Berkeley, Perceptual Relativity, and the primary/secondary quality contrast;
Hylas redux.
I. Color as a secondary quality
Unlike others I find Berkeley’s view (as Philonous) in the first of the Three
Dialogues Between Hylas and Philonous (hereafter TD) 1 convincing; that perceptual
relativity (PR) examples suggest that no standard exists (or even makes sense) to
determine the inherent 2 colors of objects. But unlike Berkeley, I think the most this
shows is that colors are Weakly Mind-Dependent (WMD). By that I mean that though
objects can have color, what color they have is essentially relative to the nature of
observers and lighting conditions. Strong mind-dependence (SMD)—Berkeley’s
view—claims that colors can’t exist unless perceived, 3
1
George Berkeley, Three Dialogues between Hylas and Philonous, (1734 ed.) in
Works vol. 2 ed. A.A. Luce and T.E Jessop, (Thomas Nelson and Sons, 1949). Page
numbers in the text.
2
A color is inherent for an object if some change in the object is necessary for a
change in its color.
3
Paul Boghossian, writes: “Finally, there is the question whether some things we are
prepared to believe in – say, colors – exist only in some mind-dependent sense. There
are two possible thoughts here; one is that colors are attributes precisely of minds, and
the other is that, although they are the attributes of external objects, nothing could
have them unless there are minds.” “Seeking the Real”, Philosophical Studies 108 (12), (2002) 223-238). I would make this “thought” weaker. Objects could have colors
and shapes even if there were no minds, but reference to what would be perceived
under certain conditions is essential to ascribing colors to objects.
Weak mind-dependence what I’ve called in the past “perspectivalism”, and
others “relationalism,” or “relativism” (differences exist between the last two) is
supported by the findings of color science. 4 Relativism is consistent with the view that
“outward objects” (Berkeley’s phrase) have color—a view to be distinguished from
color eliminativists (e.g., Galileo, Descartes, Gassendi,)—a position Hylas I believe
could have taken. 5 WMD claims the following about color; (1) Perceived colors vary
with respect to a variety of circumstances e including essential reference to visual
systems of perceivers, (2) There’s no fact of the matter as to an object’s mindindependent or “inherent” color.
In The Principles of Human Knowledge (PHK) sec.15 Berkeley famously
notes that at most PR examples entail that we don’t know the true extension or color
of “an outward object,” not that there isn’t any. That there can’t be has allegedly been
established by prior considerations on the nature of sensible objects. One
consideration, discussed below, is that we can’t perceive shape sans some quality like
color already shown to be SMD. However I accept Georges Dicker’s claim, following
4
5
See C.L. Hardin, Color for Philosophers, (Hackett, 1998)
Joshua Cohen *** makes a distinction between relationalism and relativism.(The
Red and the Real ) For my purposes that distinction is not crucial. Both relationalism
and (relativism) are “ecumenical” (Cohen); meaning roughly and at a minimum that
there is no standard, beyond stipulation, for determining the “intrinsic” color of an
object, one it would have independent of the environment and visual system of
perceivers.
Jonathan Dancy (fn 15) that when he wrote TD Berkeley believed more proof was
needed that colors can’t exist unperceived. 6
In TD1 Philonous says about color:
Even our own eyes do not always represent objects
to us after the same manner. In the jaundice 7everyone
knows that all things seem yellow. Is it not therefore highly
probable that those animals in whose eyes we discern
a very different texture from that of ours, and whose
bodies abound with different humours, do not see the same
colors in every object that we do not see the same colors
in every object that we do. From all which, should it not
seem to follow that all colors are equally apparent and
that none of
those which we perceive are really inherent
in any outward object.(TD1 Turbayne 124 (my emphasis). 8
Berkeley notes also the problem of whether visual acuteness directly tracks real color.
Philonous., assuming for the sake of argument that objects seen through microscopes
6
Dicker argues that by the time of TD Berkeley thinks he needs arguments for Strong
Mind-Dependence than in PHk; hence the detailed use of PR in TD1. See Georges
Dicker, Berkley’s Idealism, Oxford, Oxford University Press, 2011), 104, Also George
Berkeley, A Treatise Concerning The Principles of Human Knowledge, ed. Jonathan
Dancy, (Oxford, Oxford University Press, 1998), 201-202, n.45.
7
Berkeley was evidently wrong in thinking things looked yellow to people with
jaundice.
8
In PHK 14 Berkeley as well gives a number of PR examples applicable to both
“secondary” and “primary qualities.” The point again is that PR examples, if they
show tastes and colors are SMD, equally he thinks show extension and motion are
SMD.
are numerically identical with originals seen with the naked eye, puzzles Hylas by
suggesting that:
The colors, therefore, by it [the microscope] perceived
are more genuine and real then those perceived
otherwise. (TD1 124) 9
Similarly, C. L. Hardin in his book Color for Philosophers10 asks us to
consider, among a number of examples, a Seurat painting from various distances and
then describe its real color. In any case Berkeley evidently thinks a true, that is, mindindependent color of an object would be intrinsic to the object, a property independent
of perceptual circumstances, and no such standard exists. Tom Stoneham writes,
Berkeley does not deny that when we judge something
is cobalt or teal or whatever, our judgment is answerable to
how the thing would look to suitable observers in
suitable viewing conditions . . .What he wants to point
out is that we cannot give an objective justification
of the choice of these conditions as being the ones in
which the ‘true colors’ are revealed, where true means
9
In the New Theory of Vision Berkeley apparently denies the microscope gives greater
acuity since the number of minimua visibilia must be the same in what’s seen through
the microscope and what’s seen unaided. We have, he thinks, simply a new object of
vision. He also thinks what we see through the microscope, having no associative
connections with tactile experience lacks practical importance. Thus we have “only
the empty amusement of seeing,” Turbayne ed., of The New Theory of Vision, (sec 86)
p. 62. See also Catherine Wilson, The Invisible World, (Princeton, Princeton
University Press, 1995), 244-248.
10
(Indianapolis, Hackett, 1986). Also “A Spectral Reflectance Doth Not a Color
Make” The Journal of Philosophy, Vol. 100, No. 4 (Apr., 2003), 191-202.
mind-independent. 11
What about so-called “normal” perceivers, and “standard” illuminants? Hardin asks
the following:
So should not color realists [objects have inherent non-mind-dependent
color] not only claim that there are viewing conditions that are veridical,
but be prepared to specify which ones are veridical, or at least tell us
how we could in principle recognize such conditions when we encounter
them?12
Hardin’s view is that the very notion of meeting that challenge is absurd. And though
color science has advanced since Berkeley’s time, his own examples of PR (above)
convinces Hylas, that . . .” there is no such thing as color really inhering in external
bodies . . .” 13 Of course that still allows, as Stoneham and Hardin note, a viable notion
11
Tom Stoneham ***(reference?)
12
Hardin, JP, 194. Here is a partial list of reasons for denying inherent color to bodies.
Things appear differently colored depending on background color. The existence of
“metameric failure.” For example, (1) color samples seen to match in one light source
fail to match in another. (2) Samples match in color when viewed from one angle, but
fail to match when viewed from another. (3) Color vision for physiological reasons
varies among observers even under “normal conditions.” Therefore two observers
under identical lighting conditions have different color sensations. And obviously socalled typical conditions, like viewing in daylight (or “north day-light”) can’t apply to
judging the colors of stars, or the moon. Though far from being an expert I am
convinced that “ecumenism” (Jonathan Cohen) is correct, that a given object may
possess at a given time an infinite number of colors though each is indexed to a
particular set of circumstances, and that the difference between “real” and “apparent”
color is ultimately conventional.
13
It’s interesting that Berkeley puts in the mouth of Hylas an extra argument against
the claim that “outward objects” are colored; it would require action at a distance to
of “typical” viewing conditions, where “typical,” as opposed to some uses of
“normal,” is thoroughly pragmatic.
What doesn’t follow is color eliminativism, or, alternatively SMD. Berkeley of
course is not ultimately a color eliminativist. There are no colors on “outward
objects” since he thinks ultimately there are no “outward (mind-independent) objects.”
But that conclusion comes later in the Dialogues supported in part by the claim, based
on PR examples, that colors are SMD. 14
Yet we suggest for Hylas another option exists, a perspectivalist, relativist or
relationalist view of color perception.15 Jonathan Cohen outlines relationalism. as
follows:
What the relationalist proposes, then, is that colors
are not (as the physicalist maintains) subject- and
condition-independent properties of their bearers,
but relational properties that are constituted in terms
perceive them. Therefore Hylas proposes that [“light and colors ”] “in themselves are
the motions and configurations of certain insensible particles of matter.” (TD 11
Turbayne, 126. This opens Hylas to analogous semantic objections to identifying
sounds with sound waves.
14
Again, in PHK establishing SMD for sensible qualities doesn’t depend on PR
examples. See Barry Stroud, “Locke v Berkeley on Primary Qualities,” Philosophy 55,
(1980) for a good discussion.
15
Such theories have been around for a while; recently as a response to Hardin’s
eliminativism. For example, Jonathan Cohen, “it’s Not Easy Being Green: Hardin and
Color Relationalism,” In Jonathan Cohen & Mohan Matthen (eds.), Color Ontology
and Color Science. Boston, MIT Press, 2010. Cohen develops the position in The Red
and the Real, (op. cit.) and as mentioned contrasts relationalism with relativism though
I don’t discuss the distinction.
of relations to subjects and viewing conditions. . .
This view does justice to the facts about perceptual variation,
and it does so without requiring either unmotivated
choices between variants or unjustified optimism
that there is some unknown (or unknowable) fact that
could motivate such a choice. 16
A radical relativism (or relationalism) presumably could associate every
sighted being in a specific set of environmental and internal conditions with what
colors she sees in those conditions. Certainly impractical, but the thought again is
material objects do have colors, but always indexed to some set of perceptual
conditions. What’s required is a pragmatic definition of normal (or better typical)
conditions specifiable without begging the question. 17 We would rule out varieties of
red-green color-blindness, for example. 18 But (following Hardin) there are evidently
However, like relativism relationalism expresses the view that notions of normal
viewers and standard viewing conditions are conventional.
17
For a good discussion along these lines, see Margaret Atherton, “How Berkeley Can
Maintain That Snow is White?” Philosophy and Phenomenological Research, Vol.
67, No. 1 (Jul., 2003), pp. 101-113, Atherton writes: Berkeley [gives] us a method for
determining the true colors of things: they are not the ones we constantly and
unchangingly perceive, rather they are the ones that vary in a regular and predictable
manner. The true color of an object should not be conceptualized as something that
exists permanently like a Munsell chip, rather the true color of an object is in point of
fact a family of colors, each of which can be reliably anticipated in appropriate
circumstances. The snow that is brilliant white against a black background can be
reliably anticipated to be yellowish under an incandescent light bulb and purply at
twilight.” (Atherton p. ***)
18
For example, the condition called “protanomaly” “[In this condition people] are
less able to discriminate colors, and they do not see mixed lights as having the same
cases where two subjects, both considered statistically “normal”, but one a statistical
outlier, disagree whether two green patches are hue-identical. 19 Here again we
relativize perceived color to majority and minority normal perceivers. We might, for
instance, be interested in genetic and/or neurological differences in majority and
minority normals. What is important again is that relativizing color ascriptions permits
saying, against either eliminativists, or those who think colors are SMD, that outward
objects have color. Hylas could, in principle, have taken this option I think while
accepting that PR examples show no fact of the matter about an object’s inherent
color.
2. PR and Shape
PR examples about color convince Hylas that, as he says, all colors are “equally
apparent; and that there is no such thing as color really inhering in external bodies, . . .
(TD1 186) 20 Philonous notes that comparable PR examples can given for perceived
shape, or any of the qualities Hylas calls “primary.” qualities, those some
“philosophers” hold “really exist in bodies.” Though accepting that SMD applies to
colors, Hylas mentions what he takes to be the current (“philosophers”) view, that so-
colors as normal observers. They also suffer from a darkening of the red end of the
spectrum.” Encyclopedia of Philosophy (Fall 2008 Edition).
19
For details see Hardin, Color For Philosophers, 76-83. Summarizing his discussion
Hardin contends that the choice of unique green is a practical matter.
20
Hylas in this passage then suggests colors are “altogether in the light,” a suggestion
that suffers the same semantic objection Philonous made to identifying sounds with
sound waves.
called primary qualities (“extension, figure, solidity, gravity, motion, and rest,”) are
held to “exist really in bodies.” He adds that he’s “thoroughly convinced of its truth.”
(Works II 187-188) But after Berkeley offers some PR cases, particularly about shape
and motion, Hylas, rightly or wrongly accepts that shape like color is SMD, though
reserving the right to later change his mind. 21
My interest, however, is when the discussion later turns toward whether, as Hylas
suggests, a distinction can be made between “ absolute and sensible extension,” the
latter which Hylas (under some pressure) is willing to call “extension in general or
motion in general.” When Philonous expresses astonishment about whether one can
“frame” an abstract idea of extension sans any sensible quality, Hylas remarks:
What! Is it not an easy matter, to consider extension and
motion by
themselves, abstracted from all other sensible qualities? Pray how do the
mathematicians treat of them?
Philonous’s response echoes one Berkeley makes in his The Introduction to The
Principles of Human Knowledge (PHKI), Geometers, for example, can pay attention
or selectively attend to the linearity of a polygon’s line segments for the purposes of
proof, ignoring its other properties. Berkeley writes:
Thus, when I demonstrate any proposition concerning triangles
it is to be supposed that I have in view the universal idea of a triangle,
which ought not to be understood as if I can frame an idea which
was neither equilateral nor scaleon, nor equicrural, but only that
21
Controversies exist about Philonous’s examples but I choose to take the discussion
in another direction. Moreover, we should think of Philonous’s argument here as a
conditional: if Hylas thinks PR examples show that colors are SMD, then he should
think from analogous examples, that perceived shapes are SMD.
the particular triangle I consider, whether of this or that sort it matters
not, does equally stand for and represent all rectilinear triangles
whatsoever, and is in that sense universal. All of which seems very
plain and not to include any difficulty in it. (my emphasis,
(PHK I Works II, sec 15, 33-34)
This he takes to be legitimate abstraction. It doesn’t follow that mathematicians or
anyone can frame an idea of extension (or motion) in general.
22
I propose to contrast Philonous’s answer with an alternative, and argue for the
following. (1) A distinction, Berkeley would have accepted, should be made between
abstraction as selective attention and idealization. Idealizations, borrowing a phrase
from Michael Weisberg, are “intentional fictions;” Neither sensible objects nor
Platonic forms23 they are rather a certain way of treating sensible objects. Conceiving
primary qualities as idealizations. I argue below, dissolves certain issues Berkeley
raises; for example, whether particular shapes can be conceived apart from sensible
qualities, or how sensible ideas can resemble objects in principle unperceivable.
The reason to treat primary qualities—I’ll mostly consider shape—as
idealizations, concerns their role in explanations. Following Michael Jacovides, I list
some salient characteristics of primary qualities he finds in Boyle and Locke.
1. Primary qualities are explanatory; secondary qualities are not deeply
explanatory.
2. Ideas of primary qualities resemble something in bodies; ideas of secondary
22
The example, which I think misplaced, occurs in a discussion of how in a world of
particulars language can have general terms.
23
“Three Kinds of Idealizations,” The Journal of Philosophy, Vol. CIV, number 12,
(2007), 639.
qualities do not.
3. Primary qualities are not dispositions; secondary qualities are dispositions to
produce ideas in us.
4. The genera of primary qualities are inseparable from bodies; the genera of
secondary qualities are separable.
5. Primary qualities belong to bodies as they are in themselves; secondary
qualities do not. 24
For my purposes 1, and 4, are crucial in understanding what makes a quality primary.
Put simply, the inseparable properties of bodies—those they must possess to be
material bodies—allegedly at bottom explain all other phenomena both mechanical
and mental. Boyle writes:
Whether these accidents may not be conveniently enough be
called the moods or primary affections of bodies to distinguish
them from those less simple qualities (as colors tastes and odors)
that belong to bodies upon their account, or whether, with the
Epicureans, they may not be called the conjuncts of the smallest parts
of matter I shall not now stay to consider . . .25 (my italics).
We should at this point distinguish two types of mechanical explanation, (1)
Mechanical explanations of physical phenomena, particularly motion, (e.g., Galileo,
Newton), and (2) Explanatory projects that ultimately aim to explain everything,
24
Michael Jacovides, “Locke’s Distinctions between Primary and Secondary
Qualities,” in Lex Newman ed. The Cambridge Companion to Locke’s Essay
Concerning Human Understanding, (Cambridge, Cambridge University Press, 2007).
25
Robert Boyle, “The Origins and Forms of Qualities According to the Corpuscular
Philosophy,” (1666, Oxford), in Selected Papers, ed., M. A. Stewart, (Indianapolis,
Hackett, 1991), 21.
including mental phenomena, in terms of invisible corpuscles or atoms. (e.g., Galileo,
[in the Assayer] Boyle, perhaps Locke, 26 Gassendi.) The first type interests me
somewhat more in assessing Berkeley’s discussion of primary qualities in TD1 since
had no quarrel with the mathematical explanations of motion by, say, Galileo or
Newton. 27
In Galileo’s, Two New Sciences, discussing inclined plane experiments for
determining the law of free-fall, Sagredo, an interlocutor, remarks on the proposed
“postulate” that whatever a plane’s inclination, the moving ball’s degree of speed
[velocity] depends only on vertical distance from the ground, He notes the assumption
that “the planes are quite solid and smooth, and that the movable is of a perfectly
26
Michael Ayers in his paper, “Primary and Secondary Qualities in Locke’s Essay,”
(Primary and Secondary Qualities, ed. Nolan, 139-40) contends that Locke can be
seen as making a reasonable distinction between primary and secondary qualities that
doesn’t simply articulate the corpuscular program. Ayers notes about the perceived
non-minded world that: "Round things normally and understandably roll as square
things do not.” See Primary and Secondary Qualities, ed. L. Nolan, (Oxford, Oxford
University Press, 2011), 139-40. Fundamentally the same point is made by Edwin
Mann, “Locke’s Distinction between Primary Primary Qualities and Secondary
Primary Qualities,” in Primary and Secondary Qualities, ed. Nolan, op. cit., 158-189.
But even here, I suggest, ordinary working folk in the seventeenth century,
(carpenters, surveyors) would certainly use the idealizations of Euclidean geometry.
And there remains the problem of explaining apparent action at a distance, (gravity
magnetism etc).
27
Although Berkeley allows the use of the term “cause” in such explanations, the term
doesn’t refer to efficient causes. Only volitions, he consistently claims, can be strict or
efficient causes.
round shape.”28 Onora O’Neil about a different subject well expresses the difference
between abstraction (as Berkeley conceives it PHKI) and idealization.
Abstraction, taken straightforwardly, is a matter of bracketing,
but not denying, predicates that are true of the matter under
discussion. . . Idealization is another matter: it can easily lead to falsehood.
An assumption, and derivatively a theory, idealizes when it ascribes
predicates often seen as enhanced, ‘ideal’ predicates that are false
of the case in hand, and so denies predicates that are true of that case. 29
“Galilean idealizations” 30 play an important role in a number of
mathematically expressed natural laws, e.g., the law of free fall, or Newton’s law of
28
Galileo, Galilei, Two New Sciences, (1638), trans. Stillman Drake, (Madison,
University of Wisconsin Press, 1974), 162). See also Ernan McMullin, “Galilean
Idealization,” in Studies in the History and Philosophy of Science, 16, 3, (1985), 247273.
Another example making use of Galilean idealization is Another well known example
of the use of idealization in physics is in Boyle’s Gas Law: “Given any x and any y,
if all the molecules in y are perfectly elastic and spherical, possess equal
masses and volumes, have negligible size, and exert no forces on one another
except during collisions, then if x is a gas and y is a given mass of x which is
trapped in a vessel of variable size and the temperature of y is kept constant,
then any decrease of the volume of y increases the pressure of y proportionally,
and vice versa.” [Wikepedia]
29
Onora O’Neill, Towards Justice and Virtue, (Cambridge, Cambridge University
Press, ( 1996), 40-41.
30
The term is Ernan McMullins’. See the discussion in Andrew Wayne, “Expanding
the Scope of Explanatory Idealization,” Proceedings of the Philosophy of Science
Association, Vol. 78, No. 5, Part I, 830-842.
gravity. 31 They allow the application of Euclidean geometry to mechanical problems,
a point about which Berkeley was certainly cognizant. Here are three passages from
his treatise on mechanics, De Motu (DM) [1721, somewhat revised 1752, Luce and
Jessop Vol. IV.]
Mechanical Principles and universal laws of motions
or of nature, happily discoveries of the last century, treated
and applied by the aid of geometry, have shown a remarkable
light upon philosophy.” (DM 41).
In physics sense and experience which reach only to apparent effects
holds sway; in mechanics the abstract notions of mathematicians
are admitted. In first philosophy or metaphysics we are concerned with
incorporeal things, with causes truth and the existence of things. (DM 71,
my italics.) 32
In Dm 39 he writes:
And just as geometers for the sake of their art make use of many
devices which they themselves cannot describe nor find in the
nature of things, even so the mechanician makes use of certain
abstract and general terms, imagining in bodies force, action,
31
Galilean idealizations are thought of as limiting cases; although we don’t have
perfect vacuums, frictionless surfaces, or perfect spheres we think of such states as
limits we approximate to by eliminating “material hindrances” (Wayne, 832). Not all
idealizations in physics have this character.
32
Berkeley is discussing collision phenomena. He contends the debate about whether
motion in one object ceases, and another begins “de novo “ in the second, or the
numerically same motion maintains itself throughout, is spurious.
attraction, solicitation, etc. which are of first utility for theories and
formulations, as also for computations about motion, even if in the
truth of things, and in bodies actually existing, they would be looked
for in vain, just like geometers’ fictions made by mathematical
abstraction. (my italics)
It’s not entirely clear what Berkeley means by “mathematical abstraction ” but
I suggest that the best interpretation is “idealization.” treating planetary orbits as
ellipses is a simple example. 33 Idealization for Berkeley then is a legitimate form of
abstraction, but distinct from abstraction as selective attention. In the latter one pays
attention, for generalizing purposes, to a real property of an object and ignoring others,
attending, for example, to just the shape of a triangle, the color of a ball, or the
humanity of Peter.
It’s likely an exaggeration to say that all early modern philosophers have as a
conceptual requirement for primary qualities that they function in mathematical
explanations.34 But that way of conceiving them has some attraction since an obvious
question is why perceived shape has more primaryness than color or taste? With
respect to sensible shape, as Berkeley and others noted, PR examples apply to them as
33
Another possibility is that he’s thinking of Euclidean figures themselves as
abstractions.
34
This point is made by Antonia LoLordo in “Gassendi and the Seventeenth-Century
Atomists on Primary and Secondary Qualities.” Primary and Secondary Qualities; the
Historical and Ongoing Debate, ed. Lawrence Nolan, (Oxford, Oxford University
Press, 2011), 63, fn 5.
to colors. A plausible, and at least partial answer for the primacy of shape is that
shape, as idealized, not color, plays a fundamental explanatory role in
Galilean/Newtonian accounts of motion, and (at least as a research project) in
explanation of all physical phenomena in terms of atoms or corpuscles.
In any event at the point in Dialogue1 after Hylas notes about “absolute
extension” that mathematicians treat of extension sans sensible qualities, he might
have gone on as follows.
(H) “Shape, for example, a Euclidean circle or sphere, is an idealization of
sensible objects, but not itself a sensible object. It’s meaningless to ask for its color,
taste, smell, or tactile qualities. A Euclidean circle obviously has shape. After all, it’s
a circle, but that shape is stipulated—a matter of convention—not observed. In fact,
your own view, Philonous/Berkeley, of sensible extension implies that a Euclidean
sphere can’t exist since its circumference and diameter are incommensurable. And as
for frictionless planes or perfect spheres how would you know you’ve discovered them
without making use of the very law of free-fall you’re trying to establish.”
There’s nothing in this line of thought that should worry Philonous. In
Berkeley’s own reading of mathematical tracts on optics, astronomy and whatever
version of Euclid he studied 35 he would treat postulates and theorems as about
35
For an account of Euclid translations in the period see Stefan Storrie (forthcoming
2012). (I thank him for email discussion). Storrie speculates that Berkeley might have
been influenced by Isaac Barrow’s view that Euclidean objects, right lines, circles, etc.
can be constructed by “generative motion” (p. 24) But, as Storrie notes, Isaac Barrow
claims that no sensible line or circle is guaranteed to be Euclidean. Barrow in fact
writes: “But for the line to be “perfectly right‟ we must conceive of the sensible right
idealized diagrams, rather than about the drawn figures. Idealization in this case means
stipulating the diagrams meet the Euclidean postulates, for example that there can’t be
a two-sided polygon.
I mentioned above that idealizing perceived shapes for mathematical treatment
solves some problems Philonous raises in TD1. One was whether sensible extension
must always have some sensory properties, visual, tactile etc. If so, Hylas has a
difficulty, since having already accepted that color is SMD, he seems committed to
saying the same about shape. But he might have suggested that the notion that
idealized shapes possess sensible qualities is meaningless.
Moreover, we no longer have the so-called “resemblance” problem; i.e., how
can ideas of sense resemble anything not in principle perceivable? However,
Euclidean circles obviously resemble perceived circles. Apropos here is the following
selection from a dialogue of Leibniz between A (presumably Leibniz), and an
interlocutor B, about geometric constructions. B notes the importance of
“contemplating constructed figures accurately.”
A: True, but we must recognize that these figures must also be regarded
as characters, [symbols] for the circle described on paper is not a true circle
and need not be; it is enough that we take it for a circle.
B: Nevertheless it has a certain similarity to the circle, and this is surely not
arbitrary.
line as having no „roughness‟ or „exorbitances‟ by an act of reason rather than sense.
In this way geometrical objects are not sensible but objects of reason” The Usefulness
of Mathematical Learning Explained and Demonstrated, (1683) tr. Kirkby, (London,
1734), 75.
A: Granted; therefore figures are the most useful of characters. 36 (my italics)
Galilean idealizations are introduced to permit mathematical treatment. The
laws of motion require idealizations of both objects and conditions. They are limiting
cases that often can’t exist in principle. (e.g., absolute zero, a perfect vacuum,
Newton’s point masses, etc.) Explanations making use of Galilean idealizations are
strictly false, since they don’t precisely predict the phenomena. 37 But as Leibniz noted
these idealizations resemble sensible objects.
What about the project of causally explaining at least all mechanical
phenomena (leaving out now mental phenomena) in terms of atoms or corpuscles?
Here as well, idealized objects, for example, in the kinetic theory of gasses, were often
involved.38 I note in passing that the question whether the molecules postulated by the
theory exist at all is distinct 39 from the question whether they exist as Galilean
idealizations, point masses undergoing perfectly elastic collisions. The answer to that
36
Leibniz, “Dialogue on the Connection between Things and Words” (August, 1677),
in Philosophic Papers and Letters, Vol. 2, Ed. Leroy E. Loemker, (Chicago, Chicago
University Press, 1969), 184.
37
Nancy Cartwright, in How the Laws of Physics Lie, (Clarendon Press, 1999),
develops the theme that idealizations make explanations in physics, though useful,
strictly false.
38
Boyle (1662) and others discovered the law named after him, that the pressure and
volume of a gas were inversely proportional at a fixed temperature; The law was
derived later from the a theory which presupposed molecules (considered as point
masses) moving randomly in a closed container.
39
Issues about the existence of theoretical entities, exemplified by the kinetic theory
of gasses, produced a large (and continuing) literature I fortunately needn’t discuss.
clearly is ‘no.’ However, as limiting cases, they certainly resemble members of the
sequence of cases they limit.
In “The Excellency of the Mechanical Hypothesis,” Boyle, in recommending
“the Corpuscular Principles, ” writes in part:
For a figure of the portion of matter may either be one of the five regular solids
treated of by geometricians, or some determinate species of solid figures.
As that of a cone, cylinder, &c., [also irregular shapes] . . . And as the figure
so the motion of one of these particulars . . . as (besides straight) circular,
elliptical, parabolical, hyperbolical, and I know not how many others . . .
(Boyle’s italics). 40
Again, Berkeley wouldn’t countenance the actual existence of a Euclidean
regular solid, or perfectly elliptical motion. But as Leibniz noted their actual existence
doesn’t matter. These are Galilean idealizations, limiting cases, ultimately useful in a
mathematized mechanics. Perceptual relativity examples are obviously irrelevant to
whether they are mind-dependent.
40
Boyle, Selected Philosophical Papers, 141.