The Parmenides
Philosophy 190: Plato
Fall, 2014
Prof. Peter Hadreas
Course website:
http://www.sjsu.edu/people/peter.hadreas/courses/Plato
Overview of main differences of the Parmenides as
compared with other dialogues1
•Socrates is ‘very young’ (127C5) in the Parmenides, somewhere between
fifteen and nineteen years old.
•Unlike other dialogues of question and answer form, in which Socrates
typically questions others who contradict themselves, Parmenides
questions Socrates and Socrates contradicts himself.
•Parmenides argues with Socrates and wins the arguments regarding the
forms. Forms such as justice itself and good itself are mentioned. The
older Socrates of the other dialogues presents Forms as central to his
philosophy.
•The question arises as to whether this dialogue signals Plato’s revision of
the Theory of Forms.
•The Parmenides is the only dialogue in which forms are the main topic.
•The dialogue’s second part, 137C-166C, is the longest passage of
unrelenting argument in Plato’s writings and its arguments are his most
puzzling.”
1. adapted from Peterson, Sandra, “The Parmenides,” The Oxford Handbook of
Plato, edited by Gail Fine, (Oxford/New York: Oxford University Press, 2011), p.
383.
Parmenides flourished late sixth or early fifth century BCE
He was from Elea in Magna Graecia and he was the founder
of the Eleatic school of philosophy.
Zeno (c. 490 – c. 430 BCE)
•Part of Eleatic School and principal student of Parmenides.
•According to the ancient historian of philosophy, Diogenes Laertius,
Aristotle said that Zeno invented the dialectic.1
•All the extant works we have Zeno are the result of discussions or quotes
from other writers. The paradoxes of which he is best known are related by
Aristotle in Physics, 233a and 239b.
•Proclus in his commentary on Plato's Parmenides states that Zeno
produced "not less than forty arguments revealing contradictions”2. Nine of
his arguments have survived.
•Zeno’s arguments are the first examples we have of indirect proofs or
proofs by reductio ad absurdum.
•Plutarch, who usually is a fairly careful historian, says that Zeno tried to
kill the tyrant Demylus. He couldn’t do so, so "with his own teeth bit off the
tyrant’s tongue and spit it in the tyrant’s face.3
1. Diogenes Laërtius, 8.57, 9.25
2. Proclus, Commentary on Plato's Parmenides, p. 293.
3. Plutarch, Against Colotes.
Zeno shows the Doors to Truth and Falsity (Veritas et
Falsitas). Fresco in the Library of El Escorial, Madrid.
Proposed interpretation of the frame of the Parmenides:
•The Republic begins with a character named Cephalus and the main
characters are Socrates and Plato’s full brothers Adeimantus and Glaucus.
Adeimantus and Glaucus retain a sincere interest in the conversations as they
arise in the Republic.
•The Parmenides begins also with a character named Cephalus, but it’s a
different Cephalus from the Republic. In the Parmenides he is from
Clazomenae, the home of Anaxagoras. In the Republic he is presumably from
Piraeus.
•Plato’s half brother, Antiphon, is sought in the Parmenides. He’s given up
philosophy, now “he devotes most of his time to horses.” (p. 361, 126C) But
before he gave up philosophy, he memorized, after much practice, the
conversation that took place between Socrates, Zeno, Parmenides and others
that make up the dialogue.
Proposal: In the Parmenides Plato is suggesting that the results of the
Parmenides are more distantly related to his own teaching and, if taken at
their face value, dissuade people from applying philosophy to their lives.
Is the Aristotle of Plato’s Parmenides an allusion to Aristotle
the philosopher?
There would seem to be no connection.
•It is probable that the Parmenides was written before Aristotle
joined the Academy in 367 or 366 BCE at about the age of
seventeen.
•Aristotle’s early writings indicate that for years afterwards
Aristotle was, as we should expect, a faithful adherent of the
theory of Forms under the overwhelming influence of his
master.
•The objections to the theory in the Parmenides are advanced
by Parmenides, not by Aristoteles, who has nothing to say of
himself.
Argument adapted from Cornford, Francis MacDonald, Plato and Parmenides,
(Bobbs-Merrill, Indianapolis) p. 109, n. 1.
The character of the teenage Socrates at the beginning of the
Parmenides
Socrates treats Zeno rather condescendingly. He’s brash, maybe rude.1
Perhaps what we’d expect from a very bright teenager. Consider the way he
sums up the combination of Parmenides’ and Zeno’s cooperative work,
128B, p. 362:
“Parmenides,” Socrates said, “I understand that Zeno wants to be on
intimate terms with you not only in friendship, but also in his book. He has
in a way written the same thing as you, but by changing it round he tries to
fool us into thinking he is saying something different. You say in your poem
that all is one, and you give splendid and excellent proofs for that; he, for
his part, says it is not many and gives a vast array of very grand proofs of
his own. So with one of you saying ‘one,’ and the other ‘not many,’ and with
each of you speaking in a way that suggests you’ve said nothing the same –
although you mean practically the same thing – what you’ve said you
appear to have said over the heads of us.”
1. Sandra Peterson makes a similar point in “The Parmenides,” The Oxford
Handbook of Plato, edited by Gail Fine, (Oxford/New York: Oxford University
Press, 2011), p. 383-4.
In the initial conversation with Parmenides and Zeno, Socrates
summarizes a typical argument of Zeno at 127E, p. 362-31
“Zeno, what do you mean by this: If things are many, they
must be both like and unlike, But that is impossible, because
unlike things can’t be like like and unlike things likes? That
what you say, isn’t it?” – “It is,” said Zeno.
But as Socrates will later say, obviously things can be unlike
and unlike or many and one, 129D, p. 363: “He will say, when
he wants to show that I am many, that my right side is
different from my left, and my front from my back, and
likewise my upper and lower parts –since I take it I do partake
in multitude. But when he wants to show that I’m one, he will
say that I am one person among the seven of us, because I also
partake of oneness. Thus he shows both are true.”
The teenage Socrates already has an interest in and admires a
philosophy that takes seriously a theory of ‘forms.’
p. 363, 129B &E
SOCRATES: “If some showed that the likes themselves come to be unlike
or the unlike like – that I think would be marvel; but if he shows that
things that partake of both of these have properties, there seems to be
nothing strange about this, Zeno –”
…
“But if someone first distinguishes as separate the forms, themselves by
themselves, of the things I was talking about a moment ago – for example,
likeness and unlikeness, multitude and oneness, rest and motion, and
everything of that sort – and then shows that in themselves they can mix
together and separate, I for my part” he said, “would be utterly amazed,
Zeno.”
Six Properties of the Forms as collected from Parmenides
129B-130Di
1. Causality. Things take on a property by virtue of participating or
partaking in a Form. “.. things that partake of both of these [likeness and
unlikessness] have both properties.” 129B, p. 363.
2. Separation. A form is itself by not being identical with the things that
partake in it. “But if some first distinguishes as separate the form,
themselves by themselves, …” 129D, p. 363
3. Purity: Forms cannot have contrary properties. “And it’s the same with
all the others [Forms]: if he could show that the kinds and forms themselves
have in themselves these opposite properties, that would call for
astonishment.” 129C, p. 363
4. Uniqueness: There is only one Form with a perfection of a certain
property. “And what about these?” asked Parmenides. “Is there a form,
itself by itself, of just, and beautiful, and good, and everything of that
sort?” “Yes,” he [Socrates] said. 130B, p. 364.
i. This list follows Rickless’s analysis: Rickless, Samuel, "Plato's Parmenides", The Stanford
Encyclopedia of Philosophy (Winter 2012 Edition), Edward N. Zalta (ed.), URL =
<http://plato.stanford.edu/archives/win2012/entries/plato-parmenides/>.
Properties of the Forms1 [continued]
5. Self-Predication: Any Form has the property which itself is.
“If someone showed that the likes of themselves come to be
unlike or the unlikes like – that, I think, would be a marvel;
but if he shows that things that partake of both of these have
both properties, there seems to be nothing strange about that
Zeno …” 129C, p. 363.
6. Oneness: Something that can be counted as a necessarily
homogenous. “But if someone first distinguishes as separate
the forms, themselves by themselves . . . and then shows that in
themselves they can mix together and separate, I [Socrates] for
my part,” he said “would be utterly amazed Zeno.” 129E, p.
363. NOTE: Oneness is different from Uniqueness.
1. Ibid.
130A-E Parmenides’ Criticism of the Theory of the Forms –
The Extent of the Forms1
“And what about these Socrates? Things that might seem
absurd, like hair and mud and dirt or anything else totally
undignified and worthless? Are you doubtful whether you
should say that a form is separate for each of these too, which
in turn is other than anything we touch with our hands.” p.
130D. p. 364.
1. Rickless, S. Plato’s Forms in Transition, (Cambridge: Cambridge
University Press, 2007) pp. 54-55 and Miller, M., Plato’s Parmenides
(Princeton, NJ: Princeton University Press, 1986) counter-argue. Both
justice and mud have self-predication. Justice is just, mud is muddy. But
it’s difficult to see how those things that self-predicate materially, could also
be separate from sensible things. So then if there is a Form of mud or hair,
it would not be the material self-predicating hairiness and that seems to be
what is objectionable. Or perhaps there could not be Forms of such things.
Parmenides’ Criticism of the Theory of the Forms: Objections
to Participation. I (130E-131E)
A thing cannot contain either Form as a whole or as a part of
it. Samuel Rickless in the Stanford Encyclopedia of Philosophy
article p. 7ff. says this presumes what he calls the Pie Model of
the forms. According to the Pie Model, if the whole is extended
to discrete parts the whole will be made into parts. (The whole
Form is in things.)
NOTE: The Greek terms for the connection of Forms to
ordinary things are metalambabein (129A3) which Peterson
fairly translates here as ‘together or jointly get’ instead of the
traditional ‘participate’; and metechein, 129A8, which she also
fairly translates here as ‘together have’ instead of the usual,
‘share,’ ‘participate,’ or ‘partake.’1
1. Peterson, Sandra, “The Parmenides,” in The Oxford Handbook of Plato, edited by
Gail Fine, (Oxford/New York: Oxford University Press, 2011).
Parmenides’ Criticism of the Theory of the Forms: Objections
to Participation. I (130E-131E)
Socrates responds to the application of the Pie Model of the
Forms: p. 365, 131B.
“No it wouldn’t Socrates said. Not if it’s like one and the same
day. That is in many places at the same time and is none the
less not separate from itself. If it’s like that, each of the forms
might be, at the same time one and in all.”
Notice how day satisfies the six properties of Forms.”
Parmenides’ Criticism of the Theory of the Forms: Objections
to Participation. II (130E-131E)
Parmenides shift from the daylight to the sail model. A sail can
cover things – perhaps something like daylight does. But a sail
can be a whole and a part. Taking a sail as a model of the
relation of a Form to material things, leads to the sort of
contradictions we find in the Pie Model of the forms.
Parmenides’ Criticism of the Theory of the Forms: Objections
to Participation. III: The Third Man Argument 132A-B
Note: Plato never refers to the ‘Third Man argument’ as such.
The designation arises with Aristotle’s criticism of the Theory
of Forms.
Colin Strang in “Plato and the Third Man”1 sees that the
conflict enters in between the
•Unique Thesis (U)
•The One over Many thesis (OM) and the
•Non Identity Assumption (NI)
1.Strang, C. “Plato in the Third Man,” in Vlastos (ed.), Plato I, 184-200.
Strang’s concluding paragraph:
“The more you become aware of and enthralled by the
peculiar anatomy of the individual Forms, the fewer and less
important become the thing that can be said about Form in
general. They remain unchanging if only to be the subject
matter of timeless truths. (Parmenides 135C1) They remain
single; (Philebus 14E5ff.) but what they do not remain is
paradigms. (OM)
Parmenides’ Criticism of the Theory of the Forms: Objections
to Participation. IV: Making a Form into a thought in a Mind
does not provide connection to the Form in Itself
p. 366. 132B-C
If inanimate objects have forms, then presumably we require
thought for us to be aware of them. Thus thoughts seem to
have a share in forms and thus again a problem arises as to
how thoughts can be connected to Forms which are supposed
to be in themselves.
Can the objections be met by making the forms patterns or
paradeigmata of which there are likeness in things?
(132C-133A)
Again Parmenides introduces a version of what is later
referred to as the ‘Third Man Argument.’ This time
Parmenides’ formulation is closer Aristotle’s.
“If something resembles the form,” he [Parmenides] said, “can
that form not be what has ben modeled on it, to the extent that
the thing has been made like it? Or is there any way for
something like to be like what is not like it?
“There is not.”
“And isn’t there a compelling necessity for that which is to
partake of the same one form of that which is like it?”
Further development of ‘Third Man Argument.’ [continued]
(132C-133A)
“There is not.”
“But if like things are like by partaking of something, won’t
that be the form itself?
“Undoubtedly”
“Therefore nothing can be like the form, nor can the form like
anything else. Otherwise, alongside the form another form will
always make its appearance, and if that form is like anything,
yet another; and if the form proves to be like what partakes of
it, a fresh form will never cease emerging.”
“That’s very true.”
Parmenides’ Criticism of the Theory of the Forms: Objections
to Participation. V : We cannot know the Forms and the gods
cannot apply them to us
133A-134E
1.If Forms are just in themselves, they are not in real world.
2. They may have reference to each other, but they will be
unknowable to us and, further, gods cannot apply them to us.
Parmenides reintroduces the Forms
(135A-5, p. 369)
“And yet, Socrates,” said Parmenides, “the forms inevitably
involve these objections and a host of others besides – if there
are those characters for things and a person is to mark off
each form as ‘something itself.’ As a result, whoever hears
about them is doubtful and objects that they do not exist, and
that, even if they do, they must by strict necessity be
unknowable to human nature; and in saying this he seems to
have a point; and, as we said, he is extraordinarily hard to win
over. Only a very gifted man can come to know that for each
thing there is some kind, a being itself by itself; but only a
prodigy more remarkable still will discover that and be able to
teach someone else who has sifted all these difficulties
thoroughly and critically for himself.” [empasis added]
Parmenides reintroduces the Forms
(135A-5, p. 369) [continued]
“I agree with you Parmenides,” Socrates said. “That’s very
much what I think too.”
“Yet on the other hand, Socrates,” said Parmenides, “ if
someone, having an eye on all the difficulties we have just
brought up and others of the same sort, won’t allow that there
are forms of things and won’t mark off a form for each one, he
won’t have anywhere to turn his thought, since he doesn’t
allow that for each thing there is a character that is always the
same. In this way he will destroy the power of dialectic
entirely. But I think you are only too well aware of that.”
A REVIEW OF MAIN
ARGUMENTS OF
PARMENIDES AND
ZENO OUTSIDE OF
PLATO’S DIALOGUE,
PARMENIDES
From Parmenides’ Poem1
Fragment 2: “Come now, I shall tell—and convey home the tale once you
have heard—/just which ways of inquiry alone there are for
understanding:/ the one, that [it] is and that [it] is not not to be,/ is the path
of conviction, for it attends upon true reality,/ but the other, that [it] is not
and that [it] must not be,/ this, I tell you, is a path wholly without report:/
for neither could you apprehend what is not, for it is not to be
accomplished,/ nor could you indicate it.”
...
“ . . . but not ever was it, nor yet will it be, since it is now together entire,/
single, continuous; for what birth will you seek of it?/ How, whence
increased? From not being I shall not allow/ you to say or to think: for not
to be said and not to be thought/ is it that it is not. And indeed what need
could have aroused it/ later rather than before, beginning from nothing, to
grow?/ Thus it must either be altogether or not at all./
1. Translations are from Coxon, A. H. 2009. The Fragments of Parmenides: A critical
text with introduction, translation, the ancient testimonia and a commentary. Revised
and expanded edition with new translations by Richard McKirahan. Las
Vegas/Zurich/Athens: Parmenides Publishing.
From Parmenides’ Poem [continued]
“Nor ever from not being will the force of conviction allow/ something to
come to be beyond it: on account of this neither to be born/ nor to die has
Justice allowed it, having loosed its bonds,/ but she holds it fast. And the
decision about these matter lies in this:/ it is or it is not; but it has in fact
been decided, just as is necessary,/ to leave the one unthought and nameless
(for no true/ way is it), and <it has been decided> that the one that it is
indeed is genuine./ And how could What Is be hereafter? And how might it
have been?/ For if it was, it is not, nor if ever it is going to be:/ thus
generation is extinguished and destruction unheard of.”
Zeno’s Four Paradoxes of Motion
Two based on Space
Achilles and the Tortoise
In a race, the quickest runner can never overtake the slowest,
since the pursuer must first reach the point whence the
pursued started, so that the slower must always hold a lead. –
Aristotle, Physics, VI:9, 239b15
Dichotomy paradox
That which is in locomotion must arrive at the half-way stage
before it arrives at the goal.–Physics, VI:9, 239b10. The result
is that locomotion can never begin.
Note: Both these paradoxes presume that the points referred to
are part of the whole space to be traversed. If we assume they
have no extension in space – nor duration in time – the
paradoxes dissolve.
Zeno’s Four Paradoxes of Motion
One based onTime
The Arrow
If everything when it occupies an equal space is at rest, and if
that which is in locomotion is always occupying such a space at
any moment, the flying arrow is therefore motionless.
Aristotle, Physics VI:9, 239b5
Note: This paradox presumes that a whole expanse of time may be divided
into parts which are moments during which an object is in a position. If we
assume, a position in time has no duration, the paradoxes dissolve.
Zeno paradoxes rely upon types of whole/part relations.
2. Parmenides, in his poem, derives the consequences regarding
whole/part, single/many, continuous/discrete, generated, increased, etc.
from ‘it is.’ and from ‘it is not’ being unthinkable. The logic of his poem is
analogous to the method of inquiry he proposes in the Parmenides:
consequences that befall various fundamental opposites given A and not-A.
Parmenides Proposes How To Investigate Whether and How
There Are Forms
p. 370, 136-C
PARMENIDES: “If you like,” said Parmenides, “take as an
example this hypothesis that Zeno entertained: if many are,
what must the consequences be both for the many themselves
in relation to themselves and in relations to the one, and for the
one in relation to itself and in relation to the many? And, in
turn, on the hypothesis, if many are not, you must again
examine what the consequences will be both for the one and
for the many in relation to themselves and in relation to each
other. And again, in turn, if you hypothesize, if likeness is or it
is not, you must examine what the consequences will be on
each hypothesis, both for the things hypothesized themselves
and for the others, both in relation to themselves and in
relation to each other. . . .”
Problem with Parmenides’ Plan of Investigation
The plan of the Deductions is such that they rely on a condition
where the consequence is a denial of a feature and its contrary.
If the one is, for example, then it is not the case that it is at rest
and it is not the case that it is in motion, etc. But this involves a
methodical fallacy of deriving a contradiction by denying
contraries. You can get a contradiction by affirming two
contraries but not by denying them. Suppose I say that “If the
number 4 exists, then it is not at rest and it is not in motion.”
From that I cannot conclude that the number 4 does not exist.
1. Quoted very closely but not verbatim from Rickless, Samuel, "Plato's
Parmenides", The Stanford Encyclopedia of Philosophy (Winter 2012 Edition),
Edward N. Zalta (ed.), URL =
<http://plato.stanford.edu/archives/win2012/entries/plato-parmenides/>.
Problem with Parmenides’ Plan of Investigation
[continued]
Thus there is an error in supposing that the contraries are
such that one or the other must be true of the subject. Thus
some large part of the features that are used to argue against
that the One is, or is not, will not apply to the Forms, because,
as for example, with rest and motion, rest and motion do not
apply to intellectual objects, but rather only material objects.
There are in fact two ways that the denial of contraries does
not apply: 1) if there is a ‘middle,’ –Note Plato worries about
such in Symposium 202B about state in between gods and
mortals, or pleasure and pain in Philebus -- pleasure and pain
might have, as Plato but not Aristotle thought, a middle state
which is neither pleasurable not painful. 2) the contraries no
longer apply to the subject, e. g. odd/even no longer applies to
irrational numbers, or rest/motion to intellectual objects.
Parmenides, Second Part (137C-166C)
Survey of the Deductions
Hypothesis 1 (137C-142A). General logical form:
If the One is, but is not a whole with parts, then it is not F and not the
contrary of F. ‘F’ stands for many features and their contraries, such as
being many (contrary, being one); whole (contrary, part)1; limited
(contrary, unlimited); shape (contrary, opposite shape); motion (contrary,
rest); sameness (contrary, difference); being older (contrary, being
younger); knowable (contrary, being unknowable), etc.
NOTE #1: This hypothesis was appropriated in Neo-Platonic interpretations.
NOTE #2: Plato’s introduction of the notion of the ‘whole/part dichotomy plays a
central role the reductiones ad absurdum in Parmenides II. But Plato would likely
deny that the Forms are subject to the whole/part distinction. Even so, Hypothesis I
presumes that (i) anything that has parts is many; (ii) a whole is a thing with parts
from which no part is missing.
Parmenides, Second Part (137C-166C)
The Plan of the Deductions [continued]
Hypothesis 2 (142B-155D): In this hypothesis the One is said to be able to
partake of Being. Parmenides immediately then derives that the One allows
for the part/whole distinction. Even though this contrary would not be
allowed in the description of Forms in the Middle dialogues, this
hypothesis, where the ‘One’ would count for concept, types, universals of
some sort – let alone Forms -- would have to be supported to allow for
rational discourse in general. Again, it is assumed that the one has parts
and that the one is a whole.
PARMENIDES: 142D, p. 376: “ . . . If we state the ‘is’ of the one that is, and
the ‘one’ of that which is one, and if being and oneness are not the same,
but both belong to the same thing that we hypothesized, namely, the one
that is, must it not itself, since it is one being, be a whole, and the parts of
this whole be oneness and being?”
NOTE: In The Republic the Form of the Good is “beyond Being” 509B p.
1130: “Therefore, you should also say that not only do the objects of
knowledge owe their being known to the good, but their being is also due to
it, although the good is not being, but superior to it in rank and power.”
The Greater Mysteries in the Symposium 210A-212C, p.
210E3-492-4
211B6: Original
210E3-211B6: (almost) literal
translation
οὐδὲ πρὸς μὲν τὸ καλόν, πρὸς
δὲ τὸ αἰσχρόν, οὐδ’ ἔνθα μὲν καλόν,
ἔνθα δὲ αἰσχρόν, ὡς
τισὶ μὲν ὂν καλόν, τισὶ δὲ αἰσχρόν· οὐδ’
αὖ φαντασθήσεται (5)
αὐτῷ τὸ καλὸν οἷον πρόσωπόν τι οὐδὲ
χεῖρες οὐδὲ ἄλλο
οὐδὲν ὧν σῶμα μετέχει, οὐδέ τις λόγος
οὐδέ τις ἐπιστήμη,
οὐδέ που ὂν ἐν ἑτέρῳ τινι, οἷον ἐν ζώῳ
ἢ ἐν γῇ ἢ ἐν οὐρανῷ
(b.) ἢ ἔν τῳ ἄλλῳ, ἀλλ’ αὐτὸ καθ’ αὑτὸ
μεθ’ αὑτοῦ μονοειδὲς ἀεὶ
ὄν, τὰ δὲ ἄλλα πάντα καλὰ ἐκείνου
μετέχοντα τρόπον τινὰ
τοιοῦτον, οἷον γιγνομένων τε τῶν
ἄλλων καὶ ἀπολλυμένων
μηδὲν ἐκεῖνο μήτε τι πλέον μήτε ἔλαττον
γίγνεσθαι μηδὲ πάσχειν μηδέν.
neither in relation to the
beautiful/good, nor in relation to the
ugly/base, neither only at its core the
beautiful/good, nor at its core the
ugly/base, and not for some people
beautiful/good nor for others
ugly/base; nor yet will it appear to him
beautiful/good such as in a face, nor
hands, nor anything else belonging to
the body, nor yet some word, nor some
knowledge, nor as being in some other
thing, such as in an animal, or on the
earth, or in the heavens, but itself,
according to itself, with itself, always
being of one kind, and the other
beautiful/good things partake of it in
such a manner, that although they come
to be and perish, never does it become
more nor less, nor yet is ever changed.
Parmenides, Second Part (137C-166C)
The Plan of the Deductions
Hypothesis 2A, (155E-157B), Appendix to Hypotheses 1 & 2: Consideration
of Becoming in Time Becoming is not a feature F and not the contrary of a
feature F. Arguments rely on impossibility of change between motion and
rest and vice versa. The Appendix purports to show that the Conclusions of
Hypothesis 1 & 2 together entail that, for a range of properties F, if the one
is, then there is a moment outside of time (the so-called “instant”) at which
the one changes from being F to being con-F.
Rickless observes that all of the Arguments of the Appendix depend for
their soundness on there being times T1 and T2 such that T1 is distinct
from T2 and the one partakes of being at T1 and the one does not partake
of being at T2. But this premise depends for its soundness of Hypothesis 1
that the one does not partake of being. And the soundness of the One not
partaking in Being depends the Purity condition. So if the Purity condition
holds, then all the Arguments of the Appendix become unsound.1
1. Rickless, Samuel, "Plato's Parmenides", The Stanford Encyclopedia of
Philosophy (Winter 2012 Edition), Edward N. Zalta (ed.), URL =
<http://plato.stanford.edu/archives/win2012/entries/plato-parmenides/>.
Parmenides, Second Part (137C-166C)
The Plan of the Deductions
Hypothesis 3 (157B-159B) This hypothesis and the next addresses the
majority of arguments that Parmenides has brought to the Socrates’ early
working on the Theory of Forms: the relation – possibly their participation
-- of other things to the Forms:
PARMENIDES: (157B, p. 389) “Must we not examine what would be
proper for the others to undergo if one is?” – “We must.”
“Are we to say, then, what properties things other than the one must have,
if one is?” – “Let’s do.” “Well then since they are other than the one, the
others are not the one. For if they were they would not be other than the
one.” – “That’s right.”
“And yet the others are not absolutely deprived on the one, but somehow
partake of it.” – “In what way?”
“In that things other than the one are surely other because they have parts;
for if they didn’t have parts, they would be altogether one.”
Note: Assume that to be other is to have parts, otherwise they would be
“altogether one.” Thus Hypothesis 3 assumes Hypothesis 1.
Parmenides, Second Part (137C-166C)
The Plan of the Deductions
Hypothesis 4 (159B-160B)
PARMENIDES:159B, p. 390, “Well, then, suppose we now concede those
results as evident and examine again, if one is: Are things other than the
also not so; or only so?” – “Of course.” Let’s say from the beginning what
properties things other than the one must have, if one is.” – Yes. Let’s do.” –
“Must not the one be separate from the others and the others separate from
the one?” – “Why?” – “Because surely there is not something else in
addition to them that is both other than the one and other than the others;
for all things have been mentioned, since the one and the others are
mentioned.” -- “Yes, all things.”
Note: Assumes that the one + others = the totality of all things. Seems
reasonable unless there are things that are both one and other. Such a
consideration would seem to suggest that the elements of Parmenides’
arguments do not involve entities that may be transcendent.
Parmenides, Second Part (137C-166C)
The Plan of the Deductions (continued)
Hypothesis 5 (160B-163B):
Note: The alleged contradiction depends upon conceiving non-Being as
dependent on becoming, as in Hypothesis 2a.
Conclusion: 163C, p. 394
PARMENIDES: “Therefore also the one, if it is one, comes to be and ceases
to be, if it is altered, and does not come to be or cease to come to be, if it is
not altered. And thus the one, if it is not, both comes to be and ceases to
come to be, and does not come to be be or cease to come to be.” – “Yes,
you’re quite right.”
Note: Of course we need not assume that the one is not altered. If we don’t,
we are left with a cosmos without Forms and a world of Becoming – coming
to be and ceasing to come to be. Hardly an impossible conclusion. But the
problem remains that if we admit the existence of concepts, types or
universals – again let alone Forms – this hypothesis cannot be supported.
The Plan of the Deductions (continued)
Hypothesis 6 (163B-164B): Given the One is not, and has no sort of being.
This hypothesis is the contrary of Hypothesis I and results in the
consequence that the One has no character whatsoever.
Conclusion: 164A-B, p. 395:
“What about this? Can the others be related to it, if, necessarily, nothing
belongs to it?” – “They can’t.” – So the others are neither like nor unlike it,
and they are neither the same nor different from it.” – “No, they aren’t.” –
“And again: will of that, to that, something, this, of this, of another, to
another, or time past, hereafter, or now, or knowledge, opinion perception,
an account, a name, or anything else that is be applicable to what is not?” –
“It will not.” – “Thus one, since it is not, is not in any state at all.” “At any
rate, it seems to be in no state at all.”
Note: This argument would seem to lead to the conclusion, that if there is to
be a world at all some form of ‘oneness’, perhaps even as concepts,
universals, types, must exist.
Parmenides, Second Part (137C-166C)
The Plan of the Deductions (continued)
Hypothesis 7 (164B-165E) Given the One is not, means ‘nothing that is one
thing exists,’ then the Others can only be masses or bulks and will only have
appearances of some feature F’s.
Note: This would suggest a material cosmos in which, thanks to
unavoidable human misperception, we think we see and think about things.
But those things are mere appearances. What actually exists are bulks or
masses o– perhaps bulks and masses of quanta might be exemplified by a
current ‘scientistic’ metaphysical view. But of course however this
scientistic view might be supported, it is inconsistent because, quanta, or
photons, are understood as a type which would return us to Hypothesis 2.
Parmenides, Second Part (137C-166C)
The Plan of the Deductions (continued)
Hypothesis 8 (165E-160B) If the One is not, means ‘no one entity exists,’
even an entity which is a bulk or a mass, then the Others cannot even
appear as having one or many, or any character. So nothing will have any
being whatsoever. Therefore, once again one may say this hypothesis leads
to not some feature F and the contrary of some feature F, just because there
is nothing to have either F or the contrary of F.
Rickless notes that: Taken together, Hypothesis 7 and Hypothesis 8
establish that the one is. It’s argued that if the one is not, then the others
are many. It’s also shown that if the one is not, then the others are not
many. Thus Hypotheses 7 & 8 show that if the one is not, then the others
have contradictory properties. Given that nothing can have contradictory
properties, it follows directly that the one is. This reinforces the result
previously established in Hypothesis 6.”1
1. Rickless, Samuel, "Plato's Parmenides", The Stanford Encyclopedia of Philosophy (Winter
2012 Edition), Edward N. Zalta (ed.), URL =
<http://plato.stanford.edu/archives/win2012/entries/plato-parmenides/>.
Interpretations of the Parmenides
I
A Record of Socrates’ Perplexities about How to Understand
the Relation of What Will Later Be Called Universals, Types or
Essences to the Multitude of Things.1
Plato's set out to put forward difficulties for the theory of forms that he
himself did not, at least at the time he wrote the dialogue, see a way to
resolve.
But Parmenides does say as he is proposing his method that a “very gifted
man” should be able defend the existence of the forms, and thereby
explain the possibility of dialectic, through the very method Parmenides
applies in the second part of the dialogue.
1. see Vlastos (1954, 343); Gill (1996); Allen (1997).
Interpretations of the Parmenides
II
Theory of Forms Comes Out in Tact If a Distinction Is Made Between
Plato’s Writing a Phrase Meaning ‘Definitionally True’ and his Writing a
Phrase Meaning ‘Displays a Feature of Being ---’
The most influential version of this view belongs to Meinwald
(1991; 1992) and Peterson (1996; 2000; 2003). According to
Meinwald, Plato meant us to recognize the invalidity of
Parmenides' criticisms of the theory of forms by having us
focus on the in-relation-to qualifications that are supposed to
serve as one of the principles of division that explain the fact
that the second part takes the shape of eight separate
Deductions.
Interpretations of the Parmenides
II
These qualifications, properly understood, reveal that subjectpredicate sentences (of the form “X is F”) are ambiguous: to
say that X is F is to say either that X is F in relation to itself
(i.e., pros heauto) or that X is F in relation to the others (i.e.,
pros ta alla), where to say that X is F pros heauto is to say that
the F is definitionally true of X, and to say that X is F pros ta
alla is to say that X displays the feature of being F. As
Meinwald argues, if Plato meant us to recognize the existence
of such an ambiguity, then he probably meant us to recognize
that self-predicational sentences (of the form “The F is F”) are
also ambiguous, and that the ambiguity of such sentences
reveals that the Third Man argument and the Greatest
Difficulty commit the fallacy of equivocation.
Interpretations of the Parmenides
III
The Discerning Reader Would Understand that Parmenides’
Criticisms are Effective Only on the Mistaken Assumption that
Forms are Fundamentally Similar to the Material, Sensible
Things that Participate in Them.
Miller (1986), for example, argues that the point of the
dialogue is to help the discerning reader see the forms for what
they really are, transcendent beings that should be accessed by
reason rather than with the help of categories drawn from
sense experience.
IV
Parmenides II Reveals That Many Features of the Forms Hold
Up To the Scrutiny of Parmenides Eightfold Analysis. But
Certain Features of Forms Must Be Dismissed.
Rickless’s View1
Whether combined with the Pie Model conception of partaking
or with Paradigmatism, Plato's middle period theory of forms
is internally inconsistent if taken at face value. However, if
three principles are abandoned inconsistencies are eliminated.
Causality, Separation, Self-Predication, and Oneness hold up
under the test of the analyses in the Parmenides.
But Purity, Uniqueness, and No Causation by Contraries must
be abandoned.
1. Rickless, Samuel, "Plato's Parmenides", The Stanford Encyclopedia of
Philosophy (Winter 2012 Edition), Edward N. Zalta (ed.), URL =
<http://plato.stanford.edu/archives/win2012/entries/plato-parmenides/>.
Plato’s Timaeus on Fire Itself
51D
“So here’s how I cast my vote: If understanding and true opinion are
distinct, then these ‘by themselves’ things definitely exist—-these Forms,
the objects not of our sense perception, but of our understanding only. But
if – as some people think-- true opinion does not differ in any way from
understanding, then all the things we perceive through our bodily senses
must be assumed to be the most stable things there are. But we do have to
speak of understanding and true opinion as distinct, of course, because we
can come to have one without the other and the one is not like the other. It
is through instruction that we come to have understanding, and through
persuasion that we come to have true belief. Understanding always involves
a true account while true belief lacks any account. And while
understanding remains unmoved by persuasion, true belief gives into
persuasion. And of true belief, it must be said, all men have a share, but of
understanding, only the gods and a small group of people do.”
Plato’s Timaeus on Fire Itself
51D
“Is there such a thing as a Fire by itself? Do all these things of which we
always say that each of them is something “by itself” really exist? Or are
the things we see, and whatever else we perceive through the body, the only
things that possess this kind of actuality, so that there is absolutely nothing
else besides them all? Is our perpetual claim that there exists an intelligible
Form for each thing a vacuous gesture, in the end nothing but mere talk?
Now we certainly do not do justice to the question before us if we dismiss it,
leaving it undecided and unadjudicated, and just insist that such things
exist, but neither must we append a further lengthy digression to a
discourse already quite long. If, however, a significant distinction
formulated in a few words were to present itself, that would suit our
present needs best of all.
References for slides used in this powerpoint
Slide#3, bust of Parmenides: http://www.volkerdoormann.org/parmenides.htmhttp://platosymposium.files.wordpress.com/2009/04/framingnarrative41.jpg
Slide 4, portrait, “Zeno shows the doors to Truth”:
http://en.wikipedia.org/wiki/Zeno_of_Elea#mediaviewer/File:Zeno_of_Elea_Tibaldi_or_Carducci_Es
corial.jpghttp://de.wikipedia.org/wiki/Aristophanes#mediaviewer/File:Aristofanes.jpg