“Plato’s First Principles.” In Apostolos Pierris (ed.), Aristotle's Criticisms of Plato: The Metaphysical Question. Patras, Greece: Institute for Philosophical Research, 2004. 155–76.

Plato’s First Principles

Mary Louise Gill

Brown University

June 24, 2002

In Metaphysics A.6 Aristotle outlines the main features

of Plato’s metaphysics and includes a puzzling report about

his first principles, the One and the Indefinite Dyad (which

he also calls the Great and the Small). According to

Aristotle, Plato agreed with the Heracliteans that

perceptible things are always in flux and that there is no

knowledge of them (1). He says that Plato took over from

Socrates a search for definitions but unlike Socrates he

thought that definitions applied not to perceptible things

but to Forms (2), which are separate from the perceptible

things (3). Perceptible things are called after the Forms

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and are what they are by participation in Forms, but

Aristotle objects that Plato did not make clear precisely

what participation is (4). In addition to Forms and

perceptible things, Plato posited mathematical objects,

which differ from the perceptible things in being eternal

and unchanging, and from the Forms in being many of the same

kind (5). Because Forms are causes of other things (6),

Plato thought the elements of Forms are the elements of all

things (7). In sum, Plato posited only two of Aristotle’s

four causes (15). As matter, he posited the Great and the

Small as principles (8), and as formal cause (what-it-is or

substantial being), he posited the One (9). Forms are the

formal causes of other things, and the One is the formal

cause of Forms (16). The Dyad of the Great and the Small is

the subject for Forms in the case of perceptible things, and

the subject for the One in the case of Forms (17). Plato

assigned the cause of the good and the bad to each of his

two principles, one to each (18).

Although some statements in this report can be fairly

easily matched to views expressed in Plato’s dialogues, the

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claims about the first principles have been a source of

notorious difficulty and controversy. Why does Aristotle

not credit Plato with discovering his efficient and final

causes? In the fourfold division of kinds in the Philebus,

which certainly seems relevant to Aristotle’s report, Plato

distinguishes not only the limit (pe/rav) and the unlimited

(a1peiron) and their mixture, but also the cause of the

mixture, which is also responsible for its goodness.

Aristotle speaks often of the Timaeus, but Metaphysics A.6

appears to ignore it. Like the Philebus, the Timaeus posits

efficient and final causes: A divine craftsman orders the

cosmos by appeal to good and eternal models, which he copies

as far as possible into recalcitrant materials. Reflection

on the Timaeus invites a further question: Why in Metaphysics

A.6 does Aristotle not mention Plato’s Receptacle, which

plays such a prominent role in the Timaean account of the

composition of the perceptible world? Certainly Aristotle

mentions the Receptacle elsewhere, and once in a tantalizing

passage in Physics IV.2, where he complains that what Plato

said about the participant in the Timaeus and in his

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“unwritten doctrines” was different (209b5-17).1 The

discrepancies between Aristotle’s report and the theories

expressed in Plato’s dialogues have led some scholars to

suppose that Aristotle misunderstood or even knowingly

misrepresented Plato’s views (e.g., Robin, Cherniss).

Others have supposed that Aristotle recounts theories that

Plato expressed to his students in conversation or in his

lecture(s) On the Good but did not write down (Tübingen

School).

In his book, Plato’s Late Ontology, Kenneth Sayre has argued

that the account of first principles that Aristotle

attributes to Plato can be largely reconstructed from

Plato’s later dialogues, and in particular from two passages

that invoke pe/rav (limit) and a1peiron (unlimited) in the

Philebus. I endorse Sayre’s project and accept many of his

main conclusions. At the same time, I cannot agree with

Sayre that the late dialogues give up the separation of

Forms. Although separate Forms are not explicitly mentioned

in the Sophist, the Statesman, or the Philebus, separate Forms

1 Cf. 209b33-210a2; cf. GC II.1, 329a13-24.

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figure prominently in the Timaeus. Sayre follows G.E.L.

Owen in dating the Timaeus after the Republic but before the

Parmenides and the late dialogues, but I am not persuaded

that the Timaeus can have been written so early. Besides

the need to re-date the Timaeus, there remains Aristotle’s

testimony that a major problem with Plato’s theory was his

separation of Forms. Can Aristotle have been so seriously

wrong or unfair about this aspect of Plato’s late theory,

if, as Sayre believes, he got so much else right?

In this paper I shall argue that Aristotle’s account of

Plato’s first principles in Metaphysics A.6 can be traced to

the second part of the Parmenides. There Plato, using

Parmenides as his main speaker, examines in elaborate detail

the One and its relations to the so-called Others.

Parmenides discusses what the One and the Others are in

themselves and what they are in relation to each other. The

identity of the Others is never made plain, except that they

are other than the One. This indefiniteness is exactly what

we should expect if I am right that the Others, viewed apart

from the One, are what Aristotle calls the Indefinite Dyad.

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Plato mentions neither an efficient cause nor a final cause

in the Parmenides. This omission lends support to my

suggestion that the Parmenides is the main source for

Aristotle’s report in Metaphysics A.6.

It seems to me likely that the Timaeus was written as a

response to objections raised in the first part of the

Parmenides.2 In any case, the metaphysics of the Timaeus goes

unmentioned in Aristotle’s report in Metaphysics A.6.3 I

shall argue that Plato introduced the Receptacle as a third

principle in the Timaeus to vindicate the pattern-copy model

of participation, which came to grief in the first part of

the Parmenides. My paper will largely ignore Aristotle’s

report about Platonic numbers. I suspect that numbers are

2 Many other scholars have made this suggestion, e.g., Sarah Waterlow (Broadie), “The Third Man’s Contribution to Plato’s Paradigmatism.” Mind91 (1982), 339-57; R. Patterson, Image and Reality in Plato’s Metaphysics (Indianapolis, 1985); W. J. Prior, Unity and Development in Plato’s Metaphysics (London, 1985).3 Perhaps it is even possible that the Timaeus was composed after Metaphysics A.6, though nothing in my argument depends on this conjecture. Werner Jaeger argued that Metaphysics A was early, because Aristotle used the first person plural “we” in “we Platonists” in A.9, as though he still regarded himself as a member of the Academy, whereas he used the third person in Met. M (notably the discussion of Plato’s first principles is not included in M). But of course Jaeger also thought that Met. A was written after the death of Plato (because Aristotle used the imperfect in A.9 in referring to what Plato used to say). See Werner Jaeger, Aristotle: Fundamentals of the History of his Development. Trans. by R. Robinson. 2nd ed. (Oxford, 1934), 171-76.

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important for the differentiation of Forms, and that the

generation of numbers in the second deduction of the

Parmenides may be relevant to that. But I leave this issue

aside. My focus will be the first principles themselves and

the composition of the simplest determinate objects in the

perceptible realm.

The One and the Others

Recall that in the first part of the Parmenides Plato

has Socrates, as a youth, set out a theory of Forms

reminiscent of the treatment of Forms in such middle period

dialogues as the Phaedo and the Republic. According to

Socrates (128e-130a), perceptible objects can have opposite

characters at the same time, because they partake of the

corresponding opposite Forms. For instance, Socrates is

like Simmias in some respects and unlike him in other

respects. Socrates has these opposite features, likeness

and unlikeness, because he partakes of the Forms of Likeness

and Unlikeness. Furthermore, he is both one and many,

because he partakes of the Forms of Oneness and Multitude.

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Parmenides listens patiently to Socrates’ speech and then

asks him a series of penetrating questions. What Forms are

there? What are Socrates’ reasons for positing Forms in

some cases and not others? Are they good reasons? What is

participation, the relation between perceptible objects and

Forms? Can many perceptible objects participate in some one

Form and that Form still be one? If there are many

participants whose character the Form explains, why isn’t

the Form divisible into as many parts as it has participants

or duplicated ad infinitum? Socrates proves unable to

rescue his theory, and by the end of the interrogation we

wonder whether the theory itself should be abandoned. But

Parmenides surprises us by saying that, despite all the

difficulties that have just been discussed and a host of

others besides, there must be Forms. Otherwise we won’t

have anywhere to turn our thought and will destroy the power

of dialectic entirely (135b5-c3). The question, then, is

what to do about philosophy while these difficulties remain

unresolved. Socrates, now confused, has no suggestion to

offer.

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That, says Parmenides, is because he has posited Forms

too soon, before he has been properly trained. The second

part of the Parmenides presents a dialectical exercise of the

sort Parmenides is recommending. It consists of eight

deductions, plus an appendix to the first and second

deductions. Four deductions start from the positive

hypothesis that One is, and four start from the negative

hypothesis that One is not. Within the two groups of four,

two deductions in each foursome consider consequences for

the One, and two consider consequences for the Others. Of

each pair of deductions that consider consequences for the

same subject, one deduction reaches positive conclusions,

the other negative conclusions, about it (or them). The

conclusions of paired deductions conflict with each other.

So, for example, the first and second deductions examine

consequences for the One, on the hypothesis that One is, and

the first deduction reaches negative conclusions, the second

deduction positive conclusions, about it. The third and

fourth deductions again start from the positive hypothesis

that One is but examine consequences for the Others. The

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third deduction reaches positive conclusions about them, and

the fourth deduction reaches negative conclusions. Again

their conclusions conflict with each other.

Deduction 3 is the most constructive section in the

whole of Part II, because it integrates the approaches of

Deductions 1 and 2. Deduction 1 considered what the One is

solely in virtue of itself (kaq 0 au9to/)—i.e., in virtue of

its oneness—and argued that, so strictly considered, the One

is nothing at all, not even one. The One failed even to be

one, because to be one it would have to partake of Being to

connect it to its character. Deduction 2 then considered

what the One is in relation to other things (pro\v a1lla),

giving no special priority to what the One is in virtue of

itself. Examined in this way, the One wouldn’t stay put but

was shown to be everything indescriminately. Many of its

features excluded one another. These two deductions

together reveal that neither approach can succeed on its

own. The two approaches need to be integrated, so that a

thing’s relations to other things are limited by what the

thing is in its own right.

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Deduction 3 adopts this constructive strategy but turns

its focus from the One to the Others. It considers both

what the Others are in relation to the One (pro\v to\ e3n)

and what they are in virtue of themselves (au0ta\ kaq 0

au9ta/). Parmenides argues that the Others are distinct

from the One but nonetheless stand in some relation to it, a

relation he calls participation (157b-c). He proposes that

they partake of the One by being wholes and that they are

distinct from the One by having parts. Although nothing is

explicitly said about the nature of the One, Parmenide’s

statement suggests that the One itself is altogether one,

despite its many participants.4

What does participation in the One contribute to the

Others? In Deduction 3 Parmenides claims three fundamental

roles for the One. First, participation in the One makes

4 Apparently the One is not multiplied by having instance-parts (things that have a share of it). Deduction 3 ignores the idea dveloped in the Whole-Part Dilemma in Part I and in the second argument for unlimited multitude in Deduction 2 (143a-144e), that the One itself is many by having many participants. This consideration will be reintroduced in Deduction 4, with the outcome that nothing can partake of the One. Deduction 3 reaches its positive results by ignoring the problem. The solution to this problem is a proposal that was brought to grief in the Likeness Regress in Part I but is resuscitated in the Timaeus: Forms areparadigms and participation is being a likeness of.

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the others wholes, whose parts can be viewed all together as

a collection (157c8-d7).5 The One seems not to contribute to

the Others an additional determinate feature on a par with

the other features they have. Instead, the One determines

something about that entity’s features, converting them into

a whole collection that can be viewed all together. Second,

participation in the One makes each part an individual—a

singular entity that is something by itself (kaq 0 au0to\

o1n) (157e5-158a3). Again there is no indication that the

One contributes some determinate property to the participant

on a par with the participant’s own feature(s). Instead the

One simply marks off that entity from other things, so that

the entity’s own character can be discriminated from others.

Third, the One is said to limit the parts in relation to one

another (pro\v a1llhla) and in relation to the whole (pro\v

to\ o3lon), and the whole in relation to the parts (158c7-

d2). Parmenides’ claim prefigures Aristotle’s own words in

Metaphysics Z.17. Parmenides says that through the communion

of the Others with the One something different (e3tero/n ti)

5 The argument is difficult. I have offered an analysis of it in my Introduction, Plato: Parmenides (Hackett, 1996), 87-89.

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comes to be in them, which affords a limit in relation to

one another. Aristotle illustrates the idea with the

syllable “ba.” The syllable “ba” is not the letters B and A

plus another element. The syllable “ba” is B and A plus

something different, a principle that orders the parts in

relation to each other and thereby differentiates the

syllable “ba” from the syllable “ab” (1041b11-33).

According to this brief summary of Deduction 3, the One

performs three operations. It makes individuals

discriminable as the individuals they are; it enables a

plurality of individuals to be considered, not merely one by

one, but together as a group; and it orders the parts in

relation to one another and in relation to the whole. This

third function suggests that the One is responsible for a

thing’s structural unity.

The Indefinite Dyad

A valuable clue to understanding Plato’s second

principle is Aristotle’s report in Met. N that the Great and

the Small are relatives (pro/v ti). Aristotle faults Plato

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for treating relatives as fundamental principles, because in

his own view relatives, far from being substances, are

posterior even to quality and quantity. A relative, he

says, is a certain affection (pa/qov) of quantity, and not

matter (1088a21-24). Independent reports of Plato’s lecture

On the Good suggest that Plato classed what is kaq 0 au9to/

(“in itself”) under the One and what is pro/v ti

(“relative”) under excess and defect and thence under the

Indefinite Dyad.6 Given these reports it is worth asking in

what sense Plato might have regarded the Indefinite Dyad as

something relative.

I suspect that Aristotle’s own doctrine of relatives is

a source of confusion in his own and later accounts of

Plato’s second principle. To understand Plato’s view, I

suggest that we start with Parmenides’ final objection to

Forms in the first part of the Parmenides. I call this final

objection the Separation Argument (133a-134e).7 At this

6 See Hermodorus’ report of Plato’s Lecture on the Good preserved by Simplicius, In Phys. 247,30-248,20, and the report in Sextus Empiricus, Ad Math. 247-80; see also Wilpert’s diagram.7 I discuss the whole of the Parmenides in more detail in my Introductionto the Hackett translation of Plato’s Parmenides, trans. by M. L. Gill and P. Ryan (Indianapolis, 1996).

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stage of the interrogation, Socrates has failed to explain

participation in a way that avoids Parmenides’ objections.

So Parmenides now proposes that perhaps there simply is no

relation between sensible particulars and Forms. Not only

do Forms exist apart from us, they are ontologically

independent of us, and we and things that belong to us are

ontologically independent of them. Contrary to Socrates’

theory, Forms do not explain the properties that perceptible

objects have.

Parmenides spells out his proposal by focusing on Forms

of relations, such as the Form of Mastership. He suggests

that Forms are determined as what they are in relation to

one another, and that things that belong to us, such as

mastership in us, are determined as what they are, not in

relation to the Forms, but in relation to other things that

belong to us. Human masters are what they are in relation

to human slaves, not in relation to Slavery itself (133d-

134a). Although the argument initially focuses on Forms of

relations (such as mastership) and of relational properties

(such as master), the argument is later extended to all

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Forms, including those that we would not normally think of

as relational—“the Beautiful itself, the Good, and all

things we take to be Ideas themselves” (134b14-c2). Sever

the causal link between Forms and perceptible objects, and

the realm of Forms is utterly separate from our visible

realm.

Socrates finds the argument alarming, since he takes it

to show that the gods can have no knowledge of us or power

to affect our realm, and this outcome offends his sense of

piety. But we the audience are bound to ask: What is so bad

about the situation here envisaged? If things in our realm

are determined as what they are in relation to other things

in our realm, and if we can know these things without

appealing to Forms, why bother with Forms? They seem

irrelevant to us and our concerns.

But on closer inspection the passage reveals that we

have lost something of importance, if there is no causal

connection between Forms and us. Parmenides says:

“Surely you would say that if in fact there is

knowledge—a kind itself—it is much more precise than is

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knowledge that belongs to us. And the same goes for

beauty and all the others.” (134c6-8)

Sever the causal link between Forms and us, and our

knowledge is not precise like that of the gods, and beauty

in us is fuzzy, not something precise. Everything in our

realm becomes somehow nebulous.

Imagine ourselves like the prisoners in Plato’s Cave

(Rep. VII, 514a-520d). Our legs and necks bound, we can see

only shadows dancing on the wall before us. We judge the

appearances by comparing them with one another. Our

judgments must be constantly modified, because the shadows

keep changing in relation to one another. Although the

prisoners’ situation is similar to ours as envisaged in the

Separation Argument in the Parmenides, there is one major

difference. For the prisoners, the shadows are cast by

puppets being carried along the road in the firelight behind

them. The prisoners can be released from chains and turn

their vision away from the shadows to observe the puppets

themselves in the light of the fire. They can then make

their way out of the Cave and ultimately behold the Forms in

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the light of the Form of the Good. For them there is the

possibility of returning to the Cave and observing the

shadows once more but now in the light of what they have

learned. So for them there is the possibility of knowing

the shadows and what they are shadows of (520c3-6). For us

there is no such possibility. If the Forms have no relation

to us, our world is simply the shadows in motion, always

reconfiguring themselves in relation to one another. There

is nothing that the shadows are shadows of. Such a world is

utterly unstable—in fact more precarious than we might

initially think.

This unstable world is described three times in Part II

of the Parmenides, and each version is more radical than the

previous one: twice there is a world, but we can can get no

adequate grip on it; finally there is no world at all. The

descriptions of this strange world are so abstract that they

can as easily apply to a perceptible world that has no

relation to Forms, and to a world of Forms that has no

relation to the One. The arguments are cast in terms of the

One and the Others. Deduction 4 (154b-160b) describes a

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situation resembling that in the final argument in Part I:

We are asked to imagine a situation in which the One exists

but has no relation to other things. The One and the Others

are separate from each other both in the sense that they

exist apart and in the sense that they are ontologically

independent. According to the fourth deduction, since other

things do not partake of the One, they cannot partake of any

other character either. Deduction 4 argues that the Others

have no determinate features if they do not participate in

the One, but it leaves one possibility open. Perhaps the

others have features determined in relation to one another,

like the shadows in Plato’s Cave. This possibility is

explored in Deduction 7.

Deduction 7 (164b-165e) asks us to imagine what other

things would be like if there were no One. Parmenides

describes a world that exhibits vivid appearances, and those

appearances seem to permit identification and

differentiation in relation to one another. Parmenides says

that if the Others are other, they must be other than

something. Since they cannot be other than the One, if One

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is not, they must be other than one another (164c). He then

says:

“So they are each other than one another as multitudes

(plh/qh), for they couldn’t be so as ones, if One is

not. But each mass (o1gkov) of them, as it seems, is

unlimited in multitude (a1peirov e0sti plh/qei), and if

you take what seems to be smallest, in an instant, just

as in a dream, instead of seeming to be one, it appears

many, and instead of very small, immense in relation to

the bits chopped up from it.”---“That’s quite

right.”---“The Others would be other than one another

as masses of this sort, if they are other, and if One

is not.”---“Quite so.” (164c7-d6)

This passage suggests that there are a few things the Others

are: they are other than one another, and they are unlimited

in multitude. Beyond that is sheer appearance—and the

appearance keeps changing and dissolving before our eyes.

In the end even the fleeting appearance has deceived

us. In the eighth and final deduction (165e-166c), the

appearance too has vanished. Parmenides concludes: “Then if

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we were to say, to sum up, ‘If the One is not, nothing is,’

wouldn’t we speak correctly?” His young interlocutor

Aristotle replies: “Absolutely.” (166b7-c2). Consider

Parmenides’ conclusion: “If the One is not, nothing is.”

Clearly the consequent of this conditional is false, for

there is a world to be explained. So the antecedent of the

conditional is false. But that antecedent is simply the

negative hypothesis that has governed the last four

deductions in the Parmenides. If the negative hypothesis is

false, then the positive hypothesis is true. There must be

a One, and other things must somehow partake of it. This, I

take it, is the implication of the overall argument of

Parmenides Part II. There must be Forms, or stable objects

of some sort, since there is a world to be explained.

Let us return once more to the constructive Third

Deduction. Here Parmenides announced that, stripped of

oneness, things that partake of it—whether they partake of

the oneness of parts or the oneness of wholes—are in

themselves unlimited in multitude (a1peiron plh/qei) (158b5-

7). Parmenides asks us to subtract in thought the very

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least we can from those multitudes. What is subtracted,

too, he says, is a multitude and not one, if in fact it

doesn’t partake of the One (158c2-4). He says:

“So always, as we examine in this way its nature,

itself by itself (au0th\n kaq 0 au9th/n), different

from the form, won’t as much as we ever see be

unlimited in multitude (a1peiron

plh/qei)?”---“Absolutely.” (158c5-7)

Considered by itself apart from the One, what participates

in the One, or in some one Form, is unlimited in multitude.

Portions of the multitude, as well as the multitude itself,

are likewise unlimited in multitude. We can talk about

Plato’s second principle in abstraction, but as Deduction 8

showed, the unlimited multitude cannot actually exist

without participating in the One. Plato’s two principles

operate together. The unlimited multitude is sheer

qualitative content, an undifferentiated manifold in

constant flux. The One is empty of qualitative content but

altogether one.

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If I am right that these are the two principles

mentioned in Aristotle’s report, they are together the

principles of Forms, and the second principle and Forms are

together the principles of perceptible things. Many

questions remain unanswered. In the realm of Forms, how can

Plato account for there being a plurality of qualitatively

distinct Forms? What differentiates the Form of Justice

from the Form of Human Being, if they are both composed of

the same ultimate principles? Perhaps the generation of the

numbers in the second deduction provides Plato with the

wherewithal to differentiate the Forms from one another.

Questions remain in the perceptible realm as well. Suppose

there are Forms. How can they explain our world? If Forms

explain our world, perceptible things must stand in some

relation to them. Plato calls the relation “participation,”

and interprets the notion in different ways in different

places. But the first part of the Parmenides canvassed the

possibilities and found fault with each alternative. That

was why, in the final argument in Part I, Parmenides

proposed that there simply is no relation between Forms and

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us. Until the problem of participation is solved, Plato

cannot explain the composition of the perceptible world.

This is one of the main issues confronted in the

Timaeus. Plato’s answer to the problem of participation is

the Receptacle.

The Receptacle

Before we leave the second part of the Parmenides, let

me call to your attention a striking omission in Deduction

4. Recall that in Deduction 4 Parmenides reaches negative

conclusions about the Others on the assumption that the One

is. He undermines the positive conclusions of Deduction 3

by arguing that the Others cannot partake of the One without

fragmenting it into many. If they did partake of the One,

it would fail to be altogether one, because it would have

many instance-parts, as in the Whole-Part Dilemma in Part I

(130e-131e). Since the One is altogether one, Parmenides

claims in Deduction 4 that the One and the Others are

utterly separate from each other, not only in the sense that

they exist apart but also in the sense, familiar from the

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Separation Argument in Part I, that they are ontologically

independent.

Why does young Aristotle fail to resist Parmenides’

claim about the One’s fragmentation in Deduction 4? Can’t

the Others participate in the One without fragmenting it

into many? Suppose that the One is a pattern (para/deigma)

and that the Others partake of it by being copies of it. On

this conception of participation, the Others can participate

in the One, while it exists apart from them and is

altogether one. This was one of the notions of participation

considered in Part I (in a section I call the Likeness

Regress, also known as the second version of the TMA,

132c12-d4). The reason why Aristotle fails to make this

obvious objection is precisely that this model of

participation was eliminated in Part I, on the grounds that

it gave rise to an infinite regress of Forms of the same

sort. So if he were to reintroduce that proposal in

Deduction 4, he would also have to show that there is a way

to keep the pattern-copy model of participation while

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avoiding an infinite regress. Young Aristotle is even less

equipped to make the defense than was Socrates.

The Timaeus returns to pattern-copy model of

participation. I believe that Plato thinks that he has a

way to preserve this model of participation that avoids the

Parmenides regress.

Recall the problem itself in the first part of the

Parmenides (132c-133a). Socrates proposed that Forms are

like patterns (paradei/gmata) set in nature, and that other

things resemble then and are likenesses (o9moio/mata).

Partaking of Forms, he said, is simply being modeled on

them. Socrates proposed that the relation between sensibles

and Forms is an asymmetrical relation, the relation of being

a likeness of. A portrait is a likeness of Simmias; Simmias is

not a likeness of it. Parmenides made trouble for Socrates’

proposal by arguing that the asymmetrical relation is based

on an underlying symmetrical relation, the relation of being

like. If a portrait of Simmias is like Simmias, Simmias is

like it. There are various ways to construe the details of

26

Parmenides’ argument which needn’t detain us here.8 The

basic issue is that the pattern and its copies share a

feature in common in virtue of which they are like. So both

pattern and copies participate in that property. Given the

model of participation that Socrates has proposed, both

pattern1 and its copies are now likenesses of pattern2.

Pattern2 then shares a feature in common with its

participants. So there must be a pattern3. And so the

regress proceeds.

The Timaeus takes a major step to halt the regress.

Plato does not give up the self-predication of Forms: the

pattern-copy model of participation entails self-

predication, because two things that are like must share a

feature in common. Nor does he give up the separation of

Forms, at least not in this work. Instead he halts the

regress by placing constraints on what it is to be an image.

These constraints bar Forms from standing in the imaging

relation. To be an image, a thing must represent something

other than itself and come to be in a medium. Timaeus

8 I offer an interpretation of the argument in Plato: Parmenides (Indianapolis, 1996), 42-45.

27

explicitly denies that Forms satisfy the second condition.

A Form, he says, neither receives into itself anything else

from anywhere else, nor enters into anything else anywhere

(52a2-3). By contrast, the perceptible copies of Forms

depend on the Receptacle as their medium.

Timaeus opened his main discourse with only a twofold

distinction between the realm of Being and the realm of

Becoming. Using that distinction, he described the

composition of the world’s body and soul by a divine

craftsman. But he then makes a fresh start (47e) and

describes a precosmic situation before the god began to set

things in order.9 He says that whereas previously two kinds

seemed sufficient—a model, which is intelligible and always

remains the same, and a copy of the model, which becomes and

is visible—we must now add a third kind, one that is

difficult and obscure: the Receptacle of all becoming (48e2-

49a6). Timaeus spends several pages describing the nature

and function of this third entity: The Receptiacle is what

is permanent in a context of flux; it has no perceptible

9 I give an interpretation of this central section in “Matter and Flux in Plato’s Timaeus,” Phronesis 32 (1987), 34-53.

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features of its own that would intrude on those of its

contents; most importantly, it is space, the place in which

images occur and disappear.

After repeating his threefold classification for a

third time, Timaeus explains why perceptible things must

occur in the Receptacle. He starts by describing our

confusion:

We look at this [threefold distinction] as in a dream

and say that everything that is must be in some place

and occupy some room, and that what is neither on earth

nor in heaven is nothing. Because of this dreaming

state, we prove unable to rouse ourselves and to make

all these distinctions and others akin to them, even

concerning the unsleeping nature that truly is, and so

to state the truth: For an image, since that thing

itself which it has come to be about does not belong to

it,10 but it is an ever-moving semblance of something

else, for this reason it is proper that it come to be

10 In translating e0f 0 w[| ge/gonen I follow the basi idea (though not the actual translation) of Harold Cherniss, “Timaeus 52c2-5,” Mélange de Philosophie grec (1956), repr. in H. Cherniss, Selected Papers, ed. by L. Tarán(Leiden, 1977).

29

in something else, clinging to substantial being

(ou0si/av) in some way or other, or else to be nothing

at all. But what truly is has the aid of the accurate,

true account: as long as the one is distinct from the

other, neither of them ever comes to be in the other in

such a way that at the same time they become one and

the same and also two. (52b3-c5)

This passage vindicates the pattern-copy model of

participation. The second regress argument in the Parmenides

cannot get started, because Forms cannot stand in the

imaging relation to anything else. They cannot stand in

that relation because they cannot enter a medium. We

therefore cannot consider the Form and its images together

and ask what further thing they are all images of. To save

the pattern-copy model of participation, Plato has

introduced a third principle.

The precosmic chaos described in the Timaeus is not the

sheer undifferentiated multitude of the Parmenides: the

contents of the Receptacle already display minimal

differentiation even before the god sets about his work. In

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a final image, Timaeus compares the Receptacle to a

winnowing basket that is shaken by its contents and shakes

them in turn. Through this reciprocal motion, the contents

separate from one another into different regions, like to

like, much as grain separates from chaff in a winnowing

basket. Timaeus says that, although they lacked all

proportion and measure (ei]xen a0lo/gwv kai\ a0me/triwv),

the four so-called elements—earth, water, air, and fire—

possessed certain traces of themselves, even before the god

ordered them by means of forms (ei1desi) and numbers

(a0riqmoi=v) (52d4-53b5). The precosmic chaos does not

consist of properly organized stuffs even as basic as the

four bodily elements. But it does consist of discrete

entities of some simple sort that can be combined into the

elements and thence into complex organized bodies.11 Perhaps

those entities are multiple copies of the little triangles

whose construction into the bodies of the four elements

Timaeus goes on to describe.12 Or perhaps they are 11 See Timaeus 69b-c. In the precosmic situation there was nothing worthy of the names “fire,” “water,” etc. There was no proportionality,except by chance.12 So I argued in “Matter and Flux in Plato’s Timaeus,” Phronesis 32 (1987), 34-53.

31

something more ultimate, like numbers. Certainly Plato

invites this reflection, because he remarks on more than one

occasion in the Timaeus that the triangles may not be the

highest principles of bodies.13 The simples, whatever they

are, are not analytically ultimate: they are the product of

the Indefinite Dyad participating in a Form, and they are

located in the Receptacle.

I have not discussed the composition of Forms from the

One and the Indefinite Dyad, but the argument in the Timaeus

for the existence of the Receptacle bears on that issue too.

Participation of the Indefinite Dyad in the One cannot be

construed as imaging. For the Forms cannot enter a medium.

Plato therefore needs another way of explaining the

relations between Forms and a way to explain how Forms can

be one despite their many formal participants. And that, I

suspect, is the new one-many problem he confronts in the

Philebus.

13 52d, 54a.

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