it is
true to predicate man—even if it be also true to predicate not-man of it
—still grant simply that man is animal and not not-animal, (15) and the
conclusion follows: for it will still be true to say that Callias—even if it
be also true to say that not-Callias—is animal and not not-animal. The
reason is that the major term is predicable not only of the middle, but of
something other than the middle as well, (20) being of wider application;
so that the conclusion is not affected even if the middle is extended to
cover the original middle term and also what is not the original middle
term.12
The law that every predicate can be either truly affirmed or truly
denied of every subject is posited by such demonstration as uses reductio
ad impossibile, and then not always universally, but so far as it is
requisite; within the limits, that is, of the genus—the genus, (25) I mean
(as I have already explained13), to which the man of science applies his
demonstrations. In virtue of the common elements of demonstration—I
mean the common axioms which are used as premisses of
demonstration, not the subjects or the attributes demonstrated as
belonging to them—all the sciences have communion with one another,
and in communion with them all is dialectic and any science which
might attempt a universal proof of axioms such as the law of excluded
middle, (30) the law that the subtraction of equals from equals leaves
equal remainders, or other axioms of the same kind. Dialectic has no
definite sphere of this kind, not being confined to a single genus.
Otherwise its method would not be interrogative; for the interrogative
method is barred to the demonstrator, who cannot use the opposite facts
to prove the same nexus. This was shown in my work on the syllogism.14
12
If a syllogistic question15 is equivalent to a proposition embodying
one of the two sides of a contradiction, (35) and if each science has its
peculiar propositions from which its peculiar conclusion is developed,
then there is such a thing as a distinctively scientific question, and it is
the interrogative form of the premisses from which the ‘appropriate’
conclusion of each science is developed. (40) Hence it is clear that not
every question will be relevant to geometry, nor to medicine, nor to any
other science: only those questions will be geometrical which form
premisses for the proof of the theorems of geometry or of any other
science, such as optics, which uses the same basic truths as geometry.
[77b] Of the other sciences the like is true. Of these questions the
geometer is bound to give his account, using the basic truths of
geometry in conjunction with his previous conclusions; of the basic
truths the geometer, as such, is not bound to give any account. (5) The
like is true of the other sciences. There is a limit, then, to the questions
which we may put to each man of science; nor is each man of science
bound to answer all inquiries on each several subject, but only such as
fall within the defined field of his own science. If, then, in controversy
with a geometer qua geometer the disputant confines himself to
geometry and proves anything from geometrical premisses, he is clearly
to be applauded; if he goes outside these he will be at fault, (10) and
obviously cannot even refute the geometer except accidentally. One
should therefore not discuss geometry among those who are not
geometers, for in such a company an unsound argument will pass
unnoticed. This is correspondingly true in the other sciences. (15)
Since there are ‘geometrical’ questions, does it follow that there are
also distinctively ‘ungeometrical’ questions? Further, in each special
science—geometry for instance—what kind of error is it that may vitiate
questions, and yet not exclude them from that science? Again, is the
erroneous conclusion one constructed from premisses opposite to the
true premisses, or is it formal fallacy though drawn from geometrical
premisses? Or, (20) perhaps, the erroneous conclusion is due to the
drawing of premisses from another science; e. g. in a geometrical
controversy a musical question is distinctively ungeometrical, whereas
the notion that parallels meet is in one sense geometrical, being
ungeometrical in a different fashion: the reason being that
‘ungeometrical’, like ‘unrhythmical’, is equivocal, meaning in the one
case not geometry at all, (25) in the other bad geometry? It is this error,
i. e. error based on premisses of this kind—‘of’ the science but false—
that is the contrary of science. In mathematics the formal fallacy is not
so common, because it is the middle term in which the ambiguity lies,
since the major is predicated of the whole of the middle and the middle
of the whole of the minor (the predicate of course never has the prefix
‘all’); and in mathematics one can, (30) so to speak, see these middle
terms with an intellectual vision, while in dialectic the ambiguity may
escape detection. e. g. ‘Is every circle a figure?’ A diagram shows that
this is so, but the minor premiss ‘Are epics circles?’ is shown by the
diagram to be false.
If a proof has an inductive minor premiss, one should not bring an
‘objection’ against it. (35) For since every premiss must be applicable to a
number of cases (otherwise it will not be true in every instance, which,
since the syllogism proceeds from universals, it must be), then assuredly
the same is true of an ‘objection’; since premisses and ‘objections’ are so
far the same that anything which can be validly advanced as an
‘objection’ must be such that it could take the form of a premiss, (40)
either demonstrative or dialectical. On the other hand arguments
formally illogical do sometimes occur through taking as middles mere
attributes of the major and minor terms. [78a] An instance of this is
Caeneus’ proof that fire increases in geometrical proportion: ‘Fire’, he
argues, ‘increases rapidly, and so does geometrical proportion’. There is
no syllogism so, but there is a syllogism if the most rapidly increasing
proportion is geometrical and the most rapidly increasing proportion is
attributable to fire in its motion. (5) Sometimes, no doubt, it is impossible
to reason from premisses predicating mere attributes: but sometimes it is
possible, though the possibility is over-looked. If false premisses could
never give true conclusions ‘resolution’ would be easy, for premisses and
conclusion would in that case inevitably reciprocate. I might then argue
thus: let A be an existing fact; let the existence of A imply such and such
facts actually known to me to exist, which we may call B. I can now,
since they reciprocate, infer A from B.
Reciprocation of premisses and conclusion is more frequent in
mathematics, (10) because mathematics takes definitions, but never an
accident, for its premisses—a second characteristic distinguishing
mathematical reasoning from dialectical disputations.
A science expands not by the interposition of fresh middle terms, but
by the apposition of fresh extreme terms. e. g. A is predicated of B, B of
C, C of D, and so indefinitely. Or the expansion may be lateral: e. g. one
major, (15) A, may be proved of two minors, C and E. Thus let A represent
number—a number or number taken indeterminately; B determinate odd
number; C any particular odd number. We can then predicate A of C.
Next let D represent determinate even number, (20) and E even number.
Then A is predicable of E.
13
Knowledge of the fact differs from knowledge of the reasoned fact.
To begin with, they differ within the same science and in two ways: (1)
when the premisses of the syllogism are not immediate (for then the
proximate cause is not contained in them—a necessary condition of
knowledge of the reasoned fact): (2) when the premisses are immediate,
(25) but instead of the cause the better known of the two reciprocals is
taken as the middle; for of two reciprocally predicable terms the one
which is not the cause may quite easily be the better known and so
become the middle term of the demonstration. Thus (2) (a) you might
prove as follows that the planets are near because they do not twinkle:
let C be the planets, (30) B not twinkling, A proximity. Then B is
predicable of C; for the planets do not twinkle. But A is also predicable
of B, since that which does not twinkle is near—we must take this truth
as having been reached by induction or sense-perception. Therefore A is
a necessary predicate of C; so that we have demonstrated that the
planets are near. (35) This syllogism, then, proves not the reasoned fact
but only the fact; since they are not near because they do not twinkle,
but, because they are near, do not twinkle. The major and middle of the
proof, however, may be reversed, and then the demonstration will be of
the reasoned fact. (40) Thus: let C be the planets, B proximity, A not
twinkling. [78b] Then B is an attribute of C, and A—not twinkling—of
B. Consequently A is predicable of C, and the syllogism proves the
reasoned fact, since its middle term is the proximate cause. Another
example is the inference that the moon is spherical from its manner of
waxing. Thus: since that which so waxes is spherical, and since the moon
so waxes, (5) clearly the moon is spherical. Put in this form, the syllogism
turns out to be proof of the fact, but if the middle and major be reversed
it is proof of the reasoned fact; since the moon is not spherical because it
waxes in a certain manner, but waxes in such a manner because it is
spherical. (Let C be the moon, B spherical, and A waxing.) (10) Again (b),
in cases where the cause and the effect are not reciprocal and the effect
is the better known, the fact is demonstrated but not the reasoned fact.
This also occurs (1) when the middle falls outside the major and minor,
for here too the strict cause is not given, and so the demonstration is of
the fact, not of the reasoned fact. For example, (15) the question ‘Why
does not a wall breathe?’ might be answered, ‘Because it is not an
animal’; but that answer would not give the strict cause, because if not
being an animal causes the absence of respiration, then being an animal
should be the cause of respiration, according to the rule that if the
negation of x causes the non-inherence of y, (20) the affirmation of x
causes the inherence of y; e. g. if the disproportion of the hot and cold
elements is the cause of ill health, their proportion is the cause of health;
and conversely, if the assertion of x causes the inherence of y, the
negation of x must cause y’s non-inherence. But in the case given this
consequence does not result; for not every animal breathes. A syllogism
with this kind of cause takes place in the second figure. Thus: let A be
animal, B respiration, (25) C wall. Then A is predicable of all B (for all
that breathes is animal), but of no C; and consequently B is predicable of
no C; that is, the wall does not breathe. Such causes are like far-fetched
explanations, which precisely consist in making the cause too remote, (30)
as in Anacharsis’ account of why the Scythians have no flute-players;
namely because they have no vines.
Thus, then, do the syllogism of the fact and the syllogism of the
reasoned fact differ within one science and according to the position of
the middle terms. But there is another way too in which the fact and the
reasoned fact differ, and that is when they are investigated respectively
by different sciences. (35) This occurs in the case of problems related to
one another as subordinate and superior, as when optical problems are
subordinated to geometry, (40) mechanical problems to stereometry,
harmonic problems to arithmetic, the data of observation to astronomy.
[79a] (Some of these sciences bear almost the same name; e. g.
mathematical and nautical astronomy, mathematical and acoustical
harmonics.) Here it is the business of the empirical observers to know
the fact, of the mathematicians to know the reasoned fact; for the latter
are in possession of the demonstrations giving the causes, and are often
ignorant of the fact: just as we have often a clear insight into a universal,
but through lack of observation are ignorant of some of its particular
instances. These connexions16 have a perceptible existence though they
are manifestations of forms. For the mathematical sciences concern
forms: they do not demonstrate properties of a substratum, since, even
though the geometrical subjects are predicable as properties of a
perceptible substratum, it is not as thus predicable that the
mathematician demonstrates properties of them. As optics is related to
geometry, (10) so another science is related to optics, namely the theory
of the rainbow. Here knowledge of the fact is within the province of the
natural philosopher, knowledge of the reasoned fact within that of the
optician, either qua optician or qua mathematical optician. Many
sciences not standing in this mutual relation enter into it at points; e. g.
medicine and geometry: it is the physician’s business to know that
circular wounds heal more slowly, the geometer’s to know the reason
why. (15)
(5)
14
Of all the figures the most scientific is the first. Thus, it is the
vehicle of the demonstrations of all the mathematical sciences, such as
arithmetic, geometry, and optics, and practically of all sciences that
investigate causes: for the syllogism of the reasoned fact is either
exclusively or generally speaking and in most cases in this figure—a
second proof that this figure is the most scientific; for grasp of a
reasoned conclusion is the primary condition of knowledge. (20) Thirdly,
the first is the only figure which enables us to pursue knowledge of the
essence of a thing. In the second figure no affirmative conclusion is
possible, (25) and knowledge of a thing’s essence must be affirmative;
while in the third figure the conclusion can be affirmative, but cannot be
universal, and essence must have a universal character: e. g. man is not
two-footed animal in any qualified sense, but universally. Finally, the
first figure has no need of the others, (30) while it is by means of the first
that the other two figures are developed, and have their intervals closepacked until immediate premisses are reached. Clearly, therefore, the
first figure is the primary condition of knowledge.
15
Just as an attribute A may (as we saw) be atomically connected
with a subject B, so its disconnexion may be atomic. I call ‘atomic’
connexions or disconnexions which involve no intermediate term; since
in that case the connexion or disconnexion will not be mediated by
something other than the terms themselves. (35) It follows that if either A
or B, or both A and B, have a genus, their disconnexion cannot be
primary. Thus: let C be the genus of A. Then, if C is not the genus of B—
for A may well have a genus which is not the genus of B—there will be a
syllogism proving A’s disconnexion from B thus: (40)
all A is C,
no B is C,
no B is A.
[79b] Or if it is B which has a genus D, we have
all B is D,
no D is A,
no B is A, by syllogism;
and the proof will be similar if both A and B have a genus. (5) That the
genus of A need not be the genus of B and vice versa, is shown by the
existence of mutually exclusive co-ordinate series of predication. If no
term in the series ACD … is predicable of any term in the series BEF …,
and if G—a term in the former series—is the genus of A, (10) clearly G
will not be the genus of B; since, if it were, the series would not be
mutually exclusive. So also if B has a genus, it will not be the genus of A.
If, on the other hand, neither A nor B has a genus and A does not inhere
in B, this disconnexion must be atomic. If there be a middle term, one or
other of them is bound to have a genus, (15) for the syllogism will be
either in the first or the second figure. If it is in the first, B will have a
genus—for the premiss containing it must be affirmative;17 if in the
second, either A or B indifferently, since syllogism is possible if either is
contained in a negative premiss,18 but not if both premisses are negative.
(20)
Hence it is clear that one thing may be atomically disconnected from
another, and we have stated when and how this is possible.
16
Ignorance—defined not as the negation of knowledge but as a
positive state of mind—is error produced by inference.
(1) Let us first consider propositions asserting a predicate’s immediate
connexion with or disconnexion from a subject. (25) Here, it is true,
positive error may befall one in alternative ways; for it may arise where
one directly believes a connexion or disconnexion as well as where one’s
belief is acquired by inference. The error, however, that consists in a
direct belief is without complication; but the error resulting from
inference—which here concerns us—takes many forms. Thus, let A be
atomically disconnected from all B: then the conclusion inferred through
a middle term C, (30) that all B is A, will be a case of error produced by
syllogism. Now, two cases are possible. Either (a) both premisses, or (b)
one premiss only, may be false. (a) If neither A is an attribute of any C
nor C of any B, whereas the contrary was posited in both cases, both
premisses will be false. (C may quite well be so related to A and B that C
is neither subordinate to A nor a universal attribute of B: for B, (35) since
A was said to be primarily disconnected from B, cannot have a genus,
and A need not necessarily be a universal attribute of all things.
Consequently both premisses may be false.) On the other hand, (b) one
of the premisses may be true, (40) though not either indifferently but only
the major A–C; since, B having no genus, the premiss C–B will always be
false, while A–C may be true. [80a] This is the case if, for example, A is
related atomically to both C and B; because when the same term is
related atomically to more terms than one, neither of those terms will
belong to the other. It is, of course, equally the case if A–C is not atomic.
(5)
Error of attribution, then, occurs through these causes and in this form
only—for we found that no syllogism of universal attribution was
possible in any figure but the first. On the other hand, an error of nonattribution may occur either in the first or in the second figure. Let us
therefore first explain the various forms it takes in the first figure and
the character of the premisses in each case. (10)
(c) It may occur when both premisses are false; e. g. supposing A
atomically connected with both C and B, if it be then assumed that no C
is A, and all B is C, both premisses are false.
(d) It is also possible when one is false. This may be either premiss
indifferently. A–C may be true, C–B false—A–C true because A is not an
attribute of all things, (15) C–B false because C, which never has the
attribute A, cannot be an attribute of B; for if C–B were true, the premiss
A–C would no longer be true, and besides if both premisses were true,
the conclusion would be true. Or again, C–B may be true and A–C false;
e. g. if both C and A contain B as genera, (20) one of them must be
subordinate to the other, so that if the premiss takes the form No C is A,
it will be false. This makes it clear that whether either or both premisses
are false, (25) the conclusion will equally be false.
In the second figure the premisses cannot both be wholly false; for if
all B is A, no middle term can be with truth universally affirmed of one
extreme and universally denied of the other: but premisses in which the
middle is affirmed of one extreme and denied of the other are the
necessary condition if one is to get a valid inference at all. (30) Therefore
if, taken in this way, they are wholly false, their contraries conversely
should be wholly true. But this is impossible. On the other hand, there is
nothing to prevent both premisses being partially false; e. g. if actually
some A is C and some B is C, then if it is premised that all A is C and no
B is C, (35) both premisses are false, yet partially, not wholly, false. The
same is true if the major is made negative instead of the minor. Or one
premiss may be wholly false, and it may be either of them. Thus,
supposing that actually an attribute of all A must also be an attribute of
all B, then if C is yet taken to be a universal attribute of all A but
universally non-attributable to B, (40) C–A will be true but C–B false.
[80b] Again, actually that which is an attribute of no B will not be an
attribute of all A either; for if it be an attribute of all A, it will also be an
attribute of all B, which is contrary to supposition; but if C be
nevertheless assumed to be a universal attribute of A, (5) but an attribute
of no B, then the premiss C–B is true but the major is false. The case is
similar if the major is made the negative premiss. For in fact what is an
attribute of no A will not be an attribute of any B either; and if it be yet
assumed that C is universally non-attributable to A, but a universal
attribute of B, (10) the premiss C–A is true but the minor wholly false.
Again, in fact it is false to assume that that which is an attribute of all B
is an attribute of no A, for if it be an attribute of all B, it must be an
attribute of some A. If then C is nevertheless assumed to be an attribute
of all B but of no A, C–B will be true but C–A false.
It is thus clear that in the case of atomic propositions erroneous
inference will be possible not only when both premisses are false but
also when only one is false. (15)
17
(2) In the case of attributes not atomically connected with or
disconnected from their subjects, (a) (i) as long as the false conclusion is
inferred through the ‘appropriate’ middle, (20) only the major and not
both premisses can be false. By ‘appropriate middle’ I mean the middle
term through which the contradictory—i. e. the true—conclusion is
inferrible. Thus, let A be attributable to B through a middle term C: then,
since to produce a conclusion the premiss C–B must be taken
affirmatively, it is clear that this premiss must always be true, (25) for its
quality is not changed. But the major A–C is false, for it is by a change in
the quality of A–C that the conclusion becomes its contradictory—i. e.
true. Similarly (ii) if the middle is taken from another series of
predication; e. g. suppose D to be not only contained within A as a part
within its whole but also predicable of all B. Then the premiss D–B must
remain unchanged, (30) but the quality of A–D must be changed; so that
D–B is always true, A–D always false. Such error is practically identical
with that which is inferred through the ‘appropriate’ middle. On the
other hand, (b) if the conclusion is not inferred through the ‘appropriate’
middle—(i) when the middle is subordinate to A but is predicable of no
B, (35) both premisses must be false, because if there is to be a conclusion
both must be posited as asserting the contrary of what is actually the
fact, and so posited both become false: e. g. suppose that actually all D is
A but no B is D; then if these premisses are changed in quality, a
conclusion will follow and both of the new premisses will be false. (40)
When, however, (ii) the middle D is not subordinate to A, A–D will be
true, D–B false—A–D true because A was not subordinate to D, D–B false
because if it had been true, the conclusion too would have been true; but
it is ex hypothesi false. [81a]
When the erroneous inference is in the second figure, (5) both
premisses cannot be entirely false; since if B is subordinate to A, there
can be no middle predicable of all of one extreme and of none of the
other as was stated before.19 One premiss, however, may be false, and it
may be either of them. Thus, if C is actually an attribute of both A and B,
but is assumed to be an attribute of A only and not of B, (10) C–A will be
true, C–B false: or again if C be assumed to be attributable to B but to no
A, C–B will be true, C–A false.
We have stated when and through what kinds of premisses error will
result in cases where the erroneous conclusion is negative. (15) If the
conclusion is affirmative, (a) (i) it may be inferred through the
‘appropriate’ middle term. In this case both premisses cannot be false
since, as we said before,20 C–B must remain unchanged if there is to be a
conclusion, and consequently A–C, the quality of which is changed, will
always be false. This is equally true if (ii) the middle is taken from
another series of predication, (20) as was stated to be the case also with
regard to negative error;21 for D–B must remain unchanged, while the
quality of A–D must be converted, and the type of error is the same as
before.
(b) The middle may be inappropriate. Then (i) if D is subordinate to A,
(25) A–D will be true, but D–B false; since A may quite well be predicable
of several terms no one of which can be subordinated to another. If,
however, (ii) D is not subordinate to A, obviously A–D, since it is
affirmed, will always be false, while D–B may be either true or false; for
A may very well be an attribute of no D, (30) whereas all B is D, e. g. no
science is animal, all music is science. Equally well A may be an
attribute of no D, and D of no B. It emerges, then, that if the middle term
is not subordinate to the major, not only both premisses but either singly
may be false.
Thus we have made it clear how many varieties of erroneous inference
are liable to happen and through what kinds of premisses they occur, (35)
in the case both of immediate and of demonstrable truths.
18
It is also clear that the loss of any one of the senses entails the loss
of a corresponding portion of knowledge, and that, since we learn either
by induction or by demonstration, this knowledge cannot be acquired.
(40) Thus demonstration develops from universals, induction from
particulars; but since it is possible to familiarize the pupil with even the
so-called mathematical abstractions only through induction—i. e. only
because each subject genus possesses, in virtue of a determinate
mathematical character, certain properties which can be treated as
separate even though they do not exist in isolation—it is consequently
impossible to come to grasp universals except through induction. [81b]
(5) But induction is impossible for those who have not sense-perception.
For it is sense-perception alone which is adequate for grasping the
particulars: they cannot be objects of scientific knowledge, because
neither can universals give us knowledge of them without induction, nor
can we get it through induction without sense-perception.
19
Every syllogism is effected by means of three terms. (10) One kind
of syllogism serves to prove that A inheres in C by showing that A
inheres in B and B in C; the other is negative and one of its premisses
asserts one term of another, while the other denies one term of another.
It is clear, then, that these are the fundamentals and so-called
hypotheses of syllogism. (15) Assume them as they have been stated, and
proof is bound to follow—proof that A inheres in C through B, and again
that A inheres in B through some other middle term, and similarly that B
inheres in C. If our reasoning aims at gaining credence and so is merely
dialectical, it is obvious that we have only to see that our inference is
based on premisses as credible as possible: so that if a middle term
between A and B is credible though not real, (20) one can reason through
it and complete a dialectical syllogism. If, however, one is aiming at
truth, one must be guided by the real connexions of subjects and
attributes. Thus: since there are attributes which are predicated of a
subject essentially or naturally and not coincidentally—not, (25) that is, in
a sense in which we say ‘That white (thing) is a man’, which is not the
same mode of predication as when we say ‘The man is white’: the man is
white not because he is something else but because he is man, but the
white is man because ‘being white’ coincides with ‘humanity’ within one
substratum—therefore there are terms such as are naturally subjects of
predicates. (30) Suppose, then, C such a term not itself attributable to
anything else as to a subject, but the proximate subject of the attribute B
—i. e. so that B–C is immediate; suppose further E related immediately
to F, and F to B. The first question is, must this series terminate, or can it
proceed to infinity? The second question is as follows: Suppose nothing
is essentially predicated of A, but A is predicated primarily of H and of
no intermediate prior term, (35) and suppose H similarly related to G and
G to B; then must this series also terminate, or can it too proceed to
infinity? There is this much difference between the questions: the first is,
is it possible to start from that which is not itself attributable to anything
else but is the subject of attributes, and ascend to infinity? The second is
the problem whether one can start from that which is a predicate but not
itself a subject of predicates, (40) and descend to infinity? A third question
is, if the extreme terms are fixed, can there be an infinity of middles? I
mean this: suppose for example that A inheres in C and B is intermediate
between them, but between B and A there are other middles, (5) and
between these again fresh middles; can these proceed to infinity or can
they not? This is the equivalent of inquiring, do demonstrations proceed
to infinity, i. e. is everything demonstrable? [82a] Or do ultimate
subject and primary attribute limit one another?
I hold that the same questions arise with regard to negative
conclusions and premisses: viz. if A is attributable to no B, (10) then either
this predication will be primary, or there will be an intermediate term
prior to B to which A is not attributable—G, let us say, which is
attributable to all B—and there may still be another term H prior to G,
which is attributable to all G. The same questions arise, I say, because in
these cases too either the series of prior terms to which A is not
attributable is infinite or it terminates.
One cannot ask the same questions in the case of reciprocating terms,
(15) since when subject and predicate are convertible there is neither
primary nor ultimate subject, seeing that all the reciprocals qua subjects
stand in the same relation to one another, whether we say that the
subject has an infinity of attributes or that both subjects and attributes—
and we raised the question in both cases—are infinite in number. These
questions then cannot be asked—unless, indeed, the terms can
reciprocate by two different modes, by accidental predication in one
relation and natural predication in the other. (20)
20
Now, it is clear that if the predications terminate in both the
upward and the downward direction (by ‘upward’ I mean the ascent to
the more universal, by ‘downward’ the descent to the more particular),
the middle terms cannot be infinite in number. For suppose that A is
predicated of F, and that the intermediates—call them BB′ B″ …—are
infinite, (25) then clearly you might descend from A and find one term
predicated of another ad infinitum, since you have an infinity of terms
between you and F; and equally, if you ascend from F, there are infinite
terms between you and A. It follows that if these processes are
impossible there cannot be an infinity of intermediates between A and F.
(30) Nor is it of any effect to urge that some terms of the series AB … F
are contiguous so as to exclude intermediates, while others cannot be
taken into the argument at all: whichever terms of the series B … I take,
the number of intermediates in the direction either of A or of F must be
finite or infinite: where the infinite series starts, whether from the first
term or from a later one, (35) is of no moment, for the succeeding terms
in any case are infinite in number.
21
Further, if in affirmative demonstration the series terminates in
both directions, clearly it will terminate too in negative demonstration.
Let us assume that we cannot proceed to infinity either by ascending
from the ultimate term (by ‘ultimate term’ I mean a term such as F was,
not itself attributable to a subject but itself the subject of attributes), or
by descending towards an ultimate from the primary term (by ‘primary
term’ I mean a term predicable of a subject but not itself a subject22).
[82b] If this assumption is justified, the series will also terminate in the
case of negation. (5) For a negative conclusion can be proved in all three
figures. In the first figure it is proved thus: no B is A, all C is B. In
packing the interval B–C we must reach immediate propositions—as is
always the case with the minor premiss—since B–C is affirmative. As
regards the other premiss it is plain that if the major term is denied of a
term D prior to B, D will have to be predicable of all B, (10) and if the
major is denied of yet another term prior to D, this term must be
predicable of all D. Consequently, since the ascending series is finite, the
descent will also terminate and there will be a subject of which A is
primarily non-predicable. In the second figure the syllogism is, all A is B,
no C is B, ∴ no C is A. If proof of this23 is required, plainly it may be
shown either in the first figure as above, (15) in the second as here, or in
the third. The first figure has been discussed, and we will proceed to
display the second, proof by which will be as follows: all B is D, no C is
D …, since it is required that B should be a subject of which a predicate
is affirmed. Next, since D is to be proved not to belong to C, then D has a
further predicate which is denied of C. Therefore, since the succession of
predicates affirmed of an ever higher universal terminates,24 the
succession of predicates denied terminates too.25 (20)
The third figure shows it as follows: all B is A, some B is not C, ∴ some
A is not C. This premiss, i. e. C–B, will be proved either in the same
figure or in one of the two figures discussed above. (25) In the first and
second figures the series terminates. If we use the third figure, we shall
take as premisses, all E is B, some E is not C, and this premiss again will
be proved by a similar prosyllogism. But since it is assumed that the
series of descending subjects also terminates, plainly the series of more
universal non-predicables will terminate also. Even supposing that the
proof is not confined to one method, but employs them all and is now in
the first figure, now in the second or third—even so the regress will
terminate, (30) for the methods are finite in number, and if finite things
are combined in a finite number of ways, the result must be finite.
Thus it is plain that the regress of middles terminates in the case of
negative demonstration, if it does so also in the case of affirmative
demonstration. That in fact the regress terminates in both these cases
may be made clear by the following dialectical considerations. (35)
22
In the case of predicates constituting the essential nature of a
thing, it clearly terminates, seeing that if definition is possible, or in
other words, if essential form is knowable, and an infinite series cannot
be traversed, predicates constituting a thing’s essential nature must be
finite in number.26 But as regards predicates generally we have the
following prefatory remarks to make. [83a] (1) We can affirm without
falsehood ‘the white (thing) is walking’, and ‘that big (thing) is a log’; or
again, ‘the log is big’, and ‘the man walks’. But the affirmation differs in
the two cases. When I affirm ‘the white is a log’, (5) I mean that
something which happens to be white is a log—not that white is the
substratum in which log inheres, for it was not qua white or qua a
species of white that the white (thing) came to be a log, and the white
(thing) is consequently not a log except incidentally. On the other hand,
when I affirm ‘the log is white’, I do not mean that something else,
which happens also to be a log, (10) is white (as I should if I said ‘the
musician is white’, which would mean ‘the man who happens also to be
a musician is white’); on the contrary, log is here the substratum—the
substratum which actually came to be white, and did so qua wood or qua
a species of wood and qua nothing else.
If we must lay down a rule, let us entitle the latter kind of statement
predication, (15) and the former not predication at all, or not strict but
accidental predication. ‘White’ and ‘log’ will thus serve as types
respectively of predicate and subject.
We shall assume, then, that the predicate is invariably predicated
strictly and not accidentally of the subject, (20) for on such predication
demonstrations depend for their force. It follows from this that when a
single attribute is predicated of a single subject, the predicate must
affirm of the subject either some element constituting its essential
nature, or that it is in some way qualified, quantified, essentially related,
active, passive, placed, or dated.27
(2) Predicates which signify substance signify that the subject is
identical with the predicate or with a species of the predicate. (25)
Predicates not signifying substance which are predicated of a subject not
identical with themselves or with a species of themselves are accidental
or coincidental; e. g. white is a coincident of man, seeing that man is not
identical with white or a species of white, (30) but rather with animal,
since man is identical with a species of animal. These predicates which
do not signify substance must be predicates of some other subject, and
nothing can be white which is not also other than white. The Forms we
can dispense with, for they are mere sound without sense; and even if
there are such things, they are not relevant to our discussion, since
demonstrations are concerned with predicates such as we have
defined.28 (35)
(3) If A is a quality of B, B cannot be a quality of A—a quality of a
quality. Therefore A and B cannot be predicated reciprocally of one
another in strict predication: they can be affirmed without falsehood of
one another, but not genuinely predicated of each other.29 For one
alternative is that they should be substantially predicated of one
another, i. e. B would become the genus or differentia of A—the
predicate now become subject. [83b] But it has been shown that in
these substantial predications neither the ascending predicates nor the
descending subjects form an infinite series; e. g. neither the series, man
is biped, biped is animal, &c., nor the series predicating animal of man,
man of Callias, Callias of a further subject as an element of its essential
nature, is infinite. For all such substance is definable, (5) and an infinite
series cannot be traversed in thought: consequently neither the ascent
nor the descent is infinite, since a substance whose predicates were
infinite would not be definable. Hence they will not be predicated each
as the genus of the other; for this would equate a genus with one of its
own species. Nor (the other alternative) can a quale be reciprocally
predicated of a quale, (10) nor any term belonging to an adjectival
category of another such term, except by accidental predication; for all
such predicates are coincidents and are predicated of substances.30 On
the other hand—in proof of the impossibility of an infinite ascending
series—every predication displays the subject as somehow qualified or
quantified or as characterized under one of the other adjectival
categories, or else is an element in its substantial nature: these latter are
limited in number, (15) and the number of the widest kinds under which
predications fall is also limited, for every predication must exhibit its
subject as somehow qualified, quantified, essentially related, acting or
suffering, or in some place or at some time.31
I assume first that predication implies a single subject and a single
attribute, and secondly that predicates which are not substantial are not
predicated of one another. We assume this because such predicates are
all coincidents, and though some are essential coincidents, (20) others of a
different type, yet we maintain that all of them alike are predicated of
some substratum and that a coincident is never a substratum—since we
do not class as a coincident anything which does not owe its designation
to its being something other than itself, but always hold that any
coincident is predicated of some substratum other than itself, and that
another group of coincidents may have a different substratum. Subject to
these assumptions then, (25) neither the ascending nor the descending
series of predication in which a single attribute is predicated of a single
subject is infinite.32 For the subjects of which coincidents are predicated
are as many as the constitutive elements of each individual substance,
and these we have seen are not infinite in number, while in the
ascending series are contained those constitutive elements with their
coincidents—both of which are finite.33 We conclude that there is a
given subject <D> of which some attribute <C> is primarily
predicable; that there must be an attribute <B> primarily predicable of
the first attribute, (30) and that the series must end with a term <A.>
not predicable able of any term prior to the last subject of which it was
predicated <B>, and of which no term prior to it is predicable.34
The argument we have given is one of the so-called proofs; an
alternative proof follows. Predicates so related to their subjects that
there are other predicates prior to them predicable of those subjects are
demonstrable; but of demonstrable propositions one cannot have
something better than knowledge, nor can one know them without
demonstration. (35) Secondly, if a consequent is only known through an
antecedent (viz. premisses prior to it) and we neither know this
antecedent nor have something better than knowledge of it, then we
shall not have scientific knowledge of the consequent. Therefore, if it is
possible through demonstration to know anything without qualification
and not merely as dependent on the acceptance of certain premisses—
i. e. hypothetically—the series of intermediate predications must
terminate. If it does not terminate, and beyond any predicate taken as
higher than another there remains another still higher, then every
predicate is demonstrable. [84a] Consequently, since these
demonstrable predicates are infinite in number and therefore cannot not
be traversed, we shall not know them by demonstration. If, therefore, we
have not something better than knowledge of them, (5) we cannot
through demonstration have unqualified but only hypothetical science of
anything.35
As dialectical proofs of our contention these may carry conviction, but
an analytic process will show more briefly that neither the ascent nor the
descent of predication can be infinite in the demonstrative sciences
which are the object of our investigation. (10) Demonstration proves the
inherence of essential attributes in things. Now attributes may be
essential for two reasons: either because they are elements in the
essential nature of their subjects, or because their subjects are elements
in their essential nature. An example of the latter is odd as an attribute
of number—though it is number’s attribute, (15) yet number itself is an
element in the definition of odd; of the former, multiplicity or the
indivisible, which are elements in the definition of number. In neither
kind of attribution can the terms be infinite. They are not infinite where
each is related to the term below it as odd is to number, for this would
mean the inherence in odd of another attribute of odd in whose nature
odd was an essential element: but then number will be an ultimate
subject of the whole infinite chain of attributes, (20) and be an element in
the definition of each of them. Hence, since an infinity of attributes such
as contain their subject in their definition cannot inhere in a single
thing, the ascending series is equally finite.36 Note, moreover, that all
such attributes must so inhere in the ultimate subject—e. g. its attributes
in number and number in them—as to be commensurate with the
subject and not of wider extent. (25) Attributes which are essential
elements in the nature of their subjects are equally finite: otherwise
definition would be impossible. Hence, if all the attributes predicated are
essential and these cannot be infinite, the ascending series will
terminate, and consequently the descending series too.37
If this is so, it follows that the intermediates between any two terms
are also always limited in number.38 An immediately obvious
consequence of this is that demonstrations necessarily involve basic
truths, (30) and that the contention of some—referred to at the outset—
that all truths are demonstrable is mistaken. For if there are basic truths,
(a) not all truths are demonstrable, and (b) an infinite regress is
impossible; since if either (a) or (b) were not a fact, it would mean that
no interval was immediate and indivisible, but that all intervals were
divisible. This is true because a conclusion is demonstrated by the
interposition, (35) not the apposition, of a fresh term. If such interposition
could continue to infinity there might be an infinite number of terms
between any two terms; but this is impossible if both the ascending and
descending series of predication terminate; and of this fact, which before
was shown dialectically, analytic proof has now been given.39 [84b]
23
It is an evident corollary of these conclusions that if the same
attribute A inheres in two terms C and D predicable either not at all, or
not of all instances, of one another, it does not always belong to them in
virtue of a common middle term. (5) Isosceles and scalene possess the
attribute of having their angles equal to two right angles in virtue of a
common middle; for they possess it in so far as they are both a certain
kind of figure, and not in so far as they differ from one another. But this
is not always the case; for, were it so, if we take B as the common
middle in virtue of which A inheres in C and D, clearly B would inhere
in C and D through a second common middle, (10) and this in turn would
inhere in C and D through a third, so that between two terms an infinity
of intermediates would fall—an impossibility. Thus it need not always be
in virtue of a common middle term that a single attribute inheres in
several subjects, (15) since there must be immediate intervals. Yet if the
attribute to be proved common to two subjects is to be one of their
essential attributes, the middle terms involved must be within one
subject genus and be derived from the same group of immediate
premisses; for we have seen that processes of proof cannot pass from one
genus to another.40
It is also clear that when A inheres in B, this can be demonstrated if
there is a middle term. (20) Further, the ‘elements’ of such a conclusion
are the premisses containing the middle in question, and they are
identical in number with the middle terms, seeing that the immediate
propositions—or at least such immediate propositions as are universal—
are the ‘elements’. If, on the other hand, there is no middle term,
demonstration ceases to be possible: we are on the way to the basic
truths. Similarly if A does not inhere in B, (25) this can be demonstrated if
there is a middle term or a term prior to B in which A does not inhere:
otherwise there is no demonstration and a basic truth is reached. There
are, moreover, as many ‘elements’ of the demonstrated conclusion as
there are middle terms, since it is propositions containing these middle
terms that are the basic premisses on which the demonstration rests; and
as there are some indemonstrable basic truths asserting that ‘this is that’
or that ‘this inheres in that’, (30) so there are others denying that ‘this is
that’ or that ‘this inheres in that’—in fact some basic truths will affirm
and some will deny being.
When we are to prove a conclusion, we must take a primary essential
predicate—suppose it C—of the subject B, and then suppose A similarly
predicable of C. If we proceed in this manner, no proposition or attribute
which falls beyond A is admitted in the proof: the interval is constantly
condensed until subject and predicate become indivisible, (35) i. e. one.
We have our unit when the premiss becomes immediate, since the
immediate premiss alone is a single premiss in the unqualified sense of
‘single’. And as in other spheres the basic element is simple but not
identical in all—in a system of weight it is the mina, in music the
quarter-tone, and so on—so in syllogism the unit is an immediate
premiss, and in the knowledge that demonstration gives it is an
intuition. [85a] In syllogisms, then, which prove the inherence of an
attribute, nothing falls outside the major term. In the case of negative
syllogisms on the other hand, (1) in the first figure nothing falls outside
the major term whose inherence is in question; e. g. to prove through a
middle C that A does not inhere in B the premisses required are, all B is
C, no C is A. (5) Then if it has to be proved that no C is A, a middle must
be found between A and C; and this procedure will never vary.
(2) If we have to show that E is not D by means of the premisses, all D
is C; no E, or not all E,41 is C; then the middle will never fall beyond E,
and E is the subject of which D is to be denied in the conclusion.
(3) In the third figure the middle will never fall beyond the limits of
the subject and the attribute denied of it. (10)
24
Since demonstrations may be either commensurately universal or
particular,42 and either affirmative or negative; the question arises,
which form is the better? And the same question may be put in regard to
so-called ‘direct’ demonstration and reductio ad impossibile. (15) Let us first
examine the commensurately universal and the particular forms, and
when we have cleared up this problem proceed to discuss ‘direct’
demonstration and reductio ad impossibile.
The following considerations might lead some minds to prefer
particular demonstration. (20)
(1) The superior demonstration is the demonstration which gives us
greater knowledge (for this is the ideal of demonstration), and we have
greater knowledge of a particular individual when we know it in itself
than when we know it through something else; e. g. we know Coriscus
the musician better when we know that Coriscus is musical than when
we know only that man is musical, (25) and a like argument holds in all
other cases. But commensurately universal demonstration, instead of
proving that the subject itself actually is x, proves only that something
else is x—e. g. in attempting to prove that isosceles is x, it proves not
that isosceles but only that triangle is x—whereas particular
demonstration proves that the subject itself is x. The demonstration,
then, that a subject, as such, possesses an attribute is superior. If this is
so, and if the particular rather than the commensurately universal form
so demonstrates, particular demonstration is superior. (30)
(2) The universal has not a separate being over against groups of
singulars. Demonstration nevertheless creates the opinion that its
function is conditioned by something like this:—some separate entity
belonging to the real world; that, for instance, of triangle or of figure or
number, (35) over against particular triangles, figures, and numbers. But
demonstration which touches the real and will not mislead is superior to
that which moves among unrealities and is delusory. Now
commensurately universal demonstration is of the latter kind: if we
engage in it we find ourselves reasoning after a fashion well illustrated
by the argument that the proportionate is what answers to the definition
of some entity which is neither line, number, solid, nor plane, but a
proportionate apart from all these. [85b] Since, then, such a proof is
characteristically commensurate and universal, and less touches reality
than does particular demonstration, and creates a false opinion, it will
follow that commensurate and universal is inferior to particular
demonstration.
We may retort thus. (1) The first argument applies no more to
commensurate and universal than to particular demonstration. (5) If
equality to two right angles is attributable to its subject not qua isosceles
but qua triangle, he who knows that isosceles possesses that attribute
knows the subject as qua itself possessing the attribute, to a less degree
than he who knows that triangle has that attribute. To sum up the whole
matter: if a subject is proved to possess qua triangle an attribute which it
does not in fact possess qua triangle, that is not demonstration: but if it
does possess it qua triangle, the rule applies that the greater knowledge
is his who knows the subject as possessing its attribute qua that in virtue
of which it actually does possess it. (10) Since, then, triangle is the wider
term, and there is one identical definition of triangle—i. e. the term is
not equivocal—and since equality to two right angles belongs to all
triangles, it is isosceles qua triangle and not triangle qua isosceles which
has its angles so related. It follows that he who knows a connexion
universally has greater knowledge of it as it in fact is than he who knows
the particular; and the inference is that commensurate and universal is
superior to particular demonstration. (15) (2) If there is a single identical
definition—i. e. if the commensurate universal is unequivocal—then the
universal will possess being not less but more than some of the
particulars, inasmuch as it is universals which comprise the
imperishable, particulars that tend to perish.
(3) Because the universal has a single meaning, we are not therefore
compelled to suppose that in these examples it has being as a substance
apart from its particulars—any more than we need make a similar
supposition in the other cases of unequivocal universal predication, viz.
where the predicate signifies not substance but quality, essential
relatedness, or action. If such a supposition is entertained, (20) the blame
rests not with the demonstration but with the hearer.
(4) Demonstration is syllogism that proves the cause, i. e. the reasoned
fact, and it is rather the commensurate universal than the particular
which is causative (as may be shown thus: that which possesses an
attribute through its own essential nature is itself the cause of the
inherence, (25) and the commensurate universal is primary;43 hence the
commensurate universal is the cause). Consequently commensurately
universal demonstration is superior as more especially proving the cause,
that is the reasoned fact.
(5) Our search for the reason ceases, and we think that we know,
when the coming to be or existence of the fact before us is not due to the
coming to be or existence of some other fact, for the last step of a search
thus conducted is eo ipso the end and limit of the problem. (30) Thus:
‘Why did he come?’ ‘To get the money—wherewith to pay a debt—that
he might thereby do what was right.’ When in this regress we can no
longer find an efficient or final cause, we regard the last step of it as the
end of the coming—or being or coming to be—and we regard ourselves
as then only having full knowledge of the reason why he came.
If, then, all causes and reasons are alike in this respect, (35) and if this
is the means to full knowledge in the case of final causes such as we
have exemplified, it follows that in the case of the other causes also full
knowledge is attained when an attribute no longer inheres because of
something else. Thus, when we learn that exterior angles are equal to
four right angles because they are the exterior angles of an isosceles,
there still remains the question ‘Why has isosceles this attribute?’ and its
answer ‘Because it is a triangle, and a triangle has it because a triangle is
a rectilinear figure.’ [86a] If rectilinear figure possesses the property
for no further reason,44 at this point we have full knowledge—but at this
point our knowledge has become commensurately universal, and so we
conclude that commensurately universal demonstration is superior.
(6) The more demonstration becomes particular the more it sinks into
an indeterminate manifold, while universal demonstration tends to the
simple and determinate. But objects so far as they are an indeterminate
manifold are unintelligible, (5) so far as they are determinate, intelligible:
they are therefore intelligible rather in so far as they are universal than
in so far as they are particular. From this it follows that universals are
more demonstrable: but since relative and correlative increase
concomitantly, of the more demonstrable there will be fuller
demonstration. Hence the commensurate and universal form, (10) being
more truly demonstration, is the superior.
(7) Demonstration which teaches two things is preferable to
demonstration which teaches only one. He who possesses
commensurately universal demonstration knows the particular as well,
but he who possesses particular demonstration does not know the
universal. So that this is an additional reason for preferring
commensurately universal demonstration. And there is yet this further
argument:
(8) Proof becomes more and more proof of the commensurate
universal as its middle term approaches nearer to the basic truth, (15) and
nothing is so near as the immediate premiss which is itself the basic
truth. If, then, proof from the basic truth is more accurate than proof not
so derived, demonstration which depends more closely on it is more
accurate than demonstration which is less closely dependent. But
commensurately universal demonstration is characterized by this closer
dependence, and is therefore superior. Thus, if A had to be proved to
inhere in D, and the middles were B and C, (20) B being the higher term
would render the demonstration which it mediated the more universal.
Some of these arguments, however, are dialectical. The clearest
indication of the precedence of commensurately universal demonstration
is as follows: if of two propositions, a prior and a posterior, we have a
grasp of the prior, we have a kind of knowledge—a potential grasp—of
the posterior as well. For example, (25) if one knows that the angles of all
triangles are equal to two right angles, one knows in a sense—
potentially—that the isosceles’ angles also are equal to two right angles,
even if one does not know that the isosceles is a triangle; but to grasp
this posterior proposition is by no means to know the commensurate
universal either potentially or actually. Moreover, commensurately
universal demonstration is through and through intelligible; particular
demonstration issues in sense-perception. (30)
25
The preceding arguments constitute our defence of the superiority
of commensurately universal to particular demonstration. That
affirmative demonstration excels negative may be shown as follows.
(1) We may assume the superiority ceteris paribus of the demonstration
which derives from fewer postulates or hypotheses—in short from fewer
premisses; for, (35) given that all these are equally well known, where
they are fewer knowledge will be more speedily acquired, and that is a
desideratum. The argument implied in our contention that
demonstration from fewer assumptions is superior may be set out in
universal form as follows. Assuming that in both cases alike the middle
terms are known, and that middles which are prior are better known
than such as are posterior, we may suppose two demonstrations of the
inherence of A in E, the one proving it through the middles B, C and D,
the other through F and G. [86b] Then A–D is known to the same
degree as A–E (in the second proof), but A–D is better known than and
prior to A–E (in the first proof); since A–E is proved through A–D, and
the ground is more certain than the conclusion.
Hence demonstration by fewer premisses is ceteris paribus superior. (5)
Now both affirmative and negative demonstration operate through three
terms and two premisses, but whereas the former assumes only that
something is, the latter assumes both that something is and that
something else is not, and thus operating through more kinds of premiss
is inferior.
(2) It has been proved45 that no conclusion follows if both premisses
are negative, (10) but that one must be negative, the other affirmative. So
we are compelled to lay down the following additional rule: as the
demonstration expands, the affirmative premisses must increase in
number, but there cannot be more than one negative premiss in each
complete proof.46 (15) Thus, suppose no B is A, and all C is B. Then, if
both the premisses are to be again expanded, a middle must be
interposed. Let us interpose D between A and B, and E between B and C.
Then clearly E is affirmatively related to B and C, while D is
affirmatively related to B but negatively to A; for all B is D, (20) but there
must be no D which is A. Thus there proves to be a single negative
premiss, A–D. In the further prosyllogisms too it is the same, because in
the terms of an affirmative syllogism the middle is always related
affirmatively to both extremes; in a negative syllogism it must be
negatively related only to one of them, (25) and so this negation comes to
be a single negative premiss, the other premisses being affirmative. If,
then, that through which a truth is proved is a better known and more
certain truth, and if the negative proposition is proved through the
affirmative and not vice versa, affirmative demonstration, being prior
and better known and more certain, will be superior.
(3) The basic truth of demonstrative syllogism is the universal
immediate premiss, (30) and the universal premiss asserts in affirmative
demonstration and in negative denies: and the affirmative proposition is
prior to and better known than the negative (since affirmation explains
denial and is prior to denial, (35) just as being is prior to not-being). It
follows that the basic premiss of affirmative demonstration is superior to
that of negative demonstration, and the demonstration which uses
superior basic premisses is superior.
(4) Affirmative demonstration is more of the nature of a basic form of
proof, because it is a sine qua non of negative demonstration.
26
[87a] Since affirmative demonstration is superior to negative, it
is clearly superior also to reductio ad impossibile. We must first make
certain what is the difference between negative demonstration and
reductio ad impossibile. Let us suppose that no B is A, (5) and that all C is
B: the conclusion necessarily follows that no C is A. If these premisses
are assumed, therefore, the negative demonstration that no C is A is
direct. Reductio ad impossibile, on the other hand, proceeds as follows:
Supposing we are to prove that A does not inhere in B, we have to
assume that it does inhere, and further that B inheres in C, with the
resulting inference that A inheres in C. (10) This we have to suppose a
known and admitted impossibility; and we then infer that A cannot
inhere in B. Thus if the inherence of B in C is not questioned, A’s
inherence in B is impossible.
The order of the terms is the same in both proofs: they differ
according to which of the negative propositions is the better known, the
one denying A of B or the one denying A of C. (15) When the falsity of the
conclusion47 is the better known, we use reductio ad impossibile; when
the major premiss of the syllogism is the more obvious, we use direct
demonstration. All the same the proposition denying A of B is, in the
order of being, prior to that denying A of C; for premisses are prior to
the conclusion which follows from them, and ‘no C is A’ is the
conclusion, ‘no B is A’ one of its premisses. (20) For the destructive result
of reductio ad impossibile is not a proper conclusion, nor are its
antecedents proper premisses. On the contrary: the constituents of
syllogism are premisses related to one another as whole to part or part to
whole, whereas the premisses A–C and A–B are not thus related to one
another. (25) Now the superior demonstration is that which proceeds from
better known and prior premisses, and while both these forms depend
for credence on the not-being of something, yet the source of the one is
prior to that of the other. Therefore negative demonstration will have an
unqualified superiority to reductio ad impossibile, and affirmative
demonstration, being superior to negative, (30) will consequently be
superior also to reductio ad impossibile.
27
The science which is knowledge at once of the fact and of the
reasoned fact, not of the fact by itself without the reasoned fact, is the
more exact and the prior science.
A science such as arithmetic, which is not a science of properties qua
inhering in a substratum, is more exact than and prior to a science like
harmonics, which is a science of properties inhering in a substratum; and
similarly a science like arithmetic, which is constituted of fewer basic
elements, is more exact than and prior to geometry, which requires
additional elements. What I mean by ‘additional elements’ is this: a unit
is substance without position, (35) while a point is substance with
position; the latter contains an additional element.
28
A single science is one whose domain is a single genus, viz. all the
subjects constituted out of the primary entities of the genus—i. e. the
parts of this total subject—and their essential properties.
One science differs from another when their basic truths have neither
a common source nor are derived those of the one science from those of
the other. This is verified when we reach the indemonstrable premisses
of a science, for they must be within one genus with its conclusions: and
this again is verified if the conclusions proved by means of them fall
within one genus—i. e. are homogeneous. [87b]
29
One can have several demonstrations of the same connexion not
only by taking from the same series of predication middles which are
other than the immediately cohering term—e. g. by taking C, D, (5) and F
severally to prove A–B—but also by taking a middle from another series.
Thus let A be change, D alteration of a property, B feeling pleasure, and
G relaxation. We can then without falsehood predicate D of B and A of
D, for he who is pleased suffers alteration of a property, (10) and that
which alters a property changes. Again, we can predicate A of G without
falsehood, and G of B; for to feel pleasure is to relax, and to relax is to
change. So the conclusion can be drawn through middles which are
different, i. e. not in the same series—yet not so that neither of these
middles is predicable of the other, for they must both be attributable to
some one subject. (15)
A further point worth investigating is how many ways of proving the
same conclusion can be obtained by varying the figure.
30
There is no knowledge by demonstration of chance conjunctions;
for chance conjunctions exist neither by necessity nor as general
connexions but comprise what comes to be as something distinct from
these. (20) Now demonstration is concerned only with one or other of
these two; for all reasoning proceeds from necessary or general
premisses, the conclusion being necessary if the premisses are necessary
and general if the premisses are general. (25) Consequently, if chance
conjunctions are neither general nor necessary, they are not
demonstrable.
31
Scientific knowledge is not possible through the act of perception.
Even if perception as a faculty is of ‘the such’ and not merely of a ‘this
somewhat’, yet one must at any rate actually perceive a ‘this somewhat’,
(30) and at a definite present place and time: but that which is
commensurately universal and true in all cases one cannot perceive,
since it is not ‘this’ and it is not ‘now’; if it were, it would not be
commensurately universal—the term we apply to what is always and
everywhere. Seeing, therefore, that demonstrations are commensurately
universal and universals imperceptible, we clearly cannot obtain
scientific knowledge by the act of perception: nay, (35) it is obvious that
even if it were possible to perceive that a triangle has its angles equal to
two right angles, we should still be looking for a demonstration—we
should not (as some48 say) possess knowledge of it; for perception must
be of a particular, whereas scientific knowledge involves the recognition
of the commensurate universal. So if we were on the moon, and saw the
earth shutting out the sun’s light, (40) we should not know the cause of
the eclipse: we should perceive the present fact of the eclipse, but not
the reasoned fact at all, since the act of perception is not of the
commensurate universal. [88a] I do not, of course, deny that by
watching the frequent recurrence of this event we might, after tracking
the commensurate universal, possess a demonstration, for the
commensurate universal is elicited from the several groups of singulars.
(5)
The commensurate universal is precious because it makes clear the
cause; so that in the case of facts like these which have a cause other
than themselves universal knowledge49 is more precious than senseperceptions and than intuition. (As regards primary truths there is of
course a different account to be given.50) Hence it is clear that
knowledge of things demonstrable cannot be acquired by perception, (10)
unless the term perception is applied to the possession of scientific
knowledge through demonstration. Nevertheless certain points do arise
with regard to connexions to be proved which are referred for their
explanation to a failure in sense-perception: there are cases when an act
of vision would terminate our inquiry, not because in seeing we should
be knowing, but because we should have elicited the universal from
seeing; if, for example, we saw the pores in the glass and the light
passing through, the reason of the kindling would be clear to us51
because we should at the same time see it in each instance and intuit
that it must be so in all instances. (15)
32
All syllogisms cannot have the same basic truths. This may be
shown first of all by the following dialectical considerations. (1) Some
syllogisms are true and some false: for though a true inference is possible
from false premisses, (20) yet this occurs once only—I mean if A, for
instance, is truly predicable of C, but B, the middle, is false, both A–B
and B–C being false; nevertheless, if middles are taken to prove these
premisses, they will be false because every conclusion which is a
falsehood has false premisses, while true conclusions have true
premisses, (25) and false and true differ in kind. Then again, (2)
falsehoods are not all derived from a single identical set of principles:
there are falsehoods which are the contraries of one another and cannot
coexist, e. g. ‘justice is injustice’, and ‘justice is cowardice’; ‘man is
horse’, and ‘man is ox’; ‘the equal is greater’, and ‘the equal is less’. From
our established principles we may argue the case as follows, (30)
confining ourselves therefore to true conclusions. Not even all these are
inferred from the same basic truths; many of them in fact have basic
truths which differ generically and are not transferable; units, for
instance, which are without position, cannot take the place of points,
which have position. The transferred terms could only fit in as middle
terms or as major or minor terms, or else have some of the other terms
between them, (35) others outside them.
Nor can any of the common axioms—such, I mean, as the law of
excluded middle—serve as premisses for the proof of all conclusions. For
the kinds of being are different, and some attributes attach to quanta and
some to qualia only; and proof is achieved by means of the common
axioms taken in conjunction with these several kinds and their
attributes. [88b]
Again, it is not true that the basic truths are much fewer than the
conclusions, for the basic truths are the premisses, (5) and the premisses
are formed by the apposition of a fresh extreme term or the interposition
of a fresh middle. Moreover, the number of conclusions is indefinite,
though the number of middle terms is finite; and lastly some of the basic
truths are necessary, others variable.
Looking at it in this way we see that, since the number of conclusions
is indefinite, the basic truth cannot be identical or limited in number. (10)
If, on the other hand, identity is used in another sense, and it is said,
e. g., ‘these and no other are the fundamental truths of geometry, these
the fundamentals of calculation, these again of medicine’; would the
statement mean anything except that the sciences have basic truths? To
call them identical because they are self-identical is absurd, since
everything can be identified with everything in that sense of identity. (15)
Nor again can the contention that all conclusions have the same basic
truths mean that from the mass of all possible premisses any conclusion
may be drawn. That would be exceedingly naïve, for it is not the case in
the clearly evident mathematical sciences, nor is it possible in analysis,
since it is the immediate premisses which are the basic truths, and a
fresh conclusion is only formed by the addition of a new immediate
premiss: but if it be admitted that it is these primary immediate
premisses which are basic truths, (20) each subject-genus will provide one
basic truth. If, however, it is not argued that from the mass of all
possible premisses any conclusion may be proved, nor yet admitted that
basic truths differ so as to be generically different for each science, it
remains to consider the possibility that, while the basic truths of all
knowledge are within one genus, special premisses are required to prove
special conclusions. (25) But that this cannot be the case has been shown
by our proof that the basic truths of things generically different
themselves differ generically. For fundamental truths are of two kinds,
those which are premisses of demonstration and the subject-genus; and
though the former are common, the latter—number, for instance, and
magnitude—are peculiar.
33
Scientific knowledge and its object differ from opinion and the
object of opinion in that scientific knowledge is commensurately
universal and proceeds by necessary connexions, (30) and that which is
necessary cannot be otherwise. So though there are things which are
true and real and yet can be otherwise, scientific knowledge clearly does
not concern them; if it did, things which can be otherwise would be
incapable of being otherwise. (35) Nor are they any concern of rational
intuition—by rational intuition I mean an originative source of scientific
knowledge—nor of indemonstrable knowledge, which is the grasping of
the immediate premiss. [89a] Since then rational intuition, science,
and opinion, and what is revealed by these terms, are the only things
that can be ‘true’, it follows that it is opinion that is concerned with that
which may be true or false, and can be otherwise: opinion in fact is the
grasp of a premiss which is immediate but not necessary. This view also
fits the observed facts, for opinion is unstable, (5) and so is the kind of
being we have described as its object. Besides, when a man thinks a
truth incapable of being otherwise he always thinks that he knows it,
never that he opines it. He thinks that he opines when he thinks that a
connexion, though actually so, may quite easily be otherwise; for he
believes that such is the proper object of opinion, while the necessary is
the object of knowledge. (10)
In what sense, then, can the same thing be the object of both opinion
and knowledge? And if any one chooses to maintain that all that he
knows he can also opine, why should not opinion be knowledge? For he
that knows and he that opines will follow the same train of thought
through the same middle terms until the immediate premisses are
reached; because it is possible to opine not only the fact but also the
reasoned fact, (15) and the reason is the middle term; so that, since the
former knows, he that opines also has knowledge.
The truth perhaps is that if a man grasp truths that cannot be other
than they are, in the way in which he grasps the definitions through
which demonstrations take place, he will have not opinion but
knowledge: if on the other hand he apprehends these attributes as
inhering in their subjects, but not in virtue of the subjects’ substance and
essential nature, he possesses opinion and not genuine knowledge; and
his opinion, (20) if obtained through immediate premisses, will be both of
the fact and of the reasoned fact; if not so obtained, of the fact alone.
The object of opinion and knowledge is not quite identical; it is only in a
sense identical, just as the object of true and false opinion is in a sense
identical. The sense in which some maintain that true and false opinion
can have the same object leads them to embrace many strange doctrines,
(25) particularly the doctrine that what a man opines falsely he does not
opine at all. There are really many senses of ‘identical’, and in one sense
the object of true and false opinion can be the same, in another it
cannot. Thus, to have a true opinion that the diagonal is commensurate
with the side would be absurd: but because the diagonal with which
they are both concerned is the same, (30) the two opinions have objects so
far the same: on the other hand, as regards their essential definable
nature these objects differ. The identity of the objects of knowledge and
opinion is similar. Knowledge is the apprehension of, e. g. the attribute
‘animal’ as incapable of being otherwise, opinion the apprehension of
‘animal’ as capable of being otherwise—e. g. the apprehension that
animal is an element in the essential nature of man is knowledge; the
apprehension of animal as predicable of man but not as an element in
man’s essential nature is opinion: man is the subject in both judgments,
(35) but the mode of inherence differs.
This also shows that one cannot opine and know the same thing
simultaneously; for then one would apprehend the same thing as both
capable and incapable of being otherwise—an impossibility. [89b]
Knowledge and opinion of the same thing can coexist in two different
people in the sense we have explained, but not simultaneously in the
same person. That would involve a man’s simultaneously apprehending,
e. g., (1) that man is essentially animal—i. e. cannot be other than
animal—and (2) that man is not essentially animal, (5) that is, we may
assume, may be other than animal.
Further consideration of modes of thinking and their distribution
under the heads of discursive thought, intuition, science, art, practical
wisdom, and metaphysical thinking, belongs rather partly to natural
science, partly to moral philosophy.
34
Quick wit is a faculty of hitting upon the middle term
instantaneously. (10) It would be exemplified by a man who saw that the
moon has her bright side always turned towards the sun, and quickly
grasped the cause of this, namely that she borrows her light from him; or
observed somebody in conversation with a man of wealth and divined
that he was borrowing money, or that the friendship of these people
sprang from a common enmity. In all these instances he has seen the
major and minor terms and then grasped the causes, (15) the middle
terms.
Let A represent ‘bright side turned sunward’, B ‘lighted from the sun’,
C the moon. Then B, ‘lighted from the sun’, is predicable of C, the moon,
and A, ‘having her bright side towards the source of her light’, (20) is
predicable of B. So A is predicable of C through B.
1
Plato, Meno, 80 E.
2
Cf. An. Pr. ii, ch. 21.
3
Cf. the following chapter and more particularly ii, ch. 19.
4
An. Pr. i, ch. 25.
5
Ibid. ii, ch. 5.
6
Ibid. ii, cc. 5 and 6.
7
Plato, Euthydemus, 277 B.
8
Cf. Met. 1039a 9.
9
Cf. i, cc. 9 and 13.
10
sc. axioms.
11
Cf. Plato, Theaetetus, 189 E ff.
12
Lit. ‘even if the middle is itself and also what is not itself’; i. e. you may pass from the middle
term man to include not-man without affecting the conclusion.
13
Cf. 75a 42 ff. and 76b 13.
14
An. Pr. i. 1. The ‘opposite facts’ are those which would be expressed in the alternatively
possible answers to the dialectical question, the dialectician’s aim being to refute his interlocutor
whether the latter answers the question put to him affirmatively or in the negative.
15
i. e. a premiss put in the form of a question.
16
sc. ‘which require two sciences for their proof’. Cf. 78b 35.
17
i. e. in Celarent.
18
i. e. in Cesare or Camestres.
19
Cf. 80a 29.
20
Cf. 80b 17–26.
21
Cf. 80b 26–32.
22
sc. a predicate above which is no wider universal.
23
sc. ‘that no C is B’.
24
i. e. each of the successive prosyllogisms required to prove the negative minors contains an
affirmative major in which the middle is affirmed of a subject successively ‘higher’ or more
universal than the subject of the first syllogism. Thus:
Syllogism:
All B is D
No C is D
No C is B
Proyllogisms:
All D is E
All E is F
No C is E
No C is F
No C is D
No C is E
B, D, E, &c., are successively more universal subjects; and the series of affirmative majors
containing them must ex hypothesi terminate.
25
Since the series of affirmative majors terminates and since an affirmative major is required for
each prosyllogism, we shall eventually reach a minor incapable of proof and therefore
immediate.
26
If the attributes in a series of predication such as we are discussing are substantial, they must
be finite in number, because they are then the elements constituting the definition of a substance.
27
The first of three statements preliminary to a proof that predicates which are accidental—
other than substantial—cannot be unlimited in number: Accidental is to be distinguished from
essential or natural predication [cf. i, ch. 4, 73b 5 ff. and An. Pr. i, ch. 25, 43a 25–6]. The former
is alien to demonstration: hence, provided that a single attribute is predicated of a single subject,
all genuine predicates fall either under the category of substance or under one of the adjectival
categories.
28
Second preliminary statement: The precise distinction of substantive from adjectival
predication makes clear (implicitly) the two distinctions, (a) that between natural and accidental
predication, (b) that between substantival and adjectival predication, which falls within natural
predication. This enables us to reject the Platonic Forms.
29
Third preliminary statement merging into the beginning of the proof proper: Reciprocal
predication cannot produce an indefinite regress because it is not natural predication.
30
Expansion of third preliminary statement: Reciprocals A and B might be predicated of one
another (a) substantially; but it has been proved already that because a definition cannot contain
an infinity of elements substantial predication cannot generate infinity; and it would disturb the
relation of genus and species: (b) as qualia or quanta &c; but this would be unnatural predication,
because all such predicates are adjectival, i. e. accidents, or coincidents, of substances.
31
The ascent of predicates is also finite; because all predicates fall under one or other of the
categories, and (a) the series of predicates under each category terminates when the category is
reached, and (b) the number of the categories is limited. [(a) seems to mean that an attribute as
well as a substance is definable by genus and differentia, and the elements in its definition must
terminate in an upward direction at the category, and can therefore no more form an infinite
series than can the elements constituting the definition of a substance.]
32
To reinforce this brief proof that descent and ascent are both finite we may repeat the
premisses on which it depends. These are (1) the assumption that predication means the
predication of one attribute of one subject, and (2) our proof that accidents cannot be
reciprocally predicated of one another, because that would be unnatural predication. It follows
from these premisses that both ascent and descent are finite. [Actually (2) only reinforces the
proof that the descent terminates.]
33
To repeat again the proof that both ascent and descent are finite: The subjects cannot be more
in number than the constituents of a definable form, and these, we know, are not infinite in
number: hence the descent is finite. The series regarded as an ascent contains subjects and ever
more universal accidents, and neither subjects nor accidents are infinite in number.
34
Formal restatement of the last conclusion. [This is obscure: apparently Aristotle here
contemplates a hybrid series: category, accident, further specified accident … substantial genus,
subgenus … infima species, individual substance.
If this interpretation of the first portion of the chapter is at all correct, Aristotle’s first proof
that the first two questions of ch. 19 must be answered in the negative is roughly as follows: The
ultimate subject of all judgement is an individual substance, a concrete singular. Of such concrete
singulars you can predicate substantially only the elements constituting their infima species. These
are limited in number because they form an intelligible synthesis. So far, then, as substantial
predicates are concerned, the questions are answered. But these elements are also the subjects of
which accidents, or coincidents, are predicated, and therefore as regards accidental predicates, at
any rate, the descending series of subjects terminates. The ascending series of attributes also
terminates, (1) because each higher attribute in the series can only be a higher genus of the
accident predicated of the ultimate subject of its genus, and therefore an element in the
accident’s definition; (2) because the number of the categories is limited.
We may note that the first argument seems to envisage a series which, viewed as an ascent,
starts with a concrete individual of which the elements of its definition are predicated
successively, specific differentia being followed by proximate genus, which latter is the startingpoint of a succession of ever more universal attributes terminating in a category; and that the
second argument extends the scope of the dispute to the sum total of all the trains of accidental
predication which one concrete singular substance can beget. It is, as so often in Aristotle,
difficult to be sure whether he is regarding the infima species or the concrete singular as the
ultimate subject of judgement. I have assumed that he means the latter.]
35
The former proof was dialectical. So is that which follows in this paragraph. If a predicate
inheres in a subject but is subordinate to a higher predicate also predicable of that subject [i. e.
not to a wider predicate but to a middle term giving logically prior premisses and in that sense
higher], then the inherence can be known by demonstration and only by demonstration. But that
means that it is known as the consequent of an antecedent. Therefore, if demonstration gives
genuine knowledge, the series must terminate; i. e. every predicate is demonstrable and known
only as a consequent and therefore hypothetically, unless an antecedent known per se is reached.
36
As regards type (2) [the opening of the chapter has disposed of type (1)]: in any series of such
predicates any given term will contain in its definition all the lower terms, and the series will
therefore terminate at the bottom in the ultimate subject. But since every term down to and
including the ultimate subject is contained in the definition of any given term, if the series
ascend infinitely there must be a term containing an infinity of terms in its definition. But this is
impossible, and therefore the ascent terminates.
37
Note too that either type of essential attribute must be commensurate with its subject, because
the first defines, the second is defined by, its subject; and consequently no subject can possess an
infinite number of essential predicates of either type, or definition would be impossible. Hence if
the attributes predicated are all essential, the series terminates in both directions. [This passage
merely displays the ground underlying the previous argument that the ascent of attributes of type
(2) is finite, and notes in passing its more obvious and already stated application to attributes of
type (1).]
38
It follows that the intermediates between a given subject and a given attribute must also be
limited in number.
39
Corollary: (a) demonstrations necessarily involve basic truths, and therefore (b) not all truths,
as we saw [84a 32] that some maintain, are demonstrable [cf. 72b 6]. If either (a) or (b) were not
a fact, since conclusions are demonstrated by the interposition of a middle and not by the
apposition of an extreme term [cf. note on 78a15], no premiss would be an immediate indivisible
interval. This closes the analytic argument.
40
i, ch. 7.
41
Second figure, Camestres or Baroco.
42
The distinction is that of whole and part, genus and species; not that of universal and singular.
43
And therefore also essential; cf. i, ch. 4, 73b 26 ff.
44
i. e. for no reason other than its own nature.
45
An. Pr. i, ch. 7.
46
i. e. in one syllogism and two prosyllogisms proving its premisses.
47
i. e. the impossibility of A–C, the conclusion of the hypothetical syllogism.
48
Protagoras is perhaps referred to.
49
i. e. demonstration through the commensurate universal.
50
Cf. e. g. 100b 12.
51
A theory of the concentration of rays through a burning-glass which was not Aristotle’s.
BOOK II
1
The kinds of question we ask are as many as the kinds of things
which we know. They are in fact four:—(1) whether the connexion of an
attribute with a thing is a fact, (2) what is the reason of the connexion,
(25) (3) whether a thing exists, (4) what is the nature of the thing. Thus,
when our question concerns a complex of thing and attribute and we ask
whether the thing is thus or otherwise qualified—whether, e. g., the sun
suffers eclipse or not—then we are asking as to the fact of a connexion.
That our inquiry ceases with the discovery that the sun does suffer
eclipse is an indication of this; and if we know from the start that the
sun suffers eclipse, we do not inquire whether it does so or not. On the
other hand, when we know the fact we ask the reason; as, for example,
when we know that the sun is being eclipsed and that an earthquake is
in progress, (30) it is the reason of eclipse or earthquake into which we
inquire.
Where a complex is concerned, then, those are the two questions we
ask; but for some objects of inquiry we have a different kind of question
to ask, such as whether there is or is not a centaur or a God. (By ‘is or is
not’ I mean ‘is or is not, without further qualification’; as opposed to ‘is
or is not (e. g.) white’.) On the other hand, when we have ascertained
the thing’s existence, we inquire as to its nature, asking, for instance,
‘what, then, is God?’ or ‘what is man?’
2
These, (35) then, are the four kinds of question we ask, and it is in
the answers to these questions that our knowledge consists.
Now when we ask whether a connexion is a fact, or whether a thing
without qualification is, we are really asking whether the connexion or
the thing has a ‘middle’; and when we have ascertained either that the
connexion is a fact or that the thing is—i. e. ascertained either the
partial or the unqualified being of the thing—and are proceeding to ask
the reason of the connexion or the nature of the thing, then we are
asking what the ‘middle’ is. [90a]
(By distinguishing the fact of the connexion and the existence of the
thing as respectively the partial and the unqualified being of the thing, I
mean that if we ask ‘does the moon suffer eclipse?’, or ‘does the moon
wax?’, the question concerns a part of the thing’s being; for what we are
asking in such questions is whether a thing is this or that, i. e. has or has
not this or that attribute: whereas, if we ask whether the moon or night
exists, the question concerns the unqualified being of a thing.)
We conclude that in all our inquiries we are asking either whether
there is a ‘middle’ or what the ‘middle’ is: for the ‘middle’ here is
precisely the cause, (5) and it is the cause that we seek in all our
inquiries. Thus, ‘Does the moon suffer eclipse?’ means ‘Is there or is
there not a cause producing eclipse of the moon?’, and when we have
learnt that there is, our next question is, ‘What, then, is this cause?’; for
the cause through which a thing is—not is this or that, i. e. has this or
that attribute, but without qualification is—and the cause through which
it is—not is without qualification, (10) but is this or that as having some
essential attribute or some accident—are both alike the ‘middle’. By that
which is without qualification I mean the subject, e. g. moon or earth or
sun or triangle; by that which a subject is (in the partial sense) I mean a
property, e. g. eclipse, equality or inequality, interposition or noninterposition. For in all these examples it is clear that the nature of the
thing and the reason of the fact are identical: the question ‘What is
eclipse?’ and its answer ‘The privation of the moon’s light by the
interposition of the earth’ are identical with the question ‘What is the
reason of eclipse?’ or ‘Why does the moon suffer eclipse?’ and the reply
‘Because of the failure of light through the earth’s shutting it out’. (15)
Again, for ‘What is a concord? A commensurate numerical ratio of a high
and a low note’, (20) we may substitute ‘What reason makes a high and a
low note concordant? Their relation according to a commensurate
numerical ratio.’ ‘Are the high and the low note concordant?’ is
equivalent to ‘Is their ratio commensurate?’; and when we find that it is
commensurate, we ask ‘What, then, is their ratio?’.
Cases in which the ‘middle’ is sensible show that the object of our
inquiry is always the ‘middle’: we inquire, (25) because we have not
perceived it, whether there is or is not a ‘middle’ causing e. g. an eclipse.
On the other hand, if we were on the moon we should not be inquiring
either as to the fact or the reason, but both fact and reason would be
obvious simultaneously. For the act of perception would have enabled us
to know the universal too; since, the present fact of an eclipse being
evident, perception would then at the same time give us the present fact
of the earth’s screening the sun’s light, (30) and from this would arise the
universal.
Thus, as we maintain, to know a thing’s nature is to know the reason
why it is; and this is equally true of things in so far as they are said
without qualification to be as opposed to being possessed of some
attribute, and in so far as they are said to be possessed of some attribute
such as equal to two right angles, or greater or less.
3
It is clear, (35) then, that all questions are a search for a ‘middle’. Let
us now state how essential nature is revealed, and in what way it can be
reduced to demonstration;1 what definition is, and what things are
definable. And let us first discuss certain difficulties which these
questions raise, beginning what we have to say with a point most
intimately connected with our immediately preceding remarks, namely
the doubt that might be felt as to whether or not it is possible to know
the same thing in the same relation, both by definition and by
demonstration. [90b] It might, I mean, be urged that definition is held
to concern essential nature and is in every case universal and
affirmative; whereas, (5) on the other hand, some conclusions are
negative and some are not universal; e. g. all in the second figure are
negative, none in the third are universal. And again, not even all
affirmative conclusions in the first figure are definable, e. g. ‘every
triangle has its angles equal to two right angles’. An argument proving
this difference between demonstration and definition is that to have
scientific knowledge of the demonstrable is identical with possessing a
demonstration of it: hence if demonstration of such conclusions as these
is possible, (10) there clearly cannot also be definition of them. If there
could, one might know such a conclusion also in virtue of its definition
without possessing the demonstration of it; for there is nothing to stop
our having the one without the other.
Induction too will sufficiently convince us of this difference; for never
yet by defining anything—essential attribute or accident—did we get
knowledge of it. (15) Again, if to define is to acquire knowledge of a
substance, at any rate such attributes are not substances.
It is evident, then, that not everything demonstrable can be defined.
What then? Can everything definable be demonstrated, or not? There is
one of our previous arguments which covers this too. (20) Of a single
thing qua single there is a single scientific knowledge. Hence, since to
know the demonstrable scientifically is to possess the demonstration of
it, an impossible consequence will follow:—possession of its definition
without its demonstration will give knowledge of the demonstrable.
Moreover, the basic premisses of demonstrations are definitions, and it
has already been shown2 that these will be found indemonstrable; either
the basic premisses will be demonstrable and will depend on prior
premisses, (25) and the regress will be endless; or the primary truths will
be indemonstrable definitions.
But if the definable and the demonstrable are not wholly the same,
may they yet be partially the same? Or is that impossible, because there
can be no demonstration of the definable? There can be none, because
definition is of the essential nature or being of something, (30) and all
demonstrations evidently posit and assume the essential nature—
mathematical demonstrations, for example, the nature of unity and the
odd, and all the other sciences likewise. Moreover, every demonstration
proves a predicate of a subject as attaching or as not attaching to it, but
in definition one thing is not predicated of another; we do not, (35) e. g.,
predicate animal of biped nor biped of animal, nor yet figure of plane—
plane not being figure nor figure plane. Again, to prove essential nature
is not the same as to prove the fact of a connexion. [91a] Now
definition reveals essential nature, demonstration reveals that a given
attribute attaches or does not attach to a given subject; but different
things require different demonstrations—unless the one demonstration is
related to the other as part to whole. [91a] I add this because if all
triangles have been proved to possess angles equal to two right angles,
then this attribute has been proved to attach to isosceles; for isosceles is
a part of which all triangles constitute the whole. (5) But in the case
before us the fact and the essential nature are not so related to one
another, since the one is not a part of the other.
So it emerges that not all the definable is demonstrable nor all the
demonstrable definable; and we may draw the general conclusion that
there is no identical object of which it is possible to possess both a
definition and a demonstration. (10) It follows obviously that definition
and demonstration are neither identical nor contained either within the
other: if they were, their objects would be related either as identical or
as whole and part.
4
So much, then, for the first stage of our problem. The next step is to
raise the question whether syllogism—i. e. demonstration—of the
definable nature is possible or, as our recent argument assumed,
impossible.
We might argue it impossible on the following grounds:—(a) syllogism
proves an attribute of a subject through the middle term; on the other
hand (b) its definable nature is both ‘peculiar’ to a subject and
predicated of it as belonging to its essence. (15) But in that case (1) the
subject, its definition, and the middle term connecting them must be
reciprocally predicable of one another; for if A is ‘peculiar’ to C,
obviously A is ‘peculiar’ to B and B to C—in fact all three terms are
‘peculiar’ to one another: and further (2) if A inheres in the essence of all
B and B is predicated universally of all C as belonging to C’s essence, (20)
A also must be predicated of C as belonging to its essence.
If one does not take this relation as thus duplicated—if, that is, A is
predicated as being of the essence of B, but B is not of the essence of the
subjects of which it is predicated—A will not necessarily be predicated
of C as belonging to its essence. So both premisses will predicate essence,
and consequently B also will be predicated of C as its essence. (25) Since,
therefore, both premisses do predicate essence—i. e. definable form—C’s
definable form will appear in the middle term before the conclusion is
drawn.
We may generalize by supposing that it is possible to prove the
essential nature of man. Let C be man, A man’s essential nature—twofooted animal, or aught else it may be. Then, if we are to syllogize, A
must be predicated of all B. But this premiss will be mediated by a fresh
definition, which consequently will also be the essential nature of man.3
(30) Therefore the argument assumes what it has to prove, since B too is
the essential nature of man. It is, however, the case in which there are
only the two premisses—i. e. in which the premisses are primary and
immediate—which we ought to investigate, because it best illustrates the
point under discussion.
Thus they who prove the essential nature of soul or man or anything
else through reciprocating terms beg the question. (35) It would be
begging the question, for example, to contend that the soul is that which
causes its own life, and that what causes its own life is a self-moving
number; for one would have to postulate that the soul is a self-moving
number in the sense of being identical with it. [91b] For if A is
predicable as a mere consequent of B and B of C, A will not on that
account be the definable form of C: A will merely be what it was true to
say of C. Even if A is predicated of all B inasmuch as B is identical with a
species of A, still it will not follow: being an animal is predicated of
being a man—since it is true that in all instances to be human is to be
animal, (5) just as it is also true that every man is an animal—but not as
identical with being man.
We conclude, then, that unless one takes both the premisses as
predicating essence, one cannot infer that A is the definable form and
essence of C: but if one does so take them, in assuming B one will have
assumed, before drawing the conclusion, what the definable form of C is;
so that there has been no inference, for one has begged the question. (10)
5
Nor, as was said in my formal logic, is the method of division a
process of inference at all, since at no point does the characterization of
the subject follow necessarily from the premising of certain other facts:
division demonstrates as little as does induction. (15) For in a genuine
demonstration the conclusion must not be put as a question nor depend
on a concession, but must follow necessarily from its premisses, even if
the respondent deny it. The definer asks ‘Is man animal or inanimate?’
and then assumes—he has not inferred—that man is animal. Next, when
presented with an exhaustive division of animal into terrestrial and
aquatic, he assumes that man is terrestrial. Moreover, (20) that man is the
complete formula, terrestrial-animal, does not follow necessarily from
the premisses: this too is an assumption, and equally an assumption
whether the division comprises many differentiae or few. (Indeed as this
method of division is used by those who proceed by it, even truths that
can be inferred actually fail to appear as such.) (25) For why should not
the whole of this formula be true of man, and yet not exhibit his
essential nature or definable form? Again, what guarantee is there
against an unessential addition, or against the omission of the final or of
an intermediate determinant of the substantial being?
The champion of division might here urge that though these lapses do
occur, yet we can solve that difficulty if all the attributes we assume are
constituents of the definable form, and if, postulating the genus, we
produce by division the requisite uninterrupted sequence of terms, (30)
and omit nothing; and that indeed we cannot fail to fulfil these
conditions if what is to be divided falls whole into the division at each
stage, and none of it is omitted; and that this—the dividendum—must
without further question be (ultimately) incapable of fresh specific
division. Nevertheless, we reply, division does not involve inference; if it
gives knowledge, it gives it in another way. Nor is there any absurdity in
this: induction, perhaps, is not demonstration any more than is division,
yet it does make evident some truth. (35) Yet to state a definition reached
by division is not to state a conclusion: as, when conclusions are drawn
without their appropriate middles, the alleged necessity by which the
inference follows from the premisses is open to a question as to the
reason for it, so definitions reached by division invite the same question.
[92a] Thus to the question ‘What is the essential nature of man?’ the
divider replies ‘Animal, mortal, footed, biped, wingless’; and when at
each step he is asked ‘Why?’, he will say, and, as he thinks, prove by
division, that all animal is mortal or immortal: but such a formula taken
in its entirety is not definition; so that even if division does demonstrate
its formula, (5) definition at any rate does not turn out to be a conclusion
of inference.
6
Can we nevertheless actually demonstrate what a thing essentially
and substantially is, but hypothetically, i. e. by premising (1) that its
definable form is constituted by the ‘peculiar’ attributes of its essential
nature; (2) that such and such are the only attributes of its essential
nature, and that the complete synthesis of them is peculiar to the thing;
and thus—since in this synthesis consists the being of the thing—
obtaining our conclusion? Or is the truth that, (10) since proof must be
through the middle term, the definable form is once more assumed in
this minor premiss too?
Further, just as in syllogizing we do not premise what syllogistic
inference is (since the premisses from which we conclude must be
related as whole and part),4 so the definable form must not fall within
the syllogism but remain outside the premisses posited. It is only against
a doubt as to its having been a syllogistic inference at all that we have to
defend our argument as conforming to the definition of syllogism. (15) It
is only when some one doubts whether the conclusion proved is the
definable form that we have to defend it as conforming to the definition
of definable form which we assumed. Hence syllogistic inference must be
possible even without the express statement of what syllogism is or what
definable form is.
The following type of hypothetical proof also begs the question. (20) If
evil is definable as the divisible, and the definition of a thing’s contrary
—if it has one—is the contrary of the thing’s definition; then, if good is
the contrary of evil and the indivisible of the divisible, we conclude that
to be good is essentially to be indivisible. The question is begged because
definable form is assumed as a premiss, and as a premiss which is to
prove definable form. ‘But not the same definable form’, you may object.
That I admit, for in demonstrations also we premise that ‘this’ is
predicable of ‘that’; but in this premiss the term we assert of the minor is
neither the major itself nor a term identical in definition, (25) or
convertible, with the major.
Again, both proof by division and the syllogism just described are
open to the question why man should be animal-biped-terrestrial and
not merely animal and terrestrial, since what they premise does not
ensure that the predicates shall constitute a genuine unity and not
merely belong to a single subject as do musical and grammatical when
predicated of the same man. (30)
7
How then by definition shall we prove substance or essential nature?
We cannot show it as a fresh fact necessarily following from the
assumption of premisses admitted to be facts—the method of
demonstration: we may not proceed as by induction to establish a
universal on the evidence of groups of particulars which offer no
exception, (35) because induction proves not what the essential nature of
a thing is but that it has or has not some attribute. [92b] Therefore,
since presumably one cannot prove essential nature by an appeal to
sense perception or by pointing with the finger, what other method
remains?
To put it another way: how shall we by definition prove essential
nature? He who knows what human—or any other—nature is, (5) must
know also that man exists; for no one knows the nature of what does not
exist—one can know the meaning of the phrase or name ‘goat-stag’ but
not what the essential nature of a goat-stag is. But further, if definition
can prove what is the essential nature of a thing, can it also prove that it
exists? And how will it prove them both by the same process, since
definition exhibits one single thing and demonstration another single
thing, (10) and what human nature is and the fact that man exists are not
the same thing? Then too we hold that it is by demonstration that the
being of everything must be proved—unless indeed to be were its
essence; and, since being is not a genus, it is not the essence of anything.
Hence the being of anything as fact is matter for demonstration; and this
is the actual procedure of the sciences, (15) for the geometer assumes the
meaning of the word triangle, but that it is possessed of some attribute
he proves. What is it, then, that we shall prove in defining essential
nature? Triangle? In that case a man will know by definition what a
thing’s nature is without knowing whether it exists. But that is
impossible.
Moreover it is clear, if we consider the methods of defining actually in
use, that definition does not prove that the thing defined exists: since
even if there does actually exist something which is equidistant from a
centre, (20) yet why should the thing named in the definition exist? Why,
in other words, should this be the formula defining circle? One might
equally well call it the definition of mountain copper. For definitions do
not carry a further guarantee that the thing defined can exist or that it is
what they claim to define: one can always ask why. (25)
Since, therefore, to define is to prove either a thing’s essential nature
or the meaning of its name, we may conclude that definition, if it in no
sense proves essential nature, is a set of words signifying precisely what
a name signifies. But that were a strange consequence; for (1) both what
is not substance and what does not exist at all would be definable, since
even non-existents can be signified by a name: (2) all sets of words or
sentences would be definitions, (30) since any kind of sentence could be
given a name; so that we should all be talking in definitions, and even
the Iliad would be a definition: (3) no demonstration can prove that any
particular name means any particular thing: neither, therefore, do
definitions, in addition to revealing the meaning of a name, also reveal
that the name has this meaning. (35) It appears then from these
considerations that neither definition and syllogism nor their objects are
identical, and further that definition neither demonstrates nor proves
anything, and that knowledge of essential nature is not to be obtained
either by definition or by demonstration.
8
[93a] We must now start afresh and consider which of these
conclusions are sound and which are not, and what is the nature of
definition, and whether essential nature is in any sense demonstrable
and definable or in none.
Now to know its essential nature is, as we said, the same as to know
the cause of a thing’s existence, and the proof of this depends on the fact
that a thing must have a cause. (5) Moreover, this cause is either identical
with the essential nature of the thing or distinct from it;5 and if its cause
is distinct from it, the essential nature of the thing is either demonstrable
or indemonstrable. Consequently, if the cause is distinct from the thing’s
essential nature and demonstration is possible, the cause must be the
middle term, and, the conclusion proved being universal and affirmative,
the proof is in the first figure. So the method just examined of proving it
through another essential nature would be one way of proving essential
nature, (10) because a conclusion containing essential nature must be
inferred through a middle which is an essential nature just as a ‘peculiar’
property must be inferred through a middle which is a ‘peculiar’
property; so that of the two definable natures of a single thing this
method will prove one and not the other.6
Now it was said before7 that this method could not amount to
demonstration of essential nature—it is actually a dialectical proof of it
—so let us begin again and explain by what method it can be
demonstrated. (15) When we are aware of a fact we seek its reason, and
though sometimes the fact and the reason dawn on us simultaneously,
yet we cannot apprehend the reason a moment sooner than the fact; and
clearly in just the same way we cannot apprehend a thing’s definable
form without apprehending that it exists, since while we are ignorant
whether it exists we cannot know its essential nature. (20) Moreover we
are aware whether a thing exists or not sometimes through
apprehending an element in its character, and sometimes accidentally,8
as, for example, when we are aware of thunder as a noise in the clouds,
of eclipse as a privation of light, or of man as some species of animal, or
of the soul as a self-moving thing. As often as we have accidental
knowledge that the thing exists, (25) we must be in a wholly negative
state as regards awareness of its essential nature; for we have not got
genuine knowledge even of its existence, and to search for a thing’s
essential nature when we are unaware that it exists is to search for
nothing. On the other hand, whenever we apprehend an element in the
thing’s character there is less difficulty. Thus it follows that the degree of
our knowledge of a thing’s essential nature is determined by the sense in
which we are aware that it exists. Let us then take the following as our
first instance of being aware of an element in the essential nature. (30) Let
A be eclipse, C the moon, B the earth’s acting as a screen. Now to ask
whether the moon is eclipsed or not is to ask whether or not B has
occurred. But that is precisely the same as asking whether A has a
defining condition; and if this condition actually exists, we assert that A
also actually exists. Or again we may ask which side of a contradiction
the defining condition necessitates: does it make the angles of a triangle
equal or not equal to two right angles? When we have found the answer,
if the premisses are immediate, (35) we know fact and reason together; if
they are not immediate, we know the fact without the reason, as in the
following example: let C be the moon, A eclipse, B the fact that the
moon fails to produce shadows9 though she is full and though no visible
body intervenes between us and her. Then if B, failure to produce
shadows in spite of the absence of an intervening body, is attributable to
C, and A, eclipse, is attributable to B, it is clear that the moon is
eclipsed, but the reason why is not yet clear, and we know that eclipse
exists, but we do not know what its essential nature is. [93b] But when
it is clear that A is attributable to C and we proceed to ask 5 the reason
of this fact, we are inquiring what is the nature of B: is it the earth’s
acting as a screen, or the moon’s rotation or her extinction? But B is the
definition of the other term, viz., in these examples, of the major term A;
for eclipse is constituted by the earth acting as a screen. Thus, (1) ‘What
is thunder?’ ‘The quenching of fire in cloud’, and (2) ‘Why does it
thunder?’ ‘Because fire is quenched in the cloud’, are equivalent. Let C
be cloud, A thunder, B the quenching of fire. Then B is attributable to C,
cloud, (10) since fire is quenched in it; and A, noise, is attributable to B;
and B is assuredly the definition of the major term A. If there be a
further mediating cause of B, it will be one of the remaining partial
definitions of A.
We have stated then how essential nature is discovered and becomes
known, (15) and we see that, while there is no syllogism—i. e. no
demonstrative syllogism—of essential nature, yet it is through syllogism,
viz. demonstrative syllogism, that essential nature is exhibited. So we
conclude that neither can the essential nature of anything which has a
cause distinct from itself be known without demonstration, nor can it be
demonstrated; and this is what we contended in our preliminary
discussions.10 (20)
9
Now while some things have a cause distinct from themselves,
others have not. Hence it is evident that there are essential natures
which are immediate, that is, are basic premisses; and of these not only
that they are but also what they are must be assumed or revealed in some
other way. This too is the actual procedure of the arithmetician, who
assumes both the nature and the existence of unit. (25) On the other hand,
it is possible (in the manner explained) to exhibit through demonstration
the essential nature of things which have a ‘middle’,11 i. e. a cause of
their substantial being other than that being itself; but we do not thereby
demonstrate it.
10
Since definition is said to be the statement of a thing’s nature,
obviously one kind of definition will be a statement of the meaning of
the name, or of an equivalent nominal formula. (30) A definition in this
sense tells you, e. g. the meaning of the phrase ‘triangular character’.12
When we are aware that triangle exists, we inquire the reason why it
exists. But it is difficult thus to learn the definition of things the
existence of which we do not genuinely know—the cause of this
difficulty being, as we said before,13 that we only know accidentally
whether or not the thing exises. (35) Moreover, a statement may be a
unity in either of two ways, by conjunction, like the Iliad, or because it
exhibits a single predicate as inhering not accidentally in a single
subject.14
That then is one way of defining definition. Another kind of definition
is a formula exhibiting the cause of a thing’s existence. [94a] Thus the
former signifies without proving, but the latter will clearly be a quasidemonstration of essential nature, differing from demonstration in the
arrangement of its terms. For there is a difference between stating why it
thunders, and stating what is the essential nature of thunder; since the
first statement will be ‘Because fire is quenched in the clouds’, while the
statement of what the nature of thunder is will be ‘The noise of fire
being quenched in the clouds’. (5) Thus the same statement takes a
different form: in one form it is continuous15 demonstration, in the other
definition. Again, thunder can be defined as noise in the clouds, which is
the conclusion of the demonstration embodying essential nature. On the
other hand the definition of immediates is an indemonstrable positing of
essential nature. (10) We conclude then that definition is (a) an
indemonstrable statement of essential nature, or (b) a syllogism of
essential nature differing from demonstration in grammatical form, or
(c) the conclusion of a demonstration giving essential nature.
Our discussion has therefore made plain (1) in what sense and of what
things the essential nature is demonstrable, (15) and in what sense and of
what things it is not; (2) what are the various meanings of the term
definition, and in what sense and of what things it proves the essential
nature, and in what sense and of what things it does not; (3) what is the
relation of definition to demonstration, and how far the same thing is
both definable and demonstrable and how far it is not.
11
We think we have scientific knowledge when we know the cause,
(20) and there are four causes: (1) the definable form, (2) an antecedent
which necessitates a consequent,16 (3) the efficient cause, (4) the final
cause. Hence each of these can be the middle term of a proof, for17 (a)
though the inference from antecedent to necessary consequent does not
hold if only one premiss is assumed—two is the minimum—still when
there are two it holds on condition that they have a single common
middle term. (25) So it is from the assumption of this single middle term
that the conclusion follows necessarily. The following example will also
show this.18 Why is the angle in a semicircle a right angle?—or from
what assumption does it follow that it is a right angle? Thus, let A be
right angle, B the half of two right angles, C the angle in a semicircle.
Then B is the cause in virtue of which A, (30) right angle, is attributable
to C, the angle in a semicircle, since B = A and the other, viz. C, = B,
for C is half of two right angles. Therefore it is the assumption of B, the
half of two right angles, from which it follows that A is attributable to C,
i. e. that the angle in a semicircle is a right angle. Moreover, B is
identical with (b) the defining form of A, since it is what A’s definition19
signifies. Moreover, the formal cause has already been shown to be the
middle.20 (35) (c) ‘Why did the Athenians become involved in the Persian
war?’ means ‘What cause originated the waging of war against the
Athenians?’ and the answer is, ‘Because they raided Sardis with the
Eretrians’, since this originated the war. [94b] Let A be war, B
unprovoked raiding, C the Athenians. Then B, unprovoked raiding, is
true of C, the Athenians, and A is true of B, since men make war on the
unjust aggressor. So A, having war waged upon them, (5) is true of B, the
initial aggressors, and B is true of C, the Athenians, who were the
aggressors. Hence here too the cause—in this case the efficient cause—is
the middle term. (d) This is no less true where the cause is the final
cause. e. g. why does one take a walk after supper? For the sake of one’s
health. Why does a house exist? For the preservation of one’s goods. The
end in view is in the one case health, (10) in the other preservation. To
ask the reason why one must walk after supper is precisely to ask to
what end one must do it. Let C be walking after supper, B the nonregurgitation of food, A health. Then let walking after supper possess the
property of preventing food from rising to the orifice of the stomach, (15)
and let this condition be healthy; since it seems that B, the nonregurgitation of food, is attributable to C, taking a walk, and that A,
health, is attributable to B. What, then, is the cause through which A,
the final cause, inheres in C? It is B, the non-regurgitation of food; but B
is a kind of definition of A, for A will be explained by it. Why is B the
cause of A’s belonging to C? Because to be in a condition such as B is to
be in health. (20) The definitions must be transposed, and then the detail
will become clearer. Incidentally, here the order of coming to be is the
reverse of what it is in proof through the efficient cause: in the efficient
order the middle term must come to be first, (25) whereas in the
teleological order the minor, C, must first take place, and the end in
view comes last in time.
The same thing may exist for an end and be necessitated as well. For
example, light shines through a lantern (1) because that which consists
of relatively small particles necessarily passes through pores larger than
those particles—assuming that light does issue by penetration—and (2)
for an end, (30) namely to save us from stumbling. If, then, a thing can
exist through two causes, can it come to be through two causes—as for
instance if thunder be a hiss and a roar necessarily produced by the
quenching of fire, and also designed, as the Pythagoreans say, for a
threat to terrify those that lie in Tartarus? Indeed, (35) there are very
many such cases, mostly among the processes and products of the
natural world; for nature, in different senses of the term ‘nature’,
produces now for an end, now by necessity.
Necessity too is of two kinds. [95a] It may work in accordance with
a thing’s natural tendency, or by constraint and in opposition to it; as,
for instance, by necessity a stone is borne both upwards and downwards,
but not by the same necessity.
Of the products of man’s intelligence some are never due to chance or
necessity but always to an end, as for example a house or a statue;
others, (5) such as health or safety, may result from chance as well.
It is mostly in cases where the issue is indeterminate (though only
where the production does not originate in chance, and the end is
consequently good), that a result is due to an end, and this is true alike
in nature or in art. By chance, on the other hand, nothing comes to be
for an end.
12
The effect may be still coming to be, (10) or its occurrence may be
past or future, yet the cause will be the same as when it is actually
existent—for it is the middle which is the cause—except that if the effect
actually exists the cause is actually existent, if it is coming to be so is the
cause, if its occurrence is past the cause is past, if future the cause is
future. For example, the moon was eclipsed because the earth
intervened, is becoming eclipsed because the earth is in process of
intervening, (15) will be eclipsed because the earth will intervene, is
eclipsed because the earth intervenes.
To take a second example: assuming that the definition of ice is
solidified water, let C be water, A solidified, B the middle, which is the
cause, namely total failure of heat. Then B is attributed to C, and A,
solidification, to B: ice forms when B is occurring, (20) has formed when B
has occurred, and will form when B shall occur.
This sort of cause, then, and its effect come to be simultaneously when
they are in process of becoming, and exist simultaneously when they
actually exist; and the same holds good when they are past and when
they are future. But what of cases where they are not simultaneous? Can
causes and effects different from one another form, as they seem to us to
form, a continuous succession, (25) a past effect resulting from a past
cause different from itself, a future effect from a future cause different
from it, and an effect which is coming-to-be from a cause different from
and prior to it? Now on this theory it is from the posterior event that we
reason (and this though these later events actually have their source of
origin in previous events—a fact which shows that also when the effect
is coming-to-be we still reason from the posterior event), and from the
prior event we cannot reason (we cannot argue that because an event A
has occurred, (30) therefore an event B has occurred subsequently to A
but still in the past—and the same holds good if the occurrence is future)
—cannot reason because, be the time interval definite or indefinite, it
will never be possible to infer that because it is true to say that A
occurred, therefore it is true to say that B, the subsequent event,
occurred; for in the interval between the events, though A has already
occurred, the latter statement will be false. (35) And the same argument
applies also to future events; i. e. one cannot infer from an event which
occurred in the past that a future event will occur. The reason of this is
that the middle must be homogeneous, past when the extremes are past,
future when they are future, coming to be when they are coming-to-be,
actually existent when they are actually existent; and there cannot be a
middle term homogeneous with extremes respectively past and future.
And it is a further difficulty in this theory that the time interval can be
neither indefinite nor definite, (40) since during it the inference will be
false. [95b] We have also to inquire what it is that holds events
together so that the coming-to-be now occurring in actual things follows
upon a past event. It is evident, we may suggest, that a past event and a
present process cannot be ‘contiguous’, for not even two past events can
be ‘contiguous’. For past events are limits and atomic; so just as points
are not ‘contiguous’ neither are past events, (5) since both are indivisible.
For the same reason a past event and a present process cannot be
‘contiguous’, for the process is divisible, the event indivisible. Thus the
relation of present process to past event is analogous to that of line to
point, since a process contains an infinity of past events. (10) These
questions, however, must receive a more explicit treatment in our
general theory of change.21
The following must suffice as an account of the manner in which the
middle would be identical with the cause on the supposition that
coming-to-be is a series of consecutive events: for22 in the terms of such
a series too the middle and major terms must form an immediate
premiss; e. g. we argue that, (15) since C has occurred, therefore A
occurred: and C’s occurrence was posterior, A’s prior; but C is the source
of the inference because it is nearer to the present moment, and the
starting-point of time is the present. We next argue that, since D has
occurred, therefore C occurred. Then we conclude that, (20) since D has
occurred, therefore A must have occurred; and the cause is C, for since D
has occurred C must have occurred, and since C has occurred A must
previously have occurred.
If we get our middle term in this way, will the series terminate in an
immediate premiss, or since, as we said, no two events are ‘contiguous’,
will a fresh middle term always intervene because there is an infinity of
middles? No: though no two events are ‘contiguous’, yet we must start
from a premiss consisting of a middle and the present event as major. (25)
The like is true of future events too, since if it is true to say that D will
exist, it must be a prior truth to say that A will exist, and the cause of
this conclusion is C; for if D will exist, C will exist prior to D, and if C
will exist, A will exist prior to it. And here too the same infinite
divisibility might be urged, (30) since future events are not ‘contiguous’.
But here too an immediate basic premiss must be assumed. And in the
world of fact this is so: if a house has been built, then blocks must have
been quarried and shaped. The reason is that a house having been built
necessitates a foundation having been laid, and if a foundation has been
laid blocks must have been shaped beforehand. (35) Again, if a house will
be built, blocks will similarly be shaped beforehand; and proof is
through the middle in the same way, for the foundation will exist before
the house.
Now we observe in Nature a certain kind of circular process of
coming-to-be; and this is possible only if the middle and extreme terms
are reciprocal, since conversion is conditioned by reciprocity in the
terms of the proof. (40) This—the convertibility of conclusions and
premisses—has been proved in our early chapters,23 and the circular
process is an instance of this. [96a] In actual fact it is exemplified thus:
when the earth had been moistened an exhalation was bound to rise,
and when an exhalation had risen cloud was bound to form, and from
the formation of cloud rain necessarily resulted, and by the fall of rain
the earth was necessarily moistened: but this was the starting-point, (5)
so that a circle is completed; for posit any one of the terms and another
follows from it, and from that another, and from that again the first.
Some occurrences are universal (for they are, or come-to-be what they
are, always and in every case); others again are not always what they are
but only as a general rule: for instance, (10) not every man can grow a
beard, but it is the general rule. In the case of such connexions the
middle term too must be a general rule. For if A is predicated universally
of B and B of C, A too must be predicated always and in every instance
of C, since to hold in every instance and always is of the nature of the
universal. (15) But we have assumed a connexion which is a general rule;
consequently the middle term B must also be a general rule. So
connexions which embody a general rule—i. e. which exist or come to
be as a general rule—will also derive from immediate basic premisses.
1324
We have already explained how essential nature is set out in the
terms of a demonstration, (20) and the sense in which it is or is not
demonstrable or definable; so let us now discuss the method to be
adopted in tracing the elements predicated as constituting the definable
form.
Now of the attributes which inhere always in each several thing there
are some which are wider in extent than it but not wider than its genus
(by attributes of wider extent I mean all such as are universal attributes
of each several subject, (25) but in their application are not confined to
that subject). i. e. while an attribute may inhere in every triad, yet also
in a subject not a triad—as being inheres in triad but also in subjects not
numbers at all—odd on the other hand is an attribute inhering in every
triad and of wider application (inhering as it does also in pentad), but
which does not extend beyond the genus of triad; for pentad is a
number, (30) but nothing outside number is odd. It is such attributes
which we have to select, up to the exact point at which they are
severally of wider extent than the subject but collectively coextensive
with it; for this synthesis must be the substance of the thing. For
example every triad possesses the attributes number, (35) odd, and prime
in both senses, i. e. not only as possessing no divisors, but also as not
being a sum of numbers. This, then, is precisely what triad is, viz. a
number, odd, and prime in the former and also the latter sense of the
term: for these attributes taken severally apply, the first two to all odd
numbers, the last to the dyad also as well as to the triad, but, taken
collectively, to no other subject. [96b] Now since we have shown
above25 that attributes predicated as belonging to the essential nature
are necessary and that universals are necessary, and since the attributes
which we select as inhering in triad, or in any other subject whose
attributes we select in this way, (5) are predicated as belonging to its
essential nature, triad will thus possess these attributes necessarily.
Further, that the synthesis of them constitutes the substance of triad is
shown by the following argument. If it is not identical with the being of
triad, it must be related to triad as a genus named or nameless. It will
then be of wider extent than triad—assuming that wider potential extent
is the character of a genus. (10) If on the other hand this synthesis is
applicable to no subject other than the individual triads, it will be
identical with the being of triad, because we make the further
assumption that the substance of each subject is the predication of
elements in its essential nature down to the last differentia
characterizing the individuals. It follows that any other synthesis thus
exhibited will likewise be identical with the being of the subject. (15)
The author of a hand-book26 on a subject that is a generic whole
should divide the genus into its first infimae species—number e. g. into
triad and dyad—and then endeavour to seize their definitions by the
method we have described—the definition, for example, of straight line
or circle or right angle. After that, having established what the category
is to which the subaltern genus belongs—quantity or quality, (20) for
instance—he should examine the properties ‘peculiar’ to the species,
working through the proximate common differentiae. He should proceed
thus because the attributes of the genera compounded of the infimae
species will be clearly given by the definitions of the species; since the
basic element of them all27 is the definition, i. e. the simple infima
species, and the attributes inhere essentially in the simple infimae species,
in the genera only in virtue of these.
Divisions according to differentiae are a useful accessory to this
method. (25) What force they have as proofs we did, indeed, explain
above,28 but that merely towards collecting the essential nature they
may be of use we will proceed to show. They might, indeed, seem to be
of no use at all, but rather to assume everything at the start and to be no
better than an initial assumption made without division. But, (30) in fact,
the order in which the attributes are predicated does make a difference
—it matters whether we say animal—tame—biped, or biped—animal—
tame. For if every definable thing consists of two elements and ‘animaltame’ forms a unity, and again out of this and the further differentia man
(or whatever else is the unity under construction) is constituted, then the
elements we assume have necessarily been reached by division. Again,
division is the only possible method of avoiding the omission of any
element of the essential nature. (35) Thus, if the primary genus is assumed
and we then take one of the lower divisions, the dividendum will not fall
whole into this division: e. g. it is not all animal which is either wholewinged or split-winged but all winged animal, for it is winged animal to
which this differentiation belongs. [97a] The primary differentiation of
animal is that within which all animal falls. The like is true of every
other genus, whether outside animal or a subaltern genus of animal; e. g.
the primary differentiation of bird is that within which falls every bird,
of fish that within which falls every fish. So, if we proceed in this way,
we can be sure that nothing has been omitted: by any other method one
is bound to omit something without knowing it. (5)
To define and divide one need not know the whole of existence. Yet
some hold it impossible to know the differentiae distinguishing each
thing from every single other thing without knowing every single other
thing; and one cannot, they say, know each thing without knowing its
differentiae, since everything is identical with that from which it does
not differ, (10) and other than that from which it differs. Now first of all
this is a fallacy: not every differentia precludes identity, since many
differentiae inhere in things specifically identical, though not in the
substance of these nor essentially. Secondly, when one has taken one’s
differing pair of opposites and assumed that the two sides exhaust the
genus, and that the subject one seeks to define is present in one or other
of them, (15) and one has further verified its presence in one of them;
then it does not matter whether or not one knows all the other subjects
of which the differentiae are also predicated. For it is obvious that when
by this process one reaches subjects incapable of further differentiation
one will possess the formula defining the substance. Moreover, to
postulate that the division exhausts the genus is not illegitimate if the
opposites exclude a middle; since if it is the differentia of that genus, (20)
anything contained in the genus must lie on one of the two sides.
In establishing a definition by division one should keep three objects
in view: (1) the admission only of elements in the definable form, (2) the
arrangement of these in the right order, (25) (3) the omission of no such
elements. The first is feasible because one can establish genus and
differentia through the topic of the genus,29 just as one can conclude the
inherence of an accident through the topic of the accident.30 The right
order will be achieved if the right term is assumed as primary, and this
will be ensured if the term selected is predicable of all the others but not
all they of it; since there must be one such term. (30) Having assumed this
we at once proceed in the same way with the lower terms; for our
second term will be the first of the remainder, our third the first of those
which follow the second in a ‘contiguous’ series, since when the higher
term is excluded, that term of the remainder which is ‘contiguous’ to it
will be primary, and so on. Our procedure makes it clear that no
elements in the definable form have been omitted: we have taken the
differentia that comes first in the order of division, (35) pointing out that
animal e. g. is divisible exhaustively into A and B, and that the subject
accepts one of the two as its predicate. Next we have taken the
differentia of the whole thus reached, and shown that the whole we
finally reach is not further divisible—i. e. that as soon as we have taken
the last differentia to form the concrete totality, this totality admits of no
division into species. [97b] For it is clear that there is no superfluous
addition, since all these terms we have selected are elements in the
definable form; and nothing lacking, since any omission would have to
be a genus or a differentia. Now the primary term is a genus, and this
term taken in conjunction with its differentiae is a genus: moreover the
differentiae are all included, because there is now no further differentia;
if there were, (5) the final concrete would admit of division into species,
which, we said, is not the case.
To resume our account of the right method of investigation: We must
start by observing a set of similar—i. e. specifically identical—
individuals, and consider what element they have in common. We must
then apply the same process to another set of individuals which belong
to one species and are generically but not specifically identical with the
former set. When we have established what the common element is in all
members of this second species, (10) and likewise in members of further
species, we should again consider whether the results established possess
any identity, and persevere until we reach a single formula, since this
will be the definition of the thing. But if we reach not one formula but
two or more, evidently the definiendum cannot be one thing but must be
more than one. (15) I may illustrate my meaning as follows. If we were
inquiring what the essential nature of pride is, we should examine
instances of proud men we know of to see what, as such, they have in
common; e. g. if Alcibiades was proud, or Achilles and Ajax were proud,
we should find, on inquiring what they all had in common, that it was
intolerance of insult; it was this which drove Alcibiades to war, Achilles
to wrath, (20) and Ajax to suicide. We should next examine other cases,
Lysander, for example, or Socrates, and then if these have in common
indifference alike to good and ill fortune, I take these two results and
inquire what common element have equanimity amid the vicissitudes of
life and impatience of dishonour. If they have none, there will be two
genera of pride. (25) Besides, every definition is always universal and
commensurate: the physician does not prescribe what is healthy for a
single eye, but for all eyes or for a determinate species of eye. It is also
easier by this method to define the single species than the universal, and
that is why our procedure should be from the several species to the
universal genera—this for the further reason too that equivocation is less
readily detected in genera than in infimae species. (30) Indeed, perspicuity
is essential in definitions, just as inferential movement is the minimum
required in demonstrations; and we shall attain perspicuity if we can
collect separately the definition of each species through the group of
singulars which we have established—e. g. the definition of similarity
not unqualified but restricted to colours and to figures; the definition of
acuteness, (35) but only of sound—and so proceed to the common
universal with a careful avoidance of equivocation. We may add that if
dialectical disputation must not employ metaphors, clearly metaphors
and metaphorical expressions are precluded in definition: otherwise
dialectic would involve metaphors.
14
In order to formulate the connexions we wish to prove we have to
select our analyses and divisions. [98a] The method of selection
consists in laying down the common genus of all our subjects of
investigation—if e. g. they are animals, we lay down what the properties
are which inhere in every animal. These established, we next lay down
the properties essentially connected with the first of the remaining
classes—e. g. if this first subgenus is bird, (5) the essential properties of
every bird—and so on, always characterizing the proximate subgenus.
This will clearly at once enable us to say in virtue of what character the
subgenera—man, e. g., or horse—possess their properties. (10) Let A be
animal, B the properties of every animal, C, D, E, various species of
animal. Then it is clear in virtue of what character B inheres in D—
namely A—and that it inheres in C and E for the same reason: and
throughout the remaining subgenera always the same rule applies.
We are now taking our examples from the traditional class-names, but
we must not confine ourselves to considering these. (15) We must collect
any other common character which we observe, and then consider with
what species it is connected and what properties belong to it. For
example, as the common properties of horned animals we collect the
possession of a third stomach and only one row of teeth. Then since it is
clear in virtue of what character they possess these attributes—namely
their horned character—the next question is, to what species does the
possession of horns attach?
Yet a further method of selection is by analogy: for we cannot find a
single identical name to give to a squid’s pounce, (20) a fish’s spine, and
an animal’s bone, although these too possess common properties as if
there were a single osseous nature.
15
Some connexions that require proof are identical in that they
possess an identical ‘middle’—e. g. a whole group might be proved
through ‘reciprocal replacement’—and of these one class are identical in
genus, (25) namely all those whose difference consists in their concerning
different subjects or in their mode of manifestation. This latter class may
be exemplified by the questions as to the causes respectively of echo, of
reflection, and of the rainbow: the connexions to be proved which these
questions embody are identical generically, because all three are forms
of repercussion; but specifically they are different.
Other connexions that require proof only differ in that the ‘middle’ of
the one is subordinate to the ‘middle’ of the other. (30) For example: Why
does the Nile rise towards the end of the month? Because towards its
close the month is more stormy. Why is the month more stormy towards
its close? Because the moon is waning. Here the one cause is subordinate
to the other.
16
The question might be raised with regard to cause and effect
whether when the effect is present the cause also is present; whether, (35)
for instance, if a plant sheds its leaves or the moon is eclipsed, there is
present also the cause of the eclipse or of the fall of the leaves—the
possession of broad leaves, let us say, in the latter case, in the former the
earth’s interposition. [98b] For, one might argue, if this cause is not
present, these phenomena will have some other cause: if it is present, its
effect will be at once implied by it—the eclipse by the earth’s
interposition, the fall of the leaves by the possession of broad leaves; but
if so, they will be logically coincident and each capable of proof through
the other. Let me illustrate: Let A be deciduous character, (5) B the
possession of broad leaves, C vine. Now if A inheres in B (for every
broad-leaved plant is deciduous), and B in C (every vine possessing
broad leaves); then A inheres in C (every vine is deciduous), and the
middle term B is the cause. (10) But we can also demonstrate that the vine
has broad leaves because it is deciduous. Thus, let D be broad-leaved, E
deciduous, F vine. Then E inheres in F (since every vine is deciduous),
and D in E (for every deciduous plant has broad leaves): therefore every
vine has broad leaves, (15) and the cause is its deciduous character. If,31
however, they cannot each be the cause of the other (for cause is prior to
effect, and the earth’s interposition is the cause of the moon’s eclipse and
not the eclipse of the interposition)—if, then, demonstration through the
cause is of the reasoned fact and demonstration not through the cause is
of the bare fact, (20) one who knows it through the eclipse knows the fact
of the earth’s interposition but not the reasoned fact. Moreover, that the
eclipse is not the cause of the interposition, but the interposition of the
eclipse, is obvious because the interposition is an element in the
definition of eclipse, which shows that the eclipse is known through the
interposition and not vice versa.
On the other hand, can a single effect have more than one cause? One
might argue as follows: if the same attribute is predicable of more than
one thing as its primary subject, (25) let B be a primary subject in which
A inheres, and C another primary subject of A, and D and E primary
subjects of B and C respectively. A will then inhere in D and E, and B
will be the cause of A’s inherence in D, C of A’s inherence in E. The
presence of the cause thus necessitates that of the effect, (30) but the
presence of the effect necessitates the presence not of all that may cause
it but only of a cause which yet need not be the whole cause. We may,
however, suggest32 that if the connexion to be proved is always
universal and commensurate, not only will the cause be a whole but also
the effect will be universal and commensurate. For instance, deciduous
character will belong exclusively to a subject which is a whole, and, if
this whole has species, universally and commensurately to those species
—i. e. either to all species of plant or to a single species. (35) So in these
universal and commensurate connexions the ‘middle’ and its effect must
reciprocate, i. e. be convertible. Supposing, for example, that the reason
why trees are deciduous is the coagulation of sap, then if a tree is
deciduous, coagulation must be present, and if coagulation is present—
not in any subject but in a tree—then that tree must be deciduous.
17
[99a] Can the cause of an identical effect be not identical in
every instance of the effect but different? Or is that impossible? Perhaps
it is impossible if the effect is demonstrated as essential and not as
inhering in virtue of a symptom or an accident—because the middle is
then the definition of the major term—though possible if the
demonstration is not essential. Now it is possible to consider the effect
and its subject as an accidental conjunction, (5) though such conjunctions
would not be regarded as connexions demanding scientific proof. But if
they are accepted as such, the middle will correspond to the extremes,
and be equivocal if they are equivocal, generically one if they are
generically one. Take the question why proportionals alternate. The
cause when they are lines, and when they are numbers, is both different
and identical; different in so far as lines are lines and not numbers, (10)
identical as involving a given determinate increment. In all proportionals
this is so. Again, the cause of likeness between colour and colour is other
than that between figure and figure; for likeness here is equivocal,
meaning perhaps in the latter case equality of the ratios of the sides and
equality of the angles, (15) in the case of colours identity of the act of
perceiving them, or something else of the sort. Again, connexions
requiring proof which are identical by analogy have middles also
analogous.
The truth is that cause, effect, and subject are reciprocally predicable
in the following way. If the species are taken severally, the effect is
wider than the subject (e. g. the possession of external angles equal to
four right angles is an attribute wider than triangle or square), (20) but it
is coextensive with the species taken collectively (in this instance with
all figures whose external angles are equal to four right angles). And the
middle likewise reciprocates, for the middle is a definition of the major;
which is incidentally the reason why all the sciences are built up
through definition.
We may illustrate as follows. Deciduous is a universal attribute of
vine, and is at the same time of wider extent than vine; and of fig, and is
of wider extent than fig: but it is not wider than but co-extensive with
the totality of the species. (25) Then if you take the middle which is
proximate, it is a definition of deciduous. I say that, because you will
first reach a middle33 next the subject,34 and a premiss asserting it of the
whole subject, and after that a middle—the coagulation of sap or
something of the sort—proving the connexion of the first middle with
the major:35 but it is the coagulation of sap at the junction of leaf-stalk
and stem which defines deciduous.36
If an explanation in formal terms of the inter-relation of cause and
effect is demanded, (30) we shall offer the following. Let A be an attribute
of all B, and B of every species of D, but so that both A and B are wider
than their respective subjects. Then B will be a universal attribute of
each species of D (since I call such an attribute universal even if it is not
commensurate, and I call an attribute primary universal if it is
commensurate,37 not with each species severally but with their totality),
and it extends beyond each of them taken separately. Thus, B is the
cause of A’s inherence in the species of D: consequently A must be of
wider extent than B; otherwise why should B be the cause of A’s
inherence in D any more than A the cause of B’s inherence in D? Now if
A is an attribute of all the species of E, (35) all the species of E will be
united by possessing some common cause other than B: otherwise how
shall we be able to say that A is predicable of all of which E is
predicable, while E is not predicable of all of which A can be predicated?
I mean how can there fail to be some special cause of A’s inherence in E,
as there was of A’s inherence in all the species of D? Then are the species
of E, too, united by possessing some common cause? This cause we must
look for. [99b] Let us call it C.38
We conclude, then, that the same effect may have more than one
cause, but not in subjects specifically identical. For instance, (5) the cause
of longevity in quadrupeds is lack of bile, in birds a dry constitution—or
certainly something different.
18
If immediate premisses are not reached at once, and there is not
merely one middle but several middles, i. e. several causes; is the cause
of the property’s inherence in the several species the middle which is
proximate to the primary universal,39 (10) or the middle which is
proximate to the species?40 Clearly the cause is that nearest to each
species severally in which it is manifested, for that is the cause of the
subject’s falling under the universal. To illustrate formally: C is the cause
of B’s inherence in D; hence C is the cause of A’s inherence in D, B of A’s
inherence in C, while the cause of A’s inherence in B is B itself.
19
As regards syllogism and demonstration, (15) the definition of, and
the conditions required to produce each of them, are now clear, and
with that also the definition of, and the conditions required to produce,
demonstrative knowledge, since it is the same as demonstration. As to
the basic premisses, how they become known and what is the developed
state of knowledge of them is made clear by raising some preliminary
problems. (20)
We have already said41 that scientific knowledge through
demonstration is impossible unless a man knows the primary immediate
premisses. But there are questions which might be raised in respect of
the apprehension of these immediate premisses: one might not only ask
whether it is of the same kind as the apprehension of the conclusions,
but also whether there is or is not scientific knowledge of both; or
scientific knowledge of the latter, and of the former a different kind of
knowledge; and, (25) further, whether the developed states of knowledge
are not innate but come to be in us, or are innate but at first unnoticed.
Now it is strange if we possess them from birth; for it means that we
possess apprehensions more accurate than demonstration and fail to
notice them. If on the other hand we acquire them and do not previously
possess them, how could we apprehend and learn without a basis of preexistent knowledge? For that is impossible, (30) as we used to find42 in
the case of demonstration. So it emerges that neither can we possess
them from birth, nor can they come to be in us if we are without
knowledge of them to the extent of having no such developed state at
all. Therefore we must possess a capacity of some sort, but not such as to
rank higher in accuracy than these developed states. And this at least is
an obvious characteristic of all animals, for they possess a congenital
discriminative capacity which is called sense-perception. (35) But though
sense-perception is innate in all animals, in some the sense-impression
comes to persist, in others it does not. So animals in which this
persistence does not come to be have either no knowledge at all outside
the act of perceiving, or no knowledge of objects of which no impression
persists; animals in which it does come into being have perception and
can continue to retain the sense-impression in the soul: and when such
persistence is frequently repeated a further distinction at once arises
between those which out of the persistence of such sense-impressions
develop a power of systematizing them and those which do not. [100a]
So out of sense-perception comes to be what we call memory, and out of
frequently repeated memories of the same thing develops experience; for
a number of memories constitute a single experience.43 (5) From
experience again—i. e. from the universal now stabilized in its entirety
within the soul, the one beside the many which is a single identity
within them all—originate the skill of the craftsman and the knowledge
of the man of science, skill in the sphere of coming to be and science in
the sphere of being.
We conclude that these states of knowledge are neither innate in a
determinate form, nor developed from other higher states of knowledge,
(10) but from sense-perception. It is like a rout in battle stopped by first
one man making a stand and then another, until the original formation
has been restored. The soul is so constituted as to be capable of this
process.
Let us now restate the account given already, though with insufficient
clearness. When one of a number of logically indiscriminable particulars
has made a stand, (15) the earliest universal is present in the soul: for
though the act of sense-perception is of the particular, its content is
universal—is man, for example, not the man Callias. [100b] A fresh
stand is made among these rudimentary universals, and the process does
not cease until the indivisible concepts, the true universals, are
established: e. g. such and such a species of animal is a step towards the
genus animal, which by the same process is a step towards a further
generalization.
Thus it is clear that we must get to know the primary premisses by
induction; for the method by which even sense-perception implants
plants the universal is inductive. (5) Now of the thinking states by which
we grasp truth, some are unfailingly true, others admit of error—
opinion, for instance, and calculation, whereas scientific knowing and
intuition are always true: further, no other kind of thought except
intuition is more accurate than scientific knowledge, whereas primary
premisses are more knowable than demonstrations, (10) and all scientific
knowledge is discursive. From these considerations it follows that there
will be no scientific knowledge of the primary premisses, and since
except intuition nothing can be truer than scientific knowledge, it will be
intuition that apprehends the primary premisses—a result which also
follows from the fact that demonstration cannot be the originative
source of demonstration, nor, consequently, scientific knowledge of
scientific knowledge. If, therefore, it is the only other kind of true
thinking except scientific knowing, (15) intuition will be the originative
source of scientific knowledge. And the originative source of science
grasps the original basic premiss, while science as a whole is similarly
related as originative source to the whole body of fact.
1
Cf. 94a 11–14.
2
Cf. 72b 18–25 and 84a 30-b 2.
3
sc. ‘and an indefinite regress occurs’. This argument is a corollary of the proof in 15–26 that if
the proposition predicating A—its definition—of C can be a conclusion, there must be a middle
term, B, and since A, B, and C are reciprocally predicable, B too, as well as A, will be a definition
of C.
4
A reminder of a necessary condition of syllogism. If the definition of syllogism is premised the
conclusion would have to affirm some subject to be of the nature of syllogism.
5
‘distinct from it’; i. e. in the case of properties, with the definition of which Aristotle is alone
concerned in this chapter. The being of a property consists in its inherence in a substance
through a middle which defines it. Cf. the following chapter.
6
Aristotle speaks of two moments of the definable form as two essential natures. His argument
amounts to this: that if the conclusion contains the whole definition, the question has been
begged in the premisses (cf. ii, ch. 4). Hence syllogism—and even so merely dialectical syllogism
—is only possible if premisses and conclusion each contain a part of the definition.
7
ii, ch. 2.
8
The distinction is that between genuine knowledge of a connexion through its cause and
accidental knowledge of it through a middle not the cause.
9
i. e. that there is no moonlight casting shadows on the earth on a clear night at full moon.
10
ii, ch. 3.
11
Cf., however, ii, ch. 2.
12
i. e. as treated by geometry; that is, as abstracted a materia and treated as a subject. Cf. 81b 25.
13
Cf. 93a 16–27.
14
Presumably a reason for there being a kind of definition other than nominal. The reference is
obviously to 92b 32.
15
Demonstration, like a line, is continuous because its premisses are parts which are
conterminous (as linked by middle terms), and there is a movement from premisses to
conclusion. Definition resembles rather the indivisible simplicity of a point.
16
By this Aristotle appears to mean the material cause; cf. Physics ii, 195a 18, 19, where the
premisses of a syllogism are said to be the material cause of the conclusion.
17
sc. ‘lest you should suppose that (2) could not be a middle’.
18
sc. ‘that (2) can appear as a middle’.
19
Cf. Euclid, Elem. i, Def. x, but Aristotle may be referring to some earlier definition. The proof
here given that the angle in a semicircle is a right angle is not that of Euclid iii. 31; cf. Heath,
Greek Mathematics, i. pp. 339, 340.
20
The reference is to 93a 3 ff., and other passages such as 94a 5 ff., where the middle is shown to
define the major.
21
Cf. Physics vi.
22
i. e. Aristotle has had in this chapter to explain (1) how syllogisms concerning a process of
events can be brought into line with other demonstrations equally derivable from immediate
primary premisses, and (2) in what sense the middle term contains the cause. He has in fact had
(1) to show that in these syllogisms inference must find its primary premiss in the effect, and (2)
to imply that the ‘cause’ which appears as middle when cause and effect are not simultaneous is
a causa cognoscendi and not essendi.
23
i, ch. 3 and An. Pr. ii, cc. 3–5, 8–10.
24
This chapter treats only the definition of substances.
25
i, ch. 4.
26
With the remainder of the chapter compare An. Pr. i, ch. 25, where the treatment covers all
syllogism.
27
sc. genera and species.
28
ii, ch. 5 and An. Pr. i, ch. 31.
29
Cf. Topics iv.
30
Cf. Topics ii.
31
Here begins Aristotle’s answer.
32
Here begins Aristotle’s answer.
33
sc. broad-leaved.
34
Vine, fig, &c.
35
Broad-leaved with deciduous.
36
Aristotle contemplates four terms: (1) deciduous, (2) coagulation, (3) broad-leaved, (4) vine,
fig, &c.
If we get the middle proximate to (1) it is a definition of (1). But in investigating vines, figs,
&c. according to the method of chapter 13, we shall first find a common character of them in
broad-leaved, and, taking this as a middle, we shall prove that vine, fig, &c., qua broad-leaved,
are deciduous. But this proof is not demonstration, because broad-leaved is not a definition of
deciduous. So our next step will be to find a middle—coagulation—mediating the major premiss
of this proof, and demonstrate that broad-leaved plants, qua liable to coagulation, are deciduous.
This is strict demonstration, because coagulation defines deciduous.
37
But cf. i, ch. 4, 73b 21–74a 3.
38
The schema of Aristotle’s argument in this paragraph is:
39
i. e. the property.
40
the subject
41
i, ch. 2.
42
i, ch. 1.
43
Cf. Met. A 980a 28. Met. A I should be compared with this chapter.
TOPICA
Translated by W. A. Pickard-Cambridge
CONTENTS
BOOK I
INTRODUCTORY
CHAPTER
1. Programme of treatise.
2. Uses of treatise.
3. Ideal aimed at.
A. SUBJECTS AND MATERIALS OF DISCUSSIONS
4. Subjects (Problems) and materials (Propositions) classified into four groups according to
nature of Predicable concerned.
5. The four Predicables.
6. How far to be treated separately.
7. Different kinds of sameness.
8. Twofold proof of division of Predicables.
9. The ten Categories and their relation to the Predicables.
10. Dialectical Propositions.
11. Dialectical Problems:—Theses.
12. Dialectical Reasoning distinguished from Induction.
B. THE SUPPLY OF ARGUMENTS
13. Four sources of arguments:—
14. (1) How to secure propositions.
15. (2) How to distinguish ambiguous meanings.
16. (3) How to note differences.
17. (4) How to note resemblances.
18. The special uses of the last three processes.
[Books II–VIII omitted.]
TOPICA
(Topics)
BOOK I
1
[100a] Our treatise proposes to find a line of inquiry whereby we
shall be able to reason from opinions that are generally accepted about
every problem propounded to us, (18) and also shall ourselves, (20) when
standing up to an argument, avoid saying anything that will obstruct us.
First, then, we must say what reasoning is, and what its varieties are, in
order to grasp dialectical reasoning: for this is the object of our search in
the treatise before us.
Now reasoning is an argument in which, (25) certain things being laid
down, something other than these necessarily comes about through
them. (a) It is a ‘demonstration’, when the premisses from which the
reasoning starts are true and primary, or are such that our knowledge of
them has originally come through premisses which are primary and true:
(b) reasoning, (30) on the other hand, is ‘dialectical’, if it reasons from
opinions that are generally accepted. [100b] Things are ‘true’ and
‘primary’ which are believed on the strength not of anything else but of
themselves: for in regard to the first principles of science it is improper
to ask any further for the why and wherefore of them; (18) each of the
first principles should command belief in and by itself. (20) On the other
hand, those opinions are ‘generally accepted’ which are accepted by
every one or by the majority or by the philosophers—i. e. by all, or by
the majority, or by the most notable and illustrious of them. Again (c),
reasoning is ‘contentious’ if it starts from opinions that seem to be
generally accepted, but are not really such, (25) or again if it merely
seems to reason from opinions that are or seem to be generally accepted.
For not every opinion that seems to be generally accepted actually is
generally accepted. For in none of the opinions which we call generally
accepted is the illusion entirely on the surface, as happens in the case of
the principles of contentious arguments; for the nature of the fallacy in
these is obvious immediately, (30) and as a rule even to persons with little
power of comprehension. [101a] So then, of the contentious
reasonings mentioned, the former really deserves to be called ‘reasoning’
as well, but the other should be called ‘contentious reasoning’, but not
‘reasoning’, since it appears to reason, but does not really do so.
Further (d), besides all the reasonings we have mentioned there are
the mis-reasonings that start from the premisses peculiar to the special
sciences, (5) as happens (for example) in the case of geometry and her
sister sciences. For this form of reasoning appears to differ from the
reasonings mentioned above; the man who draws a false figure reasons
from things that are neither true and primary, nor yet generally
accepted. (10) For he does not fall within the definition; he does not
assume opinions that are received either by every one or by the majority
or by philosophers—that is to say, by all, or by most, or by the most
illustrious of them—but he conducts his reasoning upon assumptions
which, though appropriate to the science in question, are not true; for he
effects his mis-reasoning either by describing the semicircles wrongly or
by drawing certain lines in a way in which they could not be drawn. (15)
The foregoing must stand for an outline survey of the species of
reasoning. In general, in regard both to all that we have already
discussed and to those which we shall discuss later, (20) we may remark
that that amount of distinction between them may serve, because it is
not our purpose to give the exact definition of any of them; we merely
want to describe them in outline; we consider it quite enough from the
point of view of the line of inquiry before us to be able to recognize each
of them in some sort of way.
2 Next in order after the foregoing, we must say for how many and for
what purposes the treatise is useful. (25) They are three—intellectual
training, casual encounters, and the philosophical sciences. That it is
useful as a training is obvious on the face of it. The possession of a plan
of inquiry will enable us more easily to argue about the subject
proposed. (30) For purposes of casual encounters, it is useful because
when we have counted up the opinions held by most people, we shall
meet them on the ground not of other people’s convictions but of their
own, while we shift the ground of any argument that they appear to us
to state unsoundly. For the study of the philosophical sciences it is
useful, because the ability to raise searching difficulties on both sides of
a subject will make us detect more easily the truth and error about the
several points that arise. (35) It has a further use in relation to the
ultimate bases of the principles used in the several sciences. For it is
impossible to discuss them at all from the principles proper to the
particular science in hand, seeing that the principles are the prius of
everything else: it is through the opinions generally held on the
particular points that these have to be discussed, and this task belongs
properly, or most appropriately, to dialectic: for dialectic is a process of
criticism wherein lies the path to the principles of all inquiries. [101b]
3
We shall be in perfect possession of the way to proceed when we
are in a position like that which we occupy in regard to rhetoric and
medicine and faculties of that kind: this means the doing of that which
we choose with the materials that are available. (5) For it is not every
method that the rhetorician will employ to persuade, or the doctor to
heal: still, if he omits none of the available means, (10) we shall say that
his grasp of the science is adequate.
4
First, then, we must see of what parts our inquiry consists. Now if
we were to grasp (a) with reference to how many, and what kind of,
things arguments take place, and with what materials they start, and (b)
how we are to become well supplied with these, we should have
sufficiently won our goal. Now the materials with which arguments start
are equal in number, and are identical, (15) with the subjects on which
reasonings take place. For arguments start with ‘propositions’, while the
subjects on which reasonings take place are ‘problems’. Now every
proposition and every problem indicates either a genus or a peculiarity
or an accident—for the differentia too, applying as it does to a class (or
genus), should be ranked together with the genus. Since, however, of
what is peculiar to anything part signifies its essence, (20) while part does
not, let us divide the ‘peculiar’ into both the aforesaid parts, and call
that part which indicates the essence a ‘definition’, while of the
remainder let us adopt the terminology which is generally current about
these things, and speak of it as a ‘property’. What we have said, then,
makes it clear that according to our present division, the elements turn
out to be four, all told, (25) namely either property or definition or genus
or accident. Do not let any one suppose us to mean that each of these
enunciated by itself constitutes a proposition or problem, but only that it
is from these that both problems and propositions are formed. The
difference between a problem and a proposition is a difference in the
turn of the phrase. (30) For if it be put in this way, ‘ “An animal that
walks on two feet” is the definition of man, is it not?’ or ‘ “Animal” is the
genus of man, is it not?’ the result is a proposition: but if thus, ‘Is “an
animal that walks on two feet” a definition of man or no?’ [or ‘Is
“animal” his genus or no?’] the result is a problem. Similarly too in other
cases. Naturally, then, problems and propositions are equal in number:
for out of every proposition you will make a problem if you change the
turn of the phrase. (35)
5
We must now say what are ‘definition’, ‘property’, ‘genus’, and
‘accident’. A ‘definition’ is a phrase signifying a thing’s essence. It is
rendered in the form either of a phrase in lieu of a term, or of a phrase
in lieu of another phrase; for it is sometimes possible to define the
meaning of a phrase as well. [102a] People whose rendering consists
of a term only, try it as they may, clearly do not render the definition of
the thing in question, because a definition is always a phrase of a certain
kind. One may, however, use the word ‘definitory’ also of such a remark
as ‘The “becoming” is “beautiful”,’ (5) and likewise also of the question,
‘Are sensation and knowledge the same or different?’, for argument
about definitions is mostly concerned with questions of sameness and
difference. In a word we may call ‘definitory’ everything that falls under
the same branch of inquiry as definitions; and that all the abovementioned examples are of this character is clear on the face of them. (10)
For if we are able to argue that two things are the same or are different,
we shall be well supplied by the same turn of argument with lines of
attack upon their definitions as well: for when we have shown that they
are not the same we shall have demolished the definition. Observe,
please, that the converse of this last statement does not hold: for to show
that they are the same is not enough to establish a definition. (15) To
show, however, that they are not the same is enough of itself to
overthrow it.
A ‘property’ is a predicate which does not indicate the essence of a
thing, but yet belongs to that thing alone, and is predicated convertibly
of it. Thus it is a property of man to be capable of learning grammar: for
if A be a man, then he is capable of learning grammar, (20) and if he be
capable of learning grammar, he is a man. For no one calls anything a
‘property’ which may possibly belong to something else, e. g. ‘sleep’ in
the case of man, even though at a certain time it may happen to belong
to him alone. That is to say, if any such thing were actually to be called
a property, it will be called not a ‘property’ absolutely, (25) but a
‘temporary’ or a ‘relative’ property: for ‘being on the right hand side’ is a
temporary property, while ‘two-footed’ is in point of fact ascribed as a
property in certain relations; e. g. it is a property of man relatively to a
horse and a dog. That nothing which may belong to anything else than A
is a convertible predicate of A is clear: for it does not necessarily follow
that if something is asleep it is a man. (30)
A ‘genus’ is what is predicated in the category of essence of a number
of things exhibiting differences in kind. We should treat as predicates in
the category of essence all such things as it would be appropriate to
mention in reply to the question, ‘What is the object before you?’; as, (35)
for example, in the case of man, if asked that question, it is appropriate
to say ‘He is an animal’. The question, ‘Is one thing in the same genus as
another or in a different one?’ is also a ‘generic’ question; for a question
of that kind as well falls under the same branch of inquiry as the genus:
for having argued that ‘animal’ is the genus of man, and likewise also of
ox, we shall have argued that they are in the same genus; whereas if we
show that it is the genus of the one but not of the other, we shall have
argued that these things are not in the same genus. [102b]
An ‘accident’ is (1) something which, though it is none of the
foregoing—i. e. neither a definition nor a property nor a genus—yet
belongs to the thing: (5) (2) something which may possibly either belong
or not belong to any one and the self-same thing, as (e. g.) the ‘sitting
posture’ may belong or not belong to some self-same thing. Likewise also
‘whiteness’, for there is nothing to prevent the same thing being at one
time white, and at another not white. (10) Of the definitions of accident
the second is the better: for if he adopts the first, any one is bound, if he
is to understand it, to know already what ‘definition’ and ‘genus’ and
‘property’ are, whereas the second is sufficient of itself to tell us the
essential meaning of the term in question. (15) To Accident are to be
attached also all comparisons of things together, when expressed in
language that is drawn in any kind of way from what happens (accidit)
to be true of them; such as, for example, the question, ‘Is the honourable
or the expedient preferable?’ and ‘Is the life of virtue or the life of selfindulgence the pleasanter?’, and any other problem which may happen
to be phrased in terms like these. For in all such cases the question is ‘to
which of the two does the predicate in question happen (accidit) to
belong more closely?’ It is clear on the face of it that there is nothing to
prevent an accident from becoming a temporary or a relative property.
(20) Thus the sitting posture is an accident, but will be a temporary
property, whenever a man is the only person sitting, while if he be not
the only one sitting, it is still a property relatively to those who are not
sitting. (25) So then, there is nothing to prevent an accident from
becoming both a relative and a temporary property; but a property
absolutely it will never be.
6
We must not fail to observe that all remarks made in criticism of a
‘property’ and ‘genus’ and ‘accident’ will be applicable to ‘definitions’ as
well. For when we have shown that the attribute in question fails to
belong only to the term defined, as we do also in the case of a property,
(30) or that the genus rendered in the definition is not the true genus, or
that any of the things mentioned in the phrase used does not belong, as
would be remarked also in the case of an accident, we shall have
demolished the definition; so that, to use the phrase previously
employed,1 all the points we have enumerated might in a certain sense
be called ‘definitory’. But we must not on this account expect to find a
single line of inquiry which will apply universally to them all: for this is
not an easy thing to find, (35) and, even were one found, it would be very
obscure indeed, and of little service for the treatise before us. Rather, a
special plan of inquiry must be laid down for each of the classes we have
distinguished, and then, starting from the rules that are appropriate in
each case, it will probably be easier to make our way right through the
task before us. [103a] So then, as was said before,2 we must outline a
division of our subject, and other questions we must relegate each to the
particular branch to which it most naturally belongs, speaking of them
as ‘definitory’ and ‘generic’ questions. The questions I mean have
practically been already assigned to their several branches. (5)
7
First of all we must define the number of senses borne by the term
‘Sameness’. Sameness would be generally regarded as falling, roughly
speaking, into three divisions. We generally apply the term numerically
or specifically or generically—numerically in cases where there is more
than one name but only one thing, (10) e. g. ‘doublet’ and ‘cloak’;
specifically, where there is more than one thing, but they present no
differences in respect of their species, as one man and another, or one
horse and another: for things like this that fall under the same species
are said to be ‘specifically the same’. Similarly, too, those things are
called generically the same which fall under the same genus, such as a
horse and a man. It might appear that the sense in which water from the
same spring is called ‘the same water’ is somehow different and unlike
the senses mentioned above: but really such a case as this ought to be
ranked in the same class with the things that in one way or another are
called ‘the same’ in view of unity of species. (15) For all such things seem
to be of one family and to resemble one another. For the reason why all
water is said to be specifically the same as all other water is because of a
certain likeness it bears to it, (20) and the only difference in the case of
water drawn from the same spring is this, that the likeness is more
emphatic: that is why we do not distinguish it from the things that in
one way or another are called ‘the same’ in view of unity of species. It is
generally supposed that the term ‘the same’ is most used in a sense
agreed on by every one when applied to what is numerically one. (25) But
even so, it is apt to be rendered in more than one sense; its most literal
and primary use is found whenever the sameness is rendered in
reference to an alternative name or definition, as when a cloak is said to
be the same as a doublet, or an animal that walks on two feet is said to
be the same as a man: a second sense is when it is rendered in reference
to a property, as when what can acquire knowledge is called the same as
a man, and what naturally travels upward the same as fire: while a third
use is found when it is rendered in reference to some term drawn from
Accident, (30) as when the creature who is sitting, or who is musical, is
called the same as Socrates. For all these uses mean to signify numerical
unity. That what I have just said is true may be best seen where one
form of appellation is substituted for another. For often when we give
the order to call one of the people who are sitting down, indicating him
by name, we change our description, (35) whenever the person to whom
we give the order happens not to understand us; he will, we think,
understand better from some accidental feature; so we bid him call to us
‘the man who is sitting’ or ‘who is conversing over there’—clearly
supposing ourselves to be indicating the same object by its name and by
its accident.
8
[103b] Of ‘sameness’ then, as has been said,3 three senses are to
be distinguished. Now one way to confirm that the elements mentioned
above are those out of which and through which and to which
arguments proceed, is by induction: for if any one were to survey
propositions and problems one by one, it would be seen that each was
formed either from the definition of something or from its property or
from its genus or from its accident. (5) Another way to confirm it is
through reasoning. For every predicate of a subject must of necessity be
either convertible with its subject or not: and if it is convertible, it would
be its definition or property, for if it signifies the essence, (10) it is the
definition; if not, it is a property: for this was4 what a property is, viz.
what is predicated convertibly, but does not signify the essence. If, on
the other hand, it is not predicated convertibly of the thing, it either is
or is not one of the terms contained in the definition of the subject: and
if it be one of those terms, then it will be the genus or the differentia,
inasmuch as the definition consists of genus and differentiae; whereas,
(15) if it be not one of those terms, clearly it would be an accident, for
accident was said5 to be what belongs as an attribute to a subject
without being either its definition or its genus or a property.
9
Next, then, we must distinguish between the classes of predicates in
which the four orders in question are found. (20) These are ten in number:
Essence, Quantity, Quality, Relation, Place, Time, Position, State,
Activity, Passivity. For the accident and genus and property and
definition of anything will always be in one of these categories: for all
the propositions found through these signify either something’s essence
or its quality or quantity or some one of the other types of predicate. (25)
It is clear, too, on the face of it that the man who signifies something’s
essence signifies sometimes a substance, sometimes a quality, sometimes
some one of the other types of predicate. For when a man is set before
him and he says that what is set there is ‘a man’ or ‘an animal’, (30) he
states its essence and signifies a substance; but when a white colour is
set before him and he says that what is set there is ‘white’ or is ‘a
colour’, he states its essence and signifies a quality. Likewise, also, if a
magnitude of a cubit be set before him and he says that what is set there
is a magnitude of a cubit, he will be describing its essence and signifying
a quantity. Likewise, also, (35) in the other cases: for each of these kinds
of predicate, if either it be asserted of itself, or its genus be asserted of it,
signifies an essence: if, on the other hand, one kind of predicate is
asserted of another kind, it does not signify an essence, but a quantity or
a quality or one of the other kinds of predicate. Such, then, and so many,
are the subjects on which arguments take place, and the materials with
which they start. [104a] How we are to acquire them, and by what
means we are to become well supplied with them, falls next to be told.
10
First, then, a definition must be given of a ‘dialectical proposition’
and a ‘dialectical problem’. For it is not every proposition nor yet every
problem that is to be set down as dialectical: for no one in his senses
would make a proposition of what no one holds, (5) nor yet make a
problem of what is obvious to everybody or to most people: for the latter
admits of no doubt, while to the former no one would assent. Now a
dialectical proposition consists in asking something that is held by all
men or by most men or by the philosophers, i. e. either by all, or by
most, or by the most notable of these, (10) provided it be not contrary to
the general opinion; for a man would probably assent to the view of the
philosophers, if it be not contrary to the opinions of most men.
Dialectical propositions also include views which are like those generally
accepted; also propositions which contradict the contraries of opinions
that are taken to be generally accepted, (15) and also all opinions that are
in accordance with the recognized arts. Thus, supposing it to be a
general opinion that the knowledge of contraries is the same, it might
probably pass for a general opinion also that the perception of contraries
is the same: also, supposing it to be a general opinion that there is but
one single science of grammar, it might pass for a general opinion that
there is but one science of flute-playing as well, whereas, if it be a
general opinion that there is more than one science of grammar, it might
pass for a general opinion that there is more than one science of fluteplaying as well: for all these seem to be alike and akin. (20) Likewise,
also, propositions contradicting the contraries of general opinions will
pass as general opinions: for if it be a general opinion that one ought to
do good to one’s friends, it will also be a general opinion that one ought
not to do them harm. Here, that one ought to do harm to one’s friends is
contrary to the general view, and that one ought not to do them harm is
the contradictory of that contrary. (25) Likewise also, if one ought to do
good to one’s friends, one ought not to do good to one’s enemies: this
too is the contradictory of the view contrary to the general view; the
contrary being that one ought to do good to one’s enemies. Likewise,
also, in other cases. Also, on comparison, it will look like a general
opinion that the contrary predicate belongs to the contrary subject: e. g.
if one ought to do good to one’s friends, (30) one ought also to do evil to
one’s enemies. It might appear also as if doing good to one’s friends were
a contrary to doing evil to one’s enemies: but whether this is or is not so
in reality as well will be stated in the course of the discussion upon
contraries.6 Clearly also, all opinions that are in accordance with the arts
are dialectical propositions; for people are likely to assent to the views
held by those who have made a study of these things, (35) e. g. on a
question of medicine they will agree with the doctor, and on a question
of geometry with the geometrician; and likewise also in other cases.
11
[104b] A dialectical problem is a subject of inquiry that
contributes either to choice and avoidance, or to truth and knowledge,
and that either by itself, or as a help to the solution of some other such
problem. It must, moreover, be something on which either people hold
no opinion either way, or the masses hold a contrary opinion to the
philosophers, or the philosophers to the masses, or each of them among
themselves. (5) For some problems it is useful to know with a view to
choice or avoidance, e. g. whether pleasure is to be chosen or not, while
some it is useful to know merely with a view to knowledge, e. g.
whether the universe is eternal or not: others, again, are not useful in
and by themselves for either of these purposes, but yet help us in regard
to some such problems; for there are many things which we do not wish
to know in and by themselves, (10) but for the sake of other things, in
order that through them we may come to know something else.
Problems also include questions in regard to which reasonings conflict
(the difficulty then being whether so-and-so is so or not, there being
convincing arguments for both views); others also in regard to which we
have no argument because they are so vast, (15) and we find it difficult to
give our reasons, e. g. the question whether the universe is eternal or no:
for into questions of that kind too it is possible to inquire.
Problems, then, and propositions are to be defined as aforesaid.7 A
‘thesis’ is a supposition of some eminent philosopher that conflicts with
the general opinion; e. g. the view that contradiction is impossible, (20) as
Antisthenes said; or the view of Heraclitus that all things are in motion;
or that Being is one, as Melissus says: for to take notice when any
ordinary person expresses views contrary to men’s usual opinions would
be silly. Or it may be a view about which we have a reasoned theory
contrary to men’s usual opinions, e. g. the view maintained by the
sophists that what is need not in every case either have come to be or be
eternal: for a musician who is a grammarian ‘is’ so without ever having
‘come to be’ so, (25) or being so eternally. For even if a man does not
accept this view, he might do so on the ground that it is reasonable.
Now a ‘thesis’ also is a problem, though a problem is not always a
thesis, inasmuch as some problems are such that we have no opinion
about them either way. (30) That a thesis, however, also forms a problem,
is clear: for it follows of necessity from what has been said that either
the mass of men disagree with the philosophers about the thesis, or that
the one or the other class disagree among themselves, seeing that the
thesis is a supposition in conflict with general opinion. Practically all
dialectical problems indeed are now called ‘theses’. (35) But it should
make no difference whichever description is used; for our object in thus
distinguishing them has not been to create a terminology, but to
recognize what differences happen to be found between them. [105a]
Not every problem, nor every thesis, should be examined, but only one
which might puzzle one of those who need argument, (5) not punishment
or perception. For people who are puzzled to know whether one ought
to honour the gods and love one’s parents or not need punishment, while
those who are puzzled to know whether snow is white or not need
perception. The subjects should not border too closely upon the sphere
of demonstration, nor yet be too far removed from it: for the former
cases admit of no doubt, while the latter involve difficulties too great for
the art of the trainer.
12
Having drawn these definitions, (10) we must distinguish how
many species there are of dialectical arguments. There is on the one
hand Induction, on the other Reasoning. Now what reasoning is has been
said before:8 induction is a passage from individuals to universals, e. g.
the argument that supposing the skilled pilot is the most effective, (15)
and likewise the skilled charioteer, then in general the skilled man is the
best at his particular task. Induction is the more convincing and clear: it
is more readily learnt by the use of the senses, and is applicable
generally to the mass of men, though Reasoning is more forcible and
effective against contradictious people.
13
The classes, (20) then, of things about which, and of things out of
which, arguments are constructed, are to be distinguished in the way we
have said before. The means whereby we are to become well supplied
with reasonings are four: (1) the securing of propositions; (2) the power
to distinguish in how many senses a particular expression is used; (3) the
discovery of the differences of things; (4) the investigation of likeness.
(25) The last three, as well, are in a certain sense propositions: for it is
possible to make a proposition corresponding to each of them, e. g. (1)
‘The desirable may mean either the honourable or the pleasant or the
expedient’; and (2) ‘Sensation differs from knowledge in that the latter
may be recovered again after it has been lost, (30) while the former
cannot’; and (3) ‘The relation of the healthy to health is like that of the
vigorous to vigour’. The first proposition depends upon the use of one
term in several senses, the second upon the differences of things, the
third upon their likenesses.
14 Propositions should be selected in a number of ways corresponding
to the number of distinctions drawn in regard to the proposition: thus
one may first take in hand the opinions held by all or by most men or by
the philosophers, (35) i. e. by all, or most, or the most notable of them; or
opinions contrary to those that seem to be generally held; and, again, all
opinions that are in accordance with the arts. [105b] We must make
propositions also of the contradictories of opinions contrary to those that
seem to be generally held, as was laid down before. It is useful also to
make them by selecting not only those opinions that actually are
accepted, but also those that are like these, (5) e. g. ‘The perception of
contraries is the same’—the knowledge of them being so—and ‘we see
by admission of something into ourselves, not by an emission’; for so it
is, too, in the case of the other senses; for in hearing we admit something
into ourselves; we do not emit; and we taste in the same way. Likewise
also in the other cases. Moreover, all statements that seem to be true in
all or in most cases, (10) should be taken as a principle or accepted
position; for they are posited by those who do not also see what
exception there may be. We should select also from the written
handbooks of argument, and should draw up sketchlists of them upon
each several kind of subject, putting them down under separate
headings, e. g. ‘On Good’, or ‘On Life’—and that ‘On Good’ should deal
with every form of good, (15) beginning with the category of essence. In
the margin, too, one should indicate also the opinions of individual
thinkers, e. g. ‘Empedocles said that the elements of bodies were four’:
for any one might assent to the saying of some generally accepted
authority.
Of propositions and problems there are—to comprehend the matter in
outline—three divisions: for some are ethical propositions, (20) some are
on natural philosophy, while some are logical. Propositions such as the
following are ethical, e. g. ‘Ought one rather to obey one’s parents or the
laws, if they disagree?’; such as this are logical, e. g. ‘Is the knowledge of
opposites the same or not?’; while such as this are on natural
philosophy, e. g. ‘Is the universe eternal or not?’ Likewise also with
problems. (25) The nature of each of the aforesaid kinds of proposition is
not easily rendered in a definition, but we have to try to recognize each
of them by means of the familiarity attained through induction,
examining them in the light of the illustrations given above.
For purposes of philosophy we must treat of these things according to
their truth, (30) but for dialectic only with an eye to general opinion. All
propositions should be taken in their most universal form; then, the one
should be made into many. e. g. ‘The knowledge of opposites is the
same’; next, ‘The knowledge of contraries is the same’, and that ‘of
relative terms’. In the same way these two should again be divided, as
long as division is possible, (35) e. g. the knowledge of ‘good and evil’, of
‘white and black’, or ‘cold and hot’. Likewise also in other cases.
15
[106a] On the formation, then, of propositions, the above
remarks are enough. As regards the number of senses a term bears, we
must not only treat of those terms which bear different senses, but we
must also try to render their definitions; e. g. (5) we must not merely say
that justice and courage are called ‘good’ in one sense, and that what
conduces to vigour and what conduces to health are called so in another,
but also that the former are so called because of a certain intrinsic
quality they themselves have, the latter because they are productive of a
certain result and not because of any intrinsic quality in themselves.
Similarly also in other cases.
Whether a term bears a number of specific meanings or one only, (10)
may be considered by the following means. First, look and see if its
contrary bears a number of meanings, whether the discrepancy between
them be one of kind or one of names. For in some cases a difference is at
once displayed even in the names; e. g. the contrary of ‘sharp’ in the case
of a note is ‘flat’, while in the case of a solid edge it is ‘dull’. Clearly,
then, the contrary of ‘sharp’ bears several meanings, (15) and if so, so also
does ‘sharp’; for corresponding to each of the former terms the meaning
of its contrary will be different. For ‘sharp’ will not be the same when
contrary to ‘dull’ and to ‘flat’, though ‘sharp’ is the contrary of each.
Again baru (‘flat’, ‘heavy’) in the case of a note has ‘sharp’ as its
contrary, but in the case of a solid mass ‘light’, so that baru is used with
a number of meanings, (20) inasmuch as its contrary also is so used.
Likewise, also, ‘fine’ as applied to a picture has ‘ugly’ as its contrary, but,
as applied to a house, ‘ramshackle’; so that ‘fine’ is an ambiguous term.
In some cases there is no discrepancy of any sort in the names used,
but a difference of kind between the meanings is at once obvious: e. g. in
the case of ‘clear’ and ‘obscure’: for sound is called ‘clear’ and ‘obscure’,
(25) just as ‘colour’ is too. As regards the names, then, there is no
discrepancy, but the difference in kind between the meanings is at once
obvious: for colour is not called ‘clear’ in a like sense to sound. This is
plain also through sensation: for of things that are the same in kind we
have the same sensation, (30) whereas we do not judge clearness by the
same sensation in the case of sound and of colour, but in the latter case
we judge by sight, in the former by hearing. Likewise also with ‘sharp’
and ‘dull’ in regard to flavours and solid edges: here in the latter case we
judge by touch, but in the former by taste. For here again there is no
discrepancy in the names used, (35) in the case either of the original
terms or of their contraries: for the contrary also of sharp in either sense
is ‘dull’.
Moreover, see if one sense of a term has a contrary, while another has
absolutely none; e. g. the pleasure of drinking has a contrary in the pain
of thirst, whereas the pleasure of seeing that the diagonal is
incommensurate with the side has none, so that ‘pleasure’ is used in
more than one sense. [106b] To ‘love’ also, used of the frame of mind,
has to ‘hate’ as its contrary, while as used of the physical activity
(kissing) it has none: clearly, therefore, to ‘love’ is an ambiguous term.
Further, see in regard to their intermediates, if some meanings and their
contraries have an intermediate, while others have none, or if both have
one but not the same one, (5) as e. g. ‘clear’ and ‘obscure’ in the case of
colours have ‘grey’ as an intermediate, whereas in the case of sound they
have none, or, if they have, it is ‘harsh’, as some people say that a harsh
sound is intermediate. ‘Clear’, then, is an ambiguous term, and likewise
also ‘obscure’. See, moreover, if some of them have more than one
intermediate, (10) while others have but one, as is the case with ‘clear’
and ‘obscure’, for in the case of colours there are numbers of
intermediates, whereas in regard to sound there is but one, viz. ‘harsh’.
Again, in the case of the contradictory opposite, look and see if it
bears more than one meaning. For if this bears more than one meaning,
then the opposite of it also will be used in more than one meaning; (15)
e. g. ‘to fail to see’ is a phrase with more than one meaning, viz. (1) to
fail to possess the power of sight, (2) to fail to put that power to active
use. But if this has more than one meaning, it follows necessarily that ‘to
see’ also has more than one meaning: for there will be an opposite to
each sense of ‘to fail to see’; e. g. the opposite of ‘not to possess the
power of sight’ is to possess it, while of ‘not to put the power of sight to
active use’, the opposite is to put it to active use. (20)
Moreover, examine the case of terms that denote the privation or
presence of a certain state: for if the one term bears more than one
meaning, then so will the remaining term: e. g. if ‘to have sense’ be used
with more than one meaning, as applied to the soul and to the body,
then ‘to be wanting in sense’ too will be used with more than one
meaning, as applied to the soul and to the body. (25) That the opposition
between the terms now in question depends upon the privation or
presence of a certain state is clear, since animals naturally possess each
kind of ‘sense’, both as applied to the soul and as applied to the body.
Moreover, examine the inflected forms. For if ‘justly’ has more than
one meaning, then ‘just’, also, will be used with more than one meaning;
for there will be a meaning of ‘just’ corresponding to each of the
meanings of ‘justly’; e. g. if the word ‘justly’ be used of judging according
to one’s own opinion, (30) and also of judging as one ought, then ‘just’
also will be used in like manner. In the same way also, if ‘healthy’ has
more than one meaning, then ‘healthily’ also will be used with more
than one meaning: (35) e. g. if ‘healthy’ describes both what produces
health and what preserves health and what betokens health, then
‘healthily’ also will be used to mean ‘in such a way as to produce’ or
‘preserve’ or ‘betoken’ health. Likewise also in other cases, whenever the
original term bears more than one meaning, the inflexion also that is
formed from it will be used with more than one meaning, and vice versa.
[107a]
Look also at the classes of the predicates signified by the term, and see
if they are the same in all cases. For if they are not the same, (5) then
clearly the term is ambiguous: e. g. ‘good’ in the case of food means
‘productive of pleasure’, and in the case of medicine ‘productive of
health’, whereas as applied to the soul it means to be of a certain
quality, e. g. temperate or courageous or just: and likewise also, as
applied to ‘man’. Sometimes it signifies what happens at a certain time,
as (e. g.) the good that happens at the right time: for what happens at
the right time is called good. (10) Often it signifies what is of a certain
quantity, e. g. as applied to the proper amount: for the proper amount
too is called good. So then the term ‘good’ is ambiguous. In the same
way also ‘clear’, as applied to a body, signifies a colour, but in regard to
a note it denotes what is ‘easy to hear’. ‘Sharp’, too, is in a closely
similar case: for the same term does not bear the same meaning in all its
applications: for a sharp note is a swift note, (15) as the mathematical
theorists of harmony tell us, whereas a sharp (acute) angle is one that is
less than a right angle, while a sharp dagger is one containing a sharp
angle (point).
Look also at the genera of the objects denoted by the same term, and
see if they are different without being subaltern, as (e. g.) ‘donkey’,
which denotes both the animal and the engine. (20) For the definition of
them that corresponds to the name is different: for the one will be
declared to be an animal of a certain kind, and the other to be an engine
of a certain kind. If, however, the genera be subaltern, there is no
necessity for the definitions to be different. Thus (e. g.) ‘animal’ is the
genus of ‘raven’, and so is ‘bird’. Whenever therefore we say that the
raven is a bird, we also say that it is a certain kind of animal, (25) so that
both the genera are predicated of it. Likewise also whenever we call the
raven a ‘flying biped animal’, we declare it to be a bird: in this way,
then, as well, both the genera are predicated of raven, and also their
definition. But in the case of genera that are not subaltern this does not
happen, for whenever we call a thing an ‘engine’, (30) we do not call it an
animal, nor vice versa.
Look also and see not only if the genera of the term before you are
different without being subaltern, but also in the case of its contrary: for
if its contrary bears several senses, (35) clearly the term before you does
so as well.
It is useful also to look at the definition that arises from the use of the
term in combination, e. g. of a ‘clear (lit. white) body’ and of a ‘clear
note’. For then if what is peculiar in each case be abstracted, the same
expression ought to remain over. This does not happen in the case of
ambiguous terms, e. g. in the cases just mentioned. [107b] For the
former will be ‘a body possessing such and such a colour’, while the
latter will be ‘a note easy to hear’. Abstract, then, ‘a body’ and ‘a note’,
and the remainder in each case is not the same. It should, however, have
been had the meaning of ‘clear’ in each case been synonymous. (5)
Often in the actual definitions as well ambiguity creeps in unawares,
and for this reason the definitions also should be examined. If (e. g.) any
one describes what betokens and what produces health as ‘related
commensurably to health’, we must not desist but go on to examine in
what sense he has used the term ‘commensurably’ in each case, (10) e. g.
if in the latter case it means that ‘it is of the right amount to produce
health’, whereas in the former it means that ‘it is such as to betoken
what kind of state prevails’.
Moreover, see if the terms cannot be compared as ‘more or less’ or as
‘in like manner’, as is the case (e. g.) with a ‘clear’ (lit. white) sound and
a ‘clear’ garment, and a ‘sharp’ flavour and a ‘sharp’ note. (15) For neither
are these things said to be clear or sharp ‘in a like degree’, nor yet is the
one said to be clearer or sharper than the other. ‘Clear’, then, and ‘sharp’
are ambiguous. For synonyms are always comparable; for they will
always be used either in like manner, or else in a greater degree in one
case.
Now since of genera that are different without being subaltern the
differentiae also are different in kind, (20) e. g. those of ‘animal’ and
‘knowledge’ (for the differentiae of these are different), look and see if
the meanings comprised under the same term are differentiae of genera
that are different without being subaltern, as e. g. ‘sharp’ is of a ‘note’
and a ‘solid’. For being ‘sharp’ differentiates note from note, and likewise
also one solid from another. ‘Sharp’, then, is an ambiguous term: for it
forms differentiae of genera that are different without being subaltern.
(25)
Again, see if the actual meanings included under the same term
themselves have different differentiae, e. g. ‘colour’ in bodies and
‘colour’ in tunes: for the differentiae of ‘colour’ in bodies are
‘sightpiercing’ and ‘sight-compressing’, (30) whereas ‘colour’ in melodies
has not the same differentiae. Colour, then, is an ambiguous term; for
things that are the same have the same differentiae.
Moreover, since the species is never the differentia of anything, look
and see if one of the meanings included under the same term be a
species and another a differentia, as (e. g.) ‘clear’ (lit. (35) white) as
applied to a body is a species of colour, whereas in the case of a note it
is a differentia; for one note is differentiated from another by being
‘clear’.
16
The presence, then, of a number of meanings in a term may be
investigated by these and like means. [108a] The differences which
things present to each other should be examined within the same genera,
e. g. ‘Wherein does justice differ from courage, and wisdom from
temperance?’—for all these belong to the same genus; and also from one
genus to another, provided they be not very much too far apart, e. g.
‘Wherein does sensation differ from knowledge?’: for in the case of
genera that are very far apart, (5) the differences are entirely obvious.
17
Likeness should be studied, first, in the case of things belonging to
different genera, the formulae being ‘A : B = C : D’ (e. g. as knowledge
stands to the object of knowledge, so is sensation related to the object of
sensation), and ‘As A is in B, so is C in D’ (e. g. as sight is in the eye, (10)
so is reason in the soul, and as is a calm in the sea, so is windlessness in
the air). Practice is more especially needed in regard to terms that are
far apart; for in the case of the rest, we shall be more easily able to see
in one glance the points of likeness. We should also look at things which
belong to the same genus, (15) to see if any identical attribute belongs to
them all, e. g. to a man and a horse and a dog; for in so far as they have
any identical attribute, in so far they are alike.
18
It is useful to have examined the number of meanings of a term
both for clearness’ sake (for a man is more likely to know what it is he
asserts, if it has been made clear to him how many meanings it may
have), (20) and also with a view to ensuring that our reasonings shall be
in accordance with the actual facts and not addressed merely to the term
used. For as long as it is not clear in how many senses a term is used, it
is possible that the answerer and the questioner are not directing their
minds upon the same thing: whereas when once it has been made clear
how many meanings there are, and also upon which of them the former
directs his mind when he makes his assertion, (25) the questioner would
then look ridiculous if he failed to address his argument to this. It helps
us also both to avoid being misled and to mislead by false reasoning: for
if we know the number of meanings of a term, we shall certainly never
be misled by false reasoning, but shall know if the questioner fails to
address his argument to the same point; and when we ourselves put the
questions we shall be able to mislead him, if our answerer happens not
to know the number of meanings of our terms. (30) This, however, is not
possible in all cases, but only when of the many senses some are true
and others are false. This manner of argument, however, does not belong
properly to dialectic; dialecticians should therefore by all means beware
of this kind of verbal discussion, unless any one is absolutely unable to
discuss the subject before him in any other way. (35)
The discovery of the differences of things helps us both in reasonings
about sameness and difference, and also in recognizing what any
particular thing is. [108b] That it helps us in reasoning about sameness
and difference is clear: for when we have discovered a difference of any
kind whatever between the objects before us, we shall already have
shown that they are not the same: while it helps us in recognizing what
a thing is, because we usually distinguish the expression that is proper to
the essence of each particular thing by means of the differentiae that are
proper to it. (5)
The examination of likeness is useful with a view both to inductive
arguments and to hypothetical reasonings, and also with a view to the
rendering of definitions. It is useful for inductive arguments, (10) because
it is by means of an induction of individuals in cases that are alike that
we claim to bring the universal in evidence: for it is not easy to do this if
we do not know the points of likeness. It is useful for hypothetical
reasonings because it is a general opinion that among similars what is
true of one is true also of the rest. If, then, with regard to any of them
we are well supplied with matter for a discussion, we shall secure a
preliminary admission that however it is in these cases, (15) so it is also in
the case before us: then when we have shown the former we shall have
shown, on the strength of the hypothesis, the matter before us as well:
for we have first made the hypothesis that however it is in these cases,
so it is also in the case before us, and have then proved the point as
regards these cases. It is useful for the rendering of definitions because,
if we are able to see in one glance what is the same in each individual
case of it, (20) we shall be at no loss into what genus we ought to put the
object before us when we define it: for of the common predicates that
which is most definitely in the category of essence is likely to be the
genus. Likewise, also, in the case of objects widely divergent, the
examination of likeness is useful for purposes of definition, (25) e. g. the
sameness of a calm at sea, and windlessness in the air (each being a form
of rest), and of a point on a line and the unit in number—each being a
starting point. If, then, we render as the genus what is common to all the
cases, we shall get the credit of defining not inappropriately. Definitionmongers too nearly always render them in this way: for they declare the
unit to be the starting-point of number, (30) and the point the startingpoint of a line. It is clear, then, that they place them in that which is
common to both as their genus.
The means, then, whereby reasonings are effected, are these: the
commonplace rules, for the observance of which the aforesaid means are
useful, are as follows.
[Books II–VIII omitted.]
1a
2
9
101a 22.
3a
7
4
102a 18.
5
102b 4.
6
ii. 7.
7 b1,a8.
8
100a 25.
DE SOPHISTICIS ELENCHIS
Translated by W. A. Pickard-Cambridge
CONTENTS
INTRODUCTORY (CHAPTERS 1–2)
CHAPTER
1. General distinction of genuine from merely apparent reasonings and refutations.
2. Four classes of arguments in dialogue form:—Didactic arguments, Dialectical arguments,
Examination arguments, and Contentious arguments (the subject of the present
book).
PERPETRATION OF FALLACIES (CHAPTERS 3–15)
3. Aims of contentious reasoning fivefold.
[Chapters 4–33 omitted.]
EPILOGUE
34. (1) Our programme and its performance (183a 27−b 15).
(2) History of dialectical theory compared with that of rhetoric (183b 15–end).
DE SOPHISTICIS ELENCHIS
(On Sophistical Refutations)
1
[164a] Let us now discuss sophistic refutations, (20) i. e. what
appear to be refutations but are really fallacies instead. We will begin in
the natural order with the first.
That some reasonings are genuine, while others seem to be so but are
not, is evident. This happens with arguments, as also elsewhere, (25)
through a certain likeness between the genuine and the sham. [164b]
For physically some people are in a vigorous condition, (20) while others
merely seem to be so by blowing and rigging themselves out as the
tribesmen do their victims for sacrifice; and some people are beautiful
thanks to their beauty, while others seem to be so, by dint of
embellishing themselves. So it is, too, with inanimate things; for of
these, too, some are really silver and others gold, while others are not
and merely seem to be such to our sense; e. g. things made of litharge
and tin seem to be of silver, while those made of yellow metal look
golden. (25) In the same way both reasoning and refutation are sometimes
genuine, sometimes not, though inexperience may make them appear so:
for inexperienced people obtain only, as it were, a distant view of these
things. [165a] For reasoning rests on certain statements such that they
involve necessarily the assertion of something other than what has been
stated, through what has been stated: refutation is reasoning involving
the contradictory of the given conclusion. Now some of them do not
really achieve this, though they seem to do so for a number of reasons;
and of these the most prolific and usual domain is the argument that
turns upon names only. (5) It is impossible in a discussion to bring in the
actual things discussed: we use their names as symbols instead of them;
and therefore we suppose that what follows in the names, follows in the
things as well, just as people who calculate suppose in regard to their
counters. (10) But the two cases (names and things) are not alike. For
names are finite and so is the sum-total of formulae, while things are
infinite in number. Inevitably, then, the same formulae, and a single
name, have a number of meanings. Accordingly just as, in counting,
those who are not clever in manipulating their counters are taken in by
the experts, (15) in the same way in arguments too those who are not well
acquainted with the force of names misreason both in their own
discussions and when they listen to others. For this reason, then, and for
others to be mentioned later, there exists both reasoning and refutation
that is apparent but not real. Now for some people it is better worth
while to seem to be wise, than to be wise without seeming to be (for the
art of the sophist is the semblance of wisdom without the reality, (20) and
the sophist is one who makes money from an apparent but unreal
wisdom); for them, then, it is clearly essential also to seem to accomplish
the task of a wise man rather than to accomplish it without seeming to
do so. To reduce it to a single point of contrast it is the business of one
who knows a thing, (25) himself to avoid fallacies in the subjects which
he knows and to be able to show up the man who makes them; and of
these accomplishments the one depends on the faculty to render an
answer, and the other upon the securing of one. Those, then, who would
be sophists are bound to study the class of arguments aforesaid: for it is
worth their while: for a faculty of this kind will make a man seem to be
wise, (30) and this is the purpose they happen to have in view.
Clearly, then, there exists a class of arguments of this kind, and it is at
this kind of ability that those aim whom we call sophists. Let us now go
on to discuss how many kinds there are of sophistical arguments, and
how many in number are the elements of which this faculty is composed,
(35) and how many branches there happen to be of this inquiry, and the
other factors that contribute to this art.
2
Of arguments in dialogue form there are four classes:
Didactic, Dialectical, Examination-arguments, and Contentious
arguments. Didactic arguments are those that reason from the principles
appropriate to each subject and not from the opinions held by the
answerer (for the learner should take things on trust): dialectical
arguments are those that reason from premisses generally accepted, to
the contradictory of a given thesis: examination-arguments are those
that reason from premisses which are accepted by the answerer and
which any one who pretends to possess knowledge of the subject is
bound to know—in what manner, (5) has been defined in another
treatise: contentious arguments are those that reason or appear to reason
to a conclusion from premisses that appear to be generally accepted but
are not so. [165b] The subject, then, of demonstrative arguments has
been discussed in the Analytics, while that of dialectic arguments and
examination-arguments has been discussed elsewhere: let us proceed to
speak of the arguments used in competitions and contests. (10)
3
First we must grasp the number of aims entertained by those who
argue as competitors and rivals to the death. These are five in number,
refutation, fallacy, paradox, solecism, (15) and fifthly to reduce the
opponent in the discussion to babbling—i. e. to constrain him to repeat
himself a number of times: or it is to produce the appearance of each of
these things without the reality. For they choose if possible plainly to
refute the other party, or as the second best to show that he is
committing some fallacy, or as a third best to lead him into paradox, or
fourthly to reduce him to solecism, i. e. to make the answerer, (20) in
consequence of the argument, to use an ungrammatical expression; or, as
a last resort, to make him repeat himself.…
34
[182a] As to the number, then, and kind of sources whence
fallacies arise in discussion, and how we are to show that our opponent
is committing a fallacy and make him utter paradoxes; moreover, by the
use of what materials solecism is brought about, (30) and how to question
and what is the way to arrange the questions; moreover, as to the
question what use is served by all arguments of this kind, and
concerning the answerer’s part, both as a whole in general, and in
particular how to solve arguments and solecisms—on all these things let
the foregoing discussion suffice. It remains to recall our original proposal
and to bring our discussion to a close with a few words upon it. (35)
Our programme was, then, to discover some faculty of reasoning
about any theme put before us from the most generally accepted
premisses that there are. For that is the essential task of the art of
discussion (dialectic) and of examination (peirastic). [183b] Inasmuch,
however, as it is annexed to it, on account of the near presence of the art
of sophistry (sophistic), not only to be able to conduct an examination
dialectically but also with a show of knowledge, we therefore proposed
for our treatise not only the aforesaid aim of being able to exact an
account of any view, but also the aim of ensuring that in standing up to
an argument we shall defend our thesis in the same manner by means of
views as generally held as possible. (5) The reason of this we have
explained;1 for this, too, was why Socrates used to ask questions and not
to answer them; for he used to confess that he did not know. We have
made clear, in the course of what precedes, the number both of the
points with reference to which, and of the materials from which, this
will be accomplished, (10) and also from what sources we can become
well supplied with these: we have shown, moreover, how to question or
arrange the questioning as a whole, and the problems concerning the
answers and solutions to be used against the reasonings of the
questioner. We have also cleared up the problems concerning all other
matters that belong to the same inquiry into arguments. In addition to
this we have been through the subject of Fallacies, as we have already
stated above.2 (15)
That our programme, then, has been adequately completed is clear.
But we must not omit to notice what has happened in regard to this
inquiry. For in the case of all discoveries the results of previous labours
that have been handed down from others have been advanced bit by bit
by those who have taken them on, whereas the original discoveries
generally make an advance that is small at first though much more
useful than the development which later springs out of them. (20) For it
may be that in everything, as the saying is, ‘the first start is the main
part’: and for this reason also it is the most difficult; for in proportion as
it is most potent in its influence, so it is smallest in its compass and
therefore most difficult to see: whereas when this is once discovered, (25)
it is easier to add and develop the remainder in connexion with it. This
is in fact what has happened in regard to rhetorical speeches and to
practically all the other arts: for those who discovered the beginnings of
them advanced them in all only a little way, whereas the celebrities of
to-day are the heirs (so to speak) of a long succession of men who have
advanced them bit by bit, (30) and so have developed them to their
present form, Tisias coming next after the first founders, then
Thrasymachus after Tisias, and Theodorus next to him, while several
people have made their several contributions to it: and therefore it is not
to be wondered at that the art has attained considerable dimensions. Of
this inquiry, on the other hand, it was not the case that part of the work
had been thoroughly done before, (35) while part had not. Nothing
existed at all. For the training given by the paid professors of contentious
arguments was like the treatment of the matter by Gorgias. For they
used to hand out speeches to be learned by heart, some rhetorical, others
in the form of question and answer, each side supposing that their
arguments on either side generally fall among them. [184a] And
therefore the teaching they gave their pupils was ready but rough. For
they used to suppose that they trained people by imparting to them not
the art but its products, as though any one professing that he would
impart a form of knowledge to obviate any pain in the feet, were then
not to teach a man the art of shoe-making or the sources whence he can
acquire anything of the kind, (5) but were to present him with several
kinds of shoes of all sorts: for he has helped him to meet his need, but
has not imparted an art to him. [184b] Moreover, on the subject of
Rhetoric there exists much that has been said long ago, whereas on the
subject of reasoning we had nothing else of an earlier date to speak of at
all, but were kept at work for a long time in experimental researches. If,
then, it seems to you after inspection that, such being the situation as it
existed at the start, our investigation is in a satisfactory condition
compared with the other inquiries that have been developed by
tradition, (5) there must remain for all of you, or for our students, the
task of extending us your pardon for the shortcomings of the inquiry,
and for the discoveries thereof your warm thanks.
1
165a 19–27.
2
183a 27.
Physica
Translated by R. P. Hardie and R. K. Gaye
CONTENTS
BOOK I
CHAPTER
1. The scope and method of this book.
2. The problem: the number and character of the first principles of nature. 185a 20. Reality
is not one in the way that Parmenides and Melissus supposed.
3. Refutation of their arguments.
4. Statement and examination of the opinions of the natural philosophers.
5. The principles are contraries.
6. The principles are two, or three, in number.
7. The number and nature of the principles.
8. The true opinion removes the difficulty felt by the early philosophers.
9. Further reflections on the first principles of nature.
BOOK II
A.
1. Nature and the natural.
B.
2. Distinction of the natural philosopher from the mathematician and the metaphysician.
C. The conditions of change.
3. The essential conditions.
4. The opinions of others about chance and spontaneity.
5. Do chance and spontaneity exist? What is chance and what are its characteristics?
6. Distinction between chance and spontaneity, and between both and the essential
conditions of change.
D. Proof in natural philosophy.
7. The physicist demonstrates by means of the four conditions of change.
8. Does nature act for an end?
9. The sense in which necessity is present in natural things.
BOOK III
A. Motion.
1, 2. The nature of motion.
3. The mover and the moved.
B. The infinite.
4. Opinions of the early philosophers.
203b 15. Main arguments for belief in the infinite.
5. Criticism of the Pythagorean and Platonic belief in a separately existing infinite.
204a 34. There is no infinite sensible body.
6. That the infinite exists and how it exists.
206b 33. What the infinite is.
7. The various kinds of infinite.
207b 34. Which of the four conditions of change the infinite is to be referred to.
8. Refutation of the arguments for an actual infinite.
BOOK IV
A. Place.
1. Does place exist?
209a 2. Doubts about the nature of place.
2. Is place matter or form?
3. Can a thing be in itself or a place be in a place?
4. What place is.
5. Corollaries.
B. The void.
6. The views of others about the void.
7. What ‘void’ means.
214a 16. Refutation of the arguments for belief in the void.
8. There is no void separate from bodies.
216a 26. There is no void occupied by any body.
9. There is no void in bodies.
C. Time.
10. Doubts about the existence of time.
218a 31. Various opinions about the nature of time.
11. What time is.
219b 9. The ‘now’.
12. Various attributes of time.
220b 32. The things that are in time.
13. Definitions of temporal terms.
14. Further reflections about time.
BOOK V
1. Classification of movements and changes.
224b 35. Classification of changes per se.
2. Classification of movements per se.
226b 10. The unmovable.
3. The meaning of ‘together’, ‘apart’, ‘touch’, ‘intermediate’, ‘successive’, ‘contiguous’,
‘continuous’.
4. The unity and diversity of movements.
5. Contrariety of movement.
6. Contrariety of movement and rest.
230a 18. Contrariety of natural and unnatural movement or rest.
BOOK VI
1, 2. Every continuum consists of continuous and divisible parts.
3. A moment is indivisible and nothing is moved, or rests, in a moment.
4. Whatever is moved is divisible.
234b 21. Classification of movement.
235a 13. The time, the movement, the being-in-motion, the moving body, and the sphere
of movement, are all similarly divided.
5. Whatever has changed is, as soon as it has changed, in that to which it has changed.
235b 32. That in which (directly) it has changed is indivisible.
236a 7. In change there is a last but no first element.
6. In whatever time a thing changes (directly), it changes in any part of that time.
236b 32. Whatever changes has changed before, and whatever has changed, before was
changing.
7. The finitude or infinity of movement, of extension, and of the moved.
8. Of coming to rest, and of rest.
239a 23. A thing that is moved in any time directly is in no part of that time in a part of
the space through which it moves.
9. Refutation of the arguments against the possibility of movement.
10. That which has not parts cannot move.
241a 26. Can change be infinite?
BOOK VII
1. Whatever is moved is moved by something.
242a 19. There is a first movent which is not moved by anything else.
2. The movent and the moved are together.
3. All alteration pertains to sensible qualities.
4. Comparison of movements.
5. Proportion of movements.
BOOK VIII
1. There always has been and always will be movement.
2. Refutation of objections to the eternity of movement.
3. There are things that are sometimes in movement, sometimes at rest.
4. Whatever is in movement is moved by something else.
5. The first movent is not moved by anything outside itself.
257a 31. The first movent is immovable.
6. The immovable first movent is eternal and one.
259a 20. The first movent is not moved even incidentally.
259b 32. The primum mobile is eternal.
7. Locomotion is the primary kind of movement.
261a 28. No movement or change is continuous except locomotion.
8. Only circular movement can be continuous and infinite.
9. Circular movement is the primary kind of locomotion.
265a 27. Confirmation of the above doctrines.
10. The first movent has no parts nor magnitude, and is at the circumference of the world.
PHYSICA1
(Physics)
BOOK I
1
[184a] When the objects of an inquiry, in any department, have
principles, (10) conditions, or elements, it is through acquaintance with
these that knowledge, that is to say scientific knowledge, is attained. For
we do not think that we know a thing until we are acquainted with its
primary conditions or first principles, and have carried our analysis as
far as its simplest elements. Plainly therefore in the science of Nature, (15)
as in other branches of study, our first task will be to try to determine
what relates to its principles.
The natural way of doing this is to start from the things which are
more knowable and obvious to us and proceed towards those which are
clearer and more knowable by nature; for the same things are not
‘knowable relatively to us’ and ‘knowable’ without qualification. So in
the present inquiry we must follow this method and advance from what
is more obscure by nature, (20) but clearer to us, towards what is more
clear and more knowable by nature.
Now what is to us plain and obvious at first is rather confused masses,
the elements and principles of which become known to us later by
analysis. Thus we must advance from generalities to particulars; for it is
a whole that is best known to sense-perception, (25) and a generality is a
kind of whole, comprehending many things within it, like parts.
[184b] Much the same thing happens in the relation of the name to the
formula. (10) A name, e. g. ‘round’, means vaguely a sort of whole: its
definition analyses this into its particular senses. Similarly a child begins
by calling all men ‘father’, and all women ‘mother’, but later on
distinguishes each of them.
2
The principles in question must be either (a) one or (b) more than
one. (15)
If (a) one, it must be either (i) motionless, as Parmenides and Melissus
assert, or (ii) in motion, as the physicists hold, some declaring air to be
the first principle, others water.
If (b) more than one, then either (i) a finite or (ii) an infinite plurality.
If (i) finite (but more than one), then either two or three or four or some
other number. (20) If (ii) infinite, then either as Democritus believed one
in kind, but differing in shape or form; or different in kind and even
contrary.
A similar inquiry is made by those who inquire into the number of
existents: for they inquire whether the ultimate constituents of existing
things are one or many, and if many, whether a finite or an infinite
plurality. So they too are inquiring whether the principle or element is
one or many.
Now to investigate whether Being is one and motionless is not a
contribution to the science of Nature. (25) For just as the geometer has
nothing more to say to one who denies the principles of his science—this
being a question for a different science or for one common to all—so a
man investigating principles cannot argue with one who denies their
existence. [185a] For if Being is just one, and one in the way
mentioned, there is a principle no longer, since a principle must be the
principle of some thing or things.
To inquire therefore whether Being is one in this sense would be like
arguing against any other position maintained for the sake of argument
(such as the Heraclitean thesis, (5) or such a thesis as that Being is one
man) or like refuting a merely contentious argument—a description
which applies to the arguments both of Melissus and of Parmenides:
their premisses are false and their conclusions do not follow. (10) Or
rather the argument of Melissus is gross and palpable and offers no
difficulty at all: accept one ridiculous proposition and the rest follows—a
simple enough proceeding.
We physicists, on the other hand, must take for granted that the things
that exist by nature are, either all or some of them, in motion—which is
indeed made plain by induction. Moreover, no man of science is bound
to solve every kind of difficulty that may be raised, (15) but only as many
as are drawn falsely from the principles of the science: it is not our
business to refute those that do not arise in this way: just as it is the duty
of the geometer to refute the squaring of the circle by means of
segments, but it is not his duty to refute Antiphon’s proof.2 At the same
time the holders of the theory of which we are speaking do incidentally
raise physical questions, though Nature is not their subject: so it will
perhaps be as well to spend a few words on them, especially as the
inquiry is not without scientific interest.
The most pertinent question with which to begin will be this: (20) In
what sense is it asserted that all things are one? For ‘is’ is used in many
senses. Do they mean that all things ‘are’ substance or quantities or
qualities? And, further, are all things one substance—one man, (25) one
horse, or one soul—or quality and that one and the same—white or hot
or something of the kind? These are all very different doctrines and all
impossible to maintain.
For if both substance and quantity and quality are, then, whether these
exist independently of each other or not, Being will be many.
If on the other hand it is asserted that all things are quality or
quantity, then, whether substance exists or not, an absurdity results, (30)
if indeed the impossible can properly be called absurd. For none of the
others can exist independently: substance alone is independent: for
everything is predicated of substance as subject. Now Melissus says that
Being is infinite. It is then a quantity. For the infinite is in the category
of quantity, whereas substance or quality or affection cannot be infinite
except through a concomitant attribute, that is, if at the same time they
are also quantities. [185b] For to define the infinite you must use
quantity in your formula, but not substance or quality. If then Being is
both substance and quantity, it is two, not one: if only substance, it is
not infinite and has no magnitude; for to have that it will have to be a
quantity.
Again, (5) ‘one’ itself, no less than ‘being’, is used in many senses, so we
must consider in what sense the word is used when it is said that the All
is one.
Now we say that (a) the continuous is one or that (b) the indivisible is
one, or (c) things are said to be ‘one’, when their essence is one and the
same, as ‘liquor’ and ‘drink’.
If (a) their One is one in the sense of continuous, it is many, (10) for the
continuous is divisible ad infinitum.
There is, indeed, a difficulty about part and whole, perhaps not
relevant to the present argument, yet deserving consideration on its own
account—namely, whether the part and the whole are one or more than
one, and how they can be one or many, and, if they are more than one,
in what sense they are more than one. (Similarly with the parts of
wholes which are not continuous.) (15) Further, if each of the two parts is
indivisibly one with the whole, the difficulty arises that they will be
indivisibly one with each other also.
But to proceed: If (b) their One is one as indivisible, nothing will have
quantity or quality, and so the one will not be infinite, as Melissus says
—nor, indeed, limited, as Parmenides says, for though the limit is
indivisible, the limited is not.3
But if (c) all things are one in the sense of having the same definition,
like ‘raiment’ and ‘dress’, then it turns out that they are maintaining the
Heraclitean doctrine, (20) for it will be the same thing ‘to be good’ and ‘to
be bad’, and ‘to be good’ and ‘to be not good’, and so the same thing will
be ‘good’ and ‘not good’, and man and horse; in fact, their view will be,
not that all things are one, but that they are nothing; and that ‘to be of
such-and-such a quality’ is the same as ‘to be of such-and-such a size’.
Even the more recent of the ancient thinkers were in a pother lest the
same thing should turn out in their hands both one and many. (25) So
some, like Lycophron,4 were led to omit ‘is’, others to change the mode
of expression and say ‘the man has been whitened’ instead of ‘is white’,
and ‘walks’ instead of ‘is walking’, for fear that if they added the word
‘is’ they should be making the one to be many—as if ‘one’ and ‘being’
were always used in one and the same sense. (30) What ‘is’ may be many
either in definition (for example ‘to be white’ is one thing, ‘to be
musical’ another, yet the same thing may be both, so the one is many) or
by division, as the whole and its parts. [186a] On this point, indeed,
they were already getting into difficulties and admitted that the one was
many—as if there was any difficulty about the same thing being both
one and many, provided that these are not opposites; for ‘one’ may mean
either ‘potentially one’ or ‘actually one’.
3
If, then, we approach the thesis in this way it seems impossible for
all things to be one. Further, the arguments they use to prove their
position are not difficult to expose. (5) For both of them reason
contentiously—I mean both Melissus and Parmenides. Their premisses
are false and their conclusions do not follow. Or rather the argument of
Melissus is gross and palpable and offers no difficulty at all: admit one
ridiculous proposition and the rest follows—a simple enough proceeding.
The fallacy of Melissus is obvious. (10) For he supposes that the
assumption ‘what has come into being always has a beginning’ justifies
the assumption ‘what has not come into being has no beginning’. Then
this also is absurd, that in every case there should be a beginning of the
thing—not of the time and not only in the case of coming to be in the full
sense but also in the case of coming to have a quality—as if change
never took place suddenly. (15) Again, does it follow that Being, if one, is
motionless? Why should it not move, the whole of it within itself, as
parts of it do which are unities, e. g. this water? Again, why is
qualitative change impossible? But, (20) further, Being cannot be one in
form, though it may be in what it is made of. (Even some of the
physicists hold it to be one in the latter way, though not in the former.)
Man obviously differs from horse in form, and contraries from each
other.
The same kind of argument holds good against Parmenides also,
besides any that may apply specially to his view: the answer to him
being that ‘this is not true’ and ‘that does not follow’. His assumption that
one is used in a single sense only is false, (25) because it is used in several.
His conclusion does not follow, because if we take only white things, and
if ‘white’ has a single meaning, none the less what is white will be many
and not one. For what is white will not be one either in the sense that it
is continuous or in the sense that it must be defined in only one way.
‘Whiteness’ will be different from ‘what has whiteness’. Nor does this
mean that there is anything that can exist separately, (30) over and above
what is white. For ‘whiteness’ and ‘that which is white’ differ in
definition, not in the sense that they are things which can exist apart
from each other. But Parmenides had not come in sight of this
distinction.
It is necessary for him, then, to assume not only that ‘being’ has the
same meaning, of whatever it is predicated, but further that it means (1)
what just is and (2) what is just one.
It must be so, for (1) an attribute is predicated of some subject, (35) so
that the subject to which ‘being’ is attributed will not be, as it is
something different from ‘being’. [186b] Something, therefore, which
is not will be. Hence ‘substance’ will not be a predicate of anything else.
For the subject cannot be a being, unless ‘being’ means several things, in
such a way that each is something. But ex hypothesi ‘being’ means only
one thing.
If, then, ‘substance’ is not attributed to anything, but other things are
attributed to it, how does ‘substance’ mean what is rather than what is
not? For suppose that ‘substance’ is also ‘white’. (5) Since the definition of
the latter is different (for being cannot even be attributed to white, as
nothing is which is not ‘substance’), it follows that ‘white’ is not-being—
and that not in the sense of a particular not-being, but in the sense that
it is not at all. Hence ‘substance’ is not; for it is true to say that it is
white, (10) which we found to mean not-being. If to avoid this we say that
even ‘white’ means substance, it follows that ‘being’ has more than one
meaning.
In particular, then, Being will not have magnitude, if it is substance.
For each of the two parts must be in a different sense.
(2) Substance is plainly divisible into other substances, if we consider
the mere nature of a definition. For instance, if ‘man’ is a substance, (15)
‘animal’ and ‘biped’ must also be substances. For if not substances, they
must be attributes—and if attributes, attributes either of (a) man or of
(b) some other subject. But neither is possible.
(a) An attribute is either that which may or may not belong to the
subject or that in whose definition the subject of which it is an attribute
is involved. (20) Thus ‘sitting’ is an example of a separable attribute,
while ‘snubness’ contains the definition of ‘nose’, to which we attribute
snubness. Further, the definition of the whole is not contained in the
definitions of the contents or elements of the definitory formula; that of
‘man’ for instance in ‘biped’, or that of ‘white man’ in ‘white’. If then this
is so, and if ‘biped’ is supposed to be an attribute of ‘man’, (25) it must be
either separable, so that ‘man’ might possibly not be ‘biped’, or the
definition of ‘man’ must come into the definition of ‘biped’—which is
impossible, as the converse is the case. (30)
(b) If, on the other hand, we suppose that ‘biped’ and ‘animal’ are
attributes not of man but of something else, and are not each of them a
substance, then ‘man’ too will be an attribute of something else. But we
must assume that substance is not the attribute of anything, and that the
subject of which both ‘biped’ and ‘animal’ and each separately are
predicated is the subject also of the complex ‘biped animal’.
Are we then to say that the All is composed of indivisible substances?
Some thinkers did, (35) in point of fact, give way to both arguments.
[187a] To the argument that all things are one if being means one
thing, they conceded that not-being is; to that from bisection, they
yielded by positing atomic magnitudes. But obviously it is not true that
if being means one thing, and cannot at the same time mean the
contradictory of this, (5) there will be nothing which is not, for even if
what is not cannot be without qualification, there is no reason why it
should not be a particular not-being. To say that all things will be one, if
there is nothing besides Being itself, is absurd. For who understands
‘being itself’ to be anything but a particular substance? But if this is so,
there is nothing to prevent there being many beings, as has been said.
It is, (10) then, clearly impossible for Being to be one in this sense.
4
The physicists on the other hand have two modes of explanation.
The first set make the underlying body one—either one of the three5
or something else which is denser than fire and rarer than air—then
generate everything else from this, (15) and obtain multiplicity by
condensation and rarefaction. Now these are contraries, which may be
generalized into ‘excess and defect’. (Compare Plato’s ‘Great and
Small’—except that he makes these his matter, the one his form, while
the others treat the one which underlies as matter and the contraries as
differentiae, i. e. forms.)
The second set assert that the contrarieties are contained in the one
and emerge from it by segregation, (20) for example Anaximander and
also all those who assert that ‘what is’ is one and many, like Empedocles
and Anaxagoras; for they too produce other things from their mixture by
segregation. These differ, however, from each other in that the former
imagines a cycle of such changes, the latter a single series. (25)
Anaxagoras again made both his ‘homœomerous’ substances and his
contraries infinite in multitude, whereas Empedocles posits only the socalled elements.
The theory of Anaxagoras that the principles are infinite in multitude
was probably due to his acceptance of the common opinion of the
physicists that nothing comes into being from not-being. (30) For this is
the reason why they use the phrase ‘all things were together’ and the
coming into being of such and such a kind of thing is reduced to change
of quality, while some spoke of combination and separation. Moreover,
the fact that the contraries proceed from each other led them to the
conclusion. The one, they reasoned, must have already existed in the
other; for since everything that comes into being must arise either from
what is or from what is not, and it is impossible for it to arise from what
is not (on this point all the physicists agree), (35) they thought that the
truth of the alternative necessarily followed, namely that things come
into being out of existent things, i. e. out of things already present, but
imperceptible to our senses because of the smallness of their bulk.
[187b] So they assert that everything has been mixed in everything,
because they saw everything arising out of everything. But things, as
they say, appear different from one another and receive different names
according to the nature of the particles which are numerically
predominant among the innumerable constituents of the mixture. For
nothing, they say, is purely and entirely white or black or sweet, bone or
flesh, but the nature of a thing is held to be that of which it contains the
most. (5)
Now (1) the infinite qua infinite is unknowable, so that what is infinite
in multitude or size is unknowable in quantity, and what is infinite in
variety of kind is unknowable in quality. (10) But the principles in
question are infinite both in multitude and in kind. Therefore it is
impossible to know things which are composed of them; for it is when
we know the nature and quantity of its components that we suppose we
know a complex.
Further (2) if the parts of a whole may be of any size in the direction
either of greatness or of smallness (by ‘parts’ I mean components into
which a whole can be divided and which are actually present in it), (15) it
is necessary that the whole thing itself may be of any size. Clearly,
therefore, since it is impossible for an animal or plant to be indefinitely
big or small, neither can its parts be such, or the whole will be the same.
But flesh, bone, and the like are the parts of animals, and the fruits are
the parts of plants. Hence it is obvious that neither flesh, (20) bone, nor
any such thing can be of indefinite size in the direction either of the
greater or of the less.
Again (3) according to the theory all such things are already present in
one another and do not come into being but are constituents which are
separated out, and a thing receives its designation from its chief
constituent. Further, anything may come out of anything—water by
segregation from flesh and flesh from water. Hence, (25) since every finite
body is exhausted by the repeated abstraction of a finite body, it seems
obviously to follow that everything cannot subsist in everything else. For
let flesh be extracted from water and again more flesh be produced from
the remainder by repeating the process of separation: then, even though
the quantity separated out will continually decrease, still it will not fall
below a certain magnitude. If, (30) therefore, the process comes to an end,
everything will not be in everything else (for there will be no flesh in the
remaining water); if on the other hand it does not, and further extraction
is always possible, there will be an infinite multitude of finite equal
particles in a finite quantity—which is impossible. Another proof may be
added: Since every body must diminish in size when something is taken
from it, (35) and flesh is quantitatively definite in respect both of
greatness and smallness, it is clear that from the minimum quantity of
flesh no body can be separated out; for the flesh left would be less than
the minimum of flesh. [188a]
Lastly (4) in each of his infinite bodies there would be already present
infinite flesh and blood and brain—having a distinct existence, however,
from one another, and no less real than the infinite bodies, and each
infinite: which is contrary to reason.
The statement that complete separation never will take place is correct
enough, (5) though Anaxagoras is not fully aware of what it means. For
affections are indeed inseparable. If then colours and states had entered
into the mixture, and if separation took place, there would be a ‘white’
or a ‘healthy’ which was nothing but white or healthy, i. e. was not the
predicate of a subject. So his ‘Mind’ is an absurd person aiming at the
impossible, (10) if he is supposed to wish to separate them, and it is
impossible to do so, both in respect of quantity and of quality—of
quantity, because there is no minimum magnitude, and of quality,
because affections are inseparable.
Nor is Anaxagoras right about the coming to be of homogeneous
bodies. It is true there is a sense in which clay is divided into pieces of
clay, (15) but there is another in which it is not. Water and air are, and
are generated, ‘from’ each other, but not in the way in which bricks
come ‘from’ a house and again a house ‘from’ bricks; and it is better to
assume a smaller and finite number of principles, as Empedocles does.
5
All thinkers then agree in making the contraries principles, both
those who describe the All as one and unmoved (for even Parmenides
treats hot and cold as principles under the names of fire and earth) and
those too who use the rare and the dense. (20) The same is true of
Democritus also, with his plenum and void, both of which exist, he says,
the one as being, the other as not-being. Again he speaks of differences
in position, shape, and order, and these are genera of which the species
are contraries, namely, of position, (25) above and below, before and
behind; of shape, angular and angle-less, straight and round.
It is plain then that they all in one way or another identify the
contraries with the principles. And with good reason. For first principles
must not be derived from one another nor from anything else, while
everything has to be derived from them. But these conditions are
fulfilled by the primary contraries, which are not derived from anything
else because they are primary, nor from each other because they are
contraries.
But we must see how this can be arrived at as a reasoned result, (30) as
well as in the way just indicated.
Our first presupposition must be that in nature nothing acts on, or is
acted on by, any other thing at random, nor may anything come from
anything else, unless we mean that it does so in virtue of a concomitant
attribute. For how could ‘white’ come from ‘musical’, (35) unless ‘musical’
happened to be an attribute of the not-white or of the black? No, ‘white’
comes from ‘not-white’—and not from any ‘not-white’, but from black or
some intermediate colour. [188b] Similarly, ‘musical’ comes to be from
‘not-musical’, but not from any thing other than musical, but from
‘unmusical’ or any intermediate state there may be.
Nor again do things pass into the first chance thing; ‘white’ does not
pass into ‘musical’ (except, it may be, in virtue of a concomitant
attribute), but into ‘not-white’—and not into any chance thing which is
not white, but into black or an intermediate colour; ‘musical’ passes into
‘not-musical’—and not into any chance thing other than musical, (5) but
into ‘unmusical’ or any intermediate state there may be.
The same holds of other things also: even things which are not simple
but complex follow the same principle, (10) but the opposite state has not
received a name, so we fail to notice the fact. What is in tune must come
from what is not in tune, and vice versa; the tuned passes into
untunedness—and not into any untunedness, but into the corresponding
opposite. It does not matter whether we take attunement, (15) order, or
composition for our illustration; the principle is obviously the same in
all, and in fact applies equally to the production of a house, a statue, or
any other complex. A house comes from certain things in a certain state
of separation instead of conjunction, a statue (or any other thing that has
been shaped) from shapelessness—each of these objects being partly
order and partly composition. (20)
If then this is true, everything that comes to be or passes away comes
from, or passes into, its contrary or an intermediate state. But the
intermediates are derived from the contraries—colours, for instance,
from black and white. Everything, (25) therefore, that comes to be by a
natural process is either a contrary or a product of contraries.
Up to this point we have practically had most of the other writers on
the subject with us, as I have said already6: for all of them identify their
elements, and what they call their principles, with the contraries, giving
no reason indeed for the theory, (30) but constrained as it were by the
truth itself. They differ, however, from one another in that some assume
contraries which are more primary, others contraries which are less so:
some those more knowable in the order of explanation, others those
more familiar to sense. For some make hot and cold, or again moist and
dry, the conditions of becoming; while others make odd and even, (35) or
again Love and Strife; and these differ from each other in the way
mentioned.
Hence their principles are in one sense the same, in another different;
different certainly, as indeed most people think, but the same inasmuch
as they are analogous; for all are taken from the same table of columns,7
some of the pairs being wider, others narrower in extent. [189a] In
this way then their theories are both the same and different, some better,
some worse; some, as I have said, take as their contraries what is more
knowable in the order of explanation, (5) others what is more familiar to
sense. (The universal is more knowable in the order of explanation, the
particular in the order of sense: for explanation has to do with the
universal, sense with the particular.) ‘The great and the small’, for
example, belong to the former class, ‘the dense and the rare’ to the
latter.
It is clear then that our principles must be contraries. (10)
6 The next question is whether the principles are two or three or more
in number.
One they cannot be, for there cannot be one contrary. Nor can they be
innumerable, because, if so, Being will not be knowable: and in any one
genus there is only one contrariety, (15) and substance is one genus: also
a finite number is sufficient, and a finite number, such as the principles
of Empedocles, is better than an infinite multitude; for Empedocles
professes to obtain from his principles all that Anaxagoras obtains from
his innumerable principles. Lastly, some contraries are more primary
than others, and some arise from others—for example sweet and bitter,
white and black—whereas the principles must always remain principles.
This will suffice to show that the principles are neither one nor
innumerable. (20)
Granted, then, that they are a limited number, it is plausible to
suppose them more than two. For it is difficult to see how either density
should be of such a nature as to act in any way on rarity or rarity on
density. The same is true of any other pair of contraries; for Love does
not gather Strife together and make things out of it, (25) nor does Strife
make anything out of Love, but both act on a third thing different from
both. Some indeed assume more than one such thing from which they
construct the world of nature.
Other objections to the view that it is not necessary to assume a third
principle as a substratum may be added. (1) We do not find that the
contraries constitute the substance of any thing. (30) But what is a first
principle ought not to be the predicate of any subject. If it were, there
would be a principle of the supposed principle: for the subject is a
principle, and prior presumably to what is predicated of it. Again (2) we
hold that a substance is not contrary to another substance. How then can
substance be derived from what are not substances? Or how can nonsubstance be prior to substance?
If then we accept both the former argument8 and this one,9 we must,
to preserve both, assume a third somewhat as the substratum of the
contraries, (35) such as is spoken of by those who describe the All as one
nature—water or fire or what is intermediate between them. [189b]
What is intermediate seems preferable; for fire, earth, air, and water are
already involved with pairs of contraries. There is, therefore, much to be
said for those who make the underlying substance different from these
four; of the rest, the next best choice is air, as presenting sensible
differences in a less degree than the others; and after air, water. All,
however, agree in this, that they differentiate their One by means of the
contraries, such as density and rarity and more and less, (10) which may
of course be generalized, as has already been said,10 into excess and
defect. Indeed this doctrine too (that the One and excess and defect are
the principles of things) would appear to be of old standing, though in
different forms; for the early thinkers made the two the active and the
one the passive principle, whereas some of the more recent maintain the
reverse. (15)
To suppose then that the elements are three in number would seem,
from these and similar considerations, a plausible view, as I said
before.11 On the other hand, the view that they are more than three in
number would seem to be untenable.
For the one substratum is sufficient to be acted on; but if we have four
contraries, there will be two contrarieties, and we shall have to suppose
an intermediate nature for each pair separately. (20) If, on the other hand,
the contrarieties, being two, can generate from each other, the second
contrariety will be superfluous. Moreover, it is impossible that there
should be more than one primary contrariety. For substance is a single
genus of being, so that the principles can differ only as prior and
posterior, (25) not in genus; in a single genus there is always a single
contrariety, all the other contrarieties in it being held to be reducible to
one.
It is clear then that the number of elements is neither one nor more
than two or three; but whether two or three is, as I said, a question of
considerable difficulty.
7
We will now give our own account, (30) approaching the question
first with reference to becoming in its widest sense: for we shall be
following the natural order of inquiry if we speak first of common
characteristics, and then investigate the characteristics of special cases.
We say that one thing comes to be from another thing, and one sort of
thing from another sort of thing, both in the case of simple and of
complex things. I mean the following. We can say (1) the ‘man becomes
musical’, (35) (2) what is ‘not-musical becomes musical’, or (3) the ‘notmusical man becomes a musical man’. [190a] Now what becomes in
(1) and (2)—‘man’ and ‘not musical’—I call simple, and what each
becomes—‘musical’—simple also. But when (3) we say the ‘not-musical
man becomes a musical man’, both what becomes and what it becomes
are complex.
As regards one of these simple ‘things that become’ we say not only
‘this becomes so-and-so’, (5) but also ‘from being this, comes to be so-andso’, as ‘from being not-musical comes to be musical’; as regards the other
we do not say this in all cases, as we do not say (1) ‘from being a man he
came to be musical’ but only ‘the man became musical’.
When a ‘simple’ thing is said to become something, in one case (1) it
survives through the process, in the other (2) it does not. (10) For the man
remains a man and is such even when he becomes musical, whereas
what is not musical or is unmusical does not continue to exist, either
simply or combined with the subject.
These distinctions drawn, one can gather from surveying the various
cases of becoming in the way we are describing that, as we say, there
must always be an underlying something, namely that which becomes,
(15) and that this, though always one numerically, in form at least is not
one. (By that I mean that It can be described in different ways.) For ‘to
be man’ is not the same as ‘to be unmusical’. One part survives, the other
does not: what is not an opposite survives (for ‘man’ survives), but ‘notmusical’ or ‘unmusical’ does not survive, (20) nor does the compound of
the two, namely ‘unmusical man’.
We speak of ‘becoming that from this’ instead of ‘this becoming that’
more in the case of what does not survive the change—‘becoming
musical from unmusical’, not ‘from man’—but there are exceptions, as
we sometimes use the latter form of expression even of what survives;
we speak of ‘a statue coming to be from bronze’, (25) not of the ‘bronze
becoming a statue’. The change, however, from an opposite which does
not survive is described indifferently in both ways, ‘becoming that from
this’ or ‘this becoming that’. We say both that ‘the unmusical becomes
musical’, and that ‘from unmusical he becomes musical’. (30) And so both
forms are used of the complex, ‘becoming a musical man from an
unmusical man’, and ‘an unmusical man becoming a musical man’.
But there are different senses of ‘coming to be’. In some cases we do
not use the expression ‘come to be’, but ‘come to be so-and-so’. Only
substances are said to ‘come to be’ in the unqualified sense.
Now in all cases other than substance it is plain that there must be
some subject, namely, that which becomes. For we know that when a
thing comes to be of such a quantity or quality or in such a relation, (35)
time, or place, a subject is always presupposed, since substance alone is
not predicated of another subject, but everything else of substance.
But that substances too, and anything else that can be said ‘to be’
without qualification, come to be from some substratum, will appear on
examination. [190b] For we find in every case something that
underlies from which proceeds that which comes to be; for instance,
animals and plants from seed.
Generally things which come to be, come to be in different ways: (1)
by change of shape, (5) as a statue; (2) by addition, as things which grow;
(3) by taking away, as the Hermes from the stone; (4) by putting
together, as a house; (5) by alteration, as things which ‘turn’ in respect
of their material substance.
It is plain that these are all cases of coming to be from a substratum.
Thus, clearly, from what has been said, whatever comes to be is
always complex. (10) There is, on the one hand, (a) something which
comes into existence, and again (b) something which becomes that—the
latter (b) in two senses, either the subject or the opposite. By the
‘opposite’ I mean the ‘unmusical’, by the ‘subject’ ‘man’, and similarly I
call the absence of shape or form or order the ‘opposite’, (15) and the
bronze or stone or gold the ‘subject’.
Plainly then, if there are conditions and principles which constitute
natural objects and from which they primarily are or have come to be—
have come to be, I mean, what each is said to be in its essential nature,
not what each is in respect of a concomitant attribute—plainly, (20) I say,
everything comes to be from both subject and form. For ‘musical man’ is
composed (in a way) of ‘man’ and ‘musical’: you can analyse it into the
definitions of its elements. It is clear then that what comes to be will
come to be from these elements.
Now the subject is one numerically, though it is two in form. (For it is
the man, the gold—the ‘matter’ generally—that is counted, (25) for it is
more of the nature of a ‘this’, and what comes to be does not come from
it in virtue of a concomitant attribute; the privation, on the other hand,
and the contrary are incidental in the process.) And the positive form is
one—the order, the acquired art of music, or any similar predicate.
There is a sense, therefore, in which we must declare the principles to
be two, and a sense in which they are three; a sense in which the
contraries are the principles—say for example the musical and the
unmusical, (30) the hot and the cold, the tuned and the untuned—and a
sense in which they are not, since it is impossible for the contraries to be
acted on by each other. But this difficulty also is solved by the fact that
the substratum is different from the contraries, (35) for it is itself not a
contrary. The principles therefore are, in a way, not more in number
than the contraries, but as it were two, nor yet precisely two, since there
is a difference of essential nature, but three. [191a] For ‘to be man’ is
different from ‘to be unmusical’, and ‘to be unformed’ from ‘to be
bronze’.
We have now stated the number of the principles of natural objects
which are subject to generation, and how the number is reached: and it
is clear that there must be a substratum for the contraries, (5) and that
the contraries must be two. (Yet in another way of putting it this is not
necessary, as one of the contraries will serve to effect the change by its
successive absence and presence.)
The underlying nature is an object of scientific knowledge, by an
analogy. For as the bronze is to the statue, the wood to the bed, (10) or
the matter and the formless before receiving form to any thing which
has form, so is the underlying nature to substance, i. e. the ‘this’ or
existent.
This then is one principle (though not one or existent in the same
sense as the ‘this’), and the definition was one as we agreed; then further
there is its contrary, the privation. In what sense these are two, (15) and
in what sense more, has been stated above. Briefly, we explained first12
that only the contraries were principles, and later13 that a substratum
was indispensable, and that the principles were three; our last
statement14 has elucidated the difference between the contraries, the
mutual relation of the principles, and the nature of the substratum.
Whether the form or the substratum is the essential nature of a physical
object is not yet clear.15 But that the principles are three, (20) and in what
sense, and the way in which each is a principle, is clear.
So much then for the question of the number and the nature of the
principles.
8
We will now proceed to show that the difficulty of the early
thinkers, as well as our own, is solved in this way alone.
The first of those who studied science were misled in their search for
truth and the nature of things by their inexperience, (25) which as it were
thrust them into another path. So they say that none of the things that
are either comes to be or passes out of existence, because what comes to
be must do so either from what is or from what is not, both of which are
impossible. For what is cannot come to be (because it is already), (30) and
from what is not nothing could have come to be (because something
must be present as a substratum). So too they exaggerated the
consequence of this, and went so far as to deny even the existence of a
plurality of things, maintaining that only Being itself is. Such then was
their opinion, and such the reason for its adoption.
Our explanation on the other hand is that the phrases ‘something
comes to be from what is or from what is not’, ‘what is not or what is
does something or has something done to it or becomes some particular
thing’, (35) are to be taken (in the first way of putting our explanation) in
the same sense as ‘a doctor does something or has something done to
him’, ‘is or becomes something from being a doctor’. [191b] These
expressions may be taken in two senses, and so too, clearly, may ‘from
being’, and ‘being acts or is acted on’. A doctor builds a house, not qua
doctor, but qua housebuilder, and turns gray, (5) not qua doctor, but qua
dark-haired. On the other hand he doctors or fails to doctor qua doctor.
But we are using words most appropriately when we say that a doctor
does something or undergoes something, or becomes something from
being a doctor, if he does, undergoes, or becomes qua doctor. Clearly
then also ‘to come to be so-and-so from not-being’ means ‘qua not-being’.
It was through failure to make this distinction that those thinkers gave
the matter up, (10) and through this error that they went so much farther
astray as to suppose that nothing else comes to be or exists apart from
Being itself, thus doing away with all becoming.
We ourselves are in agreement with them in holding that nothing can
be said without qualification to come from what is not. But nevertheless
we maintain that a thing may ‘come to be from what is not’—that is, (15)
in a qualified sense. For a thing comes to be from the privation, which in
its own nature is not-being—this not surviving as a constituent of the
result. Yet this causes surprise, and it is thought impossible that
something should come to be in the way described from what is not.
In the same way we maintain that nothing comes to be from being,
and that being does not come to be except in a qualified sense. In that
way, however, it does, just as animal might come to be from animal, (20)
and an animal of a certain kind from an animal of a certain kind. Thus,
suppose a dog to come to be from a horse. The dog would then, it is
true, come to be from animal (as well as from an animal of a certain
kind) but not as animal, for that is already there. But if anything is to
become an animal, not in a qualified sense, (25) it will not be from
animal: and if being, not from being—nor from not-being either, for it
has been explained16 that by ‘from not-being’ we mean from not-being
qua not-being.
Note further that we do not subvert the principle that everything
either is or is not.
This then is one way of solving the difficulty. Another consists in
pointing out that the same things can be explained in terms of
potentiality and actuality. But this has been done with greater precision
elsewhere.17
So as we said, (30) the difficulties which constrain people to deny the
existence of some of the things we mentioned are now solved. For it was
this reason which also caused some of the earlier thinkers to turn so far
aside from the road which leads to coming to be and passing away and
change generally. If they had come in sight of this nature, all their
ignorance would have been dispelled.
9
Others,18 (35) indeed, have apprehended the nature in question, but
not adequately.
In the first place they allow that a thing may come to be without
qualification from not-being, accepting on this point the statement19 of
Parmenides. [192a] Secondly, they think that if the substratum is one
numerically, it must have also only a single potentiality—which is a very
different thing.
Now we distinguish matter and privation, and hold that one of these,
namely the matter, is not-being only in virtue of an attribute which it
has, while the privation in its own nature is not-being; and that the
matter is nearly, in a sense is, substance, (5) while the privation in no
sense is. They, on the other hand, identify their Great and Small alike
with not-being, and that whether they are taken together as one or
separately. Their triad is therefore of quite a different kind from ours.
For they got so far as to see that there must be some underlying nature,
(10) but they make it one—for even if one philosopher20 makes a dyad of
it, which he calls Great and Small, the effect is the same, for he
overlooked the other nature.21 For the one which persists is a joint
cause, with the form, of what comes to be—a mother, as it were.22 But
the negative part of the contrariety may often seem, (15) if you
concentrate your attention on it as an evil agent, not to exist at all.
For admitting with them that there is something divine, good, and
desirable, we hold that there are two other principles, the one contrary
to it, the other such as of its own nature to desire and yearn for it. But
the consequence of their view is that the contrary desires its own
extinction. Yet the form cannot desire itself, for it is not defective; nor
can the contrary desire it, (20) for contraries are mutually destructive. The
truth is that what desires the form is matter, as the female desires the
male and the ugly the beautiful—only the ugly or the female not per se
but per accidens.
The matter comes to be and ceases to be in one sense, (25) while in
another it does not. As that which contains the privation, it ceases to be
in its own nature, for what ceases to be—the privation—is contained
within it. But as potentiality it does not cease to be in its own nature,
but is necessarily outside the sphere of becoming and ceasing to be. For
if it came to be, something must have existed as a primary substratum
from which it should come and which should persist in it; but this is its
own special nature, so that it will be before coming to be. (30) (For my
definition of matter is just this—the primary substratum of each thing,
from which it comes to be without qualification, and which persists in
the result.) And if it ceases to be it will pass into that at the last, so it
will have ceased to be before ceasing to be.
The accurate determination of the first principle in respect of form,
whether it is one or many and what it is or what they are, (35) is the
province of the primary type of science;23 so these questions may stand
over till then.24 [192b] But of the natural, i. e. perishable, forms we
shall speak in the expositions which follow.
The above, then, may be taken as sufficient to establish that there are
principles and what they are and how many there are. Now let us make
a fresh start and proceed.
1
The present treatise, usually called the Physics, deals with natural body in general: the special
kinds are discussed in Aristotle’s other physical works, the De Caelo, &c. The first book is
concerned with the elements of a natural body (matter and form): the second mainly with the
different types of cause studied by the physicist. Books III–VII deal with movement, and the
notions implied in it. The subject of VIII is the prime mover, which, though not itself a natural
body, is the cause of movement in natural bodies.
2
The former method was suggested by Hippocrates of Chios, and rested on the rather obvious
geometrical fallacy of supposing that if a particular kind of lunule can be squared, another kind
can be squared also. Antiphon’s method was that of exhaustion. He drew a square in the circle,
and then isosceles triangles on its sides, and so on, and inferred that ultimately the inscribed
polygon was equal in area to the circle. This involves a denial of the geometrical principle that
every geometrical magnitude can be divided ad infinitum, and gives only an approximate result.
3
e. g. a point which terminates a line is indivisible, though the line is not.
4
An orator and a pupil of Gorgias.
5
Water, air, or fire. Aristotle points out elsewhere (Met. A. 988b 30) that no one made earth the
substratum.
6 a19–30.
7
The table is given in Met. A. 986a 23.
8
That the contraries are principles (ch. 5).
9
That the contraries need a substratum (ll. 21–34).
10
187a 16.
11 a21.
12
Ch. 5.
13
Ch. 6.
14
Ch. 7.
15
This is discussed below, Bk. II, Ch. 1.
16
l. 9.
17
Met. Bk. ix, and v. 1017a 35−b 9.
18
The Platonists.
19
That if a thing does not come to be from being, it must come to be from not-being.
20
Plato.
21
The privation.
22
Cf. Tim. 50 D, 51. A.
23
Metaphysics or ‘First philosophy’ as it is often called.
24
Met. xii 7–9.
BOOK II
1
Of things that exist, some exist by nature, some from other causes.
‘By nature’ the animals and their parts exist, (10) and the plants and the
simple bodies (earth, fire, air, water)—for we say that these and the like
exist ‘by nature’.
All the things mentioned present a feature in which they differ from
things which are not constituted by nature. Each of them has within itself
a principle of motion and of stationariness (in respect of place, (15) or of
growth and decrease, or by way of alteration). On the other hand, a bed
and a coat and anything else of that sort, qua receiving these
designations—i. e. in so far as they are products of art—have no innate
impulse to change. But in so far as they happen to be composed of stone
or of earth or of a mixture of the two, (20) they do have such an impulse,
and just to that extent—which seems to indicate that nature is a source or
cause of being moved and of being at rest in that to which it belongs
primarily, in virtue of itself and not in virtue of a concomitant attribute.
I say ‘not in virtue of a concomitant attribute’, because (for instance) a
man who is a doctor might cure himself. (25) Nevertheless it is not in so
far as he is a patient that he possesses the art of medicine: it merely has
happened that the same man is doctor and patient—and that is why
these attributes are not always found together. So it is with all other
artificial products. None of them has in itself the source of its own
production. But while in some cases (for instance houses and the other
products of manual labour) that principle is in something else external to
the thing, (30) in others—those which may cause a change in themselves
in virtue of a concomitant attribute—it lies in the things themselves (but
not in virtue of what they are).
‘Nature’ then is what has been stated. Things ‘have a nature’ which
have a principle of this kind. Each of them is a substance; for it is a
subject, and nature always implies a subject in which it inheres.
The term ‘according to nature’ is applied to all these things and also to
the attributes which belong to them in virtue of what they are, (35) for
instance the property of fire to be carried upwards—which is not a
‘nature’ nor ‘has a nature’ but is ‘by nature’ or ‘according to nature’.
What nature is, then, and the meaning of the terms ‘by nature’ and
‘according to nature’, has been stated. [193a] That nature exists, it
would be absurd to try to prove; for it is obvious that there are many
things of this kind, and to prove what is obvious by what is not is the
mark of a man who is unable to distinguish what is self-evident from
what is not. (5) (This state of mind is clearly possible. A man blind from
birth might reason about colours. Presumably therefore such persons
must be talking about words without any thought to correspond.)
Some identify the nature or substance of a natural object with that
immediate constituent of it which taken by itself is without arrangement,
(10) e. g. the wood is the ‘nature’ of the bed, and the bronze the ‘nature’
of the statue.
As an indication of this Antiphon points out that if you planted a bed
and the rotting wood acquired the power of sending up a shoot, it would
not be a bed that would come up, but wood—which shows that the
arrangement in accordance with the rules of the art is merely an
incidental attribute, (15) whereas the real nature is the other, which,
further, persists continuously through the process of making.
But if the material of each of these objects has itself the same relation
to something else, say bronze (or gold) to water, bones (or wood) to
earth and so on, that (they say) would be their nature and essence. (20)
Consequently some assert earth, others fire or air or water or some or all
of these, to be the nature of the things that are. For whatever any one of
them supposed to have this character—whether one thing or more than
one thing—this or these he declared to be the whole of substance, (25) all
else being its affections, states, or dispositions. Every such thing they
held to be eternal (for it could not pass into anything else), but other
things to come into being and cease to be times without number.
This then is one account of ‘nature’, namely that it is the immediate
material substratum of things which have in themselves a principle of
motion or change.
Another account is that ‘nature’ is the shape or form which is specified
in the definition of the thing. (30)
For the word ‘nature’ is applied to what is according to nature and the
natural in the same way as ‘art’ is applied to what is artistic or a work of
art. We should not say in the latter case that there is anything artistic
about a thing, if it is a bed only potentially, not yet having the form of a
bed; nor should we call it a work of art. (35) The same is true of natural
compounds. What is potentially flesh or bone has not yet its own
‘nature’, and does not exist ‘by nature’, until it receives the form
specified in the definition, which we name in defining what flesh or
bone is. [193b] Thus in the second sense of ‘nature’ it would be the
shape or form (not separable except in statement) of things which have
in themselves a source of motion. (5) (The combination of the two, e. g.
man, is not ‘nature’ but ‘by nature’ or ‘natural’.)
The form indeed is ‘nature’ rather than the matter; for a thing is more
properly said to be what it is when it has attained to fulfilment than
when it exists potentially. Again man is born from man, but not bed
from bed. That is why people say that the figure is not the nature of a
bed, (10) but the wood is—if the bed sprouted not a bed but wood would
come up. But even if the figure is art, then on the same principle the
shape of man is his nature. For man is born from man.
We also speak of a thing’s nature as being exhibited in the process of
growth by which its nature is attained. The ‘nature’ in this sense is not
like ‘doctoring’, (15) which leads not to the art of doctoring but to health.
Doctoring must start from the art, not lead to it. But it is not in this way
that nature (in the one sense) is related to nature (in the other). What
grows qua growing grows from something into something. Into what
then does it grow? Not into that from which it arose but into that to
which it tends. The shape then is nature.
‘Shape’ and ‘nature’, it should be added, are used in two senses. (20) For
the privation too is in a way form. But whether in unqualified coming to
be there is privation, i. e. a contrary to what comes to be, we must
consider later.1
2
We have distinguished, then, the different ways in which the term
‘nature’ is used.
The next point to consider is how the mathematician differs from the
physicist. Obviously physical bodies contain surfaces and volumes, lines
and points, and these are the subject-matter of mathematics.
Further, (25) is astronomy different from physics or a department of it?
It seems absurd that the physicist should be supposed to know the nature
of sun or moon, but not to know any of their essential attributes,
particularly as the writers on physics obviously do discuss their shape
also and whether the earth and the world are spherical or not. (30)
Now the mathematician, though he too treats of these things,
nevertheless does not treat of them as the limits of a physical body; nor
does he consider the attributes indicated as the attributes of such bodies.
That is why he separates them; for in thought they are separable from
motion, and it makes no difference, nor does any falsity result, if they
are separated. The holders of the theory of Forms do the same, (35)
though they are not aware of it; for they separate the objects of physics,
which are less separable than those of mathematics. This becomes plain
if one tries to state in each of the two cases the definitions of the things
and of their attributes. [194a] ‘Odd’ and ‘even’, ‘straight’ and ‘curved’,
and likewise ‘number’, ‘line’, and ‘figure’, do not involve motion; not so
‘flesh’ and ‘bone’ and ‘man’—these are defined like ‘snub nose’, (5) not
like ‘curved’.
Similar evidence is supplied by the more physical of the branches of
mathematics, such as optics, harmonics, and astronomy. These are in a
way the converse of geometry. While geometry investigates physical
lines but not qua physical, optics investigates mathematical lines, (10) but
qua physical, not qua mathematical.
Since ‘nature’ has two senses, the form and the matter, we must
investigate its objects as we would the essence of snubness. That is, such
things are neither independent of matter nor can be defined in terms of
matter only. Here too indeed one might raise a difficulty. (15) Since there
are two natures, with which is the physicist concerned? Or should he
investigate the combination of the two? But if the combination of the
two, then also each severally. Does it belong then to the same or to
different sciences to know each severally?
If we look at the ancients, physics would seem to be concerned with
the matter. (It was only very slightly that Empedocles and Democritus
touched on the forms and the essence. (20))
But if on the other hand art imitates nature, and it is the part of the
same discipline to know the form and the matter up to a point (e. g. the
doctor has a knowledge of health and also of bile and phlegm, in which
health is realized, and the builder both of the form of the house and of
the matter, namely that it is bricks and beams, (25) and so forth): if this is
so, it would be the part of physics also to know nature in both its senses.
Again, ‘that for the sake of which’, or the end, belongs to the same
department of knowledge as the means. But the nature is the end or ‘that
for the sake of which’. For if a thing undergoes a continuous change and
there is a stage which is last, this stage is the end or ‘that for the sake of
which’. (That is why the poet was carried away into making an absurd
statement when he said ‘he has the end2 for the sake of which he was
born’. (30) For not every stage that is last claims to be an end, but only
that which is best.)
For the arts make their material (some simply ‘make’ it, others make it
serviceable), and we use everything as if it was there for our sake. (35)
(We also are in a sense an end. ‘That for the sake of which’ has two
senses: the distinction is made in our work On Philosophy.3) The arts,
therefore, which govern the matter and have knowledge are two, namely
the art which uses the product and the art which directs the production
of it. [194b] That is why the using art also is in a sense directive; but it
differs in that it knows the form, whereas the art which is directive as
being concerned with production knows the matter. (5) For the helmsman
knows and prescribes what sort of form a helm should have, the other
from what wood it should be made and by means of what operations. In
the products of art, however, we make the material with a view to the
function, whereas in the products of nature the matter is there all along.
Again, matter is a relative term: to each form there corresponds a
special matter. (10) How far then must the physicist know the form or
essence? Up to a point, perhaps, as the doctor must know sinew or the
smith bronze (i. e. until he understands the purpose of each): and the
physicist is concerned only with things whose forms are separable
indeed, but do not exist apart from matter. Man is begotten by man and
by the sun as well. The mode of existence and essence of the separable it
is the business of the primary type of philosophy to define. (15)
3
Now that we have established these distinctions, we must proceed
to consider causes, their character and number. Knowledge is the object
of our inquiry, and men do not think they know a thing till they have
grasped the ‘why’ of it (which is to grasp its primary cause). (20) So
clearly we too must do this as regards both coming to be and passing
away and every kind of physical change, in order that, knowing their
principles, we may try to refer to these principles each of our problems.
In one sense, then, (1) that out of which a thing comes to be and
which persists, is called ‘cause’, e. g. the bronze of the statue, (25) the
silver of the bowl, and the genera of which the bronze and the silver are
species.
In another sense (2) the form or the archetype, i. e. the statement of
the essence, and its genera, are called ‘causes’ (e. g. of the octave the
relation of 2:1, and generally number), and the parts in the definition.
Again (3) the primary source of the change or coming to rest; e. g. the
man who gave advice is a cause, the father is cause of the child, (30) and
generally what makes of what is made and what causes change of what
is changed.
Again (4) in the sense of end or ‘that for the sake of which’ a thing is
done, e. g. health is the cause of walking about. (‘Why is he walking
about?’ we say. ‘To be healthy’, and, having said that, we think we have
assigned the cause.) The same is true also of all the intermediate steps
which are brought about through the action of something else as means
towards the end, (35) e. g. reduction of flesh, purging, drugs, or surgical
instruments are means towards health. [195a] All these things are ‘for
the sake of’ the end, though they differ from one another in that some
are activities, others instruments.
This then perhaps exhausts the number of ways in which the term
‘cause’ is used.
As the word has several senses, it follows that there are several causes
of the same thing (not merely in virtue of a concomitant attribute), e. g.
both the art of the sculptor and the bronze are causes of the statue. (5)
These are causes of the statue qua statue, not in virtue of anything else
that it may be—only not in the same way, the one being the material
cause, the other the cause whence the motion comes. Some things cause
each other reciprocally, e. g. hard work causes fitness and vice versa, but
again not in the same way, but the one as end, (10) the other as the origin
of change. Further the same thing is the cause of contrary results. For
that which by its presence brings about one result is sometimes blamed
for bringing about the contrary by its absence. Thus we ascribe the
wreck of a ship to the absence of the pilot whose presence was the cause
of its safety.
All the causes now mentioned fall into four familiar divisions. (15) The
letters are the causes of syllables, the material of artificial products, fire,
&c., of bodies, the parts of the whole, and the premisses of the
conclusion, in the sense of ‘that from which’. Of these pairs the one set
are causes in the sense of substratum, e. g. the parts, (20) the other set in
the sense of essence—the whole and the combination and the form. But
the seed and the doctor and the adviser, and generally the maker, are all
sources whence the change or stationariness originates, while the others
are causes in the sense of the end or the good of the rest; for ‘that for the
sake of which’ means what is best and the end of the things that lead up
to it. (Whether we say the ‘good itself’ or the ‘apparent good’ makes no
difference. (25))
Such then is the number and nature of the kinds of cause.
Now the modes of causation are many, though when brought under
heads they too can be reduced in number. For ‘cause’ is used in many
senses and even within the same kind one may be prior to another (e. g.
the doctor and the expert are causes of health, (30) the relation 2 : 1 and
number of the octave), and always what is inclusive to what is
particular. Another mode of causation is the incidental and its genera,
e. g. in one way ‘Polyclitus’, in another ‘sculptor’ is the cause of a statue,
(35) because ‘being Polyclitus’ and ‘sculptor’ are incidentally conjoined.
Also the classes in which the incidental attribute is included; thus ‘a
man’ could be said to be the cause of a statue or, generally, ‘a living
creature’. [195b] An incidental attribute too may be more or less
remote, e. g. suppose that ‘a pale man’ or ‘a musical man’ were said to
be the cause of the statue.
All causes, both proper and incidental, may be spoken of either as
potential or as actual; (5) e. g. the cause of a house being built is either
‘house-builder’ or ‘house-builder building’.
Similar distinctions can be made in the things of which the causes are
causes, e. g. of ‘this statue’ or of ‘statue’ or of ‘image’ generally, of ‘this
bronze’ or of ‘bronze’ or of ‘material’ generally. So too with the
incidental attributes. (10) Again we may use a complex expression for
either and say, e. g., neither ‘Polyclitus’ nor ‘sculptor’ but ‘Polyclitus,
sculptor’.
All these various uses, however, come to six in number, under each of
which again the usage is twofold. Cause means either what is particular
or a genus, (15) or an incidental attribute or a genus of that, and these
either as a complex or each by itself; and all six either as actual or as
potential. The difference is this much, that causes which are actually at
work and particular exist and cease to exist simultaneously with their
effect, e. g. this healing person with this being-healed person and that
housebuilding man with that being-built house; but this is not always
true of potential causes—the house and the housebuilder do not pass
away simultaneously. (20)
In investigating the cause of each thing it is always necessary to seek
what is most precise (as also in other things): thus man builds because
he is a builder, and a builder builds in virtue of his art of building. This
last cause then is prior: and so generally.
Further, (25) generic effects should be assigned to generic causes,
particular effects to particular causes, e. g. statue to sculptor, this statue
to this sculptor; and powers are relative to possible effects, actually
operating causes to things which are actually being effected.
This must suffice for our account of the number of causes and the
modes of causation. (30)
4
But chance also and spontaneity are reckoned among causes: many
things are said both to be and to come to be as a result of chance and
spontaneity. We must inquire therefore in what manner chance and
spontaneity are present among the causes enumerated, and whether they
are the same or different, and generally what chance and spontaneity
are. (35)
Some people4 even question whether they are real or not. They say
that nothing happens by chance, but that everything which we ascribe to
chance or spontaneity has some definite cause, e. g. coming ‘by chance’
into the market and finding there a man whom one wanted but did not
expect to meet is due to one’s wish to go and buy in the market.
[196a] Similarly in other cases of chance it is always possible, (5) they
maintain, to find something which is the cause; but not chance, for if
chance were real, it would seem strange indeed, and the question might
be raised, why on earth none of the wise men of old in speaking of the
causes of generation and decay took account of chance; whence it would
seem that they too did not believe that anything is by chance. (10) But
there is a further circumstance that is surprising. Many things both come
to be and are by chance and spontaneity, and although all know that
each of them can be ascribed to some cause (as the old argument said
which denied chance), (15) nevertheless they speak of some of these
things as happening by chance and others not. For this reason also they
ought to have at least referred to the matter in some way or other.
Certainly the early physicists found no place for chance among the
causes which they recognized—love, strife, mind, fire, or the like. This is
strange, whether they supposed that there is no such thing as chance or
whether they thought there is but omitted to mention it—and that too
when they sometimes used it, (20) as Empedocles does when he says that
the air is not always separated into the highest region, but ‘as it may
chance’. At any rate he says in his cosmogony that ‘it happened to run
that way at that time, but it often ran otherwise.’ He tells us also that
most of the parts of animals came to be by chance.
There are some5 too who ascribe this heavenly sphere and all the
worlds to spontaneity. (25) They say that the vortex arose spontaneously,
i. e. the motion that separated and arranged in its present order all that
exists. This statement might well cause surprise. For they are asserting
that chance is not responsible for the existence or generation of animals
and plants, nature or mind or something of the kind being the cause of
them (for it is not any chance thing that comes from a given seed but an
olive from one kind and a man from another); and yet at the same time
they assert that the heavenly sphere and the divinest of visible things
arose spontaneously, (30) (35) having no such cause as is assigned to
animals and plants. Yet if this is so, it is a fact which deserves to be
dwelt upon, and something might well have been said about it. [196b]
For besides the other absurdities of the statement, it is the more absurd
that people should make it when they see nothing coming to be
spontaneously in the heavens, but much happening by chance among the
things which as they say are not due to chance; whereas we should have
expected exactly the opposite. (5)
Others6 there are who, indeed, believe that chance is a cause, but that
it is inscrutable to human intelligence, as being a divine thing and full of
mystery.
Thus we must inquire what chance and spontaneity are, whether they
are the same or different, and how they fit into our division of causes.
5
First then we observe that some things always come to pass in the
same way, (10) and others for the most part. It is clearly of neither of
these that chance is said to be the cause, nor can the ‘effect of chance’ be
identified with any of the things that come to pass by necessity and
always, or for the most part. But as there is a third class of events
besides these two—events which all say are ‘by chance’—it is plain that
there is such a thing as chance and spontaneity; for we know that things
of this kind are due to chance and that things due to chance are of this
kind. (15)
But, secondly, some events are for the sake of something, others not.
Again, some of the former class are in accordance with deliberate
intention, others not, but both are in the class of things which are for the
sake of something. (20) Hence it is clear that even among the things
which are outside the necessary and the normal, there are some in
connexion with which the phrase ‘for the sake of something’ is
applicable. (Events that are for the sake of something include whatever
may be done as a result of thought or of nature.) Things of this kind,
then, when they come to pass incidentally are said to be ‘by chance’. (25)
For just as a thing is something either in virtue of itself or incidentally,
so may it be a cause. For instance, the housebuilding faculty is in virtue
of itself the cause of a house, whereas the pale or the musical7 is the
incidental cause. That which is per se cause of the effect is determinate,
but the incidental cause is indeterminable, for the possible attributes of
an individual are innumerable. To resume then; when a thing of this
kind comes to pass among events which are for the sake of something,
(30) it is said to be spontaneous or by chance. (The distinction between
the two must be made later8—for the present it is sufficient if it is plain
that both are in the sphere of things done for the sake of something.)
Example: A man is engaged in collecting subscriptions for a feast. He
would have gone to such and such a place for the purpose of getting the
money, if he had known. He actually went there for another purpose, (35)
and it was only incidentally that he got his money by going there; and
this was not due to the fact that he went there as a rule or necessarily,
nor is the end effected (getting the money) a cause present in himself—it
belongs to the class of things that are intentional and the result of
intelligent deliberation. [197a] It is when these conditions are satisfied
that the man is said to have gone ‘by chance’. If he had gone of
deliberate purpose and for the sake of this—if he always or normally
went there when he was collecting payments—he would not be said to
have gone ‘by chance’.
It is clear then that chance is an incidental cause in the sphere of those
actions for the sake of something which involve purpose. (5) Intelligent
reflection, then, and chance are in the same sphere, for purpose implies
intelligent reflection.
It is necessary, no doubt, that the causes of what comes to pass by
chance be indefinite; and that is why chance is supposed to belong to the
class of the indefinite and to be inscrutable to man, (10) and why it might
be thought that, in a way, nothing occurs by chance. For all these
statements are correct, because they are well grounded. Things do, in a
way, occur by chance, for they occur incidentally and chance is an
incidental cause. But strictly it is not the cause—without qualification—of
anything; for instance, a housebuilder is the cause of a house;
incidentally, a flute-player may be so.
And the causes of the man’s coming and getting the money (when he
did not come for the sake of that) are innumerable. (15) He may have
wished to see somebody or been following somebody or avoiding
somebody, or may have gone to see a spectacle. Thus to say that chance
is a thing contrary to rule is correct. For ‘rule’ applies to what is always
true or true for the most part, whereas chance belongs to a third type of
event. Hence, to conclude, since causes of this kind are indefinite, (20)
chance too is indefinite. (Yet in some cases one might raise the question
whether any incidental fact might be the cause of the chance occurrence,
e. g. of health the fresh air or the sun’s heat may be the cause, but
having had one’s hair cut cannot; for some incidental causes are more
relevant to the effect than others.)
Chance or fortune is called ‘good’ when the result is good, (25) ‘evil’
when it is evil. The terms ‘good fortune’ and ‘ill fortune’ are used when
either result is of considerable magnitude. Thus one who comes within
an ace of some great evil or great good is said to be fortunate or
unfortunate. The mind affirms the presence of the attribute, (30) ignoring
the hair’s breadth of difference. Further, it is with reason that good
fortune is regarded as unstable; for chance is unstable, as none of the
things which result from it can be invariable or normal.
Both are then, as I have said, incidental causes—both chance and
spontaneity—in the sphere of things which are capable of coming to pass
not necessarily, nor normally, (35) and with reference to such of these as
might come to pass for the sake of something.
6
They differ in that ‘spontaneity’ is the wider term. Every result of
chance is from what is spontaneous, but not everything that is from what
is spontaneous is from chance.
[197b] Chance and what results from chance are appropriate to
agents that are capable of good fortune and of moral action generally.
Therefore necessarily chance is in the sphere of moral actions. This is
indicated by the fact that good fortune is thought to be the same, or
nearly the same, as happiness, and happiness to be a kind of moral
action, (5) since it is well-doing. Hence what is not capable of moral
action cannot do anything by chance. Thus an inanimate thing or a
lower animal or a child cannot do anything by chance, because it is
incapable of deliberate intention; nor can ‘good fortune’ or ‘ill fortune’
be ascribed to them, except metaphorically, as Protarchus, for example,
said that the stones of which altars are made are fortunate because they
are held in honour, (10) while their fellows are trodden under foot. Even
these things, however, can in a way be affected by chance, when one
who is dealing with them does something to them by chance, but not
otherwise.
The spontaneous on the other hand is found both in the lower animals
and in many inanimate objects. (15) We say, for example, that the horse
came ‘spontaneously’, because, though his coming saved him, he did not
come for the sake of safety. Again, the tripod fell ‘of itself’, because,
though when it fell it stood on its feet so as to serve for a seat, it did not
fall for the sake of that.
Hence it is clear that events which (1) belong to the general class of
things that may come to pass for the sake of something, (2) do not come
to pass for the sake of what actually results, and (3) have an external
cause, may be described by the phrase ‘from spontaneity’. (20) These
‘spontaneous’ events are said to be ‘from chance’ if they have the further
characteristics of being the objects of deliberate intention and due to
agents capable of that mode of action. This is indicated by the phrase ‘in
vain’, which is used when A, which is for the sake of B, does not result in
B. For instance, taking a walk is for the sake of evacuation of the bowels;
if this does not follow after walking, we say that we have walked ‘in
vain’ and that the walking was ‘vain’. This implies that what is naturally
the means to an end is ‘in vain’, (25) when it does not effect the end
towards which it was the natural means—for it would be absurd for a
man to say that he had bathed in vain because the sun was not eclipsed,
since the one was not done with a view to the other. Thus the
spontaneous is even according to its derivation the case in which the
thing itself happens in vain. The stone that struck the man did not fall
for the purpose of striking him; therefore it fell spontaneously, (30)
because it might have fallen by the action of an agent and for the
purpose of striking. The difference between spontaneity and what results
by chance is greatest in things that come to be by nature; for when
anything comes to be contrary to nature, we do not say that it came to
be by chance, but by spontaneity. Yet strictly this too is different from
the spontaneous proper; for the cause of the latter is external, (35) that of
the former internal.
[198a] We have now explained what chance is and what spontaneity
is, and in what they differ from each other. Both belong to the mode of
causation ‘source of change’, for either some natural or some intelligent
agent is always the cause; but in this sort of causation the number of
possible causes is infinite.
Spontaneity and chance are causes of effects which, (5) though they
might result from intelligence or nature, have in fact been caused by
something incidentally. Now since nothing which is incidental is prior to
what is per se, it is clear that no incidental cause can be prior to a cause
per se. Spontaneity and chance, therefore, are posterior to intelligence
and nature. Hence, however true it may be that the heavens are due to
spontaneity, (10) it will still be true that intelligence and nature will be
prior causes of this All and of many things in it besides.
7
It is clear then that there are causes, and that the number of them is
what we have stated. The number is the same as that of the things
comprehended under the question ‘why’. (15) The ‘why’ is referred
ultimately either (1), in things which do not involve motion, e. g. in
mathematics, to the ‘what’ (to the definition of ‘straight line’ or
‘commensurable’, &c), or (2) to what initiated a motion, e. g. ‘why did
they go to war?—because there had been a raid’; or (3) we are inquiring
‘for the sake of what?’—‘that they may rule’; or (4), (20) in the case of
things that come into being, we are looking for the matter. The causes,
therefore, are these and so many in number.
Now, the causes being four, it is the business of the physicist to know
about them all, and if he refers his problems back to all of them, he will
assign the ‘why’ in the way proper to his science—the matter, (25) the
form, the mover, ‘that for the sake of which’. The last three often
coincide; for the ‘what’ and ‘that for the sake of which’ are one, while
the primary source of motion is the same in species as these (for man
generates man), and so too, in general, are all things which cause
movement by being themselves moved; and such as are not of this kind
are no longer inside the province of physics, for they cause motion not
by possessing motion or a source of motion in themselves, but being
themselves incapable of motion. Hence there are three branches of
study, (30) one of things which are incapable of motion, the second of
things in motion, but indestructible, the third of destructible things.
The question ‘why’, then, is answered by reference to the matter, to
the form, and to the primary moving cause. For in respect of coming to
be it is mostly in this last way that causes are investigated—‘what comes
to be after what? what was the primary agent or patient?’ and so at each
step of the series.
Now the principles which cause motion in a physical way are two, (35)
of which one is not physical, as it has no principle of motion in itself.
[198b] Of this kind is whatever causes movement, not being itself
moved, such as (1) that which is completely unchangeable, the primary
reality, and (2) the essence of that which is coming to be, i. e. the form;
for this is the end or ‘that for the sake of which’. Hence since nature is
for the sake of something, we must know this cause also. (5) We must
explain the ‘why’ in all the senses of the term, namely, (1) that from this
that will necessarily result (‘from this’ either without qualification or in
most cases); (2) that ‘this must be so if that is to be so’ (as the conclusion
presupposes the premisses); (3) that this was the essence of the thing;
and (4) because it is better thus (not without qualification, but with
reference to the essential nature in each case).
8
We must explain then (1) that Nature belongs to the class of causes
which act for the sake of something; (2) about the necessary and its
place in physical problems, (10) for all writers ascribe things to this cause,
arguing that since the hot and the cold, &c., are of such and such a kind,
therefore certain things necessarily are and come to be—and if they
mention any other cause (one9 his ‘friendship and strife’, (15) another10
his ‘mind’), it is only to touch on it, and then goodbye to it.
A difficulty presents itself: why should not nature work, not for the
sake of something, nor because it is better so, but just as the sky rains,
not in order to make the corn grow, but of necessity? What is drawn up
must cool, and what has been cooled must become water and descend,
(20) the result of this being that the corn grows. Similarly if a man’s crop
is spoiled on the threshing-floor, the rain did not fall for the sake of this
—in order that the crop might be spoiled—but that result just followed.
Why then should it not be the same with the parts in nature, e. g. that
our teeth should come up of necessity—the front teeth sharp, fitted for
tearing, the molars broad and useful for grinding down the food—since
they did not arise for this end, (25) but it was merely a coincident result;
and so with all other parts in which we suppose that there is purpose?
Wherever then all the parts came about just what they would have been
if they had come to be for an end, (30) such things survived, being
organized spontaneously in a fitting way; whereas those which grew
otherwise perished and continue to perish, as Empedocles says his ‘manfaced ox-progeny’ did.
Such are the arguments (and others of the kind) which may cause
difficulty on this point. Yet it is impossible that this should be the true
view. For teeth and all other natural things either invariably or normally
come about in a given way; but of not one of the results of chance or
spontaneity is this true. (35) We do not ascribe to chance or mere
coincidence the frequency of rain in winter, but frequent rain in summer
we do; nor heat in the dog-days, but only if we have it in winter.
[199a] If then, it is agreed that things are either the result of
coincidence or for an end, and these cannot be the result of coincidence
or spontaneity, it follows that they must be for an end; and that such
things are all due to nature even the champions of the theory which is
before us would agree. (5) Therefore action for an end is present in things
which come to be and are by nature.
Further, where a series has a completion, all the preceding steps are
for the sake of that. Now surely as in intelligent action, (10) so in nature;
and as in nature, so it is in each action, if nothing interferes. Now
intelligent action is for the sake of an end; therefore the nature of things
also is so. Thus if a house, e. g., had been a thing made by nature, it
would have been made in the same way as it is now by art; and if things
made by nature were made also by art, (15) they would come to be in the
same way as by nature. Each step then in the series is for the sake of the
next; and generally art partly completes what nature cannot bring to a
finish, and partly imitates her. If, therefore, artificial products are for the
sake of an end, so clearly also are natural products. The relation of the
later to the earlier terms of the series is the same in both.
This is most obvious in the animals other than man: they make things
neither by art nor after inquiry or deliberation. (20) Wherefore people
discuss whether it is by intelligence or by some other faculty that these
creatures work,—spiders, ants, and the like. By gradual advance in this
direction we come to see clearly that in plants too that is produced
which is conducive to the end—leaves, (25) e. g. grow to provide shade
for the fruit. If then it is both by nature and for an end that the swallow
makes its nest and the spider its web, and plants grow leaves for the sake
of the fruit and send their roots down (not up) for the sake of
nourishment, it is plain that this kind of cause is operative in things
which come to be and are by nature. (30) And since ‘nature’ means two
things, the matter and the form, of which the latter is the end, and since
all the rest is for the sake of the end, the form must be the cause in the
sense of ‘that for the sake of which’.
Now mistakes come to pass even in the operations of art: the
grammarian makes a mistake in writing and the doctor pours out the
wrong dose. (35) Hence clearly mistakes are possible in the operations of
nature also. [199b] If then in art there are cases in which what is
rightly produced serves a purpose, and if where mistakes occur there
was a purpose in what was attempted, only it was not attained, so must
it be also in natural products, and monstrosities will be failures in the
purposive effort. (5) Thus in the original combinations the ‘ox-progeny’ if
they failed to reach a determinate end must have arisen through the
corruption of some principle corresponding to what is now the seed.
Further, seed must have come into being first, and not straightway the
animals: the words ‘whole-natured first …’11 must have meant seed.
Again, in plants too we find the relation of means to end, (10) though
the degree of organization is less. Were there then in plants also ‘oliveheaded vine-progeny’, like the ‘man-headed ox-progeny’, or not? An
absurd suggestion; yet there must have been, if there were such things
among animals.
Moreover, among the seeds anything must have come to be at random.
But the person who asserts this entirely does away with ‘nature’ and
what exists ‘by nature’. For those things are natural which, (15) by a
continuous movement originated from an internal principle, arrive at
some completion: the same completion is not reached from every
principle; nor any chance completion, but always the tendency in each is
towards the same end, if there is no impediment.
The end and the means towards it may come about by chance. We say,
for instance, that a stranger has come by chance, (20) paid the ransom,
and gone away, when he does so as if he had come for that purpose,
though it was not for that that he came. This is incidental, for chance is
an incidental cause, as I remarked before.12 But when an event takes
place always or for the most part, it is not incidental or by chance. In
natural products the sequence is invariable, (25) if there is no
impediment.
It is absurd to suppose that purpose is not present because we do not
observe the agent deliberating. Art does not deliberate. If the shipbuilding art were in the wood, it would produce the same results by
nature. If, therefore, purpose is present in art, it is present also in nature.
The best illustration is a doctor doctoring himself: nature is like that. (30)
It is plain then that nature is a cause, a cause that operates for a
purpose.
9
As regards what is ‘of necessity’, we must ask whether the necessity
is ‘hypothetical’, or ‘simple’ as well. (35) The current view places what is
of necessity in the process of production, just as if one were to suppose
that the wall of a house necessarily comes to be because what is heavy is
naturally carried downwards and what is light to the top, wherefore the
stones and foundations take the lowest place, with earth above because
it is lighter, and wood at the top of all as being the lightest. [200a]
Whereas, though the wall does not come to be without these, (5) it is not
due to these, except as its material cause: it comes to be for the sake of
sheltering and guarding certain things. Similarly in all other things
which involve production for an end; the product cannot come to be
without things which have a necessary nature, but it is not due to these
(except as its material); it comes to be for an end. (10) For instance, why
is a saw such as it is? To effect so-and-so and for the sake of so-and-so.
This end, however, cannot be realized unless the saw is made of iron. It
is, therefore, necessary for it to be of iron, if we are to have a saw and
perform the operation of sawing. What is necessary then, is necessary on
a hypothesis; it is not a result necessarily determined by antecedents.
Necessity is in the matter, while ‘that for the sake of which’ is in the
definition.
Necessity in mathematics is in a way similar to necessity in things
which come to be through the operation of nature. (15) Since a straight
line is what it is, it is necessary that the angles of a triangle should equal
two right angles. But not conversely; though if the angles are not equal
to two right angles, then the straight line is not what it is either. But in
things which come to be for an end, the reverse is true. (20) If the end is
to exist or does exist, that also which precedes it will exist or does exist;
otherwise just as there, if the conclusion is not true, the premiss will not
be true, so here the end or ‘that for the sake of which’ will not exist. For
this too is itself a starting-point, but of the reasoning, not of the action;
while in mathematics the starting-point is the starting point of the
reasoning only, as there is no action. (25) If then there is to be a house,
such-and-such things must be made or be there already or exist, or
generally the matter relative to the end, bricks and stones if it is a house.
But the end is not due to these except as the matter, nor will it come to
exist because of them. Yet if they do not exist at all, neither will the
house, or the saw—the former in the absence of stones, the latter in the
absence of iron—just as in the other case the premisses will not be true,
if the angles of the triangle are not equal to two right angles.
The necessary in nature, (30) then, is plainly what we call by the name
of matter, and the changes in it. Both causes must be stated by the
physicist, but especially the end; for that is the cause of the matter, not
vice versa; and the end is ‘that for the sake of which’, (35) and the
beginning starts from the definition or essence; as in artificial products,
since a house is of such-and-such a kind, certain things must necessarily
come to be or be there already, or since health is this, these things must
necessarily come to be or be there already. [200b] Similarly if man is
this, then these; if these, then those. (5) Perhaps the necessary is present
also in the definition. For if one defines the operation of sawing as being
a certain kind of dividing, then this cannot come about unless the saw
has teeth of a certain kind; and these cannot be unless it is of iron. For in
the definition too there are some parts that are, as it were, its matter.
1
De Gen. et Corr. i. 3.
2
i. e. death.
3
i. e. in the dialogue De Philosophia.
4
Apparently Democritus is meant.
5
Apparently Democritus is meant.
6
Democritus.
7
Incidental attributes of the housebuilder.
8
In ch. 6.
9
Empedocles.
10
Anaxagoras.
11
Empedocles, Fr. 62. 4.
12
196b 23–7.
BOOK III
1
Nature has been defined as a ‘principle of motion and change’, (12)
and it is the subject of our inquiry. We must therefore see that we
understand the meaning of ‘motion’; for if it were unknown, the meaning
of ‘nature’ too would be unknown.
When we have determined the nature of motion, (15) our next task will
be to attack in the same way the terms which are involved in it. Now
motion is supposed to belong to the class of things which are continuous;
and the infinite presents itself first in the continuous—that is how it
comes about that ‘infinite’ is often used in definitions of the continuous
(‘what is infinitely divisible is continuous’). Besides these, place, void,
and time are thought to be necessary conditions of motion. (20)
Clearly, then, for these reasons and also because the attributes
mentioned are common to, and coextensive with, all the objects of our
science, we must first take each of them in hand and discuss it. For the
investigation of special attributes comes after that of the common
attributes.
To begin then, as we said, with motion. (25)
We may start by distinguishing (1) what exists in a state of fulfilment
only, (2) what exists as potential, (3) what exists as potential and also in
fulfilment—one being a ‘this’, another ‘so much’, a third ‘such’, and
similarly in each of the other modes of the predication of being.
Further, the word ‘relative’ is used with reference to (1) excess and
defect, (2) agent and patient and generally what can move and what can
be moved. (30) For ‘what can cause movement’ is relative to ‘what can be
moved’, and vice versa.
Again, there is no such thing as motion over and above the things. It is
always with respect to substance or to quantity or to quality or to place
that what changes changes. But it is impossible, as we assert, to find
anything common to these which is neither ‘this’ nor quantum nor quale
nor any of the other predicates. [201a] (35) Hence neither will motion
and change have reference to something over and above the things
mentioned, for there is nothing over and above them.
Now each of these belongs to all its subjects in either of two ways:
namely (1) substance—the one is positive form, (5) the other privation;
(2) in quality, white and black; (3) in quantity, complete and
incomplete; (4) in respect of locomotion, upwards and downwards or
light and heavy. Hence there are as many types of motion or change as
there are meanings of the word ‘is’.
We have now before us the distinctions in the various classes of being
between what is fully real and what is potential.
Def. (10) The fulfilment of what exists potentially, in so far as it exists
potentially, is motion—namely, of what is alterable qua alterable,
alteration: of what can be increased and its opposite what can be
decreased (there is no common name), increase and decrease: of what can
come to be and can pass away, coming to be and passing away: of what
can be carried along, locomotion.
Examples will elucidate this definition of motion. (15) When the
buildable, in so far as it is just that, is fully real, it is being built, and this
is building. Similarly, learning, doctoring, rolling, leaping, ripening,
ageing.
The same thing, if it is of a certain kind, can be both potential and
fully real, (20) not indeed at the same time or not in the same respect, but
e. g. potentially hot and actually cold. Hence at once such things will act
and be acted on by one another in many ways: each of them will be
capable at the same time of causing alteration and of being altered.
Hence, too, what effects motion as a physical agent can be moved: when
a thing of this kind causes motion, it is itself also moved. This, (25)
indeed, has led some people to suppose that every mover is moved. But
this question depends on another set of arguments, and the truth will be
made clear later.1 It is possible for a thing to cause motion, though it is
itself incapable of being moved.
It is the fulfilment of what is potential when it is already fully real and
operates not as itself but as movable, that is motion. (30) What I mean by
‘as’ is this: Bronze is potentially a statue. But it is not the fulfilment of
bronze as bronze which is motion. For ‘to be bronze’ and ‘to be a certain
potentiality’ are not the same. If they were identical without
qualification, i. e. in definition, the fulfilment of bronze as bronze would
have been motion. But they are not the same, as has been said. (This is
obvious in contraries. To be capable of health’ and ‘to be capable of
illness’ are not the same, (35) for if they were there would be no
difference between being ill and being well. [201b] Yet the subject
both of health and of sickness—whether it is humour or blood—is one
and the same.)
We can distinguish, then, between the two—just as, to give another
example, ‘colour’ and ‘visible’ are different—and clearly it is the
fulfilment of what is potential as potential that is motion. (5) So this,
precisely, is motion.
Further it is evident that motion is an attribute of a thing just when it
is fully real in this way, and neither before nor after. For each thing of
this kind is capable of being at one time actual, at another not. Take for
instance the buildable as buildable. The actuality of the buildable as
buildable is the process of building. (10) For the actuality of the buildable
must be either this or the house. But when there is a house, the
buildable is no longer buildable. On the other hand, it is the buildable
which is being built. The process then of being built must be the kind of
actuality required. But building is a kind of motion, and the same
account will apply to the other kinds also. (15)
2
The soundness of this definition is evident both when we consider
the accounts of motion that the others have given, and also from the
difficulty of defining it otherwise.
One could not easily put motion and change in another genus—this is
plain if we consider where some people put it; they identify motion with
‘difference’ or ‘inequality’2 or ‘not being’; but such things are not
necessarily moved, (20) whether they are ‘different’ or ‘unequal’ or ‘nonexistent’: Nor is change either to or from these rather than to or from
their opposites.
The reason why they put motion into these genera is that it is thought
to be something indefinite, and the principles in the second column are
indefinite because they are privative: none of them is either ‘this’ or
‘such’ or comes under any of the other modes of predication. (25) The
reason in turn why motion is thought to be indefinite is that it cannot be
classed simply as a potentiality or as an actuality—a thing that is merely
capable of having a certain size is not undergoing change, nor yet a thing
that is actually of a certain size, (30) and motion is thought to be a sort of
actuality, but incomplete, the reason for this view being that the
potential whose actuality it is is incomplete. This is why it is hard to
grasp what motion is. It is necessary to class it with privation or with
potentiality or with sheer actuality, yet none of these seems possible. (35)
There remains then the suggested mode of definition, namely that it is a
sort of actuality, or actuality of the kind described, hard to grasp, but
not incapable of existing. [202a]
The mover too is moved, as has been said—every mover, that is,
which is capable of motion, and whose immobility is rest—when a thing
is subject to motion its immobility is rest. For to act on the movable as
such is just to move it. But this it does by contact, (5) so that at the same
time it is also acted on. Hence we can define motion as the fulfilment of
the movable qua movable, the cause of the attribute being contact with what
can move, so that the mover is also acted on. The mover or agent will
always be the vehicle of a form, either a ‘this’ or a ‘such,’ (10) which,
when it acts, will be the source and cause of the change, e. g. the fullformed man begets man from what is potentially man.
3
The solution of the difficulty that is raised about the motion—
whether it is in the movable—is plain. It is the fulfilment of this
potentiality, and by the action of that which has the power of causing
motion; and the actuality of that which has the power of causing motion
is not other than the actuality of the movable, (15) for it must be the
fulfilment of both. A thing is capable of causing motion because it can do
this, it is a mover because it actually does it. But it is on the movable
that it is capable of acting. Hence there is a single actuality of both alike,
just as one to two and two to one are the same interval, (20) and the steep
ascent and the steep descent are one—for these are one and the same,
although they can be described in different ways. So it is with the mover
and the moved.
This view has a dialectical difficulty. Perhaps it is necessary that the
actuality of the agent and that of the patient should not be the same. The
one is ‘agency’ and the other ‘patiency’; and the outcome and completion
of the one is an ‘action’, that of the other a ‘passion’. (25) Since then they
are both motions, we may ask: in what are they, if they are different?
Either (a) both are in what is acted on and moved, or (b) the agency is in
the agent and the patiency in the patient. (If we ought to call the latter
also ‘agency’, the word would be used in two senses.)
Now, in alternative (b) the motion will be in the mover, for the same
statement will hold of ‘mover’ and ‘moved’.3 Hence either every mover
will be moved, (30) or, though having motion, it will not be moved.
If on the other hand (a) both are in what is moved and acted on—both
the agency and the patiency (e. g. both teaching and learning, though
they are two, in the learner), then, first, the actuality of each will not be
present in each, and, a second absurdity, (35) a thing will have two
motions at the same time. How will there be two alterations of quality in
one subject towards one definite quality? The thing is impossible: the
actualization will be one. [202b]
But (some one will say) it is contrary to reason to suppose that there
should be one identical actualization of two things which are different in
kind. Yet there will be, if teaching and learning are the same, and
agency and patiency. To teach will be the same as to learn, and to act
the same as to be acted on—the teacher will necessarily be learning
everything that he teaches, and the agent will be acted on.
One may reply:
(1) It is not absurd that the actualization of one thing should be in
another. (5) Teaching is the activity of a person who can teach, yet the
operation is performed on some patient—it is not cut adrift from a
subject, but is of A on B.
(2) There is nothing to prevent two things having one and the same
actualization, provided the actualizations are not described in the same
way, but are related as what can act to what is acting.
(3) Nor is it necessary that the teacher should learn, (10) even if to act
and to be acted on are one and the same, provided they are not the same
in definition (as ‘raiment’ and ‘dress’), but are the same merely in the
sense in which the road from Thebes to Athens and the road from Athens
to Thebes are the same, as has been explained above.4 For it is not things
which are in a way the same that have all their attributes the same, but
only such as have the same definition. (15) But indeed it by no means
follows from the fact that teaching is the same as learning, that to learn
is the same as to teach, any more than it follows from the fact that there
is one distance between two things which are at a distance from each
other, that the two vectors AB and BA are one and the same. To
generalize, teaching is not the same as learning, or agency as patiency,
in the full sense, (20) though they belong to the same subject, the motion;
for the ‘actualization of X in Y’ and the ‘actualization of Y through the
action of X’ differ in definition.
What then Motion is, has been stated both generally and particularly.
It is not difficult to see how each of its types will be defined—alteration
is the fulfilment of the alterable qua alterable (or, (25) more scientifically,
the fulfilment of what can act and what can be acted on, as such)—
generally and again in each particular case, building, healing, &c. A
similar definition will apply to each of the other kinds of motion.
4
The science of nature is concerned with spatial magnitudes and
motion and time, (30) and each of these at least is necessarily infinite or
finite, even if some things dealt with by the science are not, e. g. a
quality or a point—it is not necessary perhaps that such things should be
put under either head. Hence it is incumbent on the person who
specializes in physics to discuss the infinite and to inquire whether there
is such a thing or not, (35) and, if there is, what it is.
The appropriateness to the science of this problem is clearly indicated.
[203a] All who have touched on this kind of science in a way worth
considering have formulated views about the infinite, and indeed, to a
man, make it a principle of things.
(1) Some, as the Pythagoreans and Plato, (5) make the infinite a
principle in the sense of a self-subsistent substance, and not as a mere
attribute of some other thing. Only the Pythagoreans place the infinite
among the objects of sense (they do not regard number as separable
from these), and assert that what is outside the heaven is infinite. Plato,
on the other hand, holds that there is no body outside (the Forms are not
outside, because they are nowhere), yet that the infinite is present not
only in the objects of sense but in the Forms also.
Further, (10) the Pythagoreans identify the infinite with the even. For
this, they say, when it is cut off and shut in by the odd, provides things
with the element of infinity. An indication of this is what happens with
numbers. If the gnomons are placed round the one, and without the
one,5 in the one construction the figure that results is always different,
(15) in the other it is always the same. But Plato has two infinites, the
Great and the Small.
The physicists, on the other hand, all of them, always regard the
infinite as an attribute of a substance which is different from it and
belongs to the class of the so-called elements6—water or air or what is
intermediate between them. Those who make them limited in number
never make them infinite in amount. But those who make the elements
infinite in number, (20) as Anaxagoras and Democritus do, say that the
infinite is continuous by contact—compounded of the homogeneous
parts according to the one, of the seed-mass of the atomic shapes
according to the other.
Further, Anaxagoras held that any part is a mixture in the same way
as the All, on the ground of the observed fact that anything comes out of
anything. For it is probably for this reason that he maintains that once
upon a time all things were together. (25) (This flesh and this bone were
together, and so of any thing: therefore all things: and at the same time
too.) For there is a beginning of separation, not only for each thing, but
for all. Each thing that comes to be comes to be from a similar body, and
there is a coming to be of all things, (30) though not, it is true, at the
same time. Hence there must also be an origin of coming to be. One such
source there is which he calls Mind, and Mind begins its work of
thinking from some starting-point. So necessarily all things must have
been together at a certain time, and must have begun to be moved at a
certain time.
Democritus, for his part, asserts the contrary, namely that no element
arises from another element. Nevertheless for him the common body is a
source of all things, differing from part to part in size and in shape.
[203b]
It is clear then from these considerations that the inquiry concerns the
physicist. Nor is it without reason that they all make it a principle or
source. We cannot say that the infinite has no effect, (5) and the only
effectiveness which we can ascribe to it is that of a principle. Everything
is either a source or derived from a source. But there cannot be a source
of the infinite or limitless, for that would be a limit of it. Further, as it is
a beginning, it is both uncreatable and indestructible. For there must be
a point at which what has come to be reaches completion, and also a
termination of all passing away. That is why, (10) as we say, there is no
principle of this, but it is this which is held to be the principle of other
things, and to encompass all and to steer all, as those assert who do not
recognize, alongside the infinite, other causes, such as Mind or
Friendship. Further they identify it with the Divine, for it is ‘deathless
and imperishable’ as Anaximander says, with the majority of the
physicists.
Belief in the existence of the infinite comes mainly from five
considerations:
(1) From the nature of time—for it is infinite. (15)
(2) From the division of magnitudes—for the mathematicians also use the notion of the infinite.
(3) If coming to be and passing away do not give out, it is only because that from which things
come to be is infinite.
(4) Because the limited always finds its limit in something,
(20)
so that there must be no limit, if
everything is always limited by something different from itself.
(5) Most of all, a reason which is peculiarly appropriate and presents the difficulty that is felt
by everybody—not only number but also mathematical magnitudes and what is outside the
heaven are supposed to be infinite because they never give out in our thought.
The last fact (that what is outside is infinite) leads people to suppose
that body also is infinite, (25) and that there is an infinite number of
worlds. Why should there be body in one part of the void rather than in
another? Grant only that mass is anywhere and it follows that it must be
everywhere. Also, if void and place are infinite, there must be infinite
body too, for in the case of eternal things what may be must be.
But the problem of the infinite is difficult: many contradictions result
whether we suppose it to exist or not to exist. (30) If it exists, we have still
to ask how it exists; as a substance or as the essential attribute of some
entity? Or in neither way, yet none the less is there something which is
infinite or some things which are infinitely many?
The problem, however, which specially belongs to the physicist is to
investigate whether there is a sensible magnitude which is infinite.
[204a]
We must begin by distinguishing the various senses in which the term
‘infinite’ is used.
(1) What is incapable of being gone through, because it is not its nature to be gone through (the
sense in which the voice is ‘invisible’).
(2) What admits of being gone through, the process however having no termination,
(5)
or (3)
what scarcely admits of being gone through.
(4) What naturally admits of being gone through, but is not actually gone through or does not
actually reach an end.
Further, everything that is infinite may be so in respect of addition or
division or both.
5
Now it is impossible that the infinite should be a thing which is
itself infinite, separable from sensible objects. (10) If the infinite is neither
a magnitude nor an aggregate, but is itself a substance and not an
attribute, it will be indivisible; for the divisible must be either a
magnitude or an aggregate. But if indivisible, then not infinite, except in
the sense (1) in which the voice is ‘invisible’. But this is not the sense in
which it is used by those who say that the infinite exists, nor that in
which we are investigating it, namely as (2), ‘that which cannot be gone
through’. But if the infinite exists as an attribute, (15) it would not be, qua
infinite, an element in substances, any more than the invisible would be
an element of speech, though the voice is invisible.
Further, how can the infinite be itself any thing, unless both number
and magnitude, of which it is an essential attribute, exist in that way? If
they are not substances, a fortiori the infinite is not.
It is plain, (20) too, that the infinite cannot be an actual thing and a
substance and principle. For any part of it that is taken will be infinite, if
it has parts: for ‘to be infinite’ and ‘the infinite’ are the same, if it is a
substance and not predicated of a subject. Hence it will be either
indivisible or divisible into infinites. (25) But the same thing cannot be
many infinites. (Yet just as part of air is air, so a part of the infinite
would be infinite, if it is supposed to be a substance and principle.)
Therefore the infinite must be without parts and indivisible. But this
cannot be true of what is infinite in full completion: for it must be a
definite quantity.
Suppose then that infinity belongs to substance as an attribute. But, if
so, it cannot, as we have said, be described as a principle, (30) but rather
that of which it is an attribute—the air or the even number.
Thus the view of those who speak after the manner of the
Pythagoreans is absurd. With the same breath they treat the infinite as
substance, and divide it into parts.
This discussion, however, involves the more general question whether
the infinite can be present in mathematical objects and things which are
intelligible and do not have extension, (35) as well as among sensible
objects. [204b] Our inquiry (as physicists) is limited to its special
subject-matter, the objects of sense, and we have to ask whether there is
or is not among them a body which is infinite in the direction of
increase.
We may begin with a dialectical argument and show as follows that
there is no such thing.
If ‘bounded by a surface’ is the definition of body there cannot be an
infinite body either intelligible or sensible. (5) Nor can number taken in
abstraction be infinite, for number or that which has number is
numerable. If then the numerable can be numbered, it would also be
possible to go through the infinite.
If, on the other hand, we investigate the question more in accordance
with principles appropriate to physics, (10) we are led as follows to the
same result.
The infinite body must be either (1) compound, or (2) simple; yet
neither alternative is possible.
(1) Compound the infinite body will not be, if the elements are finite
in number. For they must be more than one, and the contraries must
always balance, and no one of them can be infinite. If one of the bodies
falls in any degree short of the other in potency—suppose fire is finite in
amount while air is infinite and a given quantity of fire exceeds in power
the same amount of air in any ratio provided it is numerically definite—
the infinite body will obviously prevail over and annihilate the finite
body. (15) On the other hand, it is impossible that each should be infinite.
‘Body’ is what has extension in all directions and the infinite is what is
boundlessly extended, (20) so that the infinite body would be extended in
all directions ad infinitum.
Nor (2) can the infinite body be one and simple, whether it is, as
some7 hold, a thing over and above the elements (from which they
generate the elements) or is not thus qualified.
(a) We must consider the former alternative; for there are some people
who make this the infinite, and not air or water, (25) in order that the
other elements may not be annihilated by the element which is infinite.
They have contrariety with each other—air is cold, water moist, fire hot;
if one were infinite, the others by now would have ceased to be. As it is,
they say, the infinite is different from them and is their source.
It is impossible, however, that there should be such a body; not
because it is infinite—on that point a general proof can be given which
applies equally to all, (30) air, water, or anything else—but simply
because there is, as a matter of fact, no such sensible body, alongside the
so-called elements. Everything can be resolved into the elements of
which it is composed. Hence the body in question would have been
present in our world here, alongside air and fire and earth and water:
but nothing of the kind is observed. (35)
(b) Nor can fire or any other of the elements be infinite. [205a] For
generally, and apart from the question how any of them could be
infinite, the All, even if it were limited, cannot either be or become one
of them, as Heraclitus says that at some time all things become fire. (5)
(The same argument applies also to the one which the physicists suppose
to exist alongside the elements: for everything changes from contrary to
contrary, e. g. from hot to cold).
The preceding consideration of the various cases serves to show us
whether it is or is not possible that there should be an infinite sensible
body. The following arguments give a general demonstration that it is
not possible.
It is the nature of every kind of sensible body to be somewhere, (10)
and there is a place appropriate to each, the same for the part and for
the whole, e. g. for the whole earth and for a single clod, and for fire and
for a spark.
Suppose (a) that the infinite sensible body is homogeneous. Then each
part will be either immovable or always being carried along. Yet neither
is possible. For why downwards rather than upwards or in any other
direction? I mean, e. g., if you take a clod, (15) where will it be moved or
where will it be at rest? For ex hypothesi the place of the body akin to it
is infinite. Will it occupy the whole place, then? And how? What then
will be the nature of its rest and of its movement, or where will they be?
It will either be at home everywhere—then it will not be moved; or it
will be moved everywhere—then it will not come to rest.
But if (b) the All has dissimilar parts, the proper places of the parts
will be dissimilar also, and the body of the All will have no unity except
that of contact. (20) Then, further, the parts will be either finite or infinite
in variety of kind. (1) Finite they cannot be, for if the All is to be infinite,
some of them would have to be infinite, while the others were not, e. g.
fire or water will be infinite. But, as we have seen before, such an
element would destroy what is contrary to it. (This indeed is the reason
why none of the physicists made fire or earth the one infinite body, (25)
but either water or air or what is intermediate between them, because
the abode of each of the two was plainly determinate, while the others
have an ambiguous place between up and down.)
But (ii) if the parts are infinite in number and simple, their proper
places too will be infinite in number, and the same will be true of the
elements themselves. If that is impossible, and the places are finite, (30)
the whole too must be finite; for the place and the body cannot but fit
each other. Neither is the whole place larger than what can be filled by
the body (and then the body would no longer be infinite), nor is the
body larger than the place; for either there would be an empty space or
a body whose nature it is to be nowhere. (35)
Anaxagoras gives an absurd account of why the infinite is at rest.
[205b] He says that the infinite itself is the cause of its being fixed.
This because it is in itself, since nothing else contains it—on the
assumption that wherever anything is, it is there by its own nature. (5)
But this is not true: a thing could be somewhere by compulsion, and not
where it is its nature to be.
Even if it is true as true can be that the whole is not moved (for what
is fixed by itself and is in itself must be immovable), yet we must explain
why it is not its nature to be moved. It is not enough just to make this
statement and then decamp. Anything else might be in a state of rest,
but there is no reason why it should not be its nature to be moved. (10)
The earth is not carried along, and would not be carried along if it were
infinite, provided it is held together by the centre. But it would not be
because there was no other region in which it could be carried along
that it would remain at the centre, but because this is its nature. Yet in
this case also we may say that it fixes itself. If then in the case of the
earth, supposed to be infinite, it is at rest, not because it is infinite, but
because it has weight and what is heavy rests at the centre and the earth
is at the centre, (15) similarly the infinite also would rest in itself, not
because it is infinite and fixes itself, but owing to some other cause.
Another difficulty emerges at the same time. Any part of the infinite
body ought to remain at rest. Just as the infinite remains at rest in itself
because it fixes itself, (20) so too any part of it you may take will remain
in itself. The appropriate places of the whole and of the part are alike,
e. g. of the whole earth and of a clod the appropriate place is the lower
region; of fire as a whole and of a spark, the upper region. If, therefore,
to be in itself is the place of the infinite, that also will be appropriate to
the part. Therefore it will remain in itself.
In general, the view that there is an infinite body is plainly
incompatible with the doctrine that there is necessarily a proper place
for each kind of body, (25) if every sensible body has either weight or
lightness, and if a body has a natural locomotion towards the centre if it
is heavy, and upwards if it is light. This would need to be true of the
infinite also. But neither character can belong to it: it cannot be either as
a whole, nor can it be half the one and half the other. (30) For how should
you divide it? or how can the infinite have the one part up and the other
down, or an extremity and a centre?
Further, every sensible body is in place, and the kinds or differences of
place are up-down, before-behind, right-left; and these distinctions hold
not only in relation to us and by arbitrary agreement, (35) but also in the
whole itself. But in the infinite body they cannot exist. In general, if it is
impossible that there should be an infinite place, and if every body is in
place, there cannot be an infinite body. [206a]
Surely what is in a special place is in place, and what is in place is in a
special place. Just, then, as the infinite cannot be quantity—that would
imply that it has a particular quantity, (5) e. g. two or three cubits;
quantity just means these—so a thing’s being in place means that it is
somewhere, and that is either up or down or in some other of the six
differences of position: but each of these is a limit.
It is plain from these arguments that there is no body which is actually
infinite.
6
But on the other hand to suppose that the infinite does not exist in
any way leads obviously to many impossible consequences: there will be
a beginning and an end of time, (10) a magnitude will not be divisible
into magnitudes, number will not be infinite. If, then, in view of the
above considerations, neither alternative seems possible, an arbiter must
be called in; and clearly there is a sense in which the infinite exists and
another in which it does not.
We must keep in mind that the word ‘is’ means either what potentially
is or what fully is.
Further, a thing is infinite either by addition or by division. (15)
Now, as we have seen, magnitude is not actually infinite. But by
division it is infinite. (There is no difficulty in refuting the theory of
indivisible lines.) The alternative then remains that the infinite has a
potential existence.
But the phrase ‘potential existence’ is ambiguous. When we speak of
the potential existence of a statue we mean that there will be an actual
statue. It is not so with the infinite. There will not be an actual infinite.
(20) The word ‘is’ has many senses, and we say that the infinite ‘is’ in the
sense in which we say ‘it is day’ or ‘it is the games’, because one thing
after another is always coming into existence. For of these things too the
distinction between potential and actual existence holds. We say that
there are Olympic games, both in the sense that they may occur and that
they are actually occurring.
The infinite exhibits itself in different ways—in time, in the
generations of man, (25) and in the division of magnitudes. For generally
the infinite has this mode of existence: one thing is always being taken
after another, and each thing that is taken is always finite, but always
different. Again, ‘being’ has more than one sense, (30) so that we must not
regard the infinite as a ‘this’, such as a man or a horse, but must suppose
it to exist in the sense in which we speak of the day or the games as
existing—things whose being has not come to them like that of a
substance, but consists in a process of coming to be or passing away;
definite if you like at each stage, yet always different.
But when this takes place in spatial magnitudes, what is taken persists,
while in the succession of time and of men it takes place by the passing
away of these in such a way that the source of supply never gives out.
[206b]
In a way the infinite by addition is the same thing as the infinite by
division. In a finite magnitude, the infinite by addition comes about in a
way inverse to that of the other. For in proportion as we see division
going on, in the same proportion we see addition being made to what is
already marked off. (5) For if we take a determinate part of a finite
magnitude and add another part determined by the same ratio (not taking
in the same amount of the original whole), and so on, we shall not
traverse the given magnitude. (10) But if we increase the ratio of the part,
so as always to take in the same amount, we shall traverse the
magnitude, for every finite magnitude is exhausted by means of any
determinate quantity however small.
The infinite, then, exists in no other way, but in this way it does exist,
potentially and by reduction. It exists fully in the sense in which we say
‘it is day’ or ‘it is the games’; and potentially as matter exists, (15) not
independently as what is finite does.
By addition then, also, there is potentially an infinite, namely, what
we have described as being in a sense the same as the infinite in respect
of division. For it will always be possible to take something ab extra. Yet
the sum of the parts taken will not exceed every determinate magnitude,
just as in the direction of division every determinate magnitude is
surpassed in smallness and there will be a smaller part.
But in respect of addition there cannot be an infinite which even
potentially exceeds every assignable magnitude, (20) unless it has the
attribute of being actually infinite, as the physicists hold to be true of the
body which is outside the world, whose essential nature is air or
something of the kind. But if there cannot be in this way a sensible body
which is infinite in the full sense, (25) evidently there can no more be a
body which is potentially infinite in respect of addition, except as the
inverse of the infinite by division, as we have said. It is for this reason
that Plato also made the infinites two in number, because it is supposed
to be possible to exceed all limits and to proceed ad infinitum in the
direction both of increase and of reduction. Yet though he makes the
infinites two, he does not use them. (30) For in the numbers the infinite in
the direction of reduction is not present, as the monad is the smallest;
nor is the infinite in the direction of increase, for the parts number only
up to the decad.
The infinite turns out to be the contrary of what it is said to be.
[207a] It is not what has nothing outside it that is infinite, but what
always has something outside it. This is indicated by the fact that rings
also that have no bezel are described as ‘endless’, because it is always
possible to take a part which is outside a given part. The description
depends on a certain similarity, but it is not true in the full sense of the
word. (5) This condition alone is not sufficient: it is necessary also that
the next part which is taken should never be the same. In the circle, the
latter condition is not satisfied: it is only the adjacent part from which
the new part is different.
Our definition then is as follows:
A quantity is infinite if it is such that we can always take a part outside
what has been already taken. On the other hand, what has nothing outside
it is complete and whole. For thus we define the whole—that from
which nothing is wanting, (10) as a whole man or a whole box. What is
true of each particular is true of the whole as such—the whole is that of
which nothing is outside. On the other hand that from which something
is absent and outside, however small that may be, is not ‘all’. ‘Whole’
and ‘complete’ are either quite identical or closely akin. Nothing is
complete (teleion) which has no end (telos); and the end is a limit.
Hence Parmenides must be thought to have spoken better than
Melissus. (15) The latter says that the whole is infinite, but the former
describes it as limited, ‘equally balanced from the middle’. For to
connect the infinite with the all and the whole is not like joining two
pieces of string; for it is from this they get the dignity they ascribe to the
infinite—its containing all things and holding the all in itself—from its
having a certain similarity to the whole. (20) It is in fact the matter of the
completeness which belongs to size, and what is potentially a whole,
though not in the full sense. It is divisible both in the direction of
reduction and of the inverse addition. It is a whole and limited; not,
however, in virtue of its own nature, but in virtue of what is other than
it. It does not contain, but, in so far as it is infinite, is contained.
Consequently, also, it is unknowable, qua infinite; for the matter has no
form. (25) (Hence it is plain that the infinite stands in the relation of part
rather than of whole. For the matter is part of the whole, as the bronze is
of the bronze statue.) If it contains in the case of sensible things, in the
case of intelligible things the great and the small ought to contain them.
But it is absurd and impossible to suppose that the unknowable and
indeterminate should contain and determine. (30)
7
It is reasonable that there should not be held to be an infinite in
respect of addition such as to surpass every magnitude, but that there
should be thought to be such an infinite in the direction of division. For
the matter and the infinite are contained inside what contains them, (35)
while it is the form which contains. [207b] It is natural too to suppose
that in number there is a limit in the direction of the minimum, and that
in the other direction every assigned number is surpassed. In magnitude,
on the contrary, every assigned magnitude is surpassed in the direction
of smallness, while in the other direction there is no infinite magnitude.
The reason is that what is one is indivisible whatever it may be, (5) e. g. a
man is one man, not many. Number on the other hand is a plurality of
‘ones’ and a certain quantity of them. Hence number must stop at the
indivisible: for ‘two’ and ‘three’ are merely derivative terms, and so with
each of the other numbers. But in the direction of largeness it is always
possible to think of a larger number: for the number of times a
magnitude can be bisected is infinite. (10) Hence this infinite is potential,
never actual: the number of parts that can be taken always surpasses any
assigned number. But this number is not separable from the process of
bisection, and its infinity is not a permanent actuality but consists in a
process of coming to be, like time and the number of time.
With magnitudes the contrary holds. (15) What is continuous is divided
ad infinitum, but there is no infinite in the direction of increase. For the
size which it can potentially be, it can also actually be. Hence since no
sensible magnitude is infinite, it is impossible to exceed every assigned
magnitude; for if it were possible there would be something bigger than
the heavens. (20)
The infinite is not the same in magnitude and movement and time, in
the sense of a single nature, but its secondary sense depends on its
primary sense, i. e. movement is called infinite in virtue of the
magnitude covered by the movement (or alteration or growth), (25) and
time because of the movement. (I use these terms for the moment. Later
I shall explain what each of them means, and also why every magnitude
is divisible into magnitudes.)
Our account does not rob the mathematicians of their science, by
disproving the actual existence of the infinite in the direction of
increase, in the sense of the untraversable. In point of fact they do not
need the infinite and do not use it. (30) They postulate only that the finite
straight line may be produced as far as they wish. It is possible to have
divided in the same ratio as the largest quantity another magnitude of
any size you like. Hence, for the purposes of proof, it will make no
difference to them to have such an infinite instead, while its existence
will be in the sphere of real magnitudes.
In the four-fold scheme of causes, (35) it is plain that the infinite is a
cause in the sense of matter, and that its essence is privation, the subject
as such being what is continuous and sensible. [208a] All the other
thinkers, too, evidently treat the infinite as matter—that is why it is
inconsistent in them to make it what contains, and not what is
contained.
8
It remains to dispose of the arguments8 which are supposed to
support the view that the infinite exists not only potentially but as a
separate thing. (5) Some have no cogency; others can be met by fresh
objections that are valid.
(1) In order that coming to be should not fail, it is not necessary that
there should be a sensible body which is actually infinite. (10) The passing
away of one thing may be the coming to be of another, the All being
limited.
(2) There is a difference between touching and being limited. The
former is relative to something and is the touching of something (for
everything that touches touches something), and further is an attribute
of some one of the things which are limited. On the other hand, what is
limited is not limited in relation to anything. Again, contact is not
necessarily possible between any two things taken at random.
(3) To rely on mere thinking is absurd, for then the excess or defect is
not in the thing but in the thought. (15) One might think that one of us is
bigger than he is and magnify him ad infinitum. But it does not follow
that he is bigger than the size we are, just because some one thinks he is,
but only because he is the size he is. The thought is an accident.
(a) Time indeed and movement are infinite, and also thinking,
(20)
in the sense that each part
that is taken passes in succession out of existence.
(b) Magnitude is not infinite either in the way of reduction or of magnification in thought.
This concludes my account of the way in which the infinite exists, and
of the way in which it does not exist, and of what it is.
1
viii. 5.
2
Plato in the Timaeus (52 E, 57 E, 58 A) makes motion depend on inequality.
3
i. e. we can substitute ‘mover’ and ‘moved’ for ‘agent’ and ‘patient’ in the formulation of the
hypothesis.
4
Cf. a18–20.
5
Aristotle’s general meaning is fairly plain. He is describing two constructions: in the one odd
gnomons are placed round the one, in the other even gnomons are placed round the two.
6
Aristotle does not regard them as elements.
7
The reference is probably to Anaximander.
8
Cf. 203b 15–30.
BOOK IV
1
The physicist must have a knowledge of Place, too, as well as of the
infinite—namely, whether there is such a thing or not, and the manner
of its existence and what it is—both because all suppose that things
which exist are somewhere (the non-existent is nowhere—where is the
goat-stag or the sphinx?), (30) and because ‘motion’ in its most general
and primary sense is change of place, which we call ‘locomotion’.
The question, what is place? presents many difficulties. An
examination of all the relevant facts seems to lead to divergent
conclusions. Moreover, we have inherited nothing from previous
thinkers, (35) whether in the way of a statement of difficulties or of a
solution.
The existence of place is held to be obvious from the fact of mutual
replacement. [208b] Where water now is, there in turn, when the
water has gone out as from a vessel, air is present. When therefore
another body occupies this same place, the place is thought to be
different from all the bodies which come to be in it and replace one
another. (5) What now contains air formerly contained water, so that
clearly the place or space into which and out of which they passed was
something different from both.
Further, the typical locomotions of the elementary natural bodies—
namely, fire, earth, and the like—show not only that place is something,
(10) but also that it exerts a certain influence. Each is carried to its own
place, if it is not hindered, the one up, the other down. Now these are
regions or kinds of place—up and down and the rest of the six
directions. Nor do such distinctions (up and down and right and left, (15)
&c.) hold only in relation to us. To us they are not always the same but
change with the direction in which we are turned: that is why the same
thing may be both right and left, up and down, before and behind. But in
nature each is distinct, taken apart by itself. It is not every chance
direction which is ‘up’, (20) but where fire and what is light are carried;
similarly, too, ‘down’ is not any chance direction but where what has
weight and what is made of earth are carried—the implication being
that these places do not differ merely in relative position, but also as
possessing distinct potencies. This is made plain also by the objects
studied by mathematics. Though they have no real place, they
nevertheless, in respect of their position relatively to us, have a right and
left as attributes ascribed to them only in consequence of their relative
position, not having by nature these various characteristics. Again, (25)
the theory that the void exists involves the existence of place: for one
would define void as place bereft of body.
These considerations then would lead us to suppose that place is
something distinct from bodies, and that every sensible body is in place.
Hesiod too might be held to have given a correct account of it when he
made chaos first. (30) At least he says:
First of all things came chaos to being, then broad-breasted earth,
implying that things need to have space first, because he thought, with
most people, that everything is somewhere and in place. If this is its
nature, the potency of place must be a marvellous thing, (35) and take
precedence of all other things. For that without which nothing else can
exist, while it can exist without the others, must needs be first; for place
does not pass out of existence when the things in it are annihilated.
[209a]
True, but even if we suppose its existence settled, the question of its
nature presents difficulty—whether it is some sort of ‘bulk’ of body or
some entity other than that, for we must first determine its genus.
(1) Now it has three dimensions, (5) length, breadth, depth, the
dimensions by which all body also is bounded. But the place cannot be
body; for if it were there would be two bodies in the same place.
(2) Further, if body has a place and space, clearly so too have surface
and the other limits of body; for the same statement will apply to them:
where the bounding planes of the water were, there in turn will be those
of the air. But when we come to a point we cannot make a distinction
between it and its place. (10) Hence if the place of a point is not different
from the point, no more will that of any of the others be different, and
place will not be something different from each of them.
(3) What in the world then are we to suppose place to be? If it has the
sort of nature described, it cannot be an element or composed of
elements, whether these be corporeal or incorporeal: for while it has
size, (15) it has not body. But the elements of sensible bodies are bodies,
while nothing that has size results from a combination of intelligible
elements.
(4) Also we may ask: of what in things is space the cause? None of the
four modes of causation can be ascribed to it. It is neither cause in the
sense of the matter of existents (for nothing is composed of it), (20) nor as
the form and definition of things, nor as end, nor does it move existents.
(5) Further, too, if it is itself an existent, where will it be? Zeno’s
difficulty demands an explanation: for if everything that exists has a
place, (25) place too will have a place, and so on ad infinitum.
(6) Again, just as every body is in place, so, too, every place has a
body in it. What then shall we say about growing things? It follows from
these premisses that their place must grow with them, if their place is
neither less nor greater than they are.
By asking these questions, then, we must raise the whole problem
about place—not only as to what it is, but even whether there is such a
thing. (30)
2
We may distinguish generally between predicating B of A because it
(A) is itself, and because it is something else; and particularly between
place which is common and in which all bodies are, and the special
place occupied primarily by each. I mean, for instance, that you are now
in the heavens because you are in the air and it is in the heavens; and
you are in the air because you are on the earth; and similarly on the
earth because you are in this place which contains no more than you. (35)
Now if place is what primarily contains each body, it would be a limit,
so that the place would be the form or shape of each body by which the
magnitude or the matter of the magnitude is defined: for this is the limit
of each body. [209b]
If, (5) then, we look at the question in this way the place of a thing is
its form. But, if we regard the place as the extension of the magnitude, it
is the matter. For this is different from the magnitude: it is what is
contained and defined by the form, as by a bounding plane. Matter or
the indeterminate is of this nature; when the boundary and attributes of
a sphere are taken away, (10) nothing but the matter is left.
This is why Plato in the Timaeus1 says that matter and space are the
same; for the ‘participant’ and space are identical. (It is true, indeed, that
the account he gives there of the ‘participant’ is different from what he
says in his so-called ‘unwritten teaching’.2 (15) Nevertheless, he did
identify place and space.) I mention Plato because, while all hold place
to be something, he alone tried to say what it is.
In view of these facts we should naturally expect to find difficulty in
determining what place is, if indeed it is one of these two things, (20)
matter or form. They demand a very close scrutiny, especially as it is not
easy to recognize them apart.
But it is at any rate not difficult to see that place cannot be either of
them. The form and the matter are not separate from the thing, whereas
the place can be separated. As we pointed out,3 where air was, (25) water
in turn comes to be, the one replacing the other; and similarly with other
bodies. Hence the place of a thing is neither a part nor a state of it, but is
separable from it. For place is supposed to be something like a vessel—
the vessel being a transportable place. But the vessel is no part of the
thing.
In so far then as it is separable from the thing, (30) it is not the form:
qua containing, it is different from the matter.
Also it is held that what is anywhere is both itself something and that
there is a different thing outside it.4 (Plato of course, if we may digress,
ought to tell us why the form and the numbers are not in place, (35) if
‘what participates’ is place—whether what participates is the Great and
the Small or the matter, as he called it in writing in the Timaeus.)
[210a]
Further, how could a body be carried to its own place, if place was the
matter or the form? It is impossible that what has no reference to motion
or the distinction of up and down can be place. So place must be looked
for among things which have these characteristics.
If the place is in the thing (it must be if it is either shape or matter)
place will have a place: for both the form and the indeterminate undergo
change and motion along with the thing, (5) and are not always in the
same place, but are where the thing is. Hence the place will have a
place.
Further, when water is produced from air, the place has been
destroyed, for the resulting body is not in the same place. (10) What sort
of destruction then is that?
This concludes my statement of the reasons why space must be
something, and again of the difficulties that may be raised about its
essential nature.
3
The next step we must take is to see in how many senses one thing
is said to be ‘in’ another.
(1) As the finger is ‘in’ the hand and generally the part ‘in’ the whole. (15)
(2) As the whole is ‘in’ the parts: for there is no whole over and above the parts.
(3) As man is ‘in’ animal and generally species ‘in’ genus.
(4) As the genus is ‘in’ the species and generally the part of the specific form ‘in’ the definition
of the specific form.
(5) As health is ‘in’ the hot and the cold and generally the form ‘in’ the matter. (20)
(6) As the affairs of Greece centre ‘in’ the king, and generally events centre ‘in’ their primary
motive agent.
(7) As the existence of a thing centres ‘in’ its good and generally ‘in’ its end, i. e. ‘in that for the
sake of which’ it exists.
(8) In the strictest sense of all, as a thing is ‘in’ a vessel, and generally ‘in’ place.
One might raise the question whether a thing can be in itself, (25) or
whether nothing can be in itself—everything being either nowhere or in
something else.
The question is ambiguous; we may mean the thing qua itself or qua
something else.
When there are parts of a whole—the one that in which a thing is, the
other the thing which is in it—the whole will be described as being in
itself. For a thing is described in terms of its parts, as well as in terms of
the thing as a whole, e. g. a man is said to be white because the visible
surface of him is white, or to be scientific because his thinking faculty
has been trained. The jar then will not be in itself and the wine will not
be in itself. (30) But the jar of wine will: for the contents and the
container are both parts of the same whole.
In this sense then, but not primarily, a thing can be in itself, namely,
as ‘white’ is in body (for the visible surface is in body), and science is in
the mind.
[210b] It is from these, which are ‘parts’ (in the sense at least of
being ‘in’ the man), that the man is called white, &c. But the jar and the
wine in separation are not parts of a whole, though together they are. So
when there are parts, a thing will be in itself, as ‘white’ is in man
because it is in body, and in body because it resides in the visible
surface. (5) We cannot go further and say that it is in surface in virtue of
something other than itself. (Yet it is not in itself: though these are in a
way the same thing,) they differ in essence, each having a special nature
and capacity, ‘surface’ and ‘white’.
Thus if we look at the matter inductively we do not find anything to
be ‘in’ itself in any of the senses that have been distinguished; and it can
be seen by argument that it is impossible. (10) For each of two things will
have to be both, e. g. the jar will have to be both vessel and wine, and
the wine both wine and jar, if it is possible for a thing to be in itself; so
that, however true it might be that they were in each other, the jar will
receive the wine in virtue not of its being wine but of the wine’s being
wine, (15) and the wine will be in the jar in virtue not of its being a jar
but of the jar’s being a jar. Now that they are different in respect of their
essence is evident; for ‘that in which something is’ and ‘that which is in
it’ would be differently defined.
Nor is it possible for a thing to be in itself even incidentally: for two
things would be at the same time in the same thing. (20) The jar would be
in itself—if a thing whose nature it is to receive can be in itself; and that
which it receives, namely (if wine) wine, will be in it. Obviously then a
thing cannot be in itself primarily.
Zeno’s problem—that if Place is something it must be in something—is
not difficult to solve. There is nothing to prevent the first place from
being ‘in’ something else—not indeed in that as ‘in’ place, (25) but as
health is ‘in’ the hot as a positive determination of it or as the hot is ‘in’
body as an affection. So we escape the infinite regress.
Another thing is plain: since the vessel is no part of what is in it (what
contains in the strict sense is different from what is contained), place
could not be either the matter or the form of the thing contained, (30) but
must be different—for the latter, both the matter and the shape, are
parts of what is contained.
This then may serve as a critical statement of the difficulties involved.
4
What then after all is place? The answer to this question may be
elucidated as follows.
Let us take for granted about it the various characteristics which are
supposed correctly to belong to it essentially. We assume then—
(1) Place is what contains that of which it is the place.
(2) Place is no part of the thing. [211a]
(3) The immediate place of a thing is neither less nor greater than the thing.
(4) Place can be left behind by the thing and is separable.
In addition:
(5) All place admits of the distinction of up and down, and each of the bodies is naturally
carried to its appropriate place and rests there, and this makes the place either up or down.
(5)
Having laid these foundations, we must complete the theory. We
ought to try to make our investigation such as will render an account of
place, and will not only solve the difficulties connected with it, but will
also show that the attributes supposed to belong to it do really belong to
it, and further will make clear the cause of the trouble and of the
difficulties about it. (10) Such is the most satisfactory kind of exposition.
First then we must understand that place would not have been
thought of, if there had not been a special kind of motion, namely that
with respect to place. It is chiefly for this reason that we suppose the
heaven also to be in place, because it is in constant movement. Of this
kind of change there are two species—locomotion on the one hand and,
(15) on the other, increase and diminution. For these too involve variation
of place: what was then in this place has now in turn changed to what is
larger or smaller.
Again, when we say a thing is ‘moved’, the predicate either (1)
belongs to it actually, in virtue of its own nature, or (2) in virtue of
something conjoined with it. In the latter case it may be either (a)
something which by its own nature is capable of being moved, (20) e. g.
the parts of the body or the nail in the ship, or (b) something which is
not in itself capable of being moved, but is always moved through its
conjunction with something else, as ‘whiteness’ or ‘science’. These have
changed their place only because the subjects to which they belong do
so.
We say that a thing is in the world, in the sense of in place, because it
is in the air, and the air is in the world; and when we say it is in the air,
(25) we do not mean it is in every part of the air, but that it is in the air
because of the outer surface of the air which surrounds it; for if all the
air were its place, the place of a thing would not be equal to the thing—
which it is supposed to be, and which the primary place in which a thing
is actually is.
When what surrounds, then, is not separate from the thing, (30) but is
in continuity with it, the thing is said to be in what surrounds it, not in
the sense of in place, but as a part in a whole. But when the thing is
separate and in contact, it is immediately ‘in’ the inner surface of the
surrounding body, and this surface is neither a part of what is in it nor
yet greater than its extension, but equal to it; for the extremities of
things which touch are coincident.
Further, if one body is in continuity with another, (35) it is not moved
in that but with that. On the other hand it is moved in that if it is
separate. It makes no difference whether what contains is moved or not.
[211b] Again, when it is not separate it is described as a part in a
whole, as the pupil in the eye or the hand in the body: when it is
separate, as the water in the cask or the wine in the jar. For the hand is
moved with the body and the water in the cask.
It will now be plain from these considerations what place is. (5) There
are just four things of which place must be one—the shape, or the
matter, or some sort of extension between the bounding surfaces of the
containing body, or this boundary itself if it contains no extension over
and above the bulk of the body which comes to be in it.
Three of these it obviously cannot be:
(1) The shape is supposed to be place because it surrounds, (10) for the
extremities of what contains and of what is contained are coincident.
Both the shape and the place, it is true, are boundaries. But not of the
same thing: the form is the boundary of the thing, the place is the
boundary of the body which contains it.
(2) The extension between the extremities is thought to be something,
because what is contained and separate may often be changed while the
container remains the same (as water may be poured from a vessel)—the
assumption being that the extension is something over and above the
body displaced. (15) But there is no such extension. One of the bodies
which change places and are naturally capable of being in contact with
the container falls in—whichever it may chance to be.
If there were an extension which were such as to exist independently
and be permanent, (20) there would be an infinity of places in the same
thing. For when the water and the air change places, all the portions of
the two together will play the same part in the whole which was
previously played by all the water in the vessel; at the same time the
place too will be undergoing change; so that there will be another place
which is the place of the place, and many places will be coincident. (25)
There is not a different place of the part, in which it is moved, when the
whole vessel changes its place: it is always the same: for it is in the
(proximate) place where they are that the air and the water (or the parts
of the water) succeed each other, not in that place in which they come to
be, which is part of the place which is the place of the whole world.
(3) The matter, too, might seem to be place, at least if we consider it
in what is at rest and is thus separate but in continuity. (30) For just as in
change of quality there is something which was formerly black and is
now white, or formerly soft and now hard—this is just why we say that
the matter exists—so place, because it presents a similar phenomenon, is
thought to exist—only in the one case we say so because what was air is
now water, (35) in the other because where air formerly was there is now
water. [212a] But the matter, as we said before,5 is neither separable
from the thing nor contains it, whereas place has both characteristics.
Well, then, if place is none of the three—neither the form nor the
matter nor an extension which is always there, different from, and over
and above, the extension of the thing which is displaced—place
necessarily is the one of the four which is left, namely, (5) the boundary
of the containing body at which it is in contact with the contained body.
(By the contained body is meant what can be moved by way of
locomotion.)
Place is thought to be something important and hard to grasp, both
because the matter and the shape present themselves along with it, and
because the displacement of the body that is moved takes place in a
stationary container, for it seems possible that there should be an
interval which is other than the bodies which are moved. (10) The air,
too, which is thought to be incorporeal, contributes something to the
belief: it is not only the boundaries of the vessel which seem to be place,
but also what is between them, regarded as empty. Just, in fact, as the
vessel is transportable place, so place is a non-portable vessel. So when
what is within a thing which is moved, is moved and changes its place,
(15) as a boat on a river, what contains plays the part of a vessel rather
than that of place. Place on the other hand is rather what is motionless:
so it is rather the whole river that is place, because as a whole it is
motionless.
Hence we conclude that the innermost motionless boundary of what
contains is place. (20)
This explains why the middle of the heaven and the surface which
faces us of the rotating system are held to be ‘up’ and ‘down’ in the strict
and fullest sense for all men: for the one is always at rest, while the
inner side of the rotating body remains always coincident with itself. (25)
Hence since the light is what is naturally carried up, and the heavy what
is carried down, the boundary which contains in the direction of the
middle of the universe, and the middle itself, are down, and that which
contains in the direction of the outermost part of the universe, and the
outermost part itself, are up.
For this reason, too, place is thought to be a kind of surface, and as it
were a vessel, i. e. a container of the thing.
Further, (30) place is coincident with the thing, for boundaries are
coincident with the bounded.
5
If then a body has another body outside it and containing it, it is in
place, and if not, not. That is why, even if there were to be water which
had not a container, the parts of it, on the one hand, will be moved (for
one part is contained in another), while, on the other hand, (35) the
whole will be moved in one sense, but not in another. For as a whole it
does not simultaneously change its place, though it will be moved in a
circle: for this place is the place of its parts. [212b] (Some things are
moved, not up and down, but in a circle; others up and down, such
things namely as admit of condensation and rarefaction.)
As was explained,6 some things are potentially in place, others
actually. So, when you have a homogeneous substance which is
continuous, (5) the parts are potentially in place: when the parts are
separated, but in contact, like a heap, they are actually in place.
Again, (1) some things are per se in place, namely every body which is
movable either by way of locomotion or by way of increase is per se
somewhere, but the heaven, as has been said,7 is not anywhere as a
whole, nor in any place, if at least, as we must suppose, (10) no body
contains it. On the line on which it is moved, its parts have place: for
each is contiguous to the next.
But (2) other things are in place indirectly, through something
conjoined with them, as the soul and the heaven. The latter is, in a way,
in place, for all its parts are: for on the orb one part contains another.
That is why the upper part is moved in a circle, while the All is not
anywhere. (15) For what is somewhere is itself something, and there must
be alongside it some other thing wherein it is and which contains it. But
alongside the All or the Whole there is nothing outside the All, and for
this reason all things are in the heaven; for the heaven, we may say, is
the All. Yet their place is not the same as the heaven. It is part of it, the
innermost part of it, which is in contact with the movable body; and for
this reason the earth is in water, (20) and this in the air, and the air in the
aether, and the aether in heaven, but we cannot go on and say that the
heaven is in anything else.
It is clear, too, from these considerations that all the problems which
were raised8 about place will be solved when it is explained in this way:
(1) There is no necessity that the place should grow with the body in it,
(2) Nor that a point should have a place,
(3) Nor that two bodies should be in the same place, (25)
(4) Nor that place should be a corporeal interval: for what is between the boundaries of the
place is any body which may chance to be there, not an interval in body.
Further, (5) place is also somewhere, not in the sense of being in a
place, but as the limit is in the limited; for not everything that is is in
place, but only movable body.
Also (6) it is reasonable that each kind of body should be carried to its
own place. For a body which is next in the series and in contact (not by
compulsion) is akin, (30) and bodies which are united do not affect each
other, while those which are in contact interact on each other.
Nor (7) is it without reason that each should remain naturally in its
proper place. For this part has the same relation to its place, (35) as a
separable part to its whole, as when one moves a part of water or air: so,
too, air is related to water, for the one is like matter, the other form—
water is the matter of air, air as it were the actuality of water, for water
is potentially air, while air is potentially water, though in another way.
[213a]
These distinctions will be drawn more carefully later.9 On the present
occasion it was necessary to refer to them: what has now been stated
obscurely will then be made more clear. (5) If the matter and the
fulfilment are the same thing (for water is both, the one potentially, the
other completely), water will be related to air in a way as part to whole.
That is why these have contact: it is organic union when both become
actually one.
This concludes my account of place—both of its existence and of its
nature. (10)
6
The investigation of similar questions about the void, also, must be
held to belong to the physicist—namely whether it exists or not, and
how it exists or what it is—just as about place. The views taken of it
involve arguments both for and against, in much the same sort of way.
(15) For those who hold that the void exists regard it as a sort of place or
vessel which is supposed to be ‘full’ when it holds the bulk which it is
capable of containing, ‘void’ when it is deprived of that—as if ‘void’ and
‘full’ and ‘place’ denoted the same thing, though the essence of the three
is different.
We must begin the inquiry by putting down the account given by
those who say that it exists, (20) then the account of those who say that it
does not exist, and third the current view on these questions.
Those who try to show that the void does not exist do not disprove
what people really mean by it, but only their erroneous way of speaking;
this is true of Anaxagoras and of those who refute the existence of the
void in this way. (25) They merely give an ingenious demonstration that
air is something—by straining wine-skins and showing the resistance of
the air, and by cutting it off in clepsydras. But people really mean that
there is an empty interval in which there is no sensible body. They hold
that everything which is is body and say that what has nothing in it at
all is void (so what is full of air is void). (30) It is not then the existence of
air that needs to be proved, but the non-existence of an interval,
different from the bodies, either separable or actual—an interval which
divides the whole body so as to break its continuity, as Democritus and
Leucippus hold, and many other physicists—or even perhaps as
something which is outside the whole body, which remains continuous.
[213b]
These people, then, have not reached even the threshold of the
problem, but rather those who say that the void exists.
(1) They argue, for one thing, (5) that change in place (i. e. locomotion
and increase) would not be. For it is maintained that motion would seem
not to exist, if there were no void, since what is full cannot contain
anything more. If it could, and there were two bodies in the same place,
it would also be true that any number of bodies could be together; for it
is impossible to draw a line of division beyond which the statement
would become untrue. If this were possible, (10) it would follow also that
the smallest body would contain the greatest; for ‘many a little makes a
mickle’: thus if many equal bodies can be together, so also can many
unequal bodies.
Melissus, indeed, infers from these considerations that the All is
immovable; for if it were moved there must, he says, be void, but void is
not among the things that exist.
This argument, then, is one way in which they show that there is a
void.
(2) They reason from the fact that some things are observed to
contract and be compressed, (15) as people say that a cask will hold the
wine which formerly filled it, along with the skins into which the wine
has been decanted, which implies that the compressed body contracts
into the voids present in it.
Again (3) increase, too, is thought to take place always by means of
void, for nutriment is body, and it is impossible for two bodies to be
together. (20) A proof of this they find also in what happens to ashes,
which absorb as much water as the empty vessel.
The Pythagoreans, too, (4) held that void exists and that it enters the
heaven itself, which as it were inhales it, from the infinite air. Further it
is the void which distinguishes the natures of things, (25) as if it were like
what separates and distinguishes the terms of a series. This holds
primarily in the numbers, for the void distinguishes their nature.
These, then, and so many, are the main grounds on which people have
argued for and against the existence of the void.
7
As a step towards settling which view is true, (30) we must determine
the meaning of the name.
The void is thought to be place with nothing in it. The reason for this
is that people take what exists to be body, and hold that while every
body is in place, void is place in which there is no body, so that where
there is no body, there must be void.
Every body, again, they suppose to be tangible; and of this nature is
whatever has weight or lightness. [214a]
Hence, by a syllogism, what has nothing heavy or light in it, is void.
This result, then, as I have said, is reached by syllogism. It would be
absurd to suppose that the point is void; for the void must be place
which has in it an interval in tangible body. (5)
But at all events we observe then that in one way the void is described
as what is not full of body perceptible to touch; and what has heaviness
and lightness is perceptible to touch. So we would raise the question:
what would they say of an interval that has colour or sound—is it void
or not? Clearly they would reply that if it could receive what is tangible
it was void, (10) and if not, not.
In another way void is that in which there is no ‘this’ or corporeal
substance. So some say that the void is the matter of the body (they
identify the place, too, with this), and in this they speak incorrectly; for
the matter is not separable from the things, (15) but they are inquiring
about the void as about something separable.
Since we have determined the nature of place, and void must, if it
exists, be place deprived of body, and we have stated both in what sense
place exists and in what sense it does not, it is plain that on this showing
void does not exist, (20) either unseparated or separated; for the void is
meant to be, not body but rather an interval in body. This is why the
void is thought to be something, viz. because place is, and for the same
reasons. For the fact of motion in respect of place comes to the aid both
of those who maintain that place is something over and above the bodies
that come to occupy it, and of those who maintain that the void is
something. They state that the void is the condition of movement in the
sense of that in which movement takes place; and this would be the kind
of thing that some say place is. (25)
But there is no necessity for there being a void if there is movement. It
is not in the least needed as a condition of movement in general, for a
reason which, incidentally, escaped Melissus; viz. that the full can suffer
qualitative change.
But not even movement in respect of place involves a void; for bodies
may simultaneously make room for one another, (30) though there is no
interval separate and apart from the bodies that are in movement. And
this is plain even in the rotation of continuous things, as in that of
liquids.
And things can also be compressed not into a void but because they
squeeze out what is contained in them (as, for instance, when water is
compressed the air within it is squeezed out); and things can increase in
size not only by the entrance of something but also by qualitative
change; e. g. if water were to be transformed into air. [214b]
In general, both the argument about increase of size and that about
the water poured on to the ashes get in their own way. (5) For either not
any and every part of the body is increased, or bodies may be increased
otherwise than by the addition of body, or there may be two bodies in
the same place (in which case they are claiming to solve a quite general
difficulty, but are not proving the existence of void), or the whole body
must be void, if it is increased in every part and is increased by means of
void. The same argument applies to the ashes.
It is evident, (10) then, that it is easy to refute the arguments by which
they prove the existence of the void.
8
Let us explain again that there is no void existing separately, as
some maintain. If each of the simple bodies has a natural locomotion,
e. g. fire upward and earth downward and towards the middle of the
universe, (15) it is clear that it cannot be the void that is the condition of
locomotion. What, then, will the void be the condition of? It is thought
to be the condition of movement in respect of place, and it is not the
condition of this.
Again, if void is a sort of place deprived of body, when there is a void
where will a body placed in it move to? It certainly cannot move into
the whole of the void. The same argument applies as against those who
think that place is something separate, (20) into which things are carried;
viz. how will what is placed in it move, or rest? Much the same
argument will apply to the void as to the ‘up’ and ‘down’ in place, as is
natural enough since those who maintain the existence of the void make
it a place.
And in what way will things be present either in place or in the void?
For the expected10 result does not take place when a body is placed as a
whole in a place conceived of as separate and permanent; for a part of it,
(25) unless it be placed apart, will not be in a place but in the whole.
Further, if separate place does not exist, neither will void.
If people say that the void must exist, as being necessary if there is to
be movement, what rather turns out to be the case, if one studies the
matter, is the opposite, that not a single thing can be moved if there is a
void; for as with those who for a like reason say the earth is at rest, (30)
so, too, in the void things must be at rest; for there is no place to which
things can move more or less than to another; since the void in so far as
it is void admits no difference.
[215a] The second reason is this: all movement is either compulsory
or according to nature, and if there is compulsory movement there must
also be natural (for compulsory movement is contrary to nature, and
movement contrary to nature is posterior to that according to nature, so
that if each of the natural bodies has not a natural movement, none of
the other movements can exist); but how can there be natural movement
if there is no difference throughout the void or the infinite? For in so far
as it is infinite, (5) there will be no up or down or middle, and in so far as
it is a void, up differs no whit from down; for as there is no difference in
what is nothing, there is none in the void (for the void seems to be a
non-existent and a privation of being), (10) but natural locomotion seems
to be differentiated, so that the things that exist by nature must be
differentiated. Either, then, nothing has a natural locomotion, or else
there is no void.
Further, in point of fact things that are thrown move though that
which gave them their impulse is not touching them, either by reason of
mutual replacement, (15) as some maintain, or because the air that has
been pushed pushes them with a movement quicker than the natural
locomotion of the projectile wherewith it moves to its proper place. But
in a void none of these things can take place, nor can anything be moved
save as that which is carried is moved.
Further, no one could say why a thing once set in motion should stop
anywhere; for why should it stop here rather than here? So that a thing
will either be at rest or must be moved ad infinitum, (20) unless something
more powerful get in its way.
Further, things are now thought to move into the void because it
yields; but in a void this quality is present equally everywhere, so that
things should move in all directions.
Further, the truth of what we assert is plain from the following
considerations. (25) We see the same weight or body moving faster than
another for two reasons, either because there is a difference in what it
moves through, as between water, air, and earth, or because, other
things being equal, the moving body differs from the other owing to
excess of weight or of lightness.
Now the medium causes a difference because it impedes the moving
thing, most of all if it is moving in the opposite direction, (30) but in a
secondary degree even if it is at rest; and especially a medium that is not
easily divided, i. e. a medium that is somewhat dense.
[215b] A, then, will move through B in time C, and through D,
which is thinner, in time E (if the length of B is equal to D), in
proportion to the density of the hindering body. For let B be water and D
air; then by so much as air is thinner and more incorporeal than water,
(5) A will move through D faster than through B. Let the speed have the
same ratio to the speed, then, that air has to water. Then if air is twice
as thin, the body will traverse B in twice the time that it does D, and the
time C will be twice the time E. And always, (10) by so much as the
medium is more incorporeal and less resistant and more easily divided,
the faster will be the movement.
Now there is no ratio in which the void is exceeded by body, as there
is no ratio of o to a number. For if 4 exceeds 3 by 1, (15) and 2 by more
than 1, and 1 by still more than it exceeds 2, still there is no ratio by
which it exceeds o; for that which exceeds must be divisible into the
excess + that which is exceeded, so that 4 will be what it exceeds o by
+ o. For this reason, too, a line does not exceed a point—unless it is
composed of points! Similarly the void can bear no ratio to the full, (20)
and therefore neither can movement through the one to movement
through the other, but if a thing moves through the thickest medium
such and such a distance in such and such a time, it moves through the
void with a speed beyond any ratio. For let F be void, equal in
magnitude to B and to D. Then if A is to traverse and move through it in
a certain time, G, a time less than E, however, (25) the void will bear this
ratio to the full. But in a time equal to G, A will traverse the part H of D.
And it will surely also traverse in that time any substance F which
exceeds air in thickness in the ratio which the time E bears to the time
G. For if the body F be as much thinner than D as E exceeds G, (30) A, if it
moves through F, will traverse it in a time inverse to the speed of the
movement, i. e. in a time equal to G. [216a] If, then, there is no body
in F, A will traverse F still more quickly. But we supposed that its
traverse of F when F was void occupied the time G. So that it will
traverse F in an equal time whether F be full or void. But this is
impossible. It is plain, then, that if there is a time in which it will move
through any part of the void, this impossible result will follow: it will be
found to traverse a certain distance, (5) whether this be full or void, in an
equal time; for there will be some body which is in the same ratio to the
other body as the time is to the time.
To sum the matter up, the cause of this result is obvious, viz. that
between any two movements there is a ratio (for they occupy time, and
there is a ratio between any two times, so long as both are finite), (10) but
there is no ratio of void to full.
These are the consequences that result from a difference in the media;
the following depend upon an excess of one moving body over another.
We see that bodies which have a greater impulse either of weight or of
lightness, if they are alike in other respects, (15) move faster over an
equal space, and in the ratio which their magnitudes bear to each other.
Therefore they will also move through the void with this ratio of speed.
But that is impossible; for why should one move faster? (In moving
through plena it must be so; for the greater divides them faster by its
force. For a moving thing cleaves the medium either by its shape, or by
the impulse which the body that is carried along or is projected
possesses.) Therefore all will possess equal velocity. (20) But this is
impossible.
It is evident from what has been said, then, that, if there is a void, a
result follows which is the very opposite of the reason for which those
who believe in a void set it up. They think that if movement in respect of
place is to exist, the void cannot exist, separated all by itself; but this is
the same as to say that place is a separate cavity; and this has already
been stated to be impossible.11 (25)
But even if we consider it on its own merits the so-called vacuum will
be found to be really vacuous. For as, if one puts a cube in water, an
amount of water equal to the cube will be displaced; so too in air; but
the effect is imperceptible to sense. And indeed always, (30) in the case of
any body that can be displaced, it must, if it is not compressed, be
displaced in the direction in which it is its nature to be displaced—
always either down, if its locomotion is downwards as in the case of
earth, or up, if it is fire, or in both directions—whatever be the nature of
the inserted body. Now in the void this is impossible; for it is not body;
the void must have penetrated the cube to a distance equal to that which
this portion of void formerly occupied in the void, (35) just as if the water
or air had not been displaced by the wooden cube, but had penetrated
right through it. [216b]
But the cube also has a magnitude equal to that occupied by the void;
a magnitude which, if it is also hot or cold, or heavy or light, (5) is none
the less different in essence from all its attributes, even if it is not
separable from them; I mean the volume of the wooden cube. So that
even if it were separated from everything else and were neither heavy
nor light, it will occupy an equal amount of void, and fill the same place,
as the part of place or of the void equal to itself. How then will the body
of the cube differ from the void or place that is equal to it? And if there
can be two such things, (10) why cannot there be any number coinciding?
This, then, is one absurd and impossible implication of the theory. It is
also evident that the cube will have this same volume even if it is
displaced, which is an attribute possessed by all other bodies also.
Therefore if this differs in no respect from its place, why need we assume
a place for bodies over and above the volume of each, (15) if their volume
be conceived of as free from attributes? It contributes nothing to the
situation if there is an equal interval attached to it as well. Further, it
ought to be clear by the study of moving things what sort of thing void
is. But in fact it is found nowhere in the world. For air is something,
though it does not seem to be so—nor, for that matter, would water, if
fishes were made of iron; for the discrimination of the tangible is by
touch.
It is clear, (20) then, from these considerations that there is no separate
void.
9
There are some who think that the existence of rarity and density
shows that there is a void. If rarity and density do not exist, they say,
neither can things contract and be compressed. But if this were not to
take place, either there would be no movement at all, (25) or the universe
would bulge, as Xuthus12 said, or air and water must always change into
equal amounts (e. g. if air has been made out of a cupful of water, at the
same time out of an equal amount of air a cupful of water must have
been made), or void must necessarily exist; for compression and
expansion cannot take place otherwise.
Now, if they mean by the rare that which has many voids existing
separately, (30) it is plain that if void cannot exist separate any more than
a place can exist with an extension all to itself, neither can the rare exist
in this sense. But if they mean that there is void, not separately existent,
but still present in the rare, this is less impossible, yet, first, the void
turns out not to be a condition of all movement, (35) but only of
movement upwards (for the rare is light, which is the reason why they
say fire is rare); second, the void turns out to be a condition of
movement not as that in which it takes place, but in that the void carries
things up as skins by being carried up themselves carry up what is
continuous with them. [217a] Yet how can void have a local
movement or a place? For thus that into which void moves is till then
void of a void.
Again, how will they explain, in the case of what is heavy, (5) its
movement downwards? And it is plain that if the rarer and more void a
thing is the quicker it will move upwards, if it were completely void it
would move with a maximum speed! But perhaps even this is
impossible, that it should move at all; the same reason which showed
that in the void all things are incapable of moving shows that the void
cannot move, viz., the fact that the speeds are incomparable.
Since we deny that a void exists, but for the rest the problem has been
truly stated, (10) that either there will be no movement, if there is not to
be condensation and rarefaction, or the universe will bulge, or a
transformation of water into air will always be balanced by an equal
transformation of air into water (for it is clear that the air produced from
water is bulkier than the water): it is necessary therefore, (15) if
compression does not exist, either that the next portion will be pushed
outwards and make the outermost part bulge, or that somewhere else
there must be an equal amount of water produced out of air, so that the
entire bulk of the whole may be equal, or that nothing moves. For when
anything is displaced this will always happen, unless it comes round in a
circle; but locomotion is not always circular, but sometimes in a straight
line.
These then are the reasons for which they might say that there is a
void; our statement is based on the assumption that there is a single
matter for contraries, (20) hot and cold and the other natural
contrarieties, and that what exists actually is produced from a potential
existent, and that matter is not separable from the contraries but its
being is different, (25) and that a single matter may serve for colour and
heat and cold.
The same matter also serves for both a large and a small body. This is
evident; for when air is produced from water, the same matter has
become something different, not by acquiring an addition to it, but has
become actually what it was potentially, and, again, (30) water is
produced from air in the same way, the change being sometimes from
smallness to greatness, and sometimes from greatness to smallness.
Similarly, therefore, if air which is large in extent comes to have a
smaller volume, or becomes greater from being smaller, it is the matter
which is potentially both that comes to be each of the two.
For as the same matter becomes hot from being cold, and cold from
being hot, because it was potentially both, so too from hot it can become
more hot, though nothing in the matter has become hot that was not hot
when the thing was less hot; just as, if the arc or curve of a greater circle
becomes that of a smaller, whether it remains the same or becomes a
different curve, convexity has not come to exist in anything that was not
convex but straight (for differences of degree do not depend on an
intermission of the quality); nor can we get any portion of a flame, (5) in
which both heat and whiteness are not present. [217b] So too, then, is
the earlier heat related to the later. So that the greatness and smallness,
also, of the sensible volume are extended, not by the matter’s acquiring
anything new, (10) but because the matter is potentially matter for both
states; so that the same thing is dense and rare, and the two qualities
have one matter.
The dense is heavy, and the rare is light. Again, as the arc of a circle
when contracted into a smaller space does not acquire a new part which
is convex, but what was there has been contracted; and as any part of
fire that one takes will be hot; so, too, it is all a question of contraction
and expansion of the same matter. (15) There are two types in each case,
both in the dense and in the rare; for both the heavy and the hard are
thought to be dense, and contrariwise both the light and the soft are
rare; and weight and hardness fail to coincide in the case of lead and
iron.
From what has been said it is evident, (20) then, that void does not exist
either separate (either absolutely separate or as a separate element in the
rare) or potentially, unless one is willing to call the condition of
movement void, whatever it may be. At that rate the matter of the heavy
and the light, qua matter of them, would be the void; for the dense and
the rare are productive of locomotion in virtue of this contrariety, and in
virtue of their hardness and softness productive of passivity and
impassivity, (25) i. e. not of locomotion but rather of qualitative change.
So much, then, for the discussion of the void, and of the sense in
which it exists and the sense in which it does not exist.
10 Next for discussion after the subjects mentioned is Time.
The best plan will be to begin by working out the difficulties
connected with it, (30) making use of the current arguments. First, does it
belong to the class of things that exist or to that of things that do not
exist? Then secondly, what is its nature? To start, then: the following
considerations would make one suspect that it either does not exist at all
or barely, and in an obscure way. One part of it has been and is not,
while the other is going to be and is not yet. [218a] Yet time—both
infinite time and any time you like to take—is made up of these. One
would naturally suppose that what is made up of things which do not
exist could have no share in reality.
Further, if a divisible thing is to exist, it is necessary that, when it
exists, all or some of its parts must exist. But of time some parts have
been, (5) while others have to be, and no part of it is, though it is
divisible. For what is ‘now’ is not a part: a part is a measure of the
whole, which must be made up of parts. Time, on the other hand, is not
held to be made up of ‘nows’.
Again, the ‘now’ which seems to bound the past and the future—does
it always remain one and the same or is it always other and other? It is
hard to say. (10)
(1) If it is always different and different, and if none of the parts in
time which are other and other are simultaneous (unless the one
contains and the other is contained, as the shorter time is by the longer),
and if the ‘now’ which is not, but formerly was, must have ceased-to-be
at some time, the ‘nows’ too cannot be simultaneous with one another,
(15) but the prior ‘now’ must always have ceased-to-be. But the prior
‘now’ cannot have ceased-to-be in13 itself (since it then existed); yet it
cannot have ceased-to-be in another ‘now’. For we may lay it down that
one ‘now’ cannot be next to another, any more than point to point. If
then it did not cease-to-be in the next ‘now’ but in another, it would
exist simultaneously with the innumerable ‘nows’ between the two—
which is impossible. (20)
Yes, but (2) neither is it possible for the ‘now’ to remain always the
same. No determinate divisible thing has a single termination, whether it
is continuously extended in one or in more than one dimension: but the
‘now’ is a termination, and it is possible to cut off a determinate time. (25)
Further, if coincidence in time (i. e. being neither prior nor posterior)
means to be ‘in one and the same “now” ’, then, if both what is before
and what is after are in this same ‘now’, things which happened ten
thousand years ago would be simultaneous with what has happened today, and nothing would be before or after anything else.
This may serve as a statement of the difficulties about the attributes of
time. (30)
As to what time is or what is its nature, the traditional accounts give
us as little light as the preliminary problems which we have worked
through.
Some assert that it is (1) the movement of the whole, others that it is
(2) the sphere itself.14 [218b]
(1) Yet part, too, of the revolution is a time, but it certainly is not a
revolution: for what is taken is part of a revolution, not a revolution.
Besides, if there were more heavens than one, the movement of any of
them equally would be time, so that there would be many times at the
same time.
(2) Those who said that time is the sphere of the whole thought so, (5)
no doubt, on the ground that all things are in time and all things are in
the sphere of the whole. The view is too naive for it to be worth while to
consider the impossibilities implied in it.
But as time is most usually supposed to be (3) motion and a kind of
change, we must consider this view. (10)
Now (a) the change or movement of each thing is only in the thing
which changes or where the thing itself which moves or changes may
chance to be. But time is present equally everywhere and with all things.
Again, (b) change is always faster or slower, (15) whereas time is not:
for ‘fast’ and ‘slow’ are defined by time—‘fast’ is what moves much in a
short time, ‘slow’ what moves little in a long time; but time is not
defined by time, by being either a certain amount or a certain kind of it.
Clearly then it is not movement. (We need not distinguish at present
between ‘movement’ and ‘change’. (20))
11
But neither does time exist without change; for when the state of
our own minds does not change at all, or we have not noticed its
changing, we do not realize that time has elapsed, any more than those
who are fabled to sleep among the heroes in Sardinia do when they are
awakened; for they connect the earlier ‘now’ with the later and make
them one, (25) cutting out the interval because of their failure to notice it.
So, just as, if the ‘now’ were not different but one and the same, there
would not have been time, so too when its difference escapes our notice
the interval does not seem to be time. If, then, the non-realization of the
existence of time happens to us when we do not distinguish any change,
(30) but the soul seems to stay in one indivisible state, and when we
perceive and distinguish we say time has elapsed, evidently time is not
independent of movement and change. It is evident, then, that time is
neither movement nor independent of movement. [219a]
We must take this as our starting-point and try to discover—since we
wish to know what time is—what exactly it has to do with movement.
Now we perceive movement and time together: for even when it is
dark and we are not being affected through the body, (5) if any
movement takes place in the mind we at once suppose that some time
also has elapsed; and not only that but also, when some time is thought
to have passed, some movement also along with it seems to have taken
place. Hence time is either movement or something that belongs to
movement. Since then it is not movement, it must be the other.
But what is moved is moved from something to something, (10) and all
magnitude is continuous. Therefore the movement goes with the
magnitude. Because the magnitude is continuous, the movement too
must be continuous, and if the movement, then the time; for the time
that has passed is always thought to be in proportion to the movement.
The distinction of ‘before’ and ‘after’ holds primarily then, in place;
and there in virtue of relative position. Since then ‘before’ and ‘after’
hold in magnitude, they must hold also in movement, (15) these
corresponding to those. But also in time the distinction of ‘before’ and
‘after’ must hold, for time and movement always correspond with each
other. The ‘before’ and ‘after’ in motion identical in substratum with
motion yet differs from it in definition, and is not identical with motion.
(20)
But we apprehend time only when we have marked motion, marking it
by ‘before’ and ‘after’; and it is only when we have perceived ‘before’
and ‘after’ in motion that we say that time has elapsed. (25) Now we mark
them by judging that A and B are different, and that some third thing is
intermediate to them. When we think of the extremes as different from
the middle and the mind pronounces that the ‘nows’ are two, one before
and one after, it is then that we say that there is time, and this that we
say is time. For what is bounded by the ‘now’ is thought to be time—we
may assume this.
When, (30) therefore, we perceive the ‘now’ as one, and neither as
before and after in a motion nor as an identity but in relation to a
‘before’ and an ‘after’, no time is thought to have elapsed, because there
has been no motion either. On the other hand, when we do perceive a
‘before’ and an ‘after’, then we say that there is time. [219b] For time
is just this—number of motion in respect of ‘before’ and ‘after’.
Hence time is not movement, but only movement in so far as it admits
of enumeration. A proof of this: we discriminate the more or the less by
number, but more or less movement by time. (5) Time then is a kind of
number. (Number, we must note, is used in two senses—both of what is
counted or the countable and also of that with which we count. Time
obviously is what is counted, not that with which we count: these are
different kinds of thing.)
Just as motion is a perpetual succession, so also is time. (10) But every
simultaneous time is self-identical; for the ‘now’ as a subject is an
identity, but it accepts different attributes.15 The ‘now’ measures time, in
so far as time involves the ‘before and after’.
The ‘now’ in one sense is the same, in another it is not the same. In so
far as it is in succession, it is different (which is just what its being now
was supposed to mean), but its substratum is an identity: for motion, (15)
as was said, goes with magnitude, and time, as we maintain, with
motion. Similarly, then, there corresponds to the point the body which is
carried along, and by which we are aware of the motion and of the
‘before and after’ involved in it. This is an identical substratum (whether
a point or a stone or something else of the kind), (20) but it has different
attributes—as the sophists assume that Coriscus’ being in the Lyceum is a
different thing from Coriscus’ being in the market-place. And the body
which is carried along is different, in so far as it is at one time here and
at another there. But the ‘now’ corresponds to the body that is carried
along, as time corresponds to the motion. For it is by means of the body
that is carried along that we become aware of the ‘before and after’ in
the motion, (25) and if we regard these as countable we get the ‘now’.
Hence in these also the ‘now’ as substratum remains the same (for it is
what is before and after in movement), but what is predicated of it is
different; for it is in so far as the ‘before and after’ is numerable that we
get the ‘now’. This is what is most knowable: for, similarly, motion is
known because of that which is moved, locomotion because of that
which is carried. For what is carried is a real thing, the movement is not.
(30) Thus what is called ‘now’ in one sense is always the same; in another
it is not the same: for this is true also of what is carried.
Clearly, too, if there were no time, there would be no ‘now’, and vice
versa. Just as the moving body and its locomotion involve each other
mutually, so too do the number of the moving body and the number of
its locomotion. [220a] For the number of the locomotion is time, while
the ‘now’ corresponds to the moving body, and is like the unit of
number.
Time, then, also is both made continuous by the ‘now’ and divided at
it. (5) For here too there is a correspondence with the locomotion and the
moving body. For the motion or locomotion is made one by the thing
which is moved, because it is one—not because it is one in its own
nature (for there might be pauses in the movement of such a thing)—but
because it is one in definition: for this determines the movement as
‘before’ and ‘after’. Here, too, there is a correspondence with the point;
for the point also both connects and terminates the length—it is the
beginning of one and the end of another. (10) But when you take it in this
way, using the one point as two, a pause is necessary, if the same point
is to be the beginning and the end. The ‘now’ on the other hand, since
the body carried is moving, is always different.
Hence time is not number in the sense in which there is ‘number’ of
the same point because it is beginning and end, but rather as the
extremities of a line form a number, and not as the parts of the line do
so, (15) both for the reason given (for we can use the middle point as two,
so that on that analogy time might stand still), and further because
obviously the ‘now’ is no part of time nor the section any part of the
movement, any more than the points are parts of the line—for it is two
lines that are parts of one line. (20)
In so far then as the ‘now’ is a boundary, it is not time, but an
attribute of it; in so far as it numbers, it is number; for boundaries
belong only to that which they bound, but number (e. g. ten) is the
number of these horses, and belongs also elsewhere.
It is clear, then, that time is ‘number of movement in respect of the
before and after’, and is continuous since it is an attribute of what is
continuous. (25)
12
The smallest number, in the strict sense of the word ‘number’, is
two. But of number as concrete, sometimes there is a minimum,
sometimes not: e. g. of a ‘line’, the smallest in respect of multiplicity is
two (or, if you like, one), but in respect of size there is no minimum; for
every line is divided ad infinitum. (30) Hence it is so with time. In respect
of number the minimum is one (or two); in point of extent there is no
minimum.
It is clear, too, that time is not described as fast or slow, but as many
or few16 and as long or short. [220b] For as continuous it is long or
short and as a number many or few, but it is not fast or slow—any more
than any number with which we number is fast or slow.
Further, (5) there is the same time everywhere at once, but not the
same time before and after, for while the present change is one, the
change which has happened and that which will happen are different.
Time is not number with which we count, but the number of things
which are counted, and this according as it occurs before or after is
always different, (10) for the ‘nows’ are different. And the number of a
hundred horses and a hundred men is the same, but the things numbered
are different—the horses from the men. Further, as a movement can be
one and the same again and again, so too can time, e. g. a year or a
spring or an autumn.
Not only do we measure the movement by the time, (15) but also the
time by the movement, because they define each other. The time marks
the movement, since it is its number, and the movement the time. We
describe the time as much or little, measuring it by the movement, just
as we know the number by what is numbered, (20) e. g. the number of the
horses by one horse as the unit. For we know how many horses there are
by the use of the number; and again by using the one horse as unit we
know the number of the horses itself. So it is with the time and the
movement; for we measure the movement by the time and vice versa. It
is natural that this should happen; for the movement goes with the
distance and the time with the movement, (25) because they are quanta
and continuous and divisible. The movement has these attributes
because the distance is of this nature, and the time has them because of
the movement. And we measure both the distance by the movement and
the movement by the distance; for we say that the road is long, if the
journey is long, and that this is long, (30) if the road is long—the time,
too, if the movement, and the movement, if the time.
[221a] Time is a measure of motion and of being moved, and it
measures the motion by determining a motion which will measure
exactly the whole motion, as the cubit does the length by determining an
amount which will measure out the whole. Further ‘to be in time’ means,
for movement, that both it and its essence are measured by time (for
simultaneously it measures both the movement and its essence, (5) and
this is what being in time means for it, that its essence should be
measured).
Clearly then ‘to be in time’ has the same meaning for other things also,
namely, that their being should be measured by time. ‘To be in time’ is
one of two things: (1) to exist when time exists, (10) (2) as we say of some
things that they are ‘in number’. The latter means either what is a part
or mode of number—in general, something which belongs to number—
or that things have a number.
Now, since time is number, the ‘now’ and the ‘before’ and the like are
in time, just as ‘unit’ and ‘odd’ and ‘even’ are in number, (15) i. e. in the
sense that the one set belongs to number, the other to time. But things
are in time as they are in number. If this is so, they are contained by
time as things in place are contained by place.
Plainly, too, to be in time does not mean to coexist with time, any
more than to be in motion or in place means to coexist with motion or
place. (20) For if ‘to be in something’ is to mean this, then all things will
be in anything, and the heaven will be in a grain; for when the grain is,
then also is the heaven. But this is a merely incidental conjunction,
whereas the other is necessarily involved: that which is in time
necessarily involves that there is time when it is, (25) and that which is in
motion that there is motion when it is.
Since what is ‘in time’ is so in the same sense as what is in number is
so, a time greater than everything in time can be found. So it is
necessary that all the things in time should be contained by time, just
like other things also which are ‘in anything’, e. g. the things ‘in place’
by place.
A thing, then, will be affected by time, just as we are accustomed to
say that time wastes things away, (30) and that all things grow old
through time, and that there is oblivion owing to the lapse of time, but
we do not say the same of getting to know or of becoming young or fair.
For time is by its nature the cause rather of decay, since it is the number
of change, and change removes what is. [221b]
Hence, plainly, things which are always are not, as such, in time, for
they are not contained by time, nor is their being measured by time. A
proof of this is that none of them is affected by time, which indicates that
they are not in time. (5)
Since time is the measure of motion, it will be the measure of rest too
—indirectly. For all rest is in time. For it does not follow that what is in
time is moved, though what is in motion is necessarily moved. (10) For
time is not motion, but ‘number of motion’: and what is at rest, also, can
be in the number of motion. Not everything that is not in motion can be
said to be ‘at rest’—but only that which can be moved, though it actually
is not moved, as was said above.17
‘To be in number’ means that there is a number of the thing, (15) and
that its being is measured by the number in which it is. Hence if a thing
is ‘in time’ it will be measured by time. But time will measure what is
moved and what is at rest, the one qua moved, the other qua at rest; for
it will measure their motion and rest respectively.
Hence what is moved will not be measurable by the time simply in so
far as it has quantity, (20) but in so far as its motion has quantity. Thus
none of the things which are neither moved nor at rest are in time: for
‘to be in time’ is ‘to be measured by time’, while time is the measure of
motion and rest.
Plainly, then, neither will everything that does not exist be in time,
i. e. those non-existent things that cannot exist, as the diagonal cannot
be commensurate with the side.
Generally, (25) if time is directly the measure of motion and indirectly
of other things, it is clear that a thing whose existence is measured by it
will have its existence in rest or motion. Those things therefore which
are subject to perishing and becoming—generally, (30) those which at one
time exist, at another do not—are necessarily in time: for there is a
greater time which will extend both beyond their existence and beyond
the time which measures their existence. [222a] Of things which do
not exist but are contained by time some were, e. g. Homer once was,
some will be, e. g. a future event; this depends on the direction in which
time contains them; if on both, they have both modes of existence. As to
such things as it does not contain in any way, they neither were nor are
nor will be. These are those non-existents whose opposites always are, (5)
as the incommensurability of the diagonal always is—and this will not
be in time. Nor will the commensurability, therefore; hence this
eternally is not, because it is contrary to what eternally is. A thing whose
contrary is not eternal can be and not be, and it is of such things that
there is coming to be and passing away.
13
The ‘now’ is the link of time, (10) as has been said18 (for it connects
past and future time), and it is a limit of time (for it is the beginning of
the one and the end of the other). But this is not obvious as it is with the
point, which is fixed. It divides potentially, (15) and in so far as it is
dividing the ‘now’ is always different, but in so far as it connects it is
always the same, as it is with mathematical lines. For the intellect it is
not always one and the same point, since it is other and other when one
divides the line; but in so far as it is one, it is the same in every respect.
So the ‘now’ also is in one way a potential dividing of time, in another
the termination of both parts, and their unity. And the dividing and the
uniting are the same thing and in the same reference, but in essence they
are not the same.
So one kind of ‘now’ is described in this way: another is when the time
is near this kind of ‘now’. (20) ‘He will come now’ because he will come
to-day; ‘he has come now’ because he came to-day. But the things in the
Iliad have not happened ‘now’, nor is the flood ‘now’—not that the time
from now to them is not continuous, but because they are not near.
‘At some time’ means a time determined in relation to the first of the
two types of ‘now’, e. g. ‘at some time’ Troy was taken, (25) and ‘at some
time’ there will be a flood; for it must be determined with reference to
the ‘now’. There will thus be a determinate time from this ‘now’ to that,
and there was such in reference to the past event. But if there be no time
which is not ‘sometime’, every time will be determined.
Will time then fail? Surely not, if motion always exists. Is time then
always different or does the same time recur? Clearly time is, (30) in the
same way as motion is. For if one and the same motion sometimes
recurs, it will be one and the same time, and if not, not.
Since the ‘now’ is an end and a beginning of time, not of the same
time however, but the end of that which is past and the beginning of
that which is to come, it follows that, as the circle has its convexity and
its concavity, in a sense, in the same thing, so time is always at a
beginning and at an end. [222b] And for this reason it seems to be
always different; for the ‘now’ is not the beginning and the end of the
same thing; if it were, (5) it would be at the same time and in the same
respect two opposites. And time will not fail; for it is always at a
beginning.
‘Presently’ or ‘just’ refers to the part of future time which is near the
indivisible present ‘now’ (‘When do you walk?’ ‘Presently’, (10) because
the time in which he is going to do so is near), and to the part of past
time which is not far from the ‘now’ (‘When do you walk?’ ‘I have just
been walking’). But to say that Troy has just been taken—we do not say
that, because it is too far from the ‘now’. ‘Lately’, too, refers to the part
of past time which is near the present ‘now’. ‘When did you go?’ ‘Lately’,
if the time is near the existing now. ‘Long ago’ refers to the distant past.
‘Suddenly’ refers to what has departed from its former condition in a
time imperceptible because of its smallness; but it is the nature of all
change to alter things from their former condition. (15) In time all things
come into being and pass away; for which reason some called it the
wisest of all things, but the Pythagorean Paron called it the most stupid,
because in it we also forget; and his was the truer view. It is clear then
that it must be in itself, as we said before19 the condition of destruction
rather than of coming into being (for change, (20) in itself, makes things
depart from their former condition), and only incidentally of coming
into being, and of being. A sufficient evidence of this is that nothing
comes into being without itself moving somehow and acting, but a thing
can be destroyed even if it does not move at all. And this is what, as a
rule, we chiefly mean by a thing’s being destroyed by time. (25) Still, time
does not work even this change; even this sort of change takes place
incidentally in time.
We have stated, then, that time exists and what it is, and in how many
senses we speak of the ‘now’, and what ‘at some time’, ‘lately’, ‘presently’
or ‘just’, ‘long ago’, and ‘suddenly’ mean.
14
These distinctions having been drawn, (30) it is evident that every
change and everything that moves is in time; for the distinction of faster
and slower exists in reference to all change, since it is found in every
instance. In the phrase ‘moving faster’ I refer to that which changes
before another into the condition in question, when it moves over the
same interval and with a regular movement; e. g. in the case of
locomotion, if both things move along the circumference of a circle, or
both along a straight line; and similarly in all other cases. [223a] (5)
But what is before is in time; for we say ‘before’ and ‘after’ with reference
to the distance from the ‘now’, and the ‘now’ is the boundary of the past
and the future; so that since ‘nows’ are in time, the before and the after
will be in time too; for in that in which the ‘now’ is, the distance from
the ‘now’ will also be. But ‘before’ is used contrariwise with reference to
past and to future time; for in the past we call ‘before’ what is farther
from the ‘now’, (10) and ‘after’ what is nearer, but in the future we call
the nearer ‘before’ and the farther ‘after’. So that since the ‘before’ is in
time, and every movement involves a ‘before’, (15) evidently every change
and every movement is in time.
It is also worth considering how time can be related to the soul; and
why time is thought to be in everything, both in earth and in sea and in
heaven. Is it because it is an attribute, or state, of movement (since it is
the number of movement) and all these things are movable (for they are
all in place), and time and movement are together, (20) both in respect of
potentiality and in respect of actuality?
Whether if soul did not exist time would exist or not, is a question that
may fairly be asked; for if there cannot be some one to count there
cannot be anything that can be counted, so that evidently there cannot
be number; for number is either what has been, or what can be, counted.
But if nothing but soul, or in soul reason, is qualified to count, (25) there
would not be time unless there were soul, but only that of which time is
an attribute, i. e. if movement can exist without soul, and the before and
after are attributes of movement, and time is these qua numerable.
One might also raise the question what sort of movement time is the
number of. Must we not say ‘of any kind’? For things both come into
being in time and pass away, (30) and grow, and are altered in time, and
are moved locally; thus it is of each movement qua movement that time
is the number. And so it is simply the number of continuous movement,
not of any particular kind of it.
But other things as well may have been moved now, and there would
be a number of each of the two movements. [223b] Is there another
time, then, and will there be two equal times at once? Surely not. For a
time that is both equal and simultaneous is one and the same time, and
even those that are not simultaneous are one in kind; for if there were
dogs, and horses, and seven of each, it would be the same number. (5) So,
too, movements that have simultaneous limits have the same time, yet
the one may in fact be fast and the other not, and one may be
locomotion and the other alteration; still the time of the two changes is
the same if their number also is equal and simultaneous; and for this
reason, while the movements are different and separate, (10) the time is
everywhere the same, because the number of equal and simultaneous
movements is everywhere one and the same.
Now there is such a thing as locomotion, and in locomotion there is
included circular movement, and everything is measured by some one
thing homogeneous with it, units by a unit, horses by a horse, and
similarly times by some definite time, and, as we said,20 time is
measured by motion as well as motion by time (this being so because by
a motion definite in time the quantity both of the motion and of the time
is measured): if, (15) then, what is first is the measure of everything
homogeneous with it, regular circular motion is above all else the
measure, because the number of this is the best known. (20) Now neither
alteration nor increase nor coming into being can be regular, but
locomotion can be. This also is why time is thought to be the movement
of the sphere, viz. because the other movements are measured by this,
and time by this movement.
This also explains the common saying that human affairs form a circle,
(25) and that there is a circle in all other things that have a natural
movement and coming into being and passing away. This is because all
other things are discriminated by time, and end and begin as though
conforming to a cycle; for even time itself is thought to be a circle. (30)
And this opinion again is held because time is the measure of this kind
of locomotion and is itself measured by such. So that to say that the
things that come into being form a circle is to say that there is a circle of
time; and this is to say that it is measured by the circular movement; for
apart from the measure nothing else to be measured is observed; the
whole is just a plurality of measures. [224a]
It is said rightly, too, that the number of the sheep and of the dogs is
the same number if the two numbers are equal, but not the same decad or
the same ten; just as the equilateral and the scalene are not the same
triangle, (5) yet they are the same figure, because they are both triangles.
For things are called the same so-and-so if they do not differ by a
differentia of that thing, but not if they do; e. g. triangle differs from
triangle by a differentia of triangle, therefore they are different triangles;
but they do not differ by a differentia of figure, but are in one and the
same division of it. For a figure of one kind is a circle and a figure of
another kind a triangle, (10) and a triangle of one kind is equilateral and a
triangle of another kind scalene. They are the same figure, then, and
that, triangle, but not the same triangle. Therefore the number of two
groups also is the same number (for their number does not differ by a
differentia of number), but it is not the same decad; for the things of
which it is asserted differ; one group are dogs, and the other horses.
We have now discussed time—both time itself and the matters
appropriate to the consideration of it. (15)
1
52.
2
Where he apparently identified ‘the participant’ with ‘the great and the small’; cf. 1. 35.
3
208b 2.
4
Cf. 212b 14–16.
5
209b 22–32.
6
211a 17–b5.
7 a32.
8
209a 2–30.
9
De Gen. et Corr. i. 3.
10
Expected by those who believe in a separately existing place or void.
11
211b 19 sqq., 213a 31.
12
A Pythagorean of Croton.
13
The argument would be clearer if we could say ‘during’ itself. If the existent perished ‘in’ itself,
it would never exist without perishing.
14
Aristotle is probably referring to Plato and the Pythagoreans respectively.
15
e. g. if you come in when I go out, the time of your coming in is in fact the time of my going
out, though for it to be the one and to be the other are different things.
16
e. g. ‘many years’.
17
202a 4.
18
220a 5.
19
221b 1.
20
220b 28.
BOOK V
1
Everything with changes does so in one of three senses. (21) It may
change (1) accidentally, as for instance when we say that something
musical walks, that which walks being something in which aptitude for
music is an accident. Again (2) a thing is said without qualification to
change because something belonging to it changes, (25) i. e. in statements
which refer to part of the thing in question: thus the body is restored to
health because the eye or the chest, that is to say a part of the whole
body, is restored to health. And above all there is (3) the case of a thing
which is in motion neither accidentally nor in respect of something else
belonging to it, but in virtue of being itself directly in motion. Here we
have a thing which is essentially movable: and that which is so is a
different thing according to the particular variety of motion: for instance
it may be a thing capable of alteration: and within the sphere of
alteration it is again a different thing according as it is capable of being
restored to health or capable of being heated. (30) And there are the same
distinctions in the case of the mover: (1) one thing causes motion
accidentally, (2) another partially (because something belonging to it
causes motion), (3) another of itself directly, as, for instance, the
physician heals, the hand strikes. We have, then, the following factors:
(a) on the one hand that which directly causes motion, and (b) on the
other hand that which is in motion: further, we have (c) that in which
motion takes place, (35) namely time, and (distinct from these three) (d)
that from which and (e) that to which it proceeds: for every motion
proceeds from something and to something, that which is directly in
motion being distinct from that to which it is in motion and that from
which it is in motion: for instance, we may take the three things ‘wood’,
‘hot’, and ‘cold’, of which the first is that which is in motion, the second
is that to which the motion proceeds, and the third is that from which it
proceeds. [224b] This being so, it is clear that the motion is in the
wood, not in its form: for the motion is neither caused nor experienced
by the form or the place or the quantity. (5) So we are left with a mover,
a moved, and a goal of motion. I do not include the starting-point of
motion: for it is the goal rather than the starting-point of motion that
gives its name to a particular process of change. Thus ‘perishing’ is
change to not-being, though it is also true that that which perishes
changes from being: and ‘becoming’ is change to being, though it is also
change from not-being.
Now a definition of motion has been given above,1a from which it will
be seen that every goal of motion, (10) whether it be a form, an affection,
or a place, is immovable, as, for instance, knowledge and heat. Here,
however, a difficulty may be raised. Affections, it may be said, are
motions, and whiteness is an affection: thus there may be change to a
motion. To this we may reply that it is not whiteness but whitening that
is a motion. (15) Here also the same distinctions are to be observed: a goal
of motion may be so accidentally, or partially and with reference to
something other than itself, or directly and with no reference to
anything else: for instance, a thing which is becoming white changes
accidentally to an object of thought, the colour being only accidentally
the object of thought; it changes to colour, (20) because white is a part of
colour, or to Europe, because Athens is a part of Europe; but it changes
essentially to white colour. It is now clear in what sense a thing is in
motion essentially, accidentally, or in respect of something other than
itself, and in what sense the phrase ‘itself directly’ is used in the case
both of the mover and of the moved: and it is also clear that the motion
is not in the form but in that which is in motion, (25) that is to say ‘the
movable in activity’. Now accidental change we may leave out of
account: for it is to be found in everything, at any time, and in any
respect. Change which is not accidental on the other hand is not to be
found in everything, but only in contraries, in things intermediate
between contraries, (30) and in contradictories, as may be proved by
induction. An intermediate may be a starting-point of change, since for
the purposes of the change it serves as contrary to either of two
contraries: for the intermediate is in a sense the extremes. Hence we
speak of the intermediate as in a sense a contrary relatively to the
extremes and of either extreme as a contrary relatively to the
intermediate: for instance, the central note is low relatively to the
highest and high relatively to the lowest, and grey is light relatively to
black and dark relatively to white. (35)
And since every change is from something to something—as the word
itself metabole indicates, implying something ‘after’ (meta) something
else, that is to say something earlier and something later—that which
changes must change in one of four ways: from subject to subject, (5)
from subject to non-subject, from non-subject to subject, or from nonsubject to non-subject, where by ‘subject’ I mean what is affirmatively
expressed. [225a] So it follows necessarily from what has been said
above that there are only three kinds of change, that from subject to
subject, that from subject to non-subject, (10) and that from non-subject
to subject: for the fourth conceivable kind, that from non-subject to nonsubject, is not change, as in that case there is no opposition either of
contraries or of contradictories.
Now change from non-subject to subject, the relation being that of
contradiction, is ‘coming to be’—‘unqualified coming to be’ when the
change takes place in an unqualified way, ‘particular coming to be’ when
the change is change in a particular character: for instance, a change
from not-white to white is a coming to be of the particular thing, (15)
white, while change from unqualified not-being to being is coming to be
in an unqualified way, in respect of which we say that a thing ‘comes to
be’ without qualification, not that it ‘comes to be’ some particular thing.
Change from subject to non-subject is ‘perishing’—‘unqualified perishing’
when the change is from being to not-being, ‘particular perishing’ when
the change is to the opposite negation, the distinction being the same as
that made in the case of coming to be.
Now the expression ‘not-being’ is used in several senses: and there can
be motion neither of that which ‘is not’ in respect of the affirmation or
negation of a predicate, (20) nor of that which ‘is not’ in the sense that it
only potentially ‘is’, that is to say the opposite of that which actually ‘is’
in an unqualified sense: for although that which is ‘not-white’ or ‘notgood’ may nevertheless be in motion accidentally (for example that
which is ‘not-white’ might be a man), yet that which is without
qualification ‘not-so-and-so’ cannot in any sense be in motion: Therefore
it is impossible for that which is not to be in motion. (25) This being so, it
follows that ‘becoming’ cannot be a motion: for it is that which ‘is not’
that ‘becomes’. For however true it may be that it accidentally ‘becomes’,
it is nevertheless correct to say that it is that which ‘is not’ that in an
unqualified sense ‘becomes’. And similarly it is impossible for that which
‘is not’ to be at rest.
There are these difficulties, then, in the way of the assumption that
that which ‘is not’ can be in motion: and it may be further objected that,
(30) whereas everything which is in motion is in space, that which ‘is not’
is not in space: for then it would be somewhere.
So, too, ‘perishing’ is not a motion: for a motion has for its contrary
either another motion or rest, whereas ‘perishing’ is the contrary of
‘becoming’.
Since, then, every motion is a kind of change, and there are only the
three kinds of change mentioned above; and since of these three those
which take the form of ‘becoming’ and ‘perishing’, (35) that is to say those
which imply a relation of contradiction, are not motions: it necessarily
follows that only change from subject to subject is motion. [225b] And
every such subject is either a contrary or an intermediate (for a privation
may be allowed to rank as a contrary) and can be affirmatively
expressed, as naked, toothless, or black. If, then, (5) the categories are
severally distinguished as Being, Quality, Place, Time, Relation,
Quantity, and Activity or Passivity, it necessarily follows that there are
three kinds of motion—qualitative, quantitative, and local.
2
In respect of Substance there is no motion, (10) because Substance
has no contrary among things that are. Nor is there motion in respect of
Relation: for it may happen that when one correlative changes, the
other, although this does not itself change, is no longer applicable, so
that in these cases the motion is accidental. Nor is there motion in
respect of Agent and Patient—in fact there can never be motion of
mover and moved, (15) because there cannot be motion of motion or
becoming of becoming or in general change of change.
For in the first place there are two senses in which motion of motion is
conceivable. (1) The motion of which there is motion might be
conceived as subject; e. g. a man is in motion because he changes from
fair to dark. Can it be that in this sense motion grows hot or cold, (20) or
changes place, or increases or decreases? Impossible: for change is not a
subject. Or (2) can there be motion of motion in the sense that some
other subject changes from a change to another mode of being, as e. g. a
man changes from falling ill to getting well? Even this is possible only in
an accidental sense. For, whatever the subject may be, movement is
change from one form to another. (25) (And the same holds good of
becoming and perishing, except that in these processes we have a change
to a particular1 kind of opposite, while the other, motion, is a change to
a different2 kind.) So, if there is to be motion of motion, that which is
changing from health to sickness must simultaneously be changing from
this very change to another. It is clear, then, that by the time that it has
become sick, it must also have changed to whatever may be the other
change concerned (for that it should be at rest, though logically possible,
is excluded by the theory). Moreover this other can never be any casual
change, (30) but must be a change from something definite to some other
definite thing. So in this case it must be the opposite change, viz.
convalescence. It is only accidentally that there can be change of change,
e. g. there is a change from remembering to forgetting only because the
subject of this change changes at one time to knowledge, at another to
ignorance.
In the second place, if there is to be change of change and becoming
of becoming, we shall have an infinite regress. [226a] Thus if one of a
series of changes is to be a change of change, (35) the preceding change
must also be so: e. g. if simple becoming was ever in process of
becoming, then that which was becoming simple becoming was also in
process of becoming, so that we should not yet have arrived at what was
in process of simple becoming but only at what was already in process of
becoming in process of becoming. And this again was sometime in
process of becoming, so that even then we should not have arrived at
what was in process of simple becoming. And since in an infinite series
there is no first term, here there will be no first stage and therefore no
following stage either. (5) On this hypothesis, then, nothing can become
or be moved or change.
Thirdly, if a thing is capable of any particular motion, it is also
capable of the corresponding contrary motion or the corresponding
coming to rest, and a thing that is capable of becoming is also capable of
perishing: consequently, if there be becoming of becoming, that which is
in process of becoming is in process of perishing at the very moment
when it has reached the stage of becoming: since it cannot be in process
of perishing when it is just beginning to become or after it has ceased to
become: for that which is in process of perishing must be in existence.
Fourthly, there must be a substrate underlying all processes of
becoming and changing. (10) What can this be in the present case? It is
either the body or the soul that undergoes alteration: what is it that
correspondingly becomes motion or becoming? And again what is the
goal of their motion? It must be the motion or becoming of something
from something to something else. But in what sense can this be so? For
the becoming of learning cannot be learning: so neither can the
becoming of becoming be becoming, (15) nor can the becoming of any
process be that process.
Finally, since there are three kinds of motion, the substratum and the
goal of motion must be one or other of these, e. g. locomotion will have
to be altered or to be locally moved.
To sum up, then, since everything that is moved is moved in one of
three ways, either accidentally, or partially, or essentially, (20) change
can change only accidentally, as e. g. when a man who is being restored
to health runs or learns: and accidental change we have long ago3
decided to leave out of account.
Since, then, motion can belong neither to Being nor to Relation nor to
Agent and Patient, it remains that there can be motion only in respect of
Quality, Quantity, and Place: for with each of these we have a pair of
contraries. (25) Motion in respect of Quality let us call alteration, a
general designation that is used to include both contraries: and by
Quality I do not here mean a property of substance (in that sense that
which constitutes a specific distinction is a quality) but a passive quality
in virtue of which a thing is said to be acted on or to be incapable of
being acted on. Motion in respect of Quantity has no name that includes
both contraries, (30) but it is called increase or decrease according as one
or the other is designated: that is to say motion in the direction of
complete magnitude is increase, motion in the contrary direction is
decrease. Motion in respect of Place has no name either general or
particular: but we may designate it by the general name of locomotion,
though strictly the term ‘locomotion’ is applicable to things that change
their place only when they have not the power to come to a stand, (35)
and to things that do not move themselves locally.
[226b] Change within the same kind from a lesser to a greater or
from a greater to a lesser degree is alteration: for it is motion either from
a contrary or to a contrary, whether in an unqualified or in a qualified
sense: for change to a lesser degree of a quality will be called change to
the contrary of that quality, and change to a greater degree of a quality
will be regarded as change from the contrary of that quality to the
quality itself. (5) It makes no difference whether the change be qualified
or unqualified, except that in the former case the contraries will have to
be contrary to one another only in a qualified sense: and a thing’s
possessing a quality in a greater or in a lesser degree means the presence
or absence in it of more or less of the opposite quality. It is now clear,
then, that there are only these three kinds of motion.
The term ‘immovable’ we apply in the first place to that which is
absolutely incapable of being moved (just as we correspondingly apply
the term invisible to sound); in the second place to that which is moved
with difficulty after a long time or whose movement is slow at the start
—in fact, (10) what we describe as hard to move; and in the third place to
that which is naturally designed for and capable of motion, but is not in
motion when, where, and as it naturally would be so. This last is the
only kind of immovable thing of which I use the term ‘being at rest’: for
rest is contrary to motion, (15) so that rest will be negation of motion in
that which is capable of admitting motion.
The foregoing remarks are sufficient to explain the essential nature of
motion and rest, the number of kinds of change, and the different
varieties of motion.
3
Let us now proceed to define the terms ‘together’ and ‘apart’, ‘in
contact’, ‘between’, ‘in succession’, ‘contiguous’, and ‘continuous’, (20)
and to show in what circumstances each of these terms is naturally
applicable.
Things are said to be together in place when they are in one place (in
the strictest sense of the word ‘place’) and to be apart when they are in
different places.
Things are said to be in contact when their extremities are together.
That which a changing thing, if it changes continuously in a natural
manner, (25) naturally reaches before it reaches that to which it changes
last, is between. Thus ‘between’ implies the presence of at least three
things: for in a process of change it is the contrary that is ‘last’: and a
thing is moved continuously if it leaves no gap or only the smallest
possible gap in the material—not in the time (for a gap in the time does
not prevent things having a ‘between’, while, on the other hand, there is
nothing to prevent the highest note sounding immediately after the
lowest) but in the material in which the motion takes place. (30) This is
manifestly true not only in local changes but in every other kind as well.
<Now every change implies a pair of opposites,7 and opposites may be
either contraries or contradictories; since then contradiction admits of no
mean term, it is obvious that ‘between’ must imply a pair of
contraries.>3a That is locally contrary which is most distant in a straight
line: for the shortest line is definitely limited, and that which is
definitely limited constitutes a measure.
A thing is ‘in succession’ when it is after the beginning in position or
in form or in some other respect in which it is definitely so regarded, (35)
and when further there is nothing of the same kind as itself between it
and that to which it is in succession, e. g. a line or lines if it is a line, a
unit or units if it is a unit, a house if it is a house (there is nothing to
prevent something of a different kind being between). [227a] For that
which is in succession is in succession to a particular thing, and is
something posterior: for one is not ‘in succession’ to two, nor is the first
day of the month to the second: in each case the latter is ‘in succession’
to the former. (5)
A thing that is in succession and touches is ‘contiguous’.
The ‘continuous’ is a subdivision of the contiguous: things are called
continuous when the touching limits of each become one and the same
and are, (10) as the word implies, contained in each other: continuity is
impossible if these extremities are two. This definition makes it plain
that continuity belongs to things that naturally in virtue of their mutual
contact form a unity. And in whatever way that which holds them
together is one, (15) so too will the whole be one, e. g. by a rivet or glue
or contact or organic union.
It is obvious that of these terms ‘in succession’ is first in order of
analysis: for that which touches is necessarily in succession, but not
everything that is in succession touches: and so succession is a property
of things prior in definition, e. g. numbers, while contact is not. (20) And
if there is continuity there is necessarily contact, but if there is contact,
that alone does not imply continuity: for the extremities of things may
be ‘together’ without necessarily being one: but they cannot be one
without being necessarily together. So natural junction is last in coming
to be: for the extremities must necessarily come into contact if they are
to be naturally joined: but things that are in contact are not all naturally
joined, (25) while where there is no contact clearly there is no natural
junction either. Hence, if as some say ‘point’ and ‘unit’ have an
independent existence of their own, it is impossible for the two to be
identical: for points can touch while units can only be in succession. (30)
Moreover, there can always be something between points (for all lines
are intermediate between points), whereas it is not necessary that there
should possibly be anything between units: for there can be nothing
between the numbers one and two.
We have now defined what is meant by ‘together’ and ‘apart’,
‘contact’, ‘between’ and ‘in succession’, ‘contiguous’ and ‘continuous’:
and we have shown in what circumstances each of these terms is
applicable. [227b]
4
There are many senses in which motion is said to be ‘one’: for we
use the term ‘one’ in many senses.
Motion is one generically according to the different categories to which
it may be assigned: thus any locomotion is one generically with any
other locomotion, (5) whereas alteration is different generically from
locomotion.
Motion is one specifically when besides being one generically it also
takes place in a species incapable of subdivision: e. g. colour has specific
differences: therefore blackening and whitening differ specifically; but at
all events every whitening will be specifically the same with every other
whitening and every blackening with every other blackening. (10) But
whiteness is not further subdivided by specific differences: hence any
whitening is specifically one with any other whitening. Where it happens
that the genus is at the same time a species, it is clear that the motion
will then in a sense be one specifically though not in an unqualified
sense: learning is an example of this, knowledge being on the one hand a
species of apprehension and on the other hand a genus including the
various knowledges. A difficulty, however, may be raised as to whether
a motion is specifically one when the same thing changes from the same
to the same, (15) e. g. when one point changes again and again from a
particular place to a particular place: if this motion is specifically one,
circular motion will be the same as rectilinear motion, and rolling the
same as walking. But is not this difficulty removed by the principle
already laid down that if that in which the motion takes place is
specifically different (as in the present instance the circular path is
specifically different from the straight) the motion itself is also different?
We have explained, (20) then, what is meant by saying that motion is one
generically or one specifically.
Motion is one in an unqualified sense when it is one essentially or
numerically: and the following distinctions will make clear what this
kind of motion is. There are three classes of things in connexion with
which we speak of motion, the ‘that which’, the ‘that in which’, and the
‘that during which’. I mean that there must be something that is in
motion, e. g. a man or gold, and it must be in motion in something, (25)
e. g. a place or an affection, and during something, for all motion takes
place during a time. Of these three it is the thing in which the motion
takes place that makes it one generically or specifically, it is the thing
moved that makes the motion one in subject, and it is the time that
makes it consecutive: but it is the three together that make it one
without qualification: to effect this, that in which the motion takes place
(the species) must be one and incapable of subdivision, (30) that during
which it takes place (the time) must be one and unintermittent, and that
which is in motion must be one—not in an accidental sense (i. e. it must
be one as the white that blackens is one or Coriscus who walks is one,
not in the accidental sense in which Coriscus and white may be one), nor
merely in virtue of community of nature (for there might be a case of
two men being restored to health at the same time in the same way, e. g.
from inflammation of the eye, yet this motion is not really one, but only
specifically one). [228a]
Suppose, however, that Socrates undergoes an alteration specifically
the same but at one time and again at another: in this case if it is
possible for that which ceased to be again to come into being and remain
numerically the same, then this motion too will be one: otherwise it will
be the same but not one. (5) And akin to this difficulty there is another;
viz. is health one? and generally are the states and affections in bodies
severally one in essence although (as is clear) the things that contain
them are obviously in motion and in flux? Thus if a person’s health at
daybreak and at the present moment is one and the same, (10) why
should not this health be numerically one with that which he recovers
after an interval? The same argument applies in each case. There is,
however, we may answer, this difference: that if the states are two then
it follows simply from this fact that the activities must also in point of
number be two (for only that which is numerically one can give rise to
an activity that is numerically one), but if the state is one, (15) this is not
in itself enough to make us regard the activity also as one: for when a
man ceases walking, the walking no longer is, but it will again be if he
begins to walk again. But, be this as it may, if in the above instance the
health is one and the same, then it must be possible for that which is one
and the same to come to be and to cease to be many times. However,
these difficulties lie outside our present inquiry.
Since every motion is continuous, (20) a motion that is one in an
unqualified sense must (since every motion is divisible) be continuous,
and a continuous motion must be one. There will not be continuity
between any motion and any other indiscriminately any more than there
is between any two things chosen at random in any other sphere: there
can be continuity only when the extremities of the two things are one.
Now some things have no extremities at all: and the extremities of others
differ specifically although we give them the same name of ‘end’: (25)
how should e. g. the ‘end’ of a line and the ‘end’ of walking touch or
come to be one? Motions that are not the same either specifically or
generically may, it is true, be consecutive (e. g. a man may run and then
at once fall ill of a fever), and again, in the torch-race we have
consecutive but not continuous locomotion: for according to our
definition there can be continuity only when the ends of the two things
are one. (30) Hence motions may be consecutive or successive in virtue of
the time being continuous, but there can be continuity only in virtue of
the motions themselves being continuous, that is when the end of each is
one with the end of the other. [228b] Motion, therefore, that is in an
unqualified sense continuous and one must be specifically the same, of
one thing, and in one time. Unity is required in respect of time in order
that there may be no interval of immobility, for where there is
intermission of motion there must be rest, and a motion that includes
intervals of rest will be not one but many, (5) so that a motion that is
interrupted by stationariness is not one or continuous, and it is so
interrupted if there is an interval of time. And though of a motion that is
not specifically one (even if the time is unintermittent) the time is one,
the motion is specifically different, and so cannot really be one, for
motion that is one must be specifically one, (10) though motion that is
specifically one is not necessarily one in an unqualified sense. We have
now explained what we mean when we call a motion one without
qualification.
Further, a motion is also said to be one generically, specifically, or
essentially when it is complete, just as in other cases completeness and
wholeness are characteristics of what is one: and sometimes a motion
even if incomplete is said to be one, provided only that it is continuous.
And besides the cases already mentioned there is another in which a
motion is said to be one, (15) viz. when it is regular: for in a sense a
motion that is irregular is not regarded as one, that title belonging rather
to that which is regular, as a straight line is regular, the irregular being
as such divisible. But the difference would seem to be one of degree. In
every kind of motion we may have regularity or irregularity: thus there
may be regular alteration, and locomotion in a regular path, (20) e. g. in a
circle or on a straight line, and it is the same with regard to increase and
decrease. The difference that makes a motion irregular is sometimes to
be found in its path: thus a motion cannot be regular if its path is an
irregular magnitude, e. g. a broken line, a spiral, or any other magnitude
that is not such that any part of it taken at random fits on to any other
that may be chosen. Sometimes it is found neither in the place nor in the
time nor in the goal but in the manner of the motion: for in some cases
the motion is differentiated by quickness and slowness: thus if its
velocity is uniform a motion is regular, (25) if not it is irregular. So
quickness and slowness are not species of motion nor do they constitute
specific differences of motion, because this distinction occurs in
connexion with all the distinct species of motion. The same is true of
heaviness and lightness when they refer to the same thing: (30) e. g. they
do not specifically distinguish earth from itself or fire from itself.
Irregular motion, therefore, while in virtue of being continuous it is one,
is so in a lesser degree, as is the case with locomotion in a broken line:
and a lesser degree of something always means an admixture of its
contrary. [229a] And since every motion that is one can be both
regular and irregular, motions that are consecutive but not specifically
the same cannot be one and continuous: for how should a motion
composed of alteration and locomotion be regular? If a motion is to be
regular its parts ought to fit one another. (5)
5
We have further to determine what motions are contrary to each
other, and to determine similarly how it is with rest. And we have first
to decide whether contrary motions are motions respectively from and to
the same thing, e. g. a motion from health and a motion to health
(where the opposition, (10) it would seem, is of the same kind as that
between coming to be and ceasing to be); or motions respectively from
contraries, e. g. a motion from health and a motion from disease; or
motions respectively to contraries, e. g. a motion to health and a motion
to disease; or motions respectively from a contrary and to the opposite
contrary, e. g. a motion from health and a motion to disease; or motions
respectively from a contrary to the opposite contrary and from the latter
to the former, e. g. a motion from health to disease and a motion from
disease to health: for motions must be contrary to one another in one or
more of these ways, (15) as there is no other way in which they can be
opposed.
Now motions respectively from a contrary and to the opposite
contrary, e. g. a motion from health and a motion to disease, are not
contrary motions: for they are one and the same. (Yet their essence is not
the same, just as changing from health is different from changing to
disease.) (20) Nor are motions respectively from a contrary and from the
opposite contrary contrary motions, for a motion from a contrary is at
the same time a motion to a contrary or to an intermediate (of this,
however, we shall speak later),4 but changing to a contrary rather than
changing from a contrary would seem to be the cause of the contrariety
of motions, the latter being the loss, the former the gain, (25) of
contrariness. Moreover, each several motion takes its name rather from
the goal than from the starting-point of change, e. g. motion to health
we call convalescence, motion to disease sickening. Thus we are left with
motions respectively to contraries, and motions respectively to contraries
from the opposite contraries. Now it would seem that motions to
contraries are at the same time motions from contraries (though their
essence may not be the same; ‘to health’ is distinct, I mean, from ‘from
disease’, and ‘from health’ from ‘to disease’).
Since then change differs from motion (motion being change from a
particular subject to a particular subject), (30) it follows that contrary
motions are motions respectively from a contrary to the opposite
contrary and from the latter to the former, e. g. a motion from health to
disease and a motion from disease to health. [229b] Moreover, the
consideration of particular examples will also show what kinds of
processes are generally recognized as contrary: thus falling ill is regarded
as contrary to recovering one’s health, these processes having contrary
goals, (5) and being taught as contrary to being led into error by another,
it being possible to acquire error, like knowledge, either by one’s own
agency or by that of another. Similarly we have upward locomotion and
downward locomotion, which are contrary lengthwise, locomotion to the
right and locomotion to the left, which are contrary breadthwise, and
forward locomotion and backward locomotion, which too are contraries.
On the other hand, (10) a process simply to a contrary, e. g. that
denoted by the expression ‘becoming white’, where no starting-point is
specified, is a change but not a motion. And in all cases of a thing that
has no contrary we have as contraries change from and change to the
same thing. Thus coming to be is contrary to ceasing to be, and losing to
gaining. But these are changes and not motions. (15) And wherever a pair
of contraries admit of an intermediate, motions to that intermediate
must be held to be in a sense motions to one or other of the contraries:
for the intermediate serves as a contrary for the purposes of the motion,
in whichever direction the change may be, e. g. grey in a motion from
grey to white takes the place of black as starting-point, in a motion from
white to grey it takes the place of black as goal, and in a motion from
black to grey it takes the place of white as goal: for the middle is
opposed in a sense to either of the extremes, (20) as has been said above.5
Thus we see that two motions are contrary to each other only when one
is a motion from a contrary to the opposite contrary and the other is a
motion from the latter to the former.
6
But since a motion appears to have contrary to it not only another
motion but also a state of rest, we must determine how this is so. A
motion has for its contrary in the strict sense of the term another
motion, but it also has for an opposite a state of rest (for rest is the
privation of motion and the privation of anything may be called its
contrary), (25) and motion of one kind has for its opposite rest of that
kind, e. g. local motion has local rest. This statement, however, needs
further qualification: there remains the question, is the opposite of
remaining at a particular place motion from or motion to that place? It is
surely clear that since there are two subjects between which motion
takes place, motion from one of these (A) to its contrary (B) has for its
opposite remaining in A, (30) while the reverse motion has for its opposite
remaining in B. At the same time these two are also contrary to each
other: for it would be absurd to suppose that there are contrary motions
and not opposite states of rest. [230a] States of rest in contraries are
opposed. To take an example, a state of rest in health is (1) contrary to a
state of rest in disease, and (2) the motion to which it is contrary is that
from health to disease. For (2) it would be absurd that its contrary
motion should be that from disease to health, since motion to that in
which a thing is at rest is rather a coming to rest, the coming to rest
being found to come into being simultaneously with the motion; and one
of these two motions it must be. (5) And (1) rest in whiteness is of course
not contrary to rest in health.
Of all things that have no contraries there are opposite changes (viz.
change from the thing and change to the thing, e. g. change from being
and change to being), but no motion. So, too, of such things there is no
remaining though there is absence of change. (10) Should there be a
particular subject, absence of change in its being will be contrary to
absence of change in its not-being. And here a difficulty may be raised: if
not-being is not a particular something, what is it, it may be asked, that
is contrary to absence of change in a thing’s being? and is this absence of
change a state of rest? If it is, then either it is not true that every state of
rest is contrary to a motion or else coming to be and ceasing to be are
motion. (15) It is clear then that, since we exclude these from among
motions, we must not say that this absence of change is a state of rest:
we must say that it is similar to a state of rest and call it absence of
change. And it will have for its contrary either nothing or absence of
change in the thing’s not-being, or the ceasing to be of the thing: for
such ceasing to be is change from it and the thing’s coming to be is
change to it.
Again, a further difficulty may be raised. How is it, it may be asked,
that whereas in local change both remaining and moving may be natural
or unnatural, (20) in the other changes this is not so? e. g. alteration is not
now natural and now unnatural, for convalescence is no more natural or
unnatural than falling ill, whitening no more natural or unnatural than
blackening; so, too, with increase and decrease: these are not contrary to
each other in the sense that either of them is natural while the other is
unnatural, (25) nor is one increase contrary to another in this sense; and
the same account may be given of becoming and perishing: it is not true
that becoming is natural and perishing unnatural (for growing old is
natural), nor do we observe one becoming to be natural and another
unnatural. We answer that if what happens under violence is unnatural,
(30) then violent perishing is unnatural and as such contrary to natural
perishing. Are there then also some becomings that are violent and not
the result of natural necessity, and are therefore contrary to natural
becomings, and violent increases and decreases, e. g. the rapid growth to
maturity of profligates and the rapid ripening of seeds even when not
packed close in the earth? And how is it with alterations? [230b]
Surely just the same: we may say that some alterations are violent while
others are natural, e. g. (5) patients alter naturally or unnaturally
according as they throw off fevers on the critical days or not. But, it may
be objected, then we shall have perishings contrary to one another, not
to becoming. Certainly: and why should not this in a sense be so? Thus it
is so if one perishing is pleasant and another painful: and so one
perishing will be contrary to another not in an unqualified sense, but in
so far as one has this quality and the other that.
Now motions and states of rest universally exhibit contrariety in the
manner described above,6 (10) e. g. upward motion and rest above are
respectively contrary to downward motion and rest below, these being
instances of local contrariety; and upward locomotion belongs naturally
to fire and downward to earth, i. e. the locomotions of the two are
contrary to each other. And again, fire moves up naturally and down
unnaturally: and its natural motion is certainly contrary to its unnatural
motion. Similarly with remaining: remaining above is contrary to motion
from above downwards, (15) and to earth this remaining comes
unnaturally, this motion naturally. So the unnatural remaining of a thing
is contrary to its natural motion, just as we find a similar contrariety in
the motion of the same thing: one of its motions, (20) the upward or the
downward, will be natural, the other unnatural.
Here, however, the question arises, has every state of rest that is not
permanent a becoming, and is this becoming a coming to a standstill? If
so, there must be a becoming of that which is at rest unnaturally, e. g. of
earth at rest above: and therefore this earth during the time that it was
being carried violently upward was coming to a standstill. But whereas
the velocity of that which comes to a standstill seems always to increase,
the velocity of that which is carried violently seems always to decrease:
so it will be in a state of rest without having become so. (25) Moreover
‘coming to a standstill’ is generally recognized to be identical or at least
concomitant with the locomotion of a thing to its proper place.
There is also another difficulty involved in the view that remaining in
a particular place is contrary to motion from that place. For when a
thing is moving from or discarding something, it still appears to have
that which is being discarded, so that if a state of rest is itself contrary to
the motion from the state of rest to its contrary, (30) the contraries rest
and motion will be simultaneously predicable of the same thing. May we
not say, however, that in so far as the thing is still stationary it is in a
state of rest in a qualified sense? For, in fact, whenever a thing is in
motion, part of it is at the starting-point while part is at the goal to
which it is changing: and consequently a motion finds its true contrary
rather in another motion than in a state of rest. [231a]
With regard to motion and rest, then, we have now explained in what
sense each of them is one and under what conditions they exhibit
contrariety.
With regard to coming to a standstill the question may be raised
whether there is an opposite state of rest to unnatural as well as to
natural motions. (5) It would be absurd if this were not the case: for a
thing may remain still merely under violence: thus we shall have a thing
being in a non-permanent state of rest without having become so. But it
is clear that it must be the case: for just as there is unnatural motion, so,
too, a thing may be in an unnatural state of rest. Further, some things
have a natural and an unnatural motion, (10) e. g. fire has a natural
upward motion and an unnatural downward motion: is it, then, this
unnatural downward motion or is it the natural downward motion of
earth that is contrary to the natural upward motion? Surely it is clear
that both are contrary to it though not in the same sense: the natural
motion of earth is contrary inasmuch as the motion of fire is also
natural, (15) whereas the upward motion of fire as being natural is
contrary to the downward motion of fire as being unnatural. The same is
true of the corresponding cases of remaining. But there would seem to
be a sense in which a state of rest and a motion are opposites.
1a
201a 10.
1
sc. a contradictory.
2
sc. a contrary.
3
224b 26.
3a
This sentence has been transposed from its place in the next paragraph in the interest of sense.
—Ed.
4
l. 28 sqq.
5
224b 32 sqq.
6
In chapter 5.
BOOK VI
1 Now if the terms ‘continuous’, (21) ‘in contact’, and ‘in succession’ are
understood as defined above1—things being ‘continuous’ if their
extrèmities are one, ‘in contact’ if their extremities are together, and ‘in
succession’ if there is nothing of their own kind intermediate between
them—nothing that is continuous can be composed of indivisibles: (25)
e. g. a line cannot be composed of points, the line being continuous and
the point indivisible. For the extremities of two points can neither be one
(since of an indivisible there can be no extremity as distinct from some
other part) nor together (since that which has no parts can have no
extremity, the extremity and the thing of which it is the extremity being
distinct).
Moreover, if that which is continuous is composed of points, (30) these
points must be either continuous or in contact with one another: and the
same reasoning applies in the case of all indivisibles. [231b] Now for
the reason given above they cannot be continuous: and one thing can be
in contact with another only if whole is in contact with whole or part
with part or part with whole. But since indivisibles have no parts, they
must be in contact with one another as whole with whole. And if they
are in contact with one another as whole with whole, they will not be
continuous: for that which is continuous has distinct parts: and these
parts into which it is divisible are different in this way, (5) i. e. spatially
separate.
Nor, again, can a point be in succession to a point or a moment to a
moment in such a way that length can be composed of points or time of
moments: for things are in succession if there is nothing of their own
kind intermediate between them, whereas that which is intermediate
between points is always a line and that which is intermediate between
moments is always a period of time.
Again, (10) if length and time could thus be composed of indivisibles,
they could be divided into indivisibles, since each is divisible into the
parts of which it is composed. But, as we saw, no continuous thing is
divisible into things without parts. Nor can there be anything of any
other kind intermediate between the parts or between the moments: for
if there could be any such thing it is clear that it must be either
indivisible or divisible, and if it is divisible, it must be divisible either
into indivisibles or into divisibles that are infinitely divisible, in which
case it is continuous.
Moreover, it is plain that everything continuous is divisible into
divisibles that are infinitely divisible: for if it were divisible into
indivisibles, (15) we should have an indivisible in contact with an
indivisible, since the extremities of things that are continuous with one
another are one and are in contact.
The same reasoning applies equally to magnitude, to time, and to
motion: either all of these are composed of indivisibles and are divisible
into indivisibles, or none. This may be made clear as follows. (20) If a
magnitude is composed of indivisibles, the motion over that magnitude
must be composed of corresponding indivisible motions: e. g. if the
magnitude ABC is composed of the indivisibles A, B, C, each
corresponding part of the motion DEF of Z over ABC is indivisible.
Therefore, since where there is motion there must be something that is
in motion, (25) and where there is something in motion there must be
motion, therefore the being-moved will also be composed of indivisibles.
So Z traversed A when its motion was D, B when its motion was E, and C
similarly when its motion was F. Now a thing that is in motion from one
place to another cannot at the moment when it was in motion both be in
motion and at the same time have completed its motion at the place to
which it was in motion: e. g. if a man is walking to Thebes, he cannot be
walking to Thebes and at the same time have completed his walk to
Thebes: and, as we saw, (30) Z traverses the partless section A in virtue of
the presence of the motion D. [232a] Consequently, if Z actually
passed through A after being in process of passing through, the motion
must be divisible: for at the time when Z was passing through, it neither
was at rest nor had completed its passage but was in an intermediate
state: while if it is passing through and has completed its passage at the
same moment, then that which is walking will at the moment when it is
walking have completed its walk and will be in the place to which it is
walking; that is to say, (5) it will have completed its motion at the place
to which it is in motion.2 And if a thing is in motion over the whole ABC
and its motion is the three D, E, and F, and if it is not in motion at all
over the partless section A but has completed its motion over it, then the
motion will consist not of motions but of starts, and will take place by a
thing’s having completed a motion without being in motion: for on this
assumption it has completed its passage through A without passing
through it. (10) So it will be possible for a thing to have completed a walk
without ever walking: for on this assumption it has completed a walk
over a particular distance without walking over that distance. Since,
then, everything must be either at rest or in motion, and Z is therefore at
rest in each of the sections A, B, and C, it follows that a thing can be
continuously at rest and at the same time in motion: for, as we saw, Z is
in motion over the whole ABC and at rest in any part (and consequently
in the whole) of it. (15) Moreover, if the indivisibles composing DEF are
motions, it would be possible for a thing in spite of the presence in it of
motion to be not in motion but at rest, while if they are not motions, it
would be possible for motion to be composed of something other than
motions.
And if length and motion are thus indivisible, it is neither more nor
less necessary that time also be similarly indivisible, that is to say be
composed of indivisible moments: for if the whole distance is divisible
and an equal velocity will cause a thing to pass through less of it in less
time, (20) the time must also be divisible, and conversely, if the time in
which a thing is carried over the section A is divisible, this section A
must also be divisible.
2
And since every magnitude is divisible into magnitudes—for we
have shown that it is impossible for anything continuous to be composed
of indivisible parts, and every magnitude is continuous—it necessarily
follows that the quicker of two things traverses a greater magnitude in
an equal time, (25) an equal magnitude in less time, and a greater
magnitude in less time, in conformity with the definition sometimes
given of ‘the quicker’. Suppose that A is quicker than B. Now since of
two things that which changes sooner is quicker, (30) in the time FG, in
which A has changed from C to D, B will not yet have arrived at D but
will be short of it: so that in an equal time the quicker will pass over a
greater magnitude. More than this, it will pass over a greater magnitude
in less time: for in the time in which A has arrived at D, B being the
slower has arrived, let us say, at E. [232b] Then since A has occupied
the whole time FG in arriving at D, it will have arrived at H in less time
than this, say FJ. Now the magnitude CH that A has passed over is
greater than the magnitude CE, and the time FJ is less than the whole
time FG: so that the quicker will pass over a greater magnitude in less
time. (5) And from this it is also clear that the quicker will pass over an
equal magnitude in less time than the slower. For since it passes over the
greater magnitude in less time than the slower, and (regarded by itself)
passes over KL the greater in more time than KN the lesser, the time PQ
in which it passes over KL will be more than the time PR in which it
passes over KN: so that, (10) the time PQ being less than the time PV in
which the slower passes over KN, the time PR will also be less than the
time PV: for it is less than the time PQ, and that which is less than
something else that is less than a thing is also itself less than that thing.
Hence it follows that the quicker will traverse an equal magnitude in less
time than the slower. Again, since the motion of anything must always
occupy either an equal time or less or more time in comparison with that
of another thing, (15) and since, whereas a thing is slower if its motion
occupies more time and of equal velocity if its motion occupies an equal
time, the quicker is neither of equal velocity nor slower, it follows that
the motion of the quicker can occupy neither an equal time nor more
time. It can only be, then, that it occupies less time, and thus we get the
necessary consequence that the quicker will pass over an equal
magnitude (as well as a greater) in less time than the slower. (20)
And since every motion is in time and a motion may occupy any time,
and the motion of everything that is in motion may be either quicker or
slower, both quicker motion and slower motion may occupy any time:
and this being so, it necessarily follows that time also is continuous. By
continuous I mean that which is divisible into divisibles that are
infinitely divisible: and if we take this as the definition of continuous, (25)
it follows necessarily that time is continuous. For since it has been
shown that the quicker will pass over an equal magnitude in less time
than the slower, suppose that A is quicker and B slower, and that the
slower has traversed the magnitude CD in the time FG. (30) Now it is
clear that the quicker will traverse the same magnitude in less time than
this: let us say in the time FH. Again, since the quicker has passed over
the whole CD in the time FH, the slower will in the same time pass over
CJ, say, which is less than CD. [233a] And since B, the slower, has
passed over CJ in the time FH, the quicker will pass over it in less time:
so that the time FH will again be divided. And if this is divided the
magnitude CJ will also be divided just as CD was: and again, if the
magnitude is divided, the time will also be divided. And we can carry on
this process for ever, (5) taking the slower after the quicker and the
quicker after the slower alternately, and using what has been
demonstrated at each stage as a new point of departure: for the quicker
will divide the time and the slower will divide the length. If, then, this
alternation always holds good, and at every turn involves a division, (10)
it is evident that all time must be continuous. And at the same time it is
clear that all magnitude is also continuous; for the divisions of which
time and magnitude respectively are susceptible are the same and equal.
Moreover, the current popular arguments make it plain that, if time is
continuous, magnitude is continuous also, (15) inasmuch as a thing passes
over half a given magnitude in half the time taken to cover the whole: in
fact without qualification it passes over a less magnitude in less time; for
the divisions of time and of magnitude will be the same. And if either is
infinite, so is the other, and the one is so in the same way as the other;
i. e. if time is infinite in respect of its extremities, length is also infinite
in respect of its extremities: if time is infinite in respect of divisibility,
length is also infinite in respect of divisibility: and if time is infinite in
both respects, (20) magnitude is also infinite in both respects.
Hence Zeno’s argument makes a false assumption in asserting that it is
impossible for a thing to pass over or severally to come in contact with
infinite things in a finite time. For there are two senses in which length
and time and generally anything continuous are called ‘infinite’: they are
called so either in respect of divisibility or in respect of their extremities.
(25) So while a thing in a finite time cannot come in contact with things
quantitatively infinite, it can come in contact with things infinite in
respect of divisibility: for in this sense the time itself is also infinite: and
so we find that the time occupied by the passage over the infinite is not
a finite but an infinite time, (30) and the contact with the infinites is made
by means of moments not finite but infinite in number.
The passage over the infinite, then, cannot occupy a finite time, and
the passage over the finite cannot occupy an infinite time: if the time is
infinite the magnitude must be infinite also, and if the magnitude is
infinite, so also is the time. This may be shown as follows. Let AB be a
finite magnitude, and let us suppose that it is traversed in infinite time
C, (35) and let a finite period CD of the time be taken. [233b] Now in
this period the thing in motion will pass over a certain segment of the
magnitude: let BE be the segment that it has thus passed over. (This will
be either an exact measure of AB or less or greater than an exact
measure: it makes no difference which it is.) Then, since a magnitude
equal to BE will always be passed over in an equal time, (5) and BE
measures the whole magnitude, the whole time occupied in passing over
AB will be finite: for it will be divisible into periods equal in number to
the segments into which the magnitude is divisible. Moreover, if it is the
case that infinite time is not occupied in passing over every magnitude,
but it is possible to pass over some magnitude, say BE, in a finite time,
and if this BE measures the whole of which it is a part, (10) and if an
equal magnitude is passed over in an equal time, then it follows that the
time like the magnitude is finite. That infinite time will not be occupied
in passing over BE is evident if the time be taken as limited in one
direction: for as the part will be passed over in less time than the whole,
the time occupied in traversing this part must be finite, the limit in one
direction being given. The same reasoning will also show the falsity of
the assumption that infinite length can be traversed in a finite time. It is
evident, then, from what has been said that neither a line nor a surface
nor in fact anything continuous can be indivisible. (15)
This conclusion follows not only from the present argument but from
the consideration that the opposite assumption implies the divisibility of
the indivisible. For since the distinction of quicker and slower may apply
to motions occupying any period of time and in an equal time the
quicker passes over a greater length, (20) it may happen that it will pass
over a length twice, or one and a half times, as great as that passed over
by the slower: for their respective velocities may stand to one another in
this proportion. Suppose, then, that the quicker has in the same time
been carried over a length one and a half times as great as that traversed
by the slower, and that the respective magnitudes are divided, that of
the quicker, the magnitude ABCD, into three indivisibles, and that of the
slower into the two indivisibles EF, FG. Then the time may also be
divided into three indivisibles, (25) for an equal magnitude will be passed
over in an equal time. Suppose then that it is thus divided into JK, KL,
LM. Again, since in the same time the slower has been carried over EF,
FG, the time may also be similarly divided into two. Thus the indivisible
will be divisible, and that which has no parts will be passed over not in
an indivisible but in a greater time.3 (30) It is evident, therefore, that
nothing continuous is without parts.
3
The present also is necessarily indivisible—the present, that is, not
in the sense in which the word is applied to one thing in virtue of
another,4 but in its proper and primary sense; in which sense it is
inherent in all time. (35) For the present is something that is an extremity
of the past (no part of the future being on this side of it) and also of the
future (no part of the past being on the other side of it): it is, as we have
said,5 a limit of both. [234a] And if it is once shown that it is
essentially of this character and one and the same, it will at once be
evident also that it is indivisible. (5)
Now the present that is the extremity of both times must be one and
the same: for if each extremity were different, the one could not be in
succession to the other, because nothing continuous can be composed of
things having no parts: and if the one is apart from the other, there will
be time intermediate between them, because everything continuous is
such that there is something intermediate between its limits and
described by the same name as itself. (10) But if the intermediate thing is
time, it will be divisible: for all time has been shown6 to be divisible.
Thus on this assumption the present is divisible. But if the present is
divisible, there will be part of the past in the future and part of the
future in the past: for past time will be marked off from future time at
the actual point of division. Also the present will be a present not in the
proper sense but in virtue of something else: for the division which
yields it will not be a division proper.7 (15) Furthermore, there will be a
part of the present that is past and a part that is future, and it will not
always be the same part that is past or future: in fact one and the same
present will not be simultaneous: for the time may be divided at many
points. If, therefore, the present cannot possibly have these
characteristics, it follows that it must be the same present that belongs to
each of the two times. (20) But if this is so it is evident that the present is
also indivisible: for if it is divisible it will be involved in the same
implications as before. It is clear, then, from what has been said that
time contains something indivisible, and this is what we call a present.
We will now show that nothing can be in motion in a present. (25) For
if this is possible, there can be both quicker and slower motion in the
present. Suppose then that in the present M the quicker has traversed the
distance AB. That being so, the slower will in the same present traverse a
distance less than AB, say AC. But since the slower will have occupied
the whole present in traversing AC, (30) the quicker will occupy less than
this in traversing it. Thus we shall have a division of the present,
whereas we found it to be indivisible. It is impossible, therefore, for
anything to be in motion in a present.
Nor can anything be at rest in a present: for, as we were saying,8 that
only can be at rest which is naturally designed to be in motion but is not
in motion when, where, or as it would naturally be so: since, therefore,
nothing is naturally designed to be in motion in a present, it is clear that
nothing can be at rest in a present either.
Moreover, inasmuch as it is the same present that belongs to both the
times,9 and it is possible for a thing to be in motion throughout one time
and to be at rest throughout the other, (35) and that which is in motion or
at rest for the whole of a time will be in motion or at rest as the case
may be in any part of it in which it is naturally designed to be in motion
or at rest: this being so, the assumption that there can be motion or rest
in a present will carry with it the implication that the same thing can at
the same time be at rest and in motion: for both the times have the same
extremity, viz. [234b] the present.
Again, when we say that a thing is at rest, we imply that its condition
in whole and in part is at the time of speaking uniform with what it was
previously: but the present contains no ‘previously’: consequently, (5)
there can be no rest in it.
It follows then that the motion of that which is in motion and the rest
of that which is at rest must occupy time.
4
Further, everything that changes must be divisible.
(10)
For since
every change is from something to something, and when a thing is at the
goal of its change it is no longer changing, and when both it itself and all
its parts are at the starting-point of its change it is not changing (for that
which is in whole and in part in an unvarying condition is not in a state
of change); it follows, therefore, (15) that part of that which is changing
must be at the starting-point and part at the goal: for as a whole it
cannot be in both or in neither. (Here by ‘goal of change’ I mean that
which comes first in the process of change: e. g. in a process of change
from white the goal in question will be grey, not black: for it is not
necessary that that which is changing should be at either of the
extremes.) It is evident, (20) therefore, that everything that changes must
be divisible.
Now motion is divisible in two senses. In the first place it is divisible
in virtue of the time that it occupies. In the second place it is divisible
according to the motions of the several parts of that which is in motion:
e. g. if the whole AC is in motion, there will be a motion of AB and a
motion of BC. That being so, let DE be the motion of the part AB and EF
the motion of the part BC. (25) Then the whole DF must be the motion of
AC: for DF must constitute the motion of AC inasmuch as DE and EF
severally constitute the motions of each of its parts. But the motion of a
thing can never be constituted by the motion or something else:
consequently the whole motion is the motion of the whole magnitude.
Again, since every motion is a motion of something, and the whole
motion DF is not the motion of either of the parts (for each of the parts
DE, EF is the motion of one of the parts AB, BC) (30) or of anything else
(for, the whole motion being the motion of a whole, the parts of the
motion are the motions of the parts of that whole: and the parts of DF
are the motions of AB, BC and of nothing else: for, as we saw,10 a motion
that is one cannot be the motion of more things than one): since this is
so, the whole motion will be the motion of the magnitude ABC.
Again, if there is a motion of the whole other than DF, say HI, the
motion of each of the parts may be subtracted from it: and these motions
will be equal to DE, (35) EF respectively: for the motion of that which is
one must be one. [235a] So if the whole motion HI may be divided
into the motions of the parts, HI will be equal to DF: if on the other hand
there is any remainder, say JI, this will be a motion of nothing: for it can
be the motion neither of the whole nor of the parts (as the motion of
that which is one must be one) nor of anything else: for a motion that is
continuous must be the motion of things that are continuous. (5) And the
same result follows if the division of HI reveals a surplus on the side of
the motions of the parts. Consequently, if this is impossible, the whole
motion must be the same as and equal to DF.
This then is what is meant by the division of motion according to the
motions of the parts: and it must be applicable to everything that is
divisible into parts.
Motion is also susceptible of another kind of division, (10) that
according to time. For since all motion is in time and all time is
divisible, and in less time the motion is less, it follows that every motion
must be divisible according to time. And since everything that is in
motion is in motion in a certain sphere and for a certain time and has a
motion belonging to it, (15) it follows that the time, the motion, the
being-in-motion, the thing that is in motion, and the sphere of the
motion must all be susceptible of the same divisions (though spheres of
motion are not all divisible in a like manner: thus quantity is essentially,
quality accidentally divisible). For suppose that A is the time occupied
by the motion B. (20) Then if all the time has been occupied by the whole
motion, it will take less of the motion to occupy half the time, less again
to occupy a further subdivision of the time, and so on to infinity. Again,
the time will be divisible similarly to the motion: for if the whole motion
occupies all the time half the motion will occupy half the time, and less
of the motion again will occupy less of the time.
In the same way the being-in-motion will also be divisible. (25) For let
C be the whole being-in-motion. Then the being-in-motion that
corresponds to half the motion will be less than the whole being-inmotion, that which corresponds to a quarter of the motion will be less
again, and so on to infinity. Moreover by setting out successively the
being-in-motion corresponding to each of the two motions DC (say) and
CE, we may argue that the whole being-in-motion will correspond to the
whole motion (for if it were some other being-in-motion that
corresponded to the whole motion, (30) there would be more than one
being-in-motion corresponding to the same motion), the argument being
the same as that whereby we showed11 that the motion of a thing is
divisible into the motions of the parts of the thing: for if we take
separately the being-in-motion corresponding to each of the two
motions, we shall see that the whole being-in-motion is continuous.
The same reasoning will show the divisibility of the length, and in fact
of everything that forms a sphere of change (though some of these are
only accidentally divisible because that which changes is so): for the
division of one term will involve the division of all. (35) So, too, in the
matter of their being finite or infinite, they will all alike be either the
one or the other. And we now see that in most cases the fact that all the
terms are divisible or infinite is a direct consequence of the fact that the
thing that changes is divisible or infinite: for the attributes ‘divisible’ and
‘infinite’ belong in the first instance to the thing that changes. [235b]
That divisibility does so we have already12 shown; that infinity does so
will be made clear in what follows.13 (5)
5
Since everything that changes changes from something to
something, that which has changed must at the moment when it has first
changed be in that to which it has changed. For that which changes
retires from or leaves that from which it changes: and leaving, if not
identical with changing, is at any rate a consequence of it. (10) And if
leaving is a consequence of changing, having left is a consequence of
having changed: for there is a like relation between the two in each case.
One kind of change, then, being change in a relation of contradiction,
where a thing has changed from not-being to being it has left not-being.
(15) Therefore it will be in being: for everything must either be or not be.
It is evident, then, that in contradictory change that which has changed
must be in that to which it has changed. And if this is true in this kind of
change, it will be true in all other kinds as well: for in this matter what
holds good in the case of one will hold good likewise in the case of the
rest.
Moreover, if we take each kind of change separately, the truth of our
conclusion will be equally evident, on the ground that that which has
changed must be somewhere or in something. (20) For, since it has left
that from which it has changed and must be somewhere, it must be
either in that to which it has changed or in something else. If, then, that
which has changed to B is in something other than B, say C, it must
again be changing from C to B: for it cannot be assumed that there is no
interval between C and B, (25) since change is continuous. Thus we have
the result that the thing that has changed, at the moment when it has
changed, is changing to that to which it has changed, which is
impossible: that which has changed, therefore, must be in that to which
it has changed. So it is evident likewise that that which has come to be,
at the moment when it has come to be, will be, and that which has
ceased to be will not-be: for what we have said applies universally to
every kind of change, and its truth is most obvious in the case of
contradictory change. (30) It is clear, then, that that which has changed,
at the moment when it has first changed, is in that to which it has
changed.
We will now show that the ‘primary when’ in which that which has
changed effected the completion of its change must be indivisible, where
by ‘primary’ I mean possessing the characteristics in question of itself
and not in virtue of the possession of them by something else belonging
to it. For let AC be divisible, and let it be divided at B. (35) If then the
completion of change has been effected in AB or again in BC, AC cannot
be the primary thing in which the completion of change has been
effected. If, on the other hand, it has been changing in both AB and BC
(for it must either have changed or be changing in each of them), it must
have been changing in the whole AC: but our assumption was that AC
contains only the completion of the change. [236a] It is equally
impossible to suppose that one part of AC contains the process and the
other the completion of the change: for then we shall have something
prior to what is primary.14 So that in which the completion of change
has been effected must be indivisible. (5) It is also evident, therefore, that
that in which that which has ceased to be has ceased to be and that in
which that which has come to be has come to be are indivisible.
But there are two senses of the expression ‘the primary when in which
something has changed’. On the one hand it may mean the primary
when containing the completion of the process of change—the moment
when it is correct to say ‘it has changed’: on the other hand it may mean
the primary when containing the beginning of the process of change. Now
the primary when that has reference to the end of the change is
something really existent: for a change may really be completed, (10) and
there is such a thing as an end of change, which we have in fact shown
to be indivisible because it is a limit. But that which has reference to the
beginning is not existent at all: for there is no such thing as a beginning
of a process of change, and the time occupied by the change does not
contain any primary when in which the change began. (15) For suppose
that AD is such a primary when. Then it cannot be indivisible: for, if it
were, the moment immediately preceding the change and the moment in
which the change begins would be consecutive (and moments cannot be
consecutive). Again, if the changing thing is at rest in the whole
preceding time CA (for we may suppose that it is at rest), it is at rest in
A also: so if AD is without parts, it will simultaneously be at rest and
have changed: for it is at rest in A and has changed in D. (20) Since then
AD is not without parts, it must be divisible, and the changing thing
must have changed in every part of it (for if it has changed in neither of
the two parts into which AD is divided, it has not changed in the whole
either: if, on the other hand, it is in process of change in both parts, it is
likewise in process of change in the whole: and if, again, it has changed
in one of the two parts, the whole is not the primary when in which it
has changed: it must therefore have changed in every part). (25) It is
evident, then, that with reference to the beginning of change there is no
primary when in which change has been effected: for the divisions are
infinite.
So, too, of that which has changed there is no primary part that has
changed. For suppose that of DE the primary part that has changed is DF
(everything that changes having been shown15 to be divisible): and let
HI be the time in which DF has changed. (30) If, then, in the whole time
DF has changed, in half the time there will be a part that has changed,
less than and therefore prior to DF: and again there will be another part
prior to this, and yet another, and so on to infinity. Thus of that which
changes there cannot be any primary part that has changed. It is evident,
then, from what has been said, (35) that neither of that which changes nor
of the time in which it changes is there any primary part. [236b]
With regard, however, to the actual subject of change—that is to say
that in respect of which a thing changes—there is a difference to be
observed. For in a process of change we may distinguish three terms—
that which changes, that in which it changes, and the actual subject of
change, e. g. the man, the time, and the fair complexion. (5) Of these the
man and the time are divisible: but with the fair complexion it is
otherwise (though they are all divisible accidentally, for that in which
the fair complexion or any other quality is an accident is divisible). For
of actual subjects of change it will be seen that those which are classed
as essentially, not accidentally, (10) divisible have no primary part. Take
the case of magnitudes: let AB be a magnitude, and suppose that it has
moved from B to a primary ‘where’ C. Then if BC is taken to be
indivisible, two things without parts will have to be contiguous (which is
impossible): if on the other hand it is taken to be divisible, there will be
something prior to C to which the magnitude has changed, and
something else again prior to that, and so on to infinity, because the
process of division may be continued without end. (15) Thus there can be
no primary ‘where’ to which a thing has changed. And if we take the
case of quantitative change, we shall get a like result, for here too the
change is in something continuous. It is evident, then, that only in
qualitative motion can there be anything essentially indivisible.
6
Now everything that changes changes in time, (20) and that in two
senses: for the time in which a thing is said to change may be the
primary time, or on the other hand it may have an extended reference,
as e. g. when we say that a thing changes in a particular year because it
changes in a particular day. That being so, that which changes must be
changing in any part of the primary time in which it changes. This is
clear from our definition of ‘primary’,16 in which the word is said to
express just this: it may also, however, (25) be made evident by the
following argument. Let VQ be the primary time in which that which is
in motion is in motion: and (as all time is divisible) let it be divided at J.
Now in the time VJ it either is in motion or is not in motion, and the
same is likewise true of the time JQ. Then if it is in motion in neither of
the two parts, it will be at rest in the whole: for it is impossible that it
should be in motion in a time in no part of which it is in motion. If on
the other hand it is in motion in only one of the two parts of the time,
(30) VQ cannot be the primary time in which it is in motion: for its
motion will have reference to a time other than VQ. It must, then, have
been in motion in any part of VQ.
And now that this has been proved, it is evident that everything that is
in motion must have been in motion before. For if that which is in
motion has traversed the distance JK in the primary time VQ, (35) in half
the time a thing that is in motion with equal velocity and began its
motion at the same time will have traversed half the distance. But if this
second thing whose velocity is equal has traversed a certain distance in a
certain time, the original thing that is in motion must have traversed the
same distance in the same time. [237a] Hence that which is in motion
must have been in motion before.
Again, if by taking the extreme moment of the time—for it is the
moment that defines the time, and time is that which is intermediate
between moments—we are enabled to say that motion has taken place in
the whole time VQ or in fact in any period of it, (5) motion may likewise
be said to have taken place in every other such period. But half the time
finds an extreme in the point of division. Therefore motion will have
taken place in half the time and in fact in any part of it: for as soon as
any division is made there is always a time defined by moments. If, then,
all time is divisible, (10) and that which is intermediate between moments
is time, everything that is changing must have completed an infinite
number of changes.
Again, since a thing that changes continuously and has not perished or
ceased from its change must either be changing or have changed in any
part of the time of its change, and since it cannot be changing in a
moment, it follows that it must have changed at every moment in the
time: consequently, since the moments are infinite in number, (15)
everything that is changing must have completed an infinite number of
changes.
And not only must that which is changing have changed, but that
which has changed must also previously have been changing, since
everything that has changed from something to something has changed
in a period of time. For suppose that a thing has changed from A to B in
a moment. (20) Now the moment in which it has changed cannot be the
same as that in which it is at A (since in that case it would be in A and B
at once): for we have shown above17 that that which has changed, when
it has changed, is not in that from which it has changed. If, on the other
hand, it is a different moment, there will be a period of time
intermediate between the two: for, (25) as we saw,18 moments are not
consecutive. Since, then, it has changed in a period of time, and all time
is divisible, in half the time it will have completed another change, in a
quarter another, and so on to infinity: consequently when it has
changed, it must have previously been changing.
Moreover, the truth of what has been said is more evident in the case
of magnitude, because the magnitude over which what is changing
changes is continuous. (30) For suppose that a thing has changed from C
to D. Then if CD is indivisible, two things without parts will be
consecutive. But since this is impossible, that which is intermediate
between them must be a magnitude and divisible into an infinite number
of segments: consequently, before the change is completed, the thing
changes to those segments. Everything that has changed, (35) therefore,
must previously have been changing: for the same proof also holds good
of change with respect to what is not continuous, changes, that is to say,
between contraries and between contradictories. [237b] In such cases
we have only to take the time in which a thing has changed and again
apply the same reasoning. So that which has changed must have been
changing and that which is changing must have changed, and a process
of change is preceded by a completion of change and a completion by a
process: and we can never take any stage and say that it is absolutely the
first. (5) The reason of this is that no two things without parts can be
contiguous, and therefore in change the process of division is infinite,
just as lines may be infinitely divided so that one part is continually
increasing and the other continually decreasing.19
So it is evident also that that which has become must previously have
been in process of becoming, (10) and that which is in process of
becoming must previously have become, everything (that is) that is
divisible and continuous: though it is not always the actual thing that is
in process of becoming of which this is true: sometimes it is something
else, that is to say, some part of the thing in question, e. g. the
foundation-stone of a house. So, too, in the case of that which is
perishing and that which has perished: for that which becomes and that
which perishes must contain an element of infiniteness as an immediate
consequence of the fact that they are continuous things: and so a thing
cannot be in process of becoming without having become or have
become without having been in process of becoming. (15) So, too, in the
case of perishing and having perished: perishing must be preceded by
having perished, and having perished must be preceded by perishing. It
is evident, then, that that which has become must previously have been
in process of becoming, and that which is in process of becoming must
previously have become: for all magnitudes and all periods of time are
infinitely divisible. (20)
Consequently no absolutely first stage of change can be represented by
any particular part of space or time which the changing thing may
occupy.
7
Now since the motion of everything that is in motion occupies a
period of time, and a greater magnitude is traversed in a longer time, it
is impossible that a thing should undergo a finite motion in an infinite
time, (25) if this is understood to mean not that the same motion or a part
of it is continually repeated, but that the whole infinite time is occupied
by the whole finite motion. In all cases where a thing is in motion with
uniform velocity it is clear that the finite magnitude is traversed in a
finite time. For if we take a part of the motion which shall be a measure
of the whole, the whole motion is completed in as many equal periods of
the time as there are parts of the motion. (30) Consequently, since these
parts are finite, both in size individually and in number collectively, the
whole time must also be finite: for it will be a multiple of the portion,
equal to the time occupied in completing the aforesaid part multiplied
by the number of the parts.
But it makes no difference even if the velocity is not uniform. For let
us suppose that the line AB represents a finite stretch over which a thing
has been moved in the given time, (35) and let CD be the infinite time.
Now if one part of the stretch must have been traversed before another
part (this is clear, that in the earlier and in the later part of the time a
different part of the stretch has been traversed: for as the time lengthens
a different part of the motion will always be completed in it, whether
the thing in motion changes with uniform velocity or not: and whether
the rate of motion increases or diminishes or remains stationary this is
none the less so), (5) let us then take AE a part of the whole stretch of
motion AB which shall be a measure of AB. [238a] Now this part of
the motion occupies a certain period of the infinite time: it cannot itself
occupy an infinite time, for we are assuming that that is occupied by the
whole AB. And if again I take another part equal to AE, that also must
occupy a finite time in consequence of the same assumption. (10) And if I
go on taking parts in this way, on the one hand there is no part which
will be a measure of the infinite time (for the infinite cannot be
composed of finite parts whether equal or unequal, because there must
be some unity which will be a measure of things finite in multitude or in
magnitude, (15) which, whether they are equal or unequal, are none the
less limited in magnitude); while on the other hand the finite stretch of
motion AB is a certain multiple of AE: consequently the motion AB must
be accomplished in a finite time. Moreover it is the same with coming to
rest as with motion. And so it is impossible for one and the same thing to
be infinitely in process of becoming or of perishing.
The same reasoning will prove that in a finite time there cannot be an
infinite extent of motion or of coming to rest, (20) whether the motion is
regular or irregular. For if we take a part which shall be a measure of the
whole time, in this part a certain fraction, not the whole, of the
magnitude will be traversed, because we assume that the traversing of
the whole occupies all the time. Again, in another equal part of the time
another part of the magnitude will be traversed: and similarly in each
part of the time that we take, (25) whether equal or unequal to the part
originally taken. It makes no difference whether the parts are equal or
not, if only each is finite: for it is clear that while the time is exhausted
by the subtraction of its parts, the infinite magnitude will not be thus
exhausted, since the process of subtraction is finite both in respect of the
quantity subtracted and of the number of times a subtraction is made.
Consequently the infinite magnitude will not be traversed in a finite
time: and it makes no difference whether the magnitude is infinite in
only one direction or in both: for the same reasoning will hold good. (30)
This having been proved, it is evident that neither can a finite
magnitude traverse an infinite magnitude in a finite time, the reason
being the same as that given above: in part of the time it will traverse a
finite magnitude and in each several part likewise, (35) so that in the
whole time it will traverse a finite magnitude.
And since a finite magnitude will not traverse an infinite in a finite
time, it is clear that neither will an infinite traverse a finite in a finite
time. [238b] For if the infinite could traverse the finite, the finite
could traverse the infinite; for it makes no difference which of the two is
the thing in motion: either case involves the traversing of the infinite by
the finite. (5) For when the infinite magnitude A is in motion a part of it,
say CD, will occupy the finite B, and then another, and then another,
and so on to infinity. Thus the two results will coincide: the infinite will
have completed a motion over the finite and the finite will have
traversed the infinite: for it would seem to be impossible for the motion
of the infinite over the finite to occur in any way other than by the finite
traversing the infinite either by locomotion over it or by measuring it.
(10) Therefore, since this is impossible, the infinite cannot traverse the
finite.
Nor again will the infinite traverse the infinite in a finite time.
Otherwise it would also traverse the finite, for the infinite includes the
finite. (15) We can further prove this in the same way by taking the time
as our starting-point.
Since, then, it is established that in a finite time neither will the finite
traverse the infinite, nor the infinite the finite, nor the infinite the
infinite, it is evident also that in a finite time there cannot be infinite
motion: for what difference does it make whether we take the motion or
the magnitude to be infinite? If either of the two is infinite, (20) the other
must be so likewise: for all locomotion is in space.
8
Since everything to which motion or rest is natural is in motion or
at rest in the natural time, place, and manner, that which is coming to a
stand, when it is coming to a stand, must be in motion: for if it is not in
motion it must be at rest: but that which is at rest cannot be coming to
rest. (25) From this it evidently follows that coming to a stand must
occupy a period of time: for the motion of that which is in motion
occupies a period of time, and that which is coming to a stand has been
shown to be in motion: consequently coming to a stand must occupy a
period of time.
Again, since the terms ‘quicker’ and ‘slower’ are used only of that
which occupies a period of time, and the process of coming to a stand
may be quicker or slower, (30) the same conclusion follows.
And that which is coming to a stand must be coming to a stand in any
part of the primary time in which it is coming to a stand. For if it is
coming to a stand in neither of two parts into which the time may be
divided, it cannot be coming to a stand in the whole time, with the
result that that which is coming to a stand will not be coming to a stand.
If on the other hand it is coming to a stand in only one of the two parts
of the time, the whole cannot be the primary time in which it is coming
to a stand: for it is coming to a stand in the whole time not primarily but
in virtue of something distinct from itself, (35) the argument being the
same as that which we used above about things in motion.20
And just as there is no primary time in which that which is in motion
is in motion, so too there is no primary time in which that which is
coming to a stand is coming to a stand, there being no primary stage
either of being in motion or of coming to a stand. [239a] For let AB be
the primary time in which a thing is coming to a stand. Now AB cannot
be without parts: for there cannot be motion in that which is without
parts, because the moving thing would necessarily have been already
moved for part of the time of its movement: and that which is coming to
a stand has been shown to be in motion. (5) But since AB is therefore
divisible, the thing is coming to a stand in every one of the parts of AB:
for we have shown above21 that it is coming to a stand in every one of
the parts in which it is primarily coming to a stand. Since, then, that in
which primarily a thing is coming to a stand must be a period of time
and not something indivisible, and since all time is infinitely divisible,
there cannot be anything in which primarily it is coming to a stand.
Nor again can there be a primary time at which the being at rest of
that which is at rest occurred: for it cannot have occurred in that which
has no parts, (10) because there cannot be motion in that which is
indivisible, and that in which rest takes place is the same as that in
which motion takes place: for we defined22 a state of rest to be the state
of a thing to which motion is natural but which is not in motion when
(that is to say in that23 in which) motion would be natural to it. Again,
our use of the phrase ‘being at rest’ also implies that the previous state of
a thing is still unaltered, (15) not one point only but two at least being
thus needed to determine its presence: consequently that in which a
thing is at rest cannot be without parts. Since, then, it is divisible, it
must be a period of time, and the thing must be at rest in every one of its
parts, as may be shown by the same method as that used above in
similar demonstrations.
So there can be no primary part of the time: and the reason is that rest
and motion are always in a period of time, (20) and a period of time has
no primary part any more than a magnitude or in fact anything
continuous: for everything continuous is divisible into an infinite
number of parts.
And since everything that is in motion is in motion in a period of time
and changes from something to something, when its motion is comprised
within a particular period of time essentially—that is to say when it fills
the whole and not merely a part of the time in question—it is impossible
that in that time that which is in motion should be over against some
particular thing primarily.24 (25) For if a thing—itself and each of its parts
—occupies the same space for a definite period of time, it is at rest: for it
is in just these circumstances that we use the term ‘being at rest’—when
at one moment after another it can be said with truth that a thing, itself
and its parts, occupies the same space. So if this is being at rest it is
impossible for that which is changing to be as a whole, at the time when
it is primarily changing, (30) over against any particular thing (for the
whole period of time is divisible), so that in one part of it after another it
will be true to say that the thing, itself and its parts, occupies the same
space. If this is not so and the aforesaid proposition is true only at a
single moment, then the thing will be over against a particular thing not
for any period of time but only at a moment that limits the time. It is
true that at any moment it is always over against something stationary:
but it is not at rest: for at a moment it is not possible for anything to be
either in motion or at rest. [239b] (35) So while it is true to say that
that which is in motion is at a moment not in motion and is opposite
some particular thing, it cannot in a period of time be over against that
which is at rest: for that would involve the conclusion that that which is
in locomotion is at rest.
9
Zeno’s reasoning, however, is fallacious, when he says that if
everything when it occupies an equal space is at rest, (5) and if that
which is in locomotion is always occupying such a space at any moment,
the flying arrow is therefore motionless. This is false, for time is not
composed of indivisible moments any more than any other magnitude is
composed of indivisibles.
Zeno’s arguments about motion, which cause so much disquietude to
those who try to solve the problems that they present, (10) are four in
number. The first asserts the non-existence of motion on the ground that
that which is in locomotion must arrive at the half-way stage before it
arrives at the goal. This we have discussed above.25
The second is the so-called ‘Achilles’, and it amounts to this, that in a
race the quickest runner can never overtake the slowest, (15) since the
pursuer must first reach the point whence the pursued started, so that
the slower must always hold a lead. This argument is the same in
principle as that which depends on bisection,26 though it differs from it
in that the spaces with which we successively have to deal are not
divided into halves. The result of the argument is that the slower is not
overtaken: but it proceeds along the same lines as the bisectionargument (for in both a division of the space in a certain way leads to
the result that the goal is not reached, (20) though the ‘Achilles’ goes
further in that it affirms that even the quickest runner in legendary
tradition must fail in his pursuit of the slowest), so that the solution
must be the same. (25) And the axiom that that which holds a lead is
never overtaken is false: it is not overtaken, it is true, while it holds a
lead: but it is overtaken nevertheless if it is granted that it traverses the
finite distance prescribed. These then are two of his arguments.
The third is that already given above, (30) to the effect that the flying
arrow is at rest, which result follows from the assumption that time is
composed of moments: if this assumption is not granted, the conclusion
will not follow.
The fourth argument is that concerning the two rows of bodies, each
row being composed of an equal number of bodies of equal size, passing
each other on a race-course as they proceed with equal velocity in
opposite directions, the one row originally occupying the space between
the goal and the middle point of the course and the other that between
the middle point and the starting-post. (35) This, he thinks, involves the
conclusion that half a given time is equal to double that time. [240a]
The fallacy of the reasoning lies in the assumption that a body occupies
an equal time in passing with equal velocity a body that is in motion and
a body of equal size that is at rest; which is false. For instance (so runs
the argument), let A, (5) A … be the stationary bodies of equal size, B,
B … the bodies, equal in number and in size to A, A …, originally
occupying the half of the course from the starting-post to the middle of
the A’s, and C, C, … those originally occupying the other half from the
goal to the middle of the A’s, equal in number, size, and velocity to B, B.
… Then three consequences follow:
First, as the B’s and the C’s pass one another, (10) the first B reaches the
last C at the same moment as the first C reaches the last B. Secondly, at
this moment the first C has passed all the A’s, whereas the first B has
passed only half the A’s, and has consequently occupied only half the
time occupied by the first C, since each of the two occupies an equal
time in passing each A. Thirdly, at the same moment all the B’s have
passed all the C’s: for the first C and the first B will simultaneously reach
the opposite ends of the course, (15) since (so says Zeno) the time
occupied by the first C in passing each of the B’s is equal to that
occupied by it in passing each of the A’s, because an equal time is
occupied by both the first B and the first C in passing all the A’s. This is
the argument, but it presupposed the aforesaid fallacious assumption.
Nor in reference to contradictory change shall we find anything
unanswerable in the argument that if a thing is changing from not-white,
(20) say, to white, and is in neither condition, then it will be neither white
nor not-white: for the fact that it is not wholly in either condition will
not preclude us from calling it white or not-white. We call a thing white
or not-white not necessarily because it is wholly either one or the other,
but because most of its parts or the most essential parts of it are so: not
being in a certain condition is different from not being wholly in that
condition. (25) So, too, in the case of being and not-being and all other
conditions which stand in a contradictory relation: while the changing
thing must of necessity be in one of the two opposites, it is never wholly
in either.
Again, in the case of circles and spheres and everything whose motion
is confined within the space that it occupies, it is not true to say that the
motion can be nothing but rest, on the ground that such things in
motion, (30) themselves and their parts, will occupy the same position for
a period of time, and that therefore they will be at once at rest and in
motion. For in the first place the parts do not occupy the same position
for any period of time: and in the second place the whole also is always
changing to a different position: for if we take the orbit as described
from a point A on a circumference, it will not be the same as the orbit as
described from B or C or any other point on the same circumference
except in an accidental sense, the sense that is to say in which a musical
man is the same as a man. [240b] (5) Thus one orbit is always changing
into another, and the thing will never be at rest. And it is the same with
the sphere and everything else whose motion is confined within the
space that it occupies.
10
Our next point is that that which is without parts cannot be in
motion except accidentally: i. e. it can be in motion only in so far as the
body or the magnitude is in motion and the partless is in motion by
inclusion therein, (10) just as that which is in a boat may be in motion in
consequence of the locomotion of the boat, or a part may be in motion
in virtue of the motion of the whole. (It must be remembered, however,
that by ‘that which is without parts’ I mean that which is quantitatively
indivisible (and that the case of the motion of a part is not exactly
parallel): for parts have motions belonging essentially and severally to
themselves distinct from the motion of the whole. (15) The distinction
may be seen most clearly in the case of a revolving sphere, in which the
velocities of the parts near the centre and of those on the surface are
different from one another and from that of the whole; this implies that
there is not one motion but many.) As we have said, then, that which is
without parts can be in motion in the sense in which a man sitting in a
boat is in motion when the boat is travelling, but it cannot be in motion
of itself. (20) For suppose that it is changing from AB to BC—either from
one magnitude to another, or from one form to another, or from some
state to its contradictory—and let D be the primary time in which it
undergoes the change. Then in the time in which it is changing it must
be either in AB or in BC or partly in one and partly in the other: for this,
(25) as we saw,27 is true of everything that is changing. Now it cannot be
partly in each of the two: for then it would be divisible into parts. Nor
again can it be in BC: for then it will have completed the change,
whereas the assumption is that the change is in process. It remains, then,
that in the time in which it is changing, it is in AB. That being so, it will
be at rest: for, as we saw,28 to be in the same condition for a period of
time is to be at rest. (30) So it is not possible for that which has no parts
to be in motion or to change in any way: for only one condition could
have made it possible for it to have motion, viz. that time should be
composed of moments, in which case at any moment it would have
completed a motion or a change, so that it would never be in motion,
but would always have been in motion. [241a] But this we have
already shown above29 to be impossible: time is not composed of
moments, just as a line is not composed of points, and motion is not
composed of starts: (5) for this theory simply makes motion consist of
indivisibles in exactly the same way as time is made to consist of
moments or a length of points.
Again, it may be shown in the following way that there can be no
motion of a point or of any other indivisible. That which is in motion
can never traverse a space greater than itself without first traversing a
space equal to or less than itself. That being so, (10) it is evident that the
point also must first traverse a space equal to or less than itself. But
since it is indivisible, there can be no space less than itself for it to
traverse first: so it will have to traverse a distance equal to itself. Thus
the line will be composed of points, for the point, as it continually
traverses a distance equal to itself, will be a measure of the whole line.
But since this is impossible, it is likewise impossible for the indivisible to
be in motion.
Again, (15) since motion is always in a period of time and never in a
moment, and all time is divisible, for everything that is in motion there
must be a time less than that in which it traverses a distance as great as
itself. For that in which it is in motion will be a time, because all motion
is in a period of time; and all time has been shown above30 to be
divisible. Therefore, if a point is in motion, there must be a time less
than that in which it has itself traversed any distance. But this is
impossible, for in less time it must traverse less distance, (20) and thus the
indivisible will be divisible into something less than itself, just as the
time is so divisible: the fact being that the only condition under which
that which is without parts and indivisible could be in motion would
have been the possibility of the infinitely small being in motion in a
moment: for in the two questions—that of motion in a moment and that
of motion of something indivisible—the same principle is involved. (25)
Our next point is that no process of change is infinite: for every
change, whether between contradictories or between contraries, is a
change from something to something. Thus in contradictory changes the
positive or the negative, as the case may be, is the limit, e. g. being is the
limit of coming to be and not-being is the limit of ceasing to be: and in
contrary changes the particular contraries are the limits, since these are
the extreme points of any such process of change, (30) and consequently
of every process of alteration: for alteration is always dependent upon
some contraries. Similarly contraries are the extreme points of processes
of increase and decrease: the limit of increase is to be found in the
complete magnitude proper to the peculiar nature of the thing that is
increasing, while the limit of decrease is the complete loss of such
magnitude. [241b] Locomotion, it is true, we cannot show to be finite
in this way, since it is not always between contraries. But since that
which cannot be cut (in the sense that it is inconceivable that it should
be cut, the term ‘cannot’ being used in several senses)—since it is
inconceivable that that which in this sense cannot be cut should be in
process of being cut, (5) and generally that that which cannot come to be
should be in process of coming to be, it follows that it is inconceivable
that that which cannot complete a change should be in process of
changing to that to which it cannot complete a change. If, then, it is to
be assumed that that which is in locomotion is in process of changing, it
must be capable of completing the change. Consequently its motion is
not infinite, and it will not be in locomotion over an infinite distance, (10)
for it cannot traverse such a distance.
It is evident, then, that a process of change cannot be infinite in the
sense that it is not defined by limits. But it remains to be considered
whether it is possible in the sense that one and the same process of
change may be infinite in respect of the time which it occupies. If it is
not one process, it would seem that there is nothing to prevent its being
infinite in this sense; e. g. if a process of locomotion be succeeded by a
process of alteration and that by a process of increase and that again by
a process of coming to be: in this way there may be motion for ever so
far as the time is concerned, (15) but it will not be one motion, because all
these motions do not compose one. If it is to be one process, no motion
can be infinite in respect of the time that it occupies, (20) with the single
exception of rotatory locomotion.
1
v. 3.
2
Which is ex hypothesi impossible (231b 28–30).
3
The slower will traverse EF in a greater time than the indivisible time in which the quicker
traverses JK.
4
i. e. in which it means a period of time including the present proper.
5
222a 12.
6
Chapter 2.
7
i. e. it will not be a point of division but merely something intermediate between past and
future.
8
226b 12 sqq.
9
viz. past and future.
10
223b 1 sqq.
11
234b 24 sqq., especially 234b 34 sqq.
12
234b 10–20.
13
Chapter 7.
14
sc. BC will have more right than AC to be regarded as that in which the change has been
completed.
15
234b 10 sqq.
16
235b 33. The ‘primary time’ is the irreducible minimum: thus the very terms of the definition
make it clear that a thing must be changing in the whole of the ‘primary time’ in which it
changes.
17
235b 6 sqq.
18
231b 6 sqq.
19
i. e. you may begin by cutting off half the line, then half of what remains, and so on, the part
cut off thus continuously increasing and the part remaining continually decreasing.
20
Ch. 6.
21
238b 31 sqq.
22
226b 12 sqq.
23
sc. time.
24
i. e. a space only just large enough to contain it, not a larger space of which only part is
occupied.
25
233a 13 sqq.
26
viz. the first argument given above, ll. 11–14.
27
234b 10 sqq.
28
239a 27.
29
231b 18 sqq.
30
232b 23 sqq.
BOOK VII
1
Everything that is in motion must be moved by something. (25) For if
it has not the source of its motion in itself it is evident that it is moved
by something other than itself, for there must be something else that
moves it. If on the other hand it has the source of its motion in itself, let
AB be taken to represent that which is in motion essentially of itself and
not in virtue of the fact that something belonging to it is in motion. Now
in the first place to assume that AB, (30) because it is in motion as a
whole and is not moved by anything external to itself, is therefore
moved by itself—this is just as if, supposing that JK is moving KL and is
also itself in motion, we were to deny that JL is moved by anything on
the ground that it is not evident which is the part that is moving it and
which the part that is moved. In the second place that which is in
motion without being moved by anything does not necessarily cease
from its motion because something else is at rest, but a thing must be
moved by something if the fact of something else having ceased from its
motion causes it to be at rest. [242a] Thus, if this is accepted,
everything that is in motion must be moved by something. (5) For AB,
which has been taken to represent that which is in motion, must be
divisible, since everything that is in motion is divisible. Let it be divided,
then, at C. Now if CB is not in motion, then AB will not be in motion: for
if it is, it is clear that AC would be in motion while BC is at rest, (10) and
thus AB cannot be in motion essentially and primarily. But ex hypothesi
AB is in motion essentially and primarily. Therefore if CB is not in
motion AB will be at rest. But we have agreed that that which is at rest if
something else is not in motion must be moved by something.
Consequently, everything that is in motion must be moved by
something: for that which is in motion will always be divisible, (15) and if
a part of it is not in motion the whole must be at rest.
Since everything that is in motion must be moved by something, let us
take the case in which a thing is in locomotion and is moved by
something that is itself in motion, and that again is moved by something
else that is in motion, and that by something else, (20) and so on
continually: then the series cannot go on to infinity, but there must be
some first movent. For let us suppose that this is not so and take the
series to be infinite. Let A then be moved by B, B by C, C by D, and so
on, each member of the series being moved by that which comes next to
it. Then since ex hypothesi the movent while causing motion is also itself
in motion, and the motion of the moved and the motion of the movent
must proceed simultaneously (for the movent is causing motion and the
moved is being moved simultaneously) it is evident that the respective
motions of A, (25) B, C, and each of the other moved movents are
simultaneous. Let us take the motion of each separately and let E be the
motion of A, F of B, and G and H respectively the motions of C and D:
for though they are all moved severally one by another, yet we may still
take the motion of each as numerically one, since every motion is from
something to something and is not infinite in respect of its extreme
points. (30) By a motion that is numerically one I mean a motion that
proceeds from something numerically one and the same to something
numerically one and the same in a period of time numerically one and
the same: for a motion may be the same generically, specifically, (35) or
numerically: it is generically the same if it belongs to the same category,
e. g. substance or quality: it is specifically the same if it proceeds from
something specifically the same to something specifically the same, e. g.
from white to black or from good to bad, which is not of a kind
specifically distinct: it is numerically the same if it proceeds from
something numerically one to something numerically one in the same
period of time, e. g. from a particular white to a particular black, or
from a particular place to a particular place, in a particular period of
time: for if the period of time were not one and the same, the motion
would no longer be numerically one though it would still be specifically
one. [242b] We have dealt with this question above.1 (4) Now let us
further take the time in which A has completed its motion, (8) and let it
be represented by J. Then since the motion of A is finite the time will
also be finite. But since the movents and the things moved are infinite,
the motion EFGH, i. e. the motion that is composed of all the individual
motions, (15) must be infinite. For the motions of A, B, and the others
may be equal, or the motions of the others may be greater: but assuming
what is conceivable, we find that whether they are equal or some are
greater, in both cases the whole motion is infinite. And since the motion
of A and that of each of the others are simultaneous, the whole motion
must occupy the same time as the motion of A: but the time occupied by
the motion of A is finite: consequently the motion will be infinite in a
finite time, which is impossible.
It might be thought that what we set out to prove has thus been
shown, (20) but our argument so far does not prove it, because it does not
yet prove that anything impossible results from the contrary supposition:
for in a finite time there may be an infinite motion, though not of one
thing, but of many: and in the case that we are considering this is so: for
each thing accomplishes its own motion, and there is no impossibility in
many things being in motion simultaneously. But if (as we see to be
universally the case) that which primarily is moved locally and
corporeally must be either in contact with or continuous with that which
moves it, (25) the things moved and the movents must be continuous or in
contact with one another, so that together they all form a single unity:
whether this unity is finite or infinite makes no difference to our present
argument; for in any case since the things in motion are infinite in
number the whole motion will be infinite, if, as is theoretically possible,
each motion is either equal to or greater than that which follows it in the
series: for we shall take as actual that which is theoretically possible. If,
(30) then, A, B, C, D form an infinite magnitude that passes through the
motion EFGH in the finite time J, this involves the conclusion that an
infinite motion is passed through in a finite time: and whether the
magnitude in question is finite or infinite this is in either case
impossible. Therefore the series must come to an end, and there must be
a first movent and a first moved: for the fact that this impossibility
results only from the assumption of a particular case is immaterial, since
the case assumed is theoretically possible, and the assumption of a
theoretically possible case ought not to give rise to any impossible result.
[243a]
2
That which is the first movent of a thing—in the sense that it
supplies not ‘that for the sake of which’ but the source of the motion—is
always together with that which is moved by it (by ‘together’ I mean
that there is nothing intermediate between them). (5) This is universally
true wherever one thing is moved by another. And since there are three
kinds of motion, local, qualitative, and quantitative, there must also be
three kinds of movent, that which causes locomotion, that which causes
alteration, and that which causes increase or decrease.
Let us begin with locomotion, (10) for this is the primary motion.
Everything that is in locomotion is moved either by itself or by
something else. In the case of things that are moved by themselves it is
evident that the moved and the movent are together: for they contain
within themselves their first movent, so that there is nothing in between.
The motion of things that are moved by something else must proceed in
one of four ways: for there are four kinds of locomotion caused by
something other than that which is in motion, (15) viz. pulling, pushing,
carrying, and twirling. All forms of locomotion are reducible to these.
Thus pushing on is a form of pushing in which that which is causing
motion away from itself follows up that which it pushes and continues to
push it: pushing off occurs when the movent does not follow up the
thing that it has moved: throwing when the movent causes a motion
away from itself more violent than the natural locomotion of the thing
moved, (20) which continues its course so long as it is controlled by the
motion imparted to it. [243b] Again, pushing apart and pushing
together are forms respectively of pushing off and pulling: pushing apart
is pushing off, which may be a motion either away from the pusher or
away from something else, while pushing together is pulling, which may
be a motion towards something else as well as towards the puller. (5) We
may similarly classify all the varieties of these last two, e. g. packing and
combing: the former is a form of pushing together, the latter a form of
pushing apart. The same is true of the other processes of combination
and separation (they will all be found to be forms of pushing apart or of
pushing together), except such as are involved in the processes of
becoming and perishing. (At the same time it is evident that there is no
other kind of motion but combination and separation: for they may all
be apportioned to one or other of those already mentioned. (10)) Again,
inhaling is a form of pulling, exhaling a form of pushing: and the same is
true of spitting and of all other motions that proceed through the body,
whether secretive or assimilative, the assimilative being forms of pulling,
the secretive of pushing off. (15) All other kinds of locomotion must be
similarly reduced, for they all fall under one or other of our four heads.
And again, of these four, carrying and twirling are reducible to pulling
and pushing. For carrying always follows one of the other three
methods, for that which is carried is in motion accidentally, because it is
in or upon something that is in motion, and that which carries it is in
doing so being either pulled or pushed or twirled; (20) thus carrying
belongs to all the other three kinds of motion in common. [244a] And
twirling is a compound of pulling and pushing, for that which is twirling
a thing must be pulling one part of the thing and pushing another part,
since it impels one part away from itself and another part towards itself.
If, therefore, it can be shown that that which is pushing and that which
is pulling are adjacent respectively to that which is being pushed and
that which is being pulled, it will be evident that in all locomotion there
is nothing intermediate between moved and movent. (5) But the former
fact is clear even from the definitions of pushing and pulling, for pushing
is motion to something else from oneself or from something else, and
pulling is motion from something else to oneself or to something else,
when the motion of that which is pulling is quicker than the motion that
would separate from one another the two things that are continuous:2
for it is this that causes one thing to be pulled on along with the other.
(10) (It might indeed be thought that there is a form of pulling that arises
in another way: that wood, e. g. pulls fire in a manner different from
that described above. But it makes no difference whether that which
pulls is in motion or is stationary when it is pulling: in the latter case it
pulls to the place where it is, while in the former it pulls to the place
where it was.) Now it is impossible to move anything either from oneself
to something else or from something else to oneself without being in
contact with it: it is evident, (15) therefore, that in all locomotion there is
nothing intermediate between moved and movent. [244b]
Nor again is there anything intermediate between that which
undergoes and that which causes alteration: this can be proved by
induction: for in every case we find that the respective extremities of
that which causes and that which undergoes alteration are adjacent. For
our assumption is that things that are undergoing alteration are altered
in virtue of their being affected in respect of their so-called affective
qualities, since that which is of a certain quality is altered in so far as it
is sensible, and the characteristics in which bodies differ from one
another are sensible characteristics: for every body differs from another
in possessing a greater or lesser number of sensible characteristics or in
possessing the same sensible characteristics in a greater or lesser degree.
But the alteration of that which undergoes alteration is also caused by
the above-mentioned characteristics, (5) which are affections of some
particular underlying quality. Thus we say that a thing is altered by
becoming hot or sweet or thick or dry or white: and we make these
assertions alike of what is inanimate and of what is animate, and further,
where animate things are in question, we make them both of the parts
that have no power of sense-perception and of the senses themselves. (10)
For in a way even the senses undergo alteration, since the active sense is
a motion through the body in the course of which the sense is affected in
a certain way. We see, then, that the animate is capable of every kind of
alteration of which the inanimate is capable: but the inanimate is not
capable of every kind of alteration of which the animate is capable, since
it is not capable of alteration in respect of the senses: moreover the
inanimate is unconscious of being affected by alteration, (15) whereas the
animate is conscious of it, though there is nothing to prevent the
animate also being unconscious of it when the process of the alteration
does not concern the senses. [245a] Since, then, the alteration of that
which undergoes alteration is caused by sensible things, in every case of
such alteration it is evident that the respective extremities of that which
causes and that which undergoes alteration are adjacent. Thus the air is
continuous with that which causes the alteration, (5) and the body that
undergoes alteration is continuous with the air. Again, the colour is
continuous with the light and the light with the sight. And the same is
true of hearing and smelling: for the primary movent in respect to the
moved is the air. Similarly, in the case of tasting, the flavour is adjacent
to the sense of taste. And it is just the same in the case of things that are
inanimate and incapable of sense-perception. (10) Thus there can be
nothing intermediate between that which undergoes and that which
causes alteration.
Nor, again, can there be anything intermediate between that which
suffers and that which causes increase: for the part of the latter that
starts the increase does so by becoming attached in such a way to the
former that the whole becomes one. Again, the decrease of that which
suffers decrease is caused by a part of the thing becoming detached. So
that which causes increase and that which causes decrease must be
continuous with that which suffers increase and that which suffers
decrease respectively: and if two things are continuous with one another
there can be nothing intermediate between them. (15)
It is evident, therefore, that between the extremities of the moved and
the movent that are respectively first and last in reference to the moved
there is nothing intermediate. [245b]
3
Everything, we say, that undergoes alteration is altered by sensible
causes, and there is alteration only in things that are said to be
essentially affected by sensible things. The truth of this is to be seen
from the following considerations. Of all other things it would be most
natural to suppose that there is alteration in figures and shapes, (5) and in
acquired states and in the processes of acquiring and losing these: but as
a matter of fact in neither of these two classes of things is there
alteration.
In the first place, when a particular formation of a thing is completed,
(10) we do not call it by the name of its material: e. g. we do not call the
statue ‘bronze’ or the pyramid3 ‘wax’ or the bed ‘wood’, but we use a
derived expression and call them ‘of bronze’, ‘waxen’, and ‘wooden’
respectively. But when a thing has been affected and altered in any way
we still call it by the original name: thus we speak of the bronze or the
wax being dry or fluid or hard or hot. (15) And not only so: we also speak
of the particular fluid or hot substance as being bronze, giving the
material the same name as that which we use to describe the affection.
[246a] Since, therefore, having regard to the figure or shape of a
thing we no longer call that which has become of a certain figure by the
name of the material that exhibits the figure, whereas having regard to a
thing’s affections or alterations we still call it by the name of its
material, it is evident that becomings of the former kind cannot be
alterations.
Moreover it would seem absurd even to speak in this way, to speak, (5)
that is to say, of a man or house or anything else that has come into
existence as having been altered. Though it may be true that every such
becoming is necessarily the result of something’s being altered, the
result, e. g. of the material’s being condensed or rarefied or heated or
cooled, nevertheless it is not the things that are coming into existence
that are altered, and their becoming is not an alteration.
Again, (10) acquired states, whether of the body or of the soul, are not
alterations. For some are excellences and others are defects, and neither
excellence nor defect is an alteration: excellence is a perfection (for
when anything acquires its proper excellence we call it perfect, (15) since
it is then if ever that we have a thing in its natural state: e. g. we have a
perfect circle when we have one as good as possible), while defect is a
perishing of or departure from this condition. So just as when speaking
of a house we do not call its arrival at perfection an alteration (for it
would be absurd to suppose that the coping or the tiling is an alteration
or that in receiving its coping or its tiling a house is altered and not
perfected), (20) the same also holds good in the case of excellences and
defects and of the persons or things that possess or acquire them: for
excellences are perfections of a thing’s nature and defects are departures
from it: consequently they are not alterations. [246b]
Further, we say that all excellences depend upon particular relations.
Thus bodily excellences such as health and a good state of body we
regard as consisting in a blending of hot and cold elements within the
body in due proportion, (5) in relation either to one another or to the
surrounding atmosphere: and in like manner we regard beauty, strength,
and all the other bodily excellences and defects. Each of them exists in
virtue of a particular relation and puts that which possesses it in a good
or bad condition with regard to its proper affections, where by ‘proper’
affections I mean those influences that from the natural constitution of a
thing tend to promote or destroy its existence. Since, then, relatives are
neither themselves alterations nor the subjects of alteration or of
becoming or in fact of any change whatever, (10) it is evident that neither
states nor the processes of losing and acquiring states are alterations,
though it may be true that their becoming or perishing is necessarily, (15)
like the becoming or perishing of a specific character or form, the result
of the alteration of certain other things, e. g. hot and cold or dry and wet
elements or the elements, whatever they may be, on which the states
primarily depend. For each several bodily defect or excellence involves a
relation with those things from which the possessor of the defect or
excellence is naturally subject to alteration: thus excellence disposes its
possessor to be unaffected by these influences or to be affected by those
of them that ought to be admitted, while defect disposes its possessor to
be affected by them or to be unaffected by those of them that ought to
be admitted.
And the case is similar in regard to the states of the soul, (20) all of
which (like those of body) exist in virtue of particular relations, the
excellences being perfections of nature and the defects departures from
it: moreover, excellence puts its possessor in good condition, while
defect puts its possessor in a bad condition, to meet his proper affections.
[247a] Consequently these cannot any more than the bodily states be
alterations, (5) nor can the processes of losing and acquiring them be so,
though their becoming is necessarily the result of an alteration of the
sensitive part of the soul, and this is altered by sensible objects: for all
moral excellence is concerned with bodily pleasures and pains, which
again depend either upon acting or upon remembering or upon
anticipating. Now those that depend upon action are determined by
sense-perception, i. e. they are stimulated by something sensible: and
those that depend upon memory or anticipation are likewise to be traced
to sense-perception, (10) for in these cases pleasure is felt either in
remembering what one has experienced or in anticipating what one is
going to experience. Thus all pleasure of this kind must be produced by
sensible things: and since the presence in any one of moral defect or
excellence involves the presence in him of pleasure or pain (with which
moral excellence and defect are always concerned), (15) and these
pleasures and pains are alterations of the sensitive part, it is evident that
the loss and acquisition of these states no less than the loss and
acquisition of the states of the body must be the result of the alteration
of something else. Consequently, though their becoming is accompanied
by an alteration, they are not themselves alterations.
[247b] Again, the states of the intellectual part of the soul are not
alterations, nor is there any becoming of them. In the first place it is
much more true of the possession of knowledge that it depends upon a
particular relation. And further, it is evident that there is no becoming of
these states. For that which is potentially possessed of knowledge
becomes actually possessed of it not by being set in motion at all itself
but by reason of the presence of something else: (5) i. e. it is when it
meets with the particular object that it knows in a manner the particular
through its knowledge of the universal. (Again, there is no becoming of
the actual use and activity of these states, unless it is thought that there
is a becoming of vision and touching and that the activity in question is
similar to these. (10)) And the original acquisition of knowledge is not a
becoming or an alteration: for the terms ‘knowing’ and ‘understanding’
imply that the intellect has reached a state of rest and come to a
standstill,4 and there is no becoming that leads to a state of rest, since,
as we have said above,5 no change at all can have a becoming.
Moreover, just as to say, when any one has passed from a state of
intoxication or sleep or disease to the contrary state, (15) that he has
become possessed of knowledge again is incorrect in spite of the fact
that he was previously incapable of using his knowledge, so, too, when
any one originally acquires the state, it is incorrect to say that he
becomes possessed of knowledge: for the possession of understanding
and knowledge is produced by the soul’s settling down6 out of the
restlessness natural to it. Hence, too, in learning and in forming
judgements on matters relating to their sense-perceptions children are
inferior to adults owing to the great amount of restlessness and motion
in their souls. [248a] Nature itself causes the soul to settle down and
come to a state of rest for the performance of some of its functions,
while for the performance of others other things do so: but in either case
the result is brought about through the alteration of something in the
body, as we see in the case of the use and activity of the intellect arising
from a man’s becoming sober or being awakened. (5) It is evident, then,
from the preceding argument that alteration and being altered occur in
sensible things and in the sensitive part of the soul and, except
accidentally, in nothing else.
4
A difficulty may be raised as to whether every motion is
commensurable with every other or not. (10) Now if they are all
commensurable and if two things to have the same velocity must
accomplish an equal motion in an equal time, then we may have a
circumference equal to a straight line, or, of course, the one may be
greater or less than the other. Further, if one thing alters and another
accomplishes a locomotion in an equal time, we may have an alteration
and a locomotion equal to one another: thus an affection will be equal to
a length, (15) which is impossible. But is it not only when an equal
motion is accomplished by two things in an equal time that the
velocities of the two are equal? Now an affection cannot be equal to a
length. Therefore there cannot be an alteration equal to or less than a
locomotion: and consequently it is not the case that every motion is
commensurable with every other.
But how will our conclusion work out in the case of the circle and the
straight line? It would be absurd to suppose that the motion of one thing
in a circle and of another in a straight line cannot be similar, (20) but that
the one must inevitably move more quickly or more slowly than the
other, just as if the course of one were downhill and of the other uphill.
Moreover it does not as a matter of fact make any difference to the
argument to say that the one motion must inevitably be quicker or
slower than the other: for then the circumference can be greater or less
than the straight line; and if so it is possible for the two to be equal. For
if in the time A the quicker (B) passes over the distance B′ and the
slower (C) passes over the distance C′, (25) B′ will be greater than C′: for
this is what we7 took ‘quicker’ to mean: and so quicker motion also
implies that one thing traverses an equal distance in less time than
another: consequently there will be a part of A in which B will pass over
a part of the circle equal to C′, while C will occupy the whole of A in
passing over C′. [248b] None the less, if the two motions are
commensurable, (5) we are confronted with the consequence stated
above, viz. that there may be a straight line equal to a circle. But these
are not commensurable: and so the corresponding motions are not
commensurable either.
But may we say that things are always commensurable if the same
terms are applied to them without equivocation? e. g. a pen, a wine, and
the highest note in a scale are not commensurable: we cannot say
whether any one of them is sharper than any other: and why is this?
they are incommensurable because it is only equivocally that the same
term ‘sharp’ is applied to them: whereas the highest note in a scale is
commensurable with the leading-note, (10) because the term ‘sharp’ has
the same meaning as applied to both. Can it be, then, that the term
‘quick’ has not the same meaning as applied to straight motion and to
circular motion respectively? If so, far less will it have the same meaning
as applied to alteration and to locomotion.
Or shall we in the first place deny that things are always
commensurable if the same terms are applied to them without
equivocation? For the term ‘much’ has the same meaning whether
applied to water or to air, yet water and air are not commensurable in
respect of it: or, if this illustration is not considered satisfactory, ‘double’
at any rate would seem to have the same meaning as applied to each
(denoting in each case the proportion of two to one), yet water and air
are not commensurable in respect of it. (15) But here again may we not
take up the same position and say that the term ‘much’ is equivocal? In
fact there are some terms of which even the definitions are equivocal;
e. g. if ‘much’ were defined as ‘so much and more’, ‘so much’ would
mean something different in different cases: ‘equal’ is similarly
equivocal; and ‘one’ again is perhaps inevitably an equivocal term; and if
‘one’ is equivocal, (20) so is ‘two’. Otherwise why is it that some things
are commensurable while others are not, if the nature of the attribute in
the two cases is really one and the same?
Can it be that the incommensurability of two things in respect of any
attribute is due to a difference in that which is primarily capable of
carrying the attribute? Thus horse and dog are so commensurable that
we may say which is the whiter, since that which primarily contains the
whiteness is the same in both, viz. the surface: and similarly they are
commensurable in respect of size. But water and speech are not
commensurable in respect of clearness, since that which primarily
contains the attribute is different in the two cases. (25) It would seem,
however, that we must reject this solution, since clearly we could thus
make all equivocal attributes univocal and say merely that that which
contains each of them is different in different cases: thus ‘equality’,
‘sweetness’, and ‘whiteness’’ will severally always be the same, though
that which contains them is different in different cases. [249a]
Moreover, it is not any casual thing that is capable of carrying any
attribute: each single attribute can be carried primarily only by one
single thing.
Must we then say that, if two things are to be commensurable in
respect of any attribute, not only must the attribute in question be
applicable to both without equivocation, but there must also be no
specific differences either in the attribute itself or in that which contains
the attribute—that these, I mean, must not be divisible in the way in
which colour is divided into kinds? Thus in this respect one thing will
not be commensurable with another, (5) i. e. we cannot say that one is
more coloured than the other where only colour in general and not any
particular colour is meant; but they are commensurable in respect of
whiteness.
Similarly in the case of motion: two things are of the same velocity if
they occupy an equal time in accomplishing a certain equal amount of
motion. Suppose, then, that in a certain time an alteration is undergone
by one half of a body’s length and a locomotion is accomplished by the
other half: can we say that in this case the alteration is equal to the
locomotion and of the same velocity? That would be absurd, (10) and the
reason is that there are different species of motion. And if in
consequence of this we must say that two things are of equal velocity if
they accomplish locomotion over an equal distance in an equal time, we
have to admit the equality of a straight line and a circumference. What,
then, is the reason of this? Is it that locomotion is a genus or that line is
a genus? (We may leave the time out of account, (15) since that is one and
the same.) If the lines are specifically different, the locomotions also
differ specifically from one another: for locomotion is specifically
differentiated according to the specific differentiation of that over which
it takes place. (It is also similarly differentiated, it would seem,
accordingly as the instrument of the locomotion is different: thus if feet
are the instrument, it is walking, if wings it is flying; but perhaps we
should rather say that this is not so, and that in this case the differences
in the locomotion are merely differences of posture in that which is in
motion.) We may say, therefore, that things are of equal velocity if in an
equal time they traverse the same magnitude: and when I call it ‘the
same’ I mean that it contains no specific difference and therefore no
difference in the motion that takes place over it. (20) So we have now to
consider how motion is differentiated: and this discussion serves to show
that the genus is not a unity but contains a plurality latent in it and
distinct from it, and that in the case of equivocal terms sometimes the
different senses in which they are used are far removed from one
another, while sometimes there is a certain likeness between them, and
sometimes again they are nearly related either generically or
analogically, with the result that they seem not to be equivocal though
they really are.
When, then, is there a difference of species? Is an attribute specifically
different if the subject is different while the attribute is the same, (25) or
must the attribute itself be different as well? And how are we to define
the limits of a species? What will enable us to decide that particular
instances of whiteness or sweetness are the same or different? Is it
enough that it appears different in one subject from what it appears in
another? Or must there be no sameness at all? And further, where
alteration is in question, how is one alteration to be of equal velocity
with another? One person may be cured quickly and another slowly, (30)
and cures may also be simultaneous: so that, recovery of health being an
alteration, we have here alterations of equal velocity, since each
alteration occupies an equal time. [249b] But what alteration? We
cannot here speak of an ‘equal’ alteration: what corresponds in the
category of quality to equality in the category of quantity is ‘likeness’.
However, let us say that there is equal velocity where the same change is
accomplished in an equal time. (5) Are we, then, to find the
commensurability in the subject of the affection or in the affection itself?
In the case that we have just been considering it is the fact that health is
one and the same that enables us to arrive at the conclusion that the one
alteration is neither more nor less than the other, but that both are alike.
If on the other hand the affection is different in the two cases, e. g. when
the alterations take the form of becoming white and becoming healthy
respectively, here there is no sameness or equality or likeness inasmuch
as the difference in the affections at once makes the alterations
specifically different, (10) and there is no unity of alteration any more
than there would be unity of locomotion under like conditions.8 So we
must find out how many species there are of alteration and of
locomotion respectively. Now if the things that are in motion—that is to
say, the things to which the motions belong essentially and not
accidentally—differ specifically, then their respective motions will also
differ specifically: if on the other hand they differ generically or
numerically, the motions also will differ generically or numerically as
the case may be. (15) But there still remains the question whether,
supposing that two alterations are of equal velocity, we ought to look for
this equality in the sameness (or likeness) of the affections, or in the
things altered, to see e. g. whether a certain quantity of each has become
white. Or ought we not rather to look for it in both? That is to say, the
alterations are the same or different according as the affections are the
same or different, while they are equal or unequal according as the
things altered are equal or unequal.
And now we must consider the same question in the case of becoming
and perishing: how is one becoming of equal velocity with another?
They are of equal velocity if in an equal time there are produced two
things that are the same and specifically inseparable, (20) e. g. two men
(not merely generically inseparable as e. g. two animals). Similarly one
is quicker than the other if in an equal time the product is different in
the two cases. I state it thus because we have no pair of terms that will
convey this ‘difference’ in the way in which unlikeness is conveyed. If
we adopt the theory that it is number that constitutes being, we may
indeed speak of a ‘greater number’ and a ‘lesser number’ within the same
species, but there is no common term that will include both relations,
nor are there terms to express each of them separately in the same way
as we indicate a higher degree or preponderance of an affection by
‘more’, (25) of a quantity by ‘greater’.
5
Now since wherever there is a movent, its motion always acts upon
something, is always in something, and always extends to something (by
‘is always in something’ I mean that it occupies a time: and by ‘extends
to something’ I mean that it involves the traversing of a certain amount
of distance: for at any moment when a thing is causing motion, it also
has caused motion, so that there must always be a certain amount of
distance that has been traversed and a certain amount of time that has
been occupied). If, then, (30) A the movent have moved B a distance C in
a time D, then in the same time the same force A will move ½ B twice
the distance C, and in ½ D it will move ½ B the whole distance C: for
thus the rules of proportion will be observed. [250a] Again if a given
force move a given weight a certain distance in a certain time and half
the distance in half the time, (5) half the motive power will move half the
weight the same distance in the same time. Let E represent half the
motive power A and F half the weight B: then the ratio between the
motive power and the weight in the one case is similar and
proportionate to the ratio in the other, so that each force will cause the
same distance to be traversed in the same time.
But if E move F a distance C in a time D, (10) it does not necessarily
follow that E can move twice F half the distance C in the same time. If,
then, A move B a distance C in a time D, it does not follow that E, being
half of A, will in the time D or in any fraction of it cause B to traverse a
part of C the ratio between which and the whole of C is proportionate to
that between A and E (whatever fraction of A E may be): in fact it might
well be that it will cause no motion at all; for it does not follow that, (15)
if a given motive power causes a certain amount of motion, half that
power will cause motion either of any particular amount or in any
length of time: otherwise one man might move a ship, since both the
motive power of the shiphaulers and the distance that they all cause the
ship to traverse are divisible into as many parts as there are men. (20)
Hence Zeno’s reasoning is false when he argues that there is no part of
the millet that does not make a sound: for there is no reason why any
such part should not in any length of time fail to move the air that the
whole bushel moves in falling. In fact it does not of itself move even
such a quantity of the air as it would move if this part were by itself: for
no part even exists otherwise than potentially.
If on the other hand we have two forces each of which separately
moves one of two weights a given distance in a given time, (25) then the
forces in combination will move the combined weights an equal distance
in an equal time: for in this case the rules of proportion apply.
Then does this hold good of alteration and of increase also? Surely it
does, for in any given case we have a definite thing that causes increase
and a definite thing that suffers increase, (30) and the one causes and the
other suffers a certain amount of increase in a certain amount of time.
Similarly we have a definite thing that causes alteration and a definite
thing that undergoes alteration, and a certain amount, or rather degree,
of alteration is completed in a certain amount of time: thus in twice as
much time twice as much alteration will be completed and conversely
twice as much alteration will occupy twice as much time: and the
alteration of half of its object will occupy half as much time and in half
as much time half of the object will be altered: or again, in the same
amount of time it will be altered twice as much. [250b]
On the other hand if that which causes alteration or increase causes a
certain amount of increase or alteration respectively in a certain amount
of time, (5) it does not necessarily follow that half the force will occupy
twice the time in altering or increasing the object, or that in twice the
time the alteration or increase will be completed by it: it may happen
that there will be no alteration or increase at all, the case being the same
as with the weight.
1
v. 4. 227b 3 sqq.
2
i. e. the thing pulling and the thing pulled. The second motion is the natural resistance of the
thing pulled, which seeks to disconnect itself from that which is pulling it.
3
sc. candle.
4
The etymological connexion between episteme and stenai can hardly be adequately given in
translation.
5
v. 2. 225b 15 sqq.
6
The same etymological connexion is here present to Aristotle’s mind as that noted above.
7
vi. 2. 232a 25 sqq.
8
sc. if there are two locomotions of different species.
BOOK VIII
1
It remains to consider the following question. (11) Was there ever a
becoming of motion before which it had no being, and is it perishing
again so as to leave nothing in motion? Or are we to say that it never
had any becoming and is not perishing, but always was and always will
be? Is it in fact an immortal never-failing property of things that are, a
sort of life as it were to all naturally constituted things?
Now the existence of motion is asserted by all who have anything to
say about nature, (15) because they all concern themselves with the
construction of the world and study the question of becoming and
perishing, which processes could not come about without the existence
of motion. But those who say that there is an infinite number of worlds,
some of which are in process of becoming while others are in process of
perishing, assert that there is always motion (for these processes of
becoming and perishing of the worlds necessarily involve motion), (20)
whereas those who hold that there is only one world, whether
everlasting or not, make corresponding assumptions in regard to motion.
If then it is possible that at any time nothing should be in motion, this
must come about in one of two ways: either in the manner described by
Anaxagoras, who says that all things were together and at rest for an
infinite period of time, (25) and that then Mind introduced motion and
separated them; or in the manner described by Empedocles, according to
whom the universe is alternately in motion and at rest—in motion, when
Love is making the one out of many, or Strife is making many out of one,
and at rest in the intermediate periods of time—his account being as
follows:
‘Since One hath learned to spring from Manifold, (30)
And One disjoined makes Manifold arise,
Thus they Become, nor stable is their life:
But since their motion must alternate be,
Thus have they ever Rest upon their round’:
for we must suppose that he means by this that they alternate from the
one motion to the other. [251a] We must consider, then, how this
matter stands, (5) for the discovery of the truth about it is of importance,
not only for the study of nature, but also for the investigation of the First
Principle.
Let us take our start from what we have already1 laid down in our
course on Physics. Motion, we say, is the fulfilment of the movable in so
far as it is movable. Each kind of motion, therefore, (10) necessarily
involves the presence of the things that are capable of that motion. In
fact, even apart from the definition of motion, every one would admit
that in each kind of motion it is that which is capable of that motion that
is in motion: thus it is that which is capable of alteration that is altered,
and that which is capable of local change that is in locomotion: and so
there must be something capable of being burned before there can be a
process of being burned, (15) and something capable of burning before
there can be a process of burning. Moreover, these things also must
either have a beginning before which they had no being, or they must be
eternal. Now if there was a becoming of every movable thing, it follows
that before the motion in question another change or motion must have
taken place in which that which was capable of being moved or of
causing motion had its becoming. To suppose, (20) on the other hand, that
these things were in being throughout all previous time without there
being any motion appears unreasonable on a moment’s thought, and still
more unreasonable, we shall find, on further consideration. For if we are
to say that, while there are on the one hand things that are movable, and
on the other hand things that are motive, there is a time when there is a
first movent and a first moved, and another time when there is no such
thing but only something that is at rest, (25) then this thing that is at rest
must previously have been in process of change: for there must have
been some cause of its rest, rest being the privation of motion.
Therefore, before this first change there will be a previous change. For
some things cause motion in only one way, while others can produce
either of two contrary motions: thus fire causes heating but not cooling,
(30) whereas it would seem that knowledge may be directed to two
contrary ends while remaining one and the same. Even in the former
class, however, there seems to be something similar, for a cold thing in a
sense causes heating by turning away and retiring, just as one possessed
of knowledge voluntarily makes an error when he uses his knowledge in
the reverse way.2 [251b] But at any rate all things that are capable
respectively of affecting and being affected, or of causing motion and
being moved, are capable of it not under all conditions, but only when
they are in a particular condition and approach one another: so it is on
the approach of one thing to another that the one causes motion and the
other is moved, and when they are present under such conditions as
rendered the one motive and the other movable. (5) So if the motion was
not always in process, it is clear that they must have been in a condition
not such as to render them capable respectively of being moved and of
causing motion, and one or other of them must have been in process of
change: for in what is relative this is a necessary consequence: e. g. if
one thing is double another when before it was not so, one or other of
them, if not both, must have been in process of change. It follows, then,
that there will be a process of change previous to the first.
(Further, (10) how can there be any ‘before’ and ‘after’ without the
existence of time? Or how can there be any time without the existence of
motion? If, then, time is the number of motion or itself a kind of motion,
it follows that, if there is always time, motion must also be eternal. But
so far as time is concerned we see that all with one exception are in
agreement in saying that it is uncreated: in fact, it is just this that
enables Democritus to show that all things cannot have had a becoming:
for time, (15) he says, is uncreated. Plato alone asserts the creation of
time, saying3 that it had a becoming together with the universe, the
universe according to him having had a becoming. Now since time
cannot exist and is unthinkable apart from the moment, and the moment
is a kind of middle-point, uniting as it does in itself both a beginning and
an end, (20) a beginning of future time and an end of past time, it follows
that there must always be time: for the extremity of the last period of
time that we take must be found in some moment, since time contains
no point of contact for us except the moment. Therefore, since the
moment is both a beginning and an end, (25) there must always be time
on both sides of it. But if this is true of time, it is evident that it must
also be true of motion, time being a kind of affection of motion.)
The same reasoning will also serve to show the imperishability of
motion: just as a becoming of motion would involve, as we saw, (30) the
existence of a process of change previous to the first, in the same way a
perishing of motion would involve the existence of a process of change
subsequent to the last: for when a thing ceases to be moved, it does not
therefore at the same time cease to be movable—e. g. the cessation of
the process of being burned does not involve the cessation of the
capacity of being burned, since a thing may be capable of being burned
without being in process of being burned—nor, when a thing ceases to
be movent, does it therefore at the same time cease to be motive. Again,
the destructive agent will have to be destroyed, after what it destroys
has been destroyed, and then that which has the capacity of destroying it
will have to be destroyed afterwards, (so that there will be a process of
change subsequent to the last,) for being destroyed also is a kind of
change. [252a] If, then, the view which we are criticizing involves
these impossible consequences, it is clear that motion is eternal and
cannot have existed at one time and not at another: in fact, such a view
can hardly be described as anything else than fantastic.
And much the same may be said of the view that such is the ordinance
of nature and that this must be regarded as a principle, (5) as would seem
to be the view of Empedocles when he says that the constitution of the
world is of necessity such that Love and Strife alternately predominate
and cause motion, while in the intermediate period of time there is a
state of rest. (10) Probably also those who, like Anaxagoras, assert a single
principle (of motion) would hold this view. But that which is produced
or directed by nature can never be anything disorderly: for nature is
everywhere the cause of order. Moreover, there is no ratio in the relation
of the infinite to the infinite, whereas order always means ratio. But if
we say that there is first a state of rest for an infinite time, and then
motion is started at some moment, (15) and that the fact that it is this
rather than a previous moment is of no importance, and involves no
order, then we can no longer say that it is nature’s work: for if anything
is of a certain character naturally, it either is so invariably and is not
sometimes of this and sometimes of another character (e. g. fire, which
travels upwards naturally, does not sometimes do so and sometimes not)
or there is a ratio in the variation. (20) It would be better, therefore, to
say with Empedocles and any one else who may have maintained such a
theory as his that the universe is alternately at rest and in motion: for in
a system of this kind we have at once a certain order. But even here the
holder of the theory ought not only to assert the fact: he ought also to
explain the cause of it: i. e. he should not make any mere assumption or
lay down any gratuitous axiom, but should employ either inductive or
demonstrative reasoning. (25) The Love and Strife postulated by
Empedocles are not in themselves causes of the fact in question, nor is it
of the essence of either that it should be so, the essential function of the
former being to unite, of the latter to separate. If he is to go on to
explain this alternate predominance, he should adduce cases where such
a state of things exists, as he points to the fact that among mankind we
have something that unites men, namely Love, (30) while on the other
hand enemies avoid one another: thus from the observed fact that this
occurs in certain cases comes the assumption that it occurs also in the
universe. Then, again, some argument is needed to explain why the
predominance of each of the two forces lasts for an equal period of time.
But it is a wrong assumption to suppose universally that we have an
adequate first principle in virtue of the fact that something always is so
or always happens so. Thus Democritus reduces the causes that explain
nature to the fact that things happened in the past in the same way as
they happen now: but he does not think fit to seek for a first principle to
explain this ‘always’: so, (35) while his theory is right in so far as it is
applied to certain individual cases, he is wrong in making it of universal
application. [252b] Thus, a triangle always has its angles equal to two
right angles, but there is nevertheless an ulterior cause of the eternity of
this truth, whereas first principles are eternal and have no ulterior cause.
Let this conclude what we have to say in support of our contention that
there never was a time when there was not motion, (5) and never will be
a time when there will not be motion.
2
The arguments that may be advanced against this position are not
difficult to dispose of. The chief considerations that might be thought to
indicate that motion may exist though at one time it had not existed at
all are the following:
First, it may be said that no process of change is eternal: for the nature
of all change is such that it proceeds from something to something, (10) so
that every process of change must be bounded by the contraries that
mark its course, and no motion can go on to infinity.
Secondly, we see that a thing that neither is in motion nor contains
any motion within itself can be set in motion; e. g. inanimate things that
are (whether the whole or some part is in question) not in motion but at
rest, are at some moment set in motion: whereas, (15) if motion cannot
have a becoming before which it had no being, these things ought to be
either always or never in motion.
Thirdly, the fact is evident above all in the case of animate beings: for
it sometimes happens that there is no motion in us and we are quite still,
and that nevertheless we are then at some moment set in motion, that is
to say it sometimes happens that we produce a beginning of motion in
ourselves spontaneously without anything having set us in motion from
without. (20) We see nothing like this in the case of inanimate things,
which are always set in motion by something else from without: the
animal, on the other hand, we say, moves itself: therefore, if an animal is
ever in a state of absolute rest, we have a motionless thing in which
motion can be produced from the thing itself, and not from without.
Now if this can occur in an animal, why should not the same be true also
of the universe as a whole? If it can occur in a small world it could also
occur in a great one: and if it can occur in the world, (25) it could also
occur in the infinite; that is, if the infinite could as a whole possibly be
in motion or at rest.
Of these objections, then, the first-mentioned—that motion to
opposites is not always the same and numerically one—is a correct
statement; in fact, (30) this may be said to be a necessary conclusion,
provided that it is possible for the motion of that which is one and the
same to be not always one and the same. (I mean that e. g. we may
question whether the note given by a single string is one and the same,
or is different each time the string is struck, although the string is in the
same condition and is moved in the same way.) But still, (35) however
this may be, there is nothing to prevent there being a motion that is the
same in virtue of being continuous and eternal: we shall have something
to say later4 that will make this point clearer. [253a]
As regards the second objection, no absurdity is involved in the fact
that something not in motion may be set in motion, that which caused
the motion from without being at one time present, and at another
absent. Nevertheless, how this can be so remains matter for inquiry; how
it comes about, I mean, that the same motive force at one time causes a
thing to be in motion, and at another does not do so: for the difficulty
raised by our objector really amounts to this—why is it that some things
are not always at rest, (5) and the rest always in motion?
The third objection may be thought to present more difficulty than the
others, namely, that which alleges that motion arises in things in which
it did not exist before, and adduces in proof the case of animate things:
thus an animal is first at rest and afterwards walks, (10) not having been
set in motion apparently by anything from without. This, however, is
false: for we observe that there is always some part of the animal’s
organism in motion, and the cause of the motion of this part is not the
animal itself, but, it may be, its environment. Moreover, we say that the
animal itself originates not all of its motions but its locomotion. (15) So it
may well be the case—or rather we may perhaps say that it must
necessarily be the case—that many motions are produced in the body by
its environment, and some of these set in motion the intellect or the
appetite, and this again then sets the whole animal in motion: this is
what happens when animals are asleep: though there is then no
perceptive motion in them, (20) there is some motion that causes them to
wake up again. But we will leave this point also to be elucidated at a
later5 stage in our discussion.
3
Our enquiry will resolve itself at the outset into a consideration of
the above-mentioned problem—what can be the reason why some things
in the world at one time are in motion and at another are at rest again?
Now one of three things must be true: either all things are always at rest,
(25) or all things are always in motion, or some things are in motion and
others at rest: and in this last case again either the things that are in
motion are always in motion and the things that are at rest are always at
rest, or they are all constituted so as to be capable alike of motion and of
rest; or there is yet a third possibility remaining—it may be that some
things in the world are always motionless, others always in motion,
while others again admit of both conditions. This last is the account of
the matter that we must give: for herein lies the solution of all the
difficulties raised and the conclusion of the investigation upon which we
are engaged. (30)
To maintain that all things are at rest, and to disregard senseperception in an attempt to show the theory to be reasonable, would be
an instance of intellectual weakness: it would call in question a whole
system, not a particular detail: moreover, it would be an attack not only
on the physicist but on almost all sciences and all received opinions, (35)
since motion plays a part in all of them. [253b] Further, just as in
arguments about mathematics objections that involve first principles do
not affect the mathematician—and the other sciences are in similar case
—so, too, objections involving the point that we have just raised do not
affect the physicist: for it is a fundamental assumption with him that
motion is ultimately referable to nature herself. (5)
The assertion that all things are in motion we may fairly regard as
equally false, though it is less subversive of physical science: for though
in our course on physics6 it was laid down that rest no less than motion
is ultimately referable to nature herself, nevertheless motion is the
characteristic fact of nature: moreover, the view is actually held by some
that not merely some things but all things in the world are in motion
and always in motion, (10) though we cannot apprehend the fact by
sense-perception. Although the supporters of this theory do not state
clearly what kind of motion they mean, or whether they mean all kinds,
it is no hard matter to reply to them: thus we may point out that there
cannot be a continuous process either of increase or of decrease: that
which comes between the two has to be included. The theory resembles
that about the stone being worn away by the drop of water or split by
plants growing out of it: if so much has been extruded or removed by the
drop, (15) it does not follow that half the amount has previously been
extruded or removed in half the time: the case of the hauled ship is
exactly comparable: here we have so many drops setting so much in
motion, but a part of them will not set as much in motion in any period
of time. The amount removed is, it is true, divisible into a number of
parts, but no one of these was set in motion separately: they were all set
in motion together. (20) It is evident, then, that from the fact that the
decrease is divisible into an infinite number of parts it does not follow
that some part must always be passing away: it all passes away at a
particular moment. Similarly, too, in the case of any alteration whatever
if that which suffers alteration is infinitely divisible it does not follow
from this that the same is true of the alteration itself, which often occurs
all at once, (25) as in freezing. Again, when any one has fallen ill, there
must follow a period of time in which his restoration to health is in the
future: the process of change cannot take place in an instant: yet the
change cannot be a change to anything else but health. The assertion,
therefore, that alteration is continuous is an extravagant calling into
question of the obvious: for alteration is a change from one contrary to
another. (30) Moreover, we notice that a stone becomes neither harder
nor softer. Again, in the matter of locomotion, it would be a strange
thing if a stone could be falling or resting on the ground without our
being able to perceive the fact. Further, it is a law of nature that earth
and all other bodies should remain in their proper places and be moved
from them only by violence: from the fact then that some of them are in
their proper places it follows that in respect of place also all things
cannot be in motion. [254a] (35) These and other similar arguments,
then, should convince us that it is impossible either that all things are
always in motion or that all things are always at rest.
Nor again can it be that some things are always at rest, others always
in motion, and nothing sometimes at rest and sometimes in motion. (5)
This theory must be pronounced impossible on the same grounds as
those previously mentioned: viz. that we see the above-mentioned
changes occurring in the case of the same things. We may further point
out that the defender of this position is fighting against the obvious, for
on this theory there can be no such thing as increase: nor can there be
any such thing as compulsory motion, (10) if it is impossible that a thing
can be at rest before being set in motion unnaturally. This theory, then,
does away with becoming and perishing. Moreover, motion, it would
seem, is generally thought to be a sort of becoming and perishing, for
that to which a thing changes comes to be, or occupancy of it comes to
be, and that from which a thing changes ceases to be, or there ceases to
be occupancy of it. It is clear, therefore, that there are cases of
occasional motion and occasional rest.
We have now to take the assertion that all things are sometimes at rest
and sometimes in motion and to confront it with the arguments
previously advanced. (15) We must take our start as before from the
possibilities that we distinguished just above. Either all things are at rest,
or all things are in motion, or some things are at rest and others in
motion. And if some things are at rest and others in motion, (20) then it
must be that either all things are sometimes at rest and sometimes in
motion, or some things are always at rest and the remainder always in
motion, or some of the things are always at rest and others always in
motion while others again are sometimes at rest and sometimes in
motion. Now we have said before that it is impossible that all things
should be at rest: nevertheless we may now repeat that assertion. We
may point out that, even if it is really the case, (25) as certain persons
assert,7 that the existent is infinite and motionless, it certainly does not
appear to be so if we follow sense-perception: many things that exist
appear to be in motion. Now if there is such a thing as false opinion at
all, there is also motion: and similarly if there is such a thing as
imagination, or if it is the case that anything seems to be different at
different times: for imagination and opinion are thought to be motions of
a kind.8 But to investigate this question at all—to see a reasoned
justification of a belief with regard to which we are too well off to
require reasoned justification—implies bad judgment of what is better
and what is worse, (30) what commends itself to belief and what does not,
what is ultimate and what is not. It is likewise impossible that all things
should be in motion or that some things should be always in motion and
the remainder always at rest. (35) We have sufficient ground for rejecting
all these theories in the single fact that we see some things that are
sometimes in motion and sometimes at rest. [254b] It is evident,
therefore, that it is no less impossible that some things should be always
in motion and the remainder always at rest than that all things should be
at rest or that all things should be in motion continuously. It remains,
then, to consider whether all things are so constituted as to be capable
both of being in motion and of being at rest, or whether, while some
things are so constituted, (5) some are always at rest and some are always
in motion: for it is this last view that we have to show to be true.
4
Now of things that cause motion or suffer motion, to some the
motion is accidental, to others essential: thus it is accidental to what
merely belongs to or contains as a part a thing that causes motion or
suffers motion, (10) essential to a thing that causes motion or suffers
motion not merely by belonging to such a thing or containing it as a
part.
Of things to which the motion is essential some derive their motion
from themselves, others from something else: and in some cases their
motion is natural, in others violent and unnatural. Thus in things that
derive their motion from themselves, e. g. all animals, (15) the motion is
natural (for when an animal is in motion its motion is derived from
itself): and whenever the source of the motion of a thing is in the thing
itself we say that the motion of that thing is natural. Therefore the
animal as a whole moves itself naturally: but the body of the animal may
be in motion unnaturally as well as naturally: it depends upon the kind
of motion that it may chance to be suffering and the kind of element9 of
which it is composed. (20) And the motion of things that derive their
motion from something else is in some cases natural, in others
unnatural: e. g. upward motion of earthy things and downward motion
of fire are unnatural. Moreover the parts of animals are often in motion
in an unnatural way, their positions and the character of the motion
being abnormal. The fact that a thing that is in motion derives its motion
from something is most evident in things that are in motion unnaturally,
(25) because in such cases it is clear that the motion is derived from
something other than the thing itself. Next to things that are in motion
unnaturally those whose motion while natural is derived from
themselves—e. g. animals—make this fact clear: for here the uncertainty
is not as to whether the motion is derived from something but as to how
we ought to distinguish in the thing between the movent and the moved.
(30) It would seem that in animals, just as in ships and things not
naturally organized, that which causes motion is separate from that
which suffers motion, and that it is only in this sense that the animal as
a whole causes its own motion.
The greatest difficulty, however, is presented by the remaining case of
those that we last distinguished. (35) Where things derive their motion
from something else we distinguished the cases in which the motion is
unnatural: we are left with those that are to be contrasted with the
others by reason of the fact that the motion is natural. [255a] It is in
these cases that difficulty would be experienced in deciding whence the
motion is derived, e. g. in the case of light and heavy things. When these
things are in motion to positions the reverse of those they would
properly occupy, their motion is violent: when they are in motion to
their proper positions—the light thing up and the heavy thing down—
their motion is natural; but in this latter case it is no longer evident, as it
is when the motion is unnatural, (5) whence their motion is derived. It is
impossible to say that their motion is derived from themselves: this is a
characteristic of life and peculiar to living things. Further, if it were, it
would have been in their power to stop themselves (I mean that if e. g. a
thing can cause itself to walk it can also cause itself not to walk), and so,
since on this supposition fire itself possesses the power of upward
locomotion, it is clear that it should also possess the power of downward
locomotion. (10) Moreover if things move themselves, it would be
unreasonable to suppose that in only one kind of motion is their motion
derived from themselves. Again, how can anything of continuous and
naturally connected substance move itself? In so far as a thing is one and
continuous not merely in virtue of contact, it is impassive: it is only in so
far as a thing is divided that one part of it is by nature active and
another passive. Therefore none of the things that we are now
considering move themselves (for they are of naturally connected
substance), (15) nor does anything else that is continuous: in each case the
movent must be separate from the moved, as we see to be the case with
inanimate things when an animate thing moves them. It is the fact that
these things also always derive their motion from something: what it is
would become evident if we were to distinguish the different kinds of
cause.
The above-mentioned distinctions can also be made in the case of
things that cause motion: (20) some of them are capable of causing
motion unnaturally (e. g. the lever is not naturally capable of moving the
weight), others naturally (e. g. what is actually hot is naturally capable
of moving10 what is potentially hot): and similarly in the case of all
other things of this kind.
In the same way, too, what is potentially of a certain quality or of a
certain quantity or in a certain place is naturally movable when it
contains the corresponding principle in itself and not accidentally (for
the same thing may be both of a certain quality and of a certain
quantity, (25) but the one is an accidental, not an essential property of the
other). So when fire or earth is moved by something the motion is
violent when it is unnatural, and natural when it brings to actuality the
proper activities11 that they potentially possess. (30) But the fact that the
term ‘potentially’ is used in more than one sense is the reason why it is
not evident whence such motions as the upward motion of fire and the
downward motion of earth are derived. One who is learning a science
potentially knows it in a different sense from one who while already
possessing the knowledge is not actually exercising it. Wherever we have
something capable of acting and something capable of being
correspondingly acted on, in the event of any such pair being in contact
what is potential becomes at times actual: (35) e. g. the learner becomes
from one potential something another potential something: for one who
possesses knowledge of a science but is not actually exercising it knows
the science potentially in a sense, though not in the same sense as he
knew it potentially before he learnt it. [255b] And when he is in this
condition, if something does not prevent him, he actively exercises his
knowledge: otherwise he would be in the contradictory state of not
knowing. In regard to natural bodies also the case is similar. (5) Thus
what is cold is potentially hot: then a change takes place and it is fire,
and it burns, unless something prevents and hinders it. So, too, with
heavy and light: light is generated from heavy, e. g. air from water (for
water is the first thing that is potentially light), (10) and air is actually
light, and will at once realize its proper activity as such unless
something prevents it. The activity of lightness consists in the light thing
being in a certain situation, namely high up: when it is in the contrary
situation, it is being prevented from rising. The case is similar also in
regard to quantity and quality. But, be it noted, this is the question we
are trying to answer—how can we account for the motion of light things
and heavy things to their proper situations? The reason for it is that they
have a natural tendency respectively towards a certain position: and this
constitutes the essence of lightness and heaviness, (15) the former being
determined by an upward, the latter by a downward, tendency. As we
have said, a thing may be potentially light or heavy in more senses than
one. Thus not only when a thing is water is it in a sense potentially light,
but when it has become air it may be still potentially light: for it may be
that through some hindrance it does not occupy an upper position, (20)
whereas, if what hinders it is removed, it realizes its activity and
continues to rise higher. The process whereby what is of a certain
quality changes to a condition of active existence is similar: thus the
exercise of knowledge follows at once upon the possession of it unless
something prevents it. So, too, what is of a certain quantity extends itself
over a certain space unless something prevents it. The thing in a sense is
and in a sense is not moved by one who moves what is obstructing and
preventing its motion (e. g. one who pulls away a pillar from under a
roof or one who removes a stone from a wine-skin in the water is the
accidental cause of motion):12 (25) and in the same way the real cause of
the motion of a ball rebounding from a wall is not the wall but the
thrower. So it is clear that in all these cases the thing does not move
itself, (30) but it contains within itself the source of motion—not of
moving something or of causing motion, but of suffering it.
If then the motion of all things that are in motion is either natural or
unnatural and violent, and all things whose motion is violent and
unnatural are moved by something, and something other than
themselves, and again all things whose motion is natural are moved by
something—both those that are moved by themselves and those that are
not moved by themselves (e. g. light things and heavy things, which are
moved either by that which brought the thing into existence as such and
made it light and heavy, (35) or by that which released what was
hindering and preventing it); then all things that are in motion must be
moved by something. [256a]
5
Now this may come about in either of two ways. Either the movent
is not itself responsible for the motion, which is to be referred to
something else which moves the movent, or the movent is itself
responsible for the motion. (5) Further, in the latter case, either the
movent immediately precedes the last thing in the series,13 or there may
be one or more intermediate links: e. g. the stick moves the stone and is
moved by the hand, which again is moved by the man: in the man,
however, we have reached a movent that is not so in virtue of being
moved by something else. Now we say that the thing is moved both by
the last and by the first movent in the series, but more strictly by the
first, since the first movent moves the last, whereas the last does not
move the first, (10) and the first will move the thing without the last, but
the last will not move it without the first: e. g. the stick will not move
anything unless it is itself moved by the man. If then everything that is
in motion must be moved by something, and the movent must either
itself be moved by something else or not, and in the former case there
must be some first movent that is not itself moved by anything else, (15)
while in the case of the immediate movent being of this kind there is no
need of an intermediate movent that is also moved (for it is impossible
that there should be an infinite series of movents, each of which is itself
moved by something else, since in an infinite series there is no first
term)—if then everything that is in motion is moved by something, and
the first movent is moved but not by anything else, (20) it must be moved
by itself.
This same argument may also be stated in another way as follows.
Every movent moves something and moves it with something, either
with itself or with something else: e. g. a man moves a thing either
himself or with a stick, and a thing is knocked down either by the wind
itself or by a stone propelled by the wind. But it is impossible for that
with which a thing is moved to move it without being moved by that
which imparts motion by its own agency: on the other hand, (25) if a
thing imparts motion by its own agency, it is not necessary that there
should be anything else with which it imparts motion, whereas if there is
a different thing with which it imparts motion, there must be something
that imparts motion not with something else but with itself, or else there
will be an infinite series. If, then, anything is a movent while being itself
moved, the series must stop somewhere and not be infinite. (30) Thus, if
the stick moves something in virtue of being moved by the hand, the
hand moves the stick: and if something else moves with the hand, the
hand also is moved by something different from itself. So when motion
by means of an instrument is at each stage caused by something different
from the instrument, this must always be preceded by something else
which imparts motion with itself. Therefore, if this last movent is in
motion and there is nothing else that moves it, it must move itself.
[256b] So this reasoning also shows that, when a thing is moved, if it
is not moved immediately by something that moves itself, the series
brings us at some time or other to a movent of this kind.
And if we consider the matter in yet a third way we shall get this same
result as follows: If everything that is in motion is moved by something
that is in motion, (5) either this being in motion is an accidental attribute
of the movents in question, so that each of them moves something while
being itself in motion, but not always because it is itself in motion, or it
is not an accidental but an essential attribute. Let us consider the former
alternative. If then it is an accidental attribute, it is not necessary that
that which is in motion should be in motion: and if this is so it is clear
that there may be a time when nothing that exists is in motion, since the
accidental is not necessary but contingent. (10) Now if we assume the
existence of a possibility, any conclusion that we thereby reach will not
be an impossibility, though it may be contrary to fact. But the nonexistence of motion is an impossibility: for we have shown above14 that
there must always be motion.
Moreover, the conclusion to which we have been led is a reasonable
one. (15) For there must be three things—the moved, the movent, and the
instrument of motion. Now the moved must be in motion, but it need
not move anything else: the instrument of motion must both move
something else and be itself in motion (for it changes together with the
moved, with which it is in contact and continuous, as is clear in the case
of things that move other things locally, in which case the two things
must up to a certain point15 be in contact): and the movent—that is to
say, that which causes motion in such a manner that it is not merely the
instrument of motion—must be unmoved. (20) Now we have visual
experience of the last term in this series, namely that which has the
capacity of being in motion, but does not contain a motive principle, and
also of that which is in motion but is moved by itself and not by
anything else: it is reasonable, therefore, not to say necessary, to suppose
the existence of the third term also, that which causes motion but is
itself unmoved. So, too, Anaxagoras is right when he says that Mind is
impassive and unmixed, (25) since he makes it the principle of motion: for
it could cause motion in this sense only by being itself unmoved, and
have supreme control only by being unmixed.
We will now take the second alternative. If the movent is not
accidentally but necessarily in motion—so that, if it were not in motion,
it would not move anything—then the movent, in so far as it is in
motion, must be in motion in one of two ways: it is moved either as that
is which is moved with the same kind of motion, (30) or with a different
kind—either that which is heating, I mean, is itself in process of
becoming hot, that which is making healthy in process of becoming
healthy, and that which is causing locomotion in process of locomotion,
or else that which is making healthy is, let us say, in process of
locomotion, and that which is causing locomotion in process of, say,
increase. But it is evident that this is impossible. For if we adopt the first
assumption we have to make it apply within each of the very lowest
species into which motion can be divided: e. g. we must say that if some
one is teaching some lesson in geometry, he is also in process of being
taught that same lesson in geometry, and that if he is throwing he is in
process of being thrown in just the same manner. [257a] Or if we
reject this assumption we must say that one kind of motion is derived
from another; e. g. that that which is causing locomotion is in process of
increase, that which is causing this increase is in process of being altered
by something else, (5) and that which is causing this alteration is in
process of suffering some different kind of motion. But the series must
stop somewhere, since the kinds of motion are limited; and if we say that
the process is reversible, and that that which is causing alteration is in
process of locomotion, we do no more than if we had said at the outset
that that which is causing locomotion is in process of locomotion, and
that one who is teaching is in process of being taught: for it is clear that
everything that is moved is moved by the movent that is further back in
the series as well as by that which immediately moves it: in fact the
earlier movent is that which more strictly moves it. (10) But this is of
course impossible: for it involves the consequence that one who is
teaching is in process of learning what he is teaching, whereas teaching
necessarily implies possessing knowledge, and learning not possessing it.
Still more unreasonable is the consequence involved that, since
everything that is moved is moved by something that is itself moved by
something else, (15) everything that has a capacity for causing motion has
as such a corresponding capacity for being moved: i. e. it will have a
capacity for being moved in the sense in which one might say that
everything that has a capacity for making healthy, and exercises that
capacity, has as such a capacity for being made healthy, and that which
has a capacity for building has as such a capacity for being built. It will
have the capacity for being thus moved either immediately or through
one or more links (as it will if, while everything that has a capacity for
causing motion has as such a capacity for being moved by something
else, (20) the motion that it has the capacity for suffering is not that with
which it affects what is next to it, but a motion of a different kind; e. g.
that which has a capacity for making healthy might as such have a
capacity for learning: the series, however, could be traced back, as we
said before, until at some time or other we arrived at the same kind of
motion). Now the first alternative is impossible, and the second is
fantastic: it is absurd that that which has a capacity for causing
alteration should as such necessarily have a capacity, (25) let us say, for
increase. It is not necessary, therefore, that that which is moved should
always be moved by something else that is itself moved by something
else: so there will be an end to the series. Consequently the first thing
that is in motion will derive its motion either from something that is at
rest or from itself. But if there were any need to consider which of the
two, that which moves itself or that which is moved by something else,
(30) is the cause and principle of motion, every one would decide for the
former: for that which is itself independently a cause is always prior as a
cause to that which is so only in virtue of being itself dependent upon
something else that makes it so.
We must therefore make a fresh start and consider the question; if a
thing moves itself, in what sense and in what manner does it do so? Now
everything that is in motion must be infinitely divisible, for it has been
shown already16 in our general course on Physics, that everything that is
essentially in motion is continuous. [257b] Now it is impossible that
that which moves itself should in its entirety move itself: for then, while
being specifically one and indivisible, it would as a whole both undergo
and cause the same locomotion or alteration: thus it would at the same
time be both teaching and being taught (the same thing), (5) or both
restoring to and being restored to the same health. Moreover, we have17
established the fact that it is the movable that is moved; and this is
potentially, not actually, in motion, but the potential is in process to
actuality, and motion is an incomplete actuality of the movable. The
movent on the other hand is already in activity: e. g. it is that which is
hot that produces heat: in fact, that which produces the form18 is always
something that possesses it. Consequently (if a thing can move itself as a
whole), (10) the same thing in respect of the same thing19 may be at the
same time both hot and not hot. So, too, in every other case where the
movent must be described by the same name in the same sense as the
moved. Therefore when a thing moves itself it is one part of it that is the
movent and another part that is moved. But it is not self-moving in the
sense that each of the two parts is moved by the other part: the
following considerations make this evident. In the first place, if each of
the two parts is to move the other, there will be no first movent. (15) If a
thing is moved by a series of movents, that which is earlier in the series
is more the cause of its being moved than that which comes next, and
will be more truly the movent: for we found that there are two kinds of
movent, that which is itself moved by something else and that which
derives its motion from itself: and that which is further from the thing
that is moved is nearer to the principle of motion than that which is
intermediate. In the second place, (20) there is no necessity for the
movent part to be moved by anything but itself: so it can only be
accidentally that the other part moves it in return. I take then the
possible case of its not moving it: then there will be a part that is moved
and a part that is an unmoved movent. In the third place, there is no
necessity for the movent to be moved in return: on the contrary the
necessity that there should always be motion makes it necessary that
there should be some movent that is either unmoved or moved by itself.
In the fourth place we should then have a thing undergoing the same
motion that it is causing—that which is producing heat, (25) therefore,
being heated. But as a matter of fact that which primarily moves itself
cannot contain either a single part that moves itself or a number of parts
each of which moves itself. For, if the whole is moved by itself, it must
be moved either by some part of itself or as a whole by itself as a whole.
If, then, it is moved in virtue of some part of it being moved by that part
itself, (30) it is this part that will be the primary self-movent, since, if this
part is separated from the whole, the part will still move itself, but the
whole will do so no longer. If on the other hand the whole is moved by
itself as a whole, it must be accidentally that the parts move themselves:
and therefore, their self-motion not being necessary, we may take the
case of their not being moved by themselves. [258a] Therefore in the
whole of the thing we may distinguish that which imparts motion
without itself being moved and that which is moved: for only in this way
is it possible for a thing to be self-moved. Further, if the whole moves
itself we may distinguish in it that which imparts the motion and that
which is moved: so while we say that AB is moved by itself, (5) we may
also say that it is moved by A. And since that which imparts motion may
be either a thing that is moved by something else or a thing that is
unmoved, and that which is moved may be either a thing that imparts
motion to something else or a thing that does not, that which moves
itself must be composed of something that is unmoved but imparts
motion and also of something that is moved but does not necessarily
impart motion but may or may not do so. Thus let A be something that
imparts motion but is unmoved, B something that is moved by A and
moves C, (10) C something that is moved by B but moves nothing (granted
that we eventually arrive at C we may take it that there is only one
intermediate term, though there may be more). Then the whole ABC
moves itself. But if I take away C, AB will move itself, A imparting
motion and B being moved, (15) whereas C will not move itself or in fact
be moved at all. Nor again will BC move itself apart from A: for B
imparts motion only through being moved by something else, not
through being moved by any part of itself. So only AB moves itself. That
which moves itself, therefore, must comprise something that imparts
motion but is unmoved and something that is moved but does not
necessarily move anything else: and each of these two things, (20) or at
any rate one of them, must be in contact with the other. If, then, that
which imparts motion is a continuous substance—that which is moved
must of course be so—it is clear that it is not through some part of the
whole being of such a nature as to be capable of moving itself that the
whole moves itself: it moves itself as a whole, both being moved and
imparting motion through containing a part that imparts motion and a
part that is moved. (25) It does not impart motion as a whole nor is it
moved as a whole: it is A alone that imparts motion and B alone that is
moved. It is not true, further, that C is moved by A, which is impossible.
Here a difficulty arises: if something is taken away from A (supposing
that that which imparts motion but is unmoved is a continuous
substance), or from B the part that is moved, will the remainder of A
continue to impart motion or the remainder of B continue to be moved?
If so, (30) it will not be AB primarily that is moved by itself, since, when
something is taken away from AB, the remainder of AB will still
continue to move itself. [258b] Perhaps we may state the case thus:
there is nothing to prevent each of the two parts, or at any rate one of
them, that which is moved, being divisible though actually undivided, so
that if it is divided it will not continue in the possession of the same
capacity: and so there is nothing to prevent self-motion residing
primarily in things that are potentially divisible.
From what has been said, then, it is evident that that which primarily
imparts motion is unmoved: for, (5) whether the series is closed at once
by that which is in motion but moved by something else deriving its
motion directly from the first unmoved, or whether the motion is
derived from what is in motion but moves itself and stops its own
motion, on both suppositions we have the result that in all cases of
things being in motion that which primarily imparts motion is unmoved.
6
Since there must always be motion without intermission, (10) there
must necessarily be something, one thing or it may be a plurality, that
first imparts motion, and this first movent must be unmoved. Now the
question whether each of the things that are unmoved but impart
motion20 is eternal is irrelevant to our present argument: but the
following considerations will make it clear that there must necessarily be
some such thing, which, while it has the capacity of moving something
else, is itself unmoved and exempt from all change, (15) which can affect
it neither in an unqualified nor in an accidental sense. Let us suppose, if
any one likes, that in the case of certain things it is possible for them at
different times to be and not to be, without any process of becoming and
perishing (in fact it would seem to be necessary, if a thing that has not
parts at one time is and at another time is not, that any such thing
should without undergoing any process of change at one time be and at
another time not be). And let us further suppose it possible that some
principles that are unmoved but capable of imparting motion at one time
are and at another time are not. (20) Even so, this cannot be true of all
such principles, since there must clearly be something that causes things
that move themselves at one time to be and at another not to be. For,
since nothing that has not parts can be in motion, that which moves
itself must as a whole have magnitude, though nothing that we have said
makes this necessarily true of every movent. (25) So the fact that some
things become and others perish, and that this is so continuously, cannot
be caused by any one of those things that, though they are unmoved, do
not always exist: nor again can it be caused by any of those which move
certain particular things, while others move other things. The eternity
and continuity of the process cannot be caused either by any one of
them singly or by the sum of them, (30) because this causal relation must
be eternal and necessary, whereas the sum of these movents is infinite
and they do not all exist together. It is clear, then, that though there may
be countless instances of the perishing of some principles that are
unmoved but impart motion, and though many things that move
themselves perish and are succeeded by others that come into being, and
though one thing that is unmoved moves one thing while another moves
another, nevertheless there is something that comprehends them all, and
that as something apart from each one of them, and this it is that is the
cause of the fact that some things are and others are not and of the
continuous process of change: and this causes the motion of the other
movents, (5) while they are the causes of the motion of other things.
[259a] Motion, then, being eternal, the first movent, if there is but
one, will be eternal also: if there are more than one, there will be a
plurality of such eternal movents. We ought, however, to suppose that
there is one rather than many, and a finite rather than an infinite
number. When the consequences of either assumption are the same, we
should always assume that things are finite rather than infinite in
number, (10) since in things constituted by nature that which is finite and
that which is better ought, if possible, to be present rather than the
reverse: and here it is sufficient to assume only one movent, the first of
unmoved things, which being eternal will be the principle of motion to
everything else.
The following argument also makes it evident that the first movent
must be something that is one and eternal. (15) We have shown21 that
there must always be motion. That being so, motion must also be
continuous, because what is always is continuous, whereas what is
merely in succession is not continuous. But further, if motion is
continuous, it is one: and it is one only if the movent and the moved that
constitute it are each of them one, since in the event of a thing’s being
moved now by one thing and now by another the whole motion will not
be continuous but successive.
Moreover a conviction that there is a first unmoved something may be
reached not only from the foregoing arguments, (20) but also by
considering again the principles operative in movents. Now it is evident
that among existing things there are some that are sometimes in motion
and sometimes at rest. This fact has served above22 to make it clear that
it is not true either that all things are in motion or that all things are at
rest or that some things are always at rest and the remainder always in
motion: on this matter proof is supplied by things that fluctuate between
the two and have the capacity of being sometimes in motion and
sometimes at rest. (25) The existence of things of this kind is clear to all:
but we wish to explain also the nature of each of the other two kinds
and show that there are some things that are always unmoved and some
things that are always in motion. In the course of our argument directed
to this end we established the fact that everything that is in motion is
moved by something,23 and that the movent is either unmoved or in
motion, (30) and that, if it is in motion, it is moved either by itself or by
something else and so on throughout the series: and so we proceeded to
the position24 that the first principle that directly causes things that are
in motion to be moved is that which moves itself, and the first principle
of the whole series is the unmoved. Further it is evident from actual
observation that there are things that have the characteristic of moving
themselves, e. g. the animal kingdom and the whole class of living
things. [259b] This being so, then, the view was suggested25 that
perhaps it may be possible for motion to come to be in a thing without
having been in existence at all before, because we see this actually
occurring in animals: they are unmoved at one time and then again they
are in motion, (5) as it seems. We must grasp the fact, therefore, that
animals move themselves only with one kind of motion,26 and that this
is not strictly originated by them. The cause of it is not derived from the
animal itself: it is connected with other natural motions in animals,
which they do not experience through their own instrumentality, e. g.
increase, decrease, and respiration: these are experienced by every
animal while it is at rest and not in motion in respect of the motion set
up by its own agency:27 here the motion is caused by the atmosphere
and by many things that enter into the animal: thus in some cases the
cause is nourishment: when it is being digested animals sleep, (10) and
when it is being distributed through the system they awake and move
themselves, the first principle of this motion being thus originally
derived from outside. Therefore animals are not always in continuous
motion by their own agency: it is something else that moves them, (15)
itself being in motion and changing as it comes into relation with each
several thing that moves itself. (Moreover in all these self-moving things
the first movent and cause of their self-motion is itself moved by itself,
though in an accidental sense: that is to say, the body changes its place,
so that that which is in the body changes its place also and is a selfmovent through its exercise of leverage.) (20) Hence we may confidently
conclude that if a thing belongs to the class of unmoved movents that
are also themselves moved accidentally, it is impossible that it should
cause continuous motion. So the necessity that there should be motion
continuously requires that there should be a first movent that is
unmoved even accidentally, if, as we have said,28 there is to be in the
world of things an unceasing and undying motion, (25) and the world is to
remain permanently self-contained and within the same limits: for if the
first principle is permanent, the universe must also be permanent, since
it is continuous with the first principle. (We must distinguish, however,
between accidental motion of a thing by itself and such motion by
something else, the former being confined to perishable things, whereas
the latter belongs also to certain first principles of heavenly bodies, (30) of
all those, that is to say, that experience more than one locomotion.29)
And further, if there is always something of this nature, a movent that
is itself unmoved and eternal, then that which is first moved by it must
be eternal. [260a] Indeed this is clear also from the consideration that
there would otherwise be no becoming and perishing and no change of
any kind in other things, which require something that is in motion to
move them: for the motion imparted by the unmoved will always be
imparted in the same way and be one and the same, since the unmoved
does not itself change in relation to that which is moved by it. (5) But
that30 which is moved by something that, though it is in motion, is
moved directly by the unmoved stands in varying relations to the things
that it moves, so that the motion that it causes will not be always the
same: by reason of the fact that it occupies contrary positions or assumes
contrary forms at different times it will produce contrary motions in
each several thing that it moves and will cause it to be at one time at
rest and at another time in motion. (10)
The foregoing argument, then, has served to clear up the point about
which we raised a difficulty at the outset31—why is it that instead of all
things being either in motion or at rest, or some things being always in
motion and the remainder always at rest, there are things that are
sometimes in motion and sometimes not? The cause of this is now plain:
it is because, while some things are moved by an eternal unmoved
movent and are therefore always in motion, other things are moved by a
movent that is in motion and changing, (15) so that they too must change.
But the unmoved movent, as has been said, since it remains permanently
simple and unvarying and in the same state, will cause motion that is
one and simple.
7
This matter will be made clearer, however, if we start afresh from
another point. (20) We must consider whether it is or is not possible that
there should be a continuous motion, and, if it is possible, which motion
this is, and which is the primary motion: for it is plain that if there must
always be motion, and a particular motion is primary and continuous,
then it is this motion that is imparted by the first movent, (25) and so it is
necessarily one and the same and continuous and primary.
Now of the three kinds of motion that there are—motion in respect of
magnitude, motion in respect of affection, and motion in respect of place
—it is this last, which we call locomotion, that must be primary. This
may be shown as follows. It is impossible that there should be increase
without the previous occurrence of alteration: for that which is
increased, (30) although in a sense it is increased by what is like itself, is
in a sense increased by what is unlike itself: thus it is said that contrary
is nourishment to contrary:32 but growth is effected only by things
becoming like to like. There must be alteration, then, in that there is this
change from contrary to contrary. [260b] But the fact that a thing is
altered requires that there should be something that alters it, something
e. g. that makes the potentially hot into the actually hot: so it is plain
that the movent does not maintain a uniform relation to it but is at one
time nearer to and at another farther from that which is altered: and we
cannot have this without locomotion. (5) If, therefore, there must always
be motion, there must also always be locomotion as the primary motion,
and, if there is a primary as distinguished from a secondary form of
locomotion, it must be the primary form. Again, all affections have their
origin in condensation and rarefaction: thus heavy and light, soft and
hard, (10) hot and cold, are considered to be forms of density and rarity.
But condensation and rarefaction are nothing more than combination
and separation, processes in accordance with which substances are said
to become and perish: and in being combined and separated things must
change in respect of place. And further, when a thing is increased or
decreased its magnitude changes in respect of place.
Again, there is another point of view from which it will be clearly seen
that locomotion is primary. (15) As in the case of other things so too in
the case of motion the word ‘primary’ may be used in several senses. A
thing is said to be prior to other things when, if it does not exist, the
others will not exist, whereas it can exist without the others: and there is
also priority in time and priority in perfection of existence. Let us begin,
then, with the first sense. Now there must be motion continuously, (20)
and there may be continuously either continuous motion or successive
motion, the former, however, in a higher degree than the latter:
moreover it is better that it should be continuous rather than successive
motion, and we always assume the presence in nature of the better, if it
be possible: since, then, continuous motion is possible (this will be
proved later:33 for the present let us take it for granted), and no other
motion can be continuous except locomotion, (25) locomotion must be
primary. For there is no necessity for the subject of locomotion to be the
subject either of increase or of alteration, nor need it become or perish:
on the other hand there cannot be any one of these processes without
the existence of the continuous motion imparted by the first movent.
Secondly, locomotion must be primary in time: for this is the only
motion possible for eternal things. (30) It is true indeed that, in the case of
any individual thing that has a becoming, locomotion must be the last of
its motions: for after its becoming it first experiences alteration and
increase, and locomotion is a motion that belongs to such things only
when they are perfected. [261a] But there must previously be
something else that is in process of locomotion to be the cause even of
the becoming of things that become, without itself being in process of
becoming, as e. g. the begotten is preceded by what begot it: otherwise
becoming might be thought to be the primary motion on the ground that
the thing must first become. (5) But though this is so in the case of any
individual thing that becomes, nevertheless before anything becomes,
something else must be in motion, not itself becoming but being, and
before this there must again be something else. And since becoming
cannot be primary—for, if it were, everything that is in motion would be
perishable—it is plain that no one of the motions next in order can be
prior to locomotion. (10) By the motions next in order I mean increase
and then alteration, decrease, and perishing. All these are posterior to
becoming: consequently, if not even becoming is prior to locomotion,
then no one of the other processes of change is so either.
Thirdly, that which is in process of becoming appears universally as
something imperfect and proceeding to a first principle: and so what is
posterior in the order of becoming is prior in the order of nature. Now
all things that go through the process of becoming acquire locomotion
last. It is this that accounts for the fact that some living things, (15) e. g.
plants and many kinds of animals, owing to lack of the requisite organ,
are entirely without motion, whereas others acquire it in the course of
their being perfected. Therefore, if the degree in which things possess
locomotion corresponds to the degree in which they have realized their
natural development, then this motion must be prior to all others in
respect of perfection of existence: and not only for this reason but also
because a thing that is in motion loses its essential character less in the
process of locomotion than in any other kind of motion: it is the only
motion that does not involve a change of being in the sense in which
there is a change in quality when a thing is altered and a change in
quantity when a thing is increased or decreased. (20) Above all it is plain
that this motion, motion in respect of place, is what is in the strictest
sense produced by that which moves itself; but it is the self-movent that
we declare to be the first principle of things that are moved and impart
motion and the primary source to which things that are in motion are to
be referred. (25)
It is clear, then, from the foregoing arguments that locomotion is the
primary motion. We have now to show which kind of locomotion is
primary. The same process of reasoning will also make clear at the same
time the truth of the assumption we have made both now and at a
previous stage34 that it is possible that there should be a motion that is
continuous and eternal. (30) Now it is clear from the following
considerations that no other than locomotion can be continuous. Every
other motion and change is from an opposite to an opposite: thus for the
processes of becoming and perishing the limits are the existent and the
non-existent, for alteration the various pairs of contrary affections, and
for increase and decrease either greatness and smallness or perfection
and imperfection of magnitude: and changes to the respective contraries
are contrary changes. (35) Now a thing that is undergoing any particular
kind of motion, but though previously existent has not always undergone
it, must previously have been at rest so far as that motion is concerned.
[261b] It is clear, then, that for the changing thing the contraries will
be states of rest. And we have a similar result in the case of changes that
are not motions: for becoming and perishing, whether regarded simply
as such without qualification or as affecting something in particular, are
opposites: therefore provided it is impossible for a thing to undergo
opposite changes at the same time, (5) the change will not be continuous,
but a period of time will intervene between the opposite processes. The
question whether these contradictory changes are contraries or not
makes no difference, provided only it is impossible for them both to be
present to the same thing at the same time: the point is of no importance
to the argument. (10) Nor does it matter if the thing need not rest in the
contradictory state, or if there is no state of rest as a contrary to the
process of change: it may be true that the nonexistent is not at rest, and
that perishing is a process to the nonexistent. All that matters is the
intervention of a time: it is this that prevents the change from being
continuous: so, too, in our previous instances the important thing was
not the relation of contrariety but the impossibility of the two processes
being present to a thing at the same time. (15) And there is no need to be
disturbed by the fact that on this showing there may be more than one
contrary to the same thing, that a particular motion will be contrary
both to rest and to motion in the contrary direction. We have only to
grasp the fact that a particular motion is in a sense the opposite both of
a state of rest and of the contrary motion, in the same way as that which
is of equal or standard measure is the opposite both of that which
surpasses it and of that which it surpasses, (20) and that it is impossible
for the opposite motions or changes to be present to a thing at the same
time. Furthermore, in the case of becoming and perishing it would seem
to be an utterly absurd thing if as soon as anything has become it must
necessarily perish and cannot continue to exist for any time: and, if this
is true of becoming and perishing, (25) we have fair grounds for inferring
the same to be true of the other kinds of change, since it would be in the
natural order of things that they should be uniform in this respect.
8
Let us now proceed to maintain that it is possible that there should
be an infinite motion that is single and continuous, and that this motion
is rotatory motion. The motion of everything that is in process of
locomotion is either rotatory or rectilinear or a compound of the two:
consequently, if one of the former two is not continuous, (30) that which
is composed of them both cannot be continuous either. Now it is plain
that if the locomotion of a thing is rectilinear and finite it is not
continuous locomotion: for the thing must turn back, and that which
turns back in a straight line undergoes two contrary locomotions, since,
so far as motion in respect of place is concerned, upward motion is the
contrary of downward motion, forward motion. (35) of backward motion,
and motion to the left of motion to the right, these being the pairs of
contraries in the sphere of place. But we have already35 defined single
and continuous motion to be motion of a single thing in a single period
of time and operating within a sphere admitting of no further specific
differentiation (for we have three things to consider, first that which is
in motion, e. g. a man or a god, secondly the ‘when’ of the motion, that
is to say, the time, and thirdly the sphere within which it operates,
which may be either place or affection or essential form or magnitude):
and contraries are specifically not one and the same but distinct: and
within the sphere of place we have the above-mentioned distinctions.
[262a]
Moreover we have an indication that motion from A to B is
the contrary of motion from B to A in the fact that, if they occur at the
same time, they arrest and stop each other. And the same is true in the
case of a circle: the motion from A towards B is the contrary of the
motion from A towards C: for even if they are continuous and there is no
turning back they arrest each other, (10) because contraries annihilate or
obstruct one another. On the other hand lateral motion is not the
contrary of upward motion. But what shows most clearly that rectilinear
motion cannot be continuous is the fact that turning back necessarily
implies coming to a stand, not only when it is a straight line that is
traversed, but also in the case of locomotion in a circle (which is not the
same thing as rotatory locomotion: for, (15) when a thing merely traverses
a circle, it may either proceed on its course without a break or turn back
again when it has reached the same point from which it started). We
may assure ourselves of the necessity of this coming to a stand not only
on the strength of observation, but also on theoretical grounds. We may
start as follows: we have three points, starting-point, middle-point, and
finishing-point, of which the middle-point in virtue of the relations in
which it stands severally to the other two is both a starting-point and a
finishing-point, (20) and though numerically one is theoretically two. We
have further the distinction between the potential and the actual. So in
the straight line in question any one of the points lying between the two
extremes is potentially a middle-point: but it is not actually so unless
that which is in motion divides the line by coming to a stand at that
point and beginning its motion again: thus the middle-point becomes
both a starting-point and a goal, (25) the starting-point of the latter part
and the finishing-point of the first part of the motion. This is the case
e. g. when A in the course of its locomotion comes to a stand at B and
starts again towards C: but when its motion is continuous A cannot
either have come to be or have ceased to be at the point B: it can only
have been there at the moment of passing, (30) its passage not being
contained within any period of time except the whole of which the
particular moment is a dividing-point. To maintain that it has come to
be and ceased to be there will involve the consequence that A in the
course of its locomotion will always be coming to a stand: for it is
impossible that A should simultaneously have come to be at B and
(5)
ceased to be there, so that the two things must have happened at
different points of time, and therefore there will be the intervening
period of time: consequently A will be in a state of rest at B, and
similarly at all other points, (5) since the same reasoning holds good in
every case. [262b] When to A, that which is in process of locomotion,
B, the middle-point, serves both as a finishing-point and as a startingpoint for its motion, A must come to a stand at B, because it makes it
two just as one might do in thought. However, the point A is the real
starting-point at which the moving body has ceased to be, and it is at C
that it has really come to be when its course is finished and it comes to a
stand. So this is how we must meet the difficulty that then arises, (10)
which is as follows. Suppose the line E is equal to the line F, that A
proceeds in continuous locomotion from the extreme point of E to C, and
that, at the moment when A is at the point B, D is proceeding in uniform
locomotion and with the same velocity as A from the extremity of F to G:
then, says the argument, D will have reached G before A has reached C:
for that which makes an earlier start and departure must make an earlier
arrival: the reason, (15) then, for the late arrival of A is that it has not
simultaneously come to be and ceased to be at B: otherwise it will not
arrive later: for this to happen it will be necessary that it should come to
a stand there. Therefore we must not hold that there was a moment
when A came to be at B and that at the same moment D was in motion
from the extremity of F: for the fact of A’s having come to be at B will
involve the fact of its also ceasing to be there, (20) and the two events will
not be simultaneous, whereas the truth is that A is at B at a sectional
point of time and does not occupy time there. In this case, therefore,
where the motion of a thing is continuous, it is impossible to use this
form of expression. On the other hand in the case of a thing that turns
back in its course we must do so. For suppose G in the course of its
locomotion proceeds to D and then turns back and proceeds downwards
again: then the extreme point D has served as finishing-point and as
starting-point for it, (25) one point thus serving as two: therefore G must
have come to a stand there: it cannot have come to be at D and departed
from D simultaneously, for in that case it would simultaneously be there
and not be there at the same moment. And here we cannot apply the
argument used to solve the difficulty stated above: we cannot argue that
G is at D at a sectional point of time and has not come to be or ceased to
be there. For here the goal that is reached is necessarily one that is
actually, (30) not potentially, existent. Now the point in the middle is
potential: but this one is actual, and regarded from below it is a
finishing-point, while regarded from above it is a starting-point, so that
it stands in these same two respective relations to the two motions.
[263a] Therefore that which turns back in traversing a rectilinear
course must in so doing come to a stand. Consequently there cannot be a
continuous rectilinear motion that is eternal.
The same method should also be adopted in replying to those who ask,
in the terms of Zeno’s argument, whether we admit that before any
distance can be traversed half the distance must be traversed, (5) that
these half-distances are infinite in number, and that it is impossible to
traverse distances infinite in number—or some on the lines of this same
argument put the questions in another form, and would have us grant
that in the time during which a motion is in progress it should be
possible to reckon a half-motion before the whole for every half-distance
that we get, so that we have the result that when the whole distance is
traversed we have reckoned an infinite number, (10) which is admittedly
impossible. Now when we first discussed the question of motion we put
forward a solution36 of this difficulty turning on the fact that the period
of time occupied in traversing the distance contains within itself an
infinite number of units: there is no absurdity, we said, in supposing the
traversing of infinite distances in infinite time, and the element of
infinity is present in the time no less than in the distance. But, although
this solution is adequate as a reply to the questioner (the question asked
being whether it is possible in a finite time to traverse or reckon an
infinite number of units), (15) nevertheless as an account of the fact and
explanation of its true nature it is inadequate. For suppose the distance
to be left out of account and the question asked to be no longer whether
it is possible in a finite time to traverse an infinite number of distances,
(20) and suppose that the inquiry is made to refer to the time taken by
itself (for the time contains an infinite number of divisions): then this
solution will no longer be adequate, and we must apply the truth that we
enunciated in our recent discussion, stating it in the following way. In
the act of dividing the continuous distance into two halves one point is
treated as two, since we make it a starting-point and a finishing-point:
and this same result is also produced by the act of reckoning halves as
well as by the act of dividing into halves. (25) But if divisions are made in
this way, neither the distance nor the motion will be continuous: for
motion if it is to be continuous must relate to what is continuous: and
though what is continuous contains an infinite number of halves, they
are not actual but potential halves. If the halves are made actual, we
shall get not a continuous but an intermittent motion. (30) In the case of
reckoning the halves, it is clear that this result follows: for then one
point must be reckoned as two: it will be the finishing-point of the one
half and the starting-point of the other, if we reckon not the one
continuous whole but the two halves. [263b] Therefore to the question
whether it is possible to pass through an infinite number of units either
of time or of distance we must reply that in a sense it is and in a sense it
is not. (5) If the units are actual, it is not possible: if they are potential, it
is possible. For in the course of a continuous motion the traveller has
traversed an infinite number of units in an accidental sense but not in an
unqualified sense: for though it is an accidental characteristic of the
distance to be an infinite number of half-distances, this is not its real and
essential character. It is also plain that unless we hold that the point of
time that divides earlier from later always belongs only to the later so
far as the thing is concerned, (10) we shall be involved in the consequence
that the same thing is at the same moment existent and not existent, and
that a thing is not existent at the moment when it has become. It is true
that the point is common to both times, the earlier as well as the later,
and that, while numerically one and the same, it is theoretically not so,
being the finishing-point of the one and the starting-point of the other:
but so far as the thing is concerned it belongs to the later stage of what
happens to it. (15) Let us suppose a time KBC and a thing D, D being
white in the time A and not-white in the time B. Then D is at the
moment C white and not-white: for if we were right in saying that it is
white during the whole time A, it is true to call it white at any moment
of A, and not-white in B, and C is in both A and B. We must not allow,
(20) therefore, that it is white in the whole of A, but must say that it is so
in all of it except the last moment C. C belongs already to the later
period, and if in the whole of A not-white was in process of becoming
and white of perishing, at C the process is complete. And so C is the first
moment at which it is true to call the thing white or not-white
respectively. Otherwise a thing may be non-existent at the moment when
it has become and existent at the moment when it has perished: or else it
must be possible for a thing at the same time to be white and not white
and in fact to be existent and non-existent. (25) Further, if anything that
exists after having been previously non-existent must become existent
and does not exist when it is becoming, time cannot be divisible into
time-atoms. For suppose that D was becoming white in the time A and
that at another time B, a time-atom consecutive with the last atom of A,
D has already become white and so is white at that moment: then,
inasmuch as in the time A it was becoming white and so was not white
and at the moment B it is white, (30) there must have been a becoming
between A and B and therefore also a time in which the becoming took
place. On the other hand, those who deny atoms of time (as we do) are
not affected by this argument: according to them D has become and so is
white at the last point of the actual time in which it was becoming
white: and this point has no other point consecutive with or in
succession to it, whereas time-atoms are conceived as successive.
[264a] Moreover it is clear that if D was becoming white in the whole
time A, the time occupied by it in having become white in addition to
having been in process of becoming white is no more than all that it
occupied in the mere process of becoming white. (5)
These and such-like, then, are the arguments for our conclusion that
derive cogency from the fact that they have a special bearing on the
point at issue. If we look at the question from the point of view of
general theory, the same result would also appear to be indicated by the
following arguments. Everything whose motion is continuous must, on
arriving at any point in the course of its locomotion, (10) have been
previously also in process of locomotion to that point, if it is not forced
out of its path by anything: e. g. on arriving at B a thing must also have
been in process of locomotion to B, and that not merely when it was
near to B, but from the moment of its starting on its course, since there
can be no reason for its being so at any particular stage rather than at an
earlier one. So, too, in the case of the other kinds of motion. Now we are
to suppose that a thing proceeds in locomotion from A to C and that at
the moment of its arrival at C the continuity of its motion is unbroken
and will remain so until it has arrived back at A. (15) Then when it is
undergoing locomotion from A to C it is at the same time undergoing
also its locomotion to A from C: consequently it is simultaneously
undergoing two contrary motions, since the two motions that follow the
same straight line are contrary to each other. With this consequence
there also follows another: we have a thing that is in process of change
from a position in which it has not yet been: so, inasmuch as this is
impossible, the thing must come to a stand at C. Therefore the motion is
not a single motion, (20) since motion that is interrupted by stationariness
is not single.
Further, the following argument will serve better to make this point
clear universally in respect of every kind of motion. If the motion
undergone by that which is in motion is always one of those already
enumerated, and the state of rest that it undergoes is one of those that
are the opposites of the motions (for we found37 that there could be no
other besides these), and moreover that which is undergoing but does
not always undergo a particular motion (by this I mean one of the
various specifically distinct motions, (25) not some particular part of the
whole motion) must have been previously undergoing the state of rest
that is the opposite of the motion, the state of rest being privation of
motion; then, inasmuch as the two motions that follow the same straight
line are contrary motions, and it is impossible for a thing to undergo
simultaneously two contrary motions, (30) that which is undergoing
locomotion from A to C cannot also simultaneously be undergoing
locomotion from C to A: and since the latter locomotion is not
simultaneous with the former but is still to be undergone, before it is
undergone there must occur a state of rest at C: for this, as we found,38
is the state of rest that is the opposite of the motion from C. The
foregoing argument, then, makes it plain that the motion in question is
not continuous.
[264b] Our next argument has a more special bearing than the
foregoing on the point at issue. We will suppose that there has occurred
in something simultaneously a perishing of not-white and a becoming of
white. Then if the alteration to white and from white is a continuous
process and the white does not remain any time, (5) there must have
occurred simultaneously a perishing of not-white, a becoming of white,
and a becoming of not-white: for the time of the three will be the same.
Again, from the continuity of the time in which the motion takes place
we cannot infer continuity in the motion, but only successiveness: in
fact, how could contraries, e. g. whiteness and blackness, meet in the
same extreme point?
On the other hand, in motion on a circular line we shall find
singleness and continuity: for here we are met by no impossible
consequence: that which is in motion from A will in virtue of the same
direction of energy be simultaneously in motion to A (since it is in
motion to the point at which it will finally arrive), (10) and yet will not be
undergoing two contrary or opposite motions: for a motion to a point
and a motion from that point are not always contraries or opposites:
they are contraries only if they are on the same straight line (for then
they are contrary to one another in respect of place, (15) as e. g. the two
motions along the diameter of the circle, since the ends of this are at the
greatest possible distance from one another), and they are opposites only
if they are along the same line. Therefore in the case we are now
considering there is nothing to prevent the motion being continuous and
free from all intermission: for rotatory motion is motion of a thing from
its place to its place, (20) whereas rectilinear motion is motion from its
place to another place.
Moreover the progress of rotatory motion is never localized within
certain fixed limits, whereas that of rectilinear motion repeatedly is so.
Now a motion that is always shifting its ground from moment to
moment can be continuous: but a motion that is repeatedly localized
within certain fixed limits cannot be so, since then the same thing would
have to undergo simultaneously two opposite motions. So, too, there
cannot be continuous motion in a semicircle or in any other arc of a
circle, (25) since here also the same ground must be traversed repeatedly
and two contrary processes of change must occur. The reason is that in
these motions the starting-point and the termination do not coincide,
whereas in motion over a circle they do coincide, and so this is the only
perfect motion.39
This differentiation also provides another means of showing that the
other kinds of motion cannot be continuous either: for in all of them we
find that there is the same ground to be traversed repeatedly: thus in
alteration there are the intermediate stages of the process, (30) and in
quantitative change there are the intervening degrees of magnitude: and
in becoming and perishing the same thing is true. It makes no difference
whether we take the intermediate stages of the process to be few or
many, or whether we add or subtract one: for in either case we find that
there is still the same ground to be traversed repeatedly. [265a]
Moreover it is plain from what has been said that those physicists who
assert that all sensible things are always in motion are wrong: for their
motion must be one or other of the motions just mentioned: in fact they
mostly conceive it as alteration (things are always in flux and decay, (5)
they say), and they go so far as to speak even of becoming and perishing
as a process of alteration. On the other hand, our argument has enabled
us to assert the fact, applying universally to all motions, that no motion
admits of continuity except rotatory motion: consequently neither
alteration nor increase admits of continuity. (10) We need now say no
more in support of the position that there is no process of change that
admits of infinity or continuity except rotatory locomotion.
9
It can now be shown plainly that rotation is the primary
locomotion. Every locomotion, as we said before,40 is either rotatory or
rectilinear or a compound of the two: and the two former must be prior
to the last, (15) since they are the elements of which the latter consists.
Moreover rotatory locomotion is prior to rectilinear locomotion, because
it is more simple and complete, which may be shown as follows. The
straight line traversed in rectilinear motion cannot be infinite: for there
is no such thing as an infinite straight line; and even if there were, it
would not be traversed by anything in motion: for the impossible does
not happen and it is impossible to traverse an infinite distance. (20) On
the other hand rectilinear motion on a finite straight line is if it turns
back a composite motion, in fact two motions, while if it does not turn
back it is incomplete and perishable: and in the order of nature, of
definition, and of time alike the complete is prior to the incomplete and
the imperishable to the perishable. Again, a motion that admits of being
eternal is prior to one that does not. (25) Now rotatory motion can be
eternal: but no other motion, whether locomotion or motion of any other
kind, can be so, since in all of them rest must occur, and with the
occurrence of rest the motion has perished. Moreover the result at which
we have arrived, that rotatory motion is single and continuous, and