Kenny Anthony. Ancient Philosophy: A New History of Western Philosophy Volume 1

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regard them as valid? Either way, what is the relevance of the second part to

the assault on the Ideas in the Wrst part?1

Before outlining the main problems for the Theory of Ideas that are put

forward in the Wrst part, it is worth repeating at this point the six principles

that we identiWed in Chapter 1 as constituting the core of the classical

Theory.

(1) The Principle of Commonality. Wherever several things are F, this is

because they participate in or imitate a single Idea of F (Rep. 5. 476a).

(2) The Principle of Separation. The Idea of F is distinct from all the things

that are F (Phd. 74c).

(3) The Principle of Self-Predication. The Idea of F is itself F.

(4) The Principle of Purity. The Idea of F is nothing but F (Phd. 74c).

(5) The Principle of Uniqueness. Nothing but the Idea of F is really, truly,

altogether F (Phd. 74d; Rep. 5. 479a–d).

(6) The Principle of Sublimity. Ideas are everlasting, they have no parts and

undergo no change, and they are not perceptible to the senses (Phd.

78d).

The problems set out in the Wrst part of the dialogue are as follows.

1. According to the theory, particular Fs are F because they participate in

the Idea of F. But what does ‘participation’ mean? Does a particular F share

only a part of the Idea, or does it contain the whole of the Idea? There are

diYculties either way. If a particular large thing L has the whole Idea of Large,

then the Idea seems to be scattered and lack the unity of an Idea; but if

L shares only a part of the Large, then it is large by something which is itself

small, because being only a part it must be smaller than the Large (131a V.).

2. It is essential to the theory that wherever several things are F they

derive this from some other entity which is the Idea of F. Thus, the several

large things derive their largeness from the Idea of Large. But if we put

together the original set of large things plus the Idea, we have a new set of

large things, which must derive their largeness from some other entity. ‘So

another form of largeness will appear, alongside the Idea of Large and the

things that participated in it, and then another again over all of these’—so

that we are set oV on an inWnite regress (132b). This line of thought much

1 In what follows I am indebted to Constance C. Meinwald’s Plato’s Parmenides (New York:

Oxford University Press, 1991), though I diVer from her on important points of interpretation.

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impressed Aristotle, who, substituting ‘man’ instead of ‘large’ for F in the

original premiss, named it the Third Man argument, after the Man who

would appear as a Super-idea, after (a) the men in the world and (b) the

Ideal Man.

3. There is a special diYculty with relational predicates. Suppose I am a

slave. According to the theory, that must be because I resemble the Ideal

Slave. But who is the Ideal Slave’s owner? Surely, the Ideal Owner. But I am

not a slave of the Ideal Owner but of whoever is my terrestrial slave-owner.

So the relationships between entities in the world cannot be explained by

relationships between the Ideas (133e).

These diY culties are genuine problems for the Theory of Ideas, and surely

Plato means us to realize this. At the very least they demand substantial

modiWcation of the theory, and in other dialogues Plato undertakes such

modiWcation. In the Parmenides, however, he does not explicitly present the

necessary modiW cations. We might expect, though, that the second part of

the dialogue oVers some guidance over the lines the modiWcation needs to

take.

A major problem with the second part is that it is not clear exactly what

is the pair of hypotheses from which Parmenides starts his argument

(137b). He describes the hypotheses as hypotheses about the One itself,

but the Greek in which they are stated can be rendered in several ways. The

two following pairs are the most promisi ng translations:

(1) If the One is v. If the One is not.

(2) If it is one v. If it is not one.

(2) is the reading that best Wts the Greek of the received text of this passage of

the dialogue, where no deW nite article occurs before the word ‘one’ (hen).

Indeed, even the most enthusiastic partisans of the Wrst reading agree that it

can only be sustained if one amends the text at this point. On the other hand,

(1) seems to be a better Wt not only to the immediately preceding wording,

but to the whole series of subsequent arguments, which quite frequent ly

unambiguously refer to the One, with a de W nite article. Moreover, anyone

who accepts reading (2) has to answer the question what the ‘it’ stands for.

On my view, there is no need to amend the text. The second reading,

which is the most natural translation, can easily be reconciled with the

subsequent argument. There are two ways to do this.

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The Wrst is to take the ‘it’ in question to be the same as the ‘it’ which is the

subject of the Way of Truth in the poem of the historical Parmenides: namely,

Being. The references to the One in the course of the subsequent arguments

are easy to account for. They occur in the course of following out the

hypothesis that ‘It (sc. Being) is One’. If that hypothesis is true, then there is

one pre-eminent subject to which the predicate ‘One’ applies, namely Being

itself. This subject can quite naturally be referred to as ‘the One’, and it is

proleptically so referred to by Parmenides at 137b3. However, this interpret-

ation becomes harder to sustain when Parmenides proceeds to examine the

negative hypothesis, which on this account would be ‘that Being is not one’.

A second interpretation, therefore, is preferable. The ‘it’ should be read

as ‘the One’. In that case, the two hypotheses are ‘The One is one’ and ‘The

One is not one’. Initially, this may seem a very implausible reading: surely

the second hypothesis rules itself out instantly as being self-contradictory.

But if we reXe ct, we see that this is not so. Some of the major problems

with the Theory of Ideas that were laid out in the Wrst part of the dialogue

derived from the principle of self-predication, namely that the Idea of F is

itself F (see p. 208 above). It is appropriate that the second part of the

dialogue should not take self-predication for granted, but explore

the consequences, in the case of one pre-eminent Idea, of its denial as

well as of its aYrmation.

The dialectic begins with the protagonist Parmenides inquiring what

predicates attach to the One, and what predicates attach to other things, on

the basis of the Wrst hypothesis. If the One is one, then the One is not a

whole with parts (137d). It is without limit and without place (138b). It is

unchanging, but it is also not at rest (139b). It is neither diVerent from, nor

the same as, itself or another (139e), and it is neither like nor unlike itself or

anything else (140b). It is neither greater nor less than itself or anything else

(140d). It is not situated in time, and since it does not belong in the past,

present, or future, it cannot have any share in being at all. The conclusion

is this:

Therefore the One in no way is. Therefore it is not in such a way as to be one,

because in that case it would be a being and a partaker of being. But, as it seems,

the One is not one and is not at all, if we have to trust this argument. But if

something is not, then nothing can belong to it or be about it. So it has no name,

no sentence or thought can be about it, and there can be no sensation or

knowledge of it. (142a)

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We are pretty clearly not intended to accept this conclusion as a true

statement about the One. Parmenides’ interlocutor in the dialogue, Aris-

totle (no relation), who is commonly a complete yes-man, interposes a rare

note of dissent when asked if this conclusion is possible. If it were true, it

would cut the ground from under the arguments that lead to it, since they

all purport to speak about the One, which according to this conclusion

cannot be done. The dialectic up to this point must be intended as a reductio

ad absurdum: but a reductio of what? Surely of the hypothesis that the One is

one and nothing but one. But of course an important part of the Theory of Ideas

was the Principle of Purity: that the Idea of F was F and nothing but F. So

the dialectic, to this point, is a recantation of an important element in the

theory.

At this point Parmenides makes a fresh start from the hypothesis that

the One is one and proves that the One is a whole with ever so many parts

(142b, 143a), bounded and shaped (145b), located both in itself and else-

where, both in motion and at rest, both the same as and diVerent from

itself and from other things (146b), both like and unlike itself and other

things (148c), simultaneously equal to, greater than, and less than itself and

other things (151b). It is and becomes older and younger than itself and

other things, but equally it neither is nor becomes older or younger than

itself nor other things (155c). It belongs to past, present, and future, and it

partakes in being, though being and oneness are not the same (if they were,

Plato argues, ‘is one’ would mean the same as ‘one one’) (142c). So there is

no problem in naming it, speaking of it, and arguing about it (155e).

There is clearly a close parallel between these two Wrst sections of

the dialectic. At each stage of each argument we are presented with a

pair of opposite predicates (e.g. in motion, at rest). In the Wrst section

Parmenides argues that neither of these predicates apply to the One. In the

second section he argues that both of these predicates apply to the One.

Between them, the two sections throw a damaging light on the Theory of

Ideas. The Wrst section shows the folly of holding that the Idea of F is

nothing but F (the Principle of Purity). The second section shows the

falsehood of holding that nothing but the Idea of F is F (the Principle of

Uniqueness).

But the two sections are not meant to be on all fours with each other.

The conclusion of the Wrst section is, as we have seen, self-stultifying and

the whole argument can only be taken seriously as a reductio ad absurdum. The

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second section, however, leads to a conclusion that, though it may be

surprising, can be understood in a way which is in no way self-refuting.

Summing up the results of this section, Parmenides says that the One

sometimes partakes of being and sometimes does not. His words echo the

complaint made in the Republ ic about the ordinary objects of sense-percep-

tion, namely that they roll about between being and non-being. But now it

is a form that displays this pattern, whereas in the heyday of the theory

what m arked oV Ideas from common or garden objects was that they did

not roll about. The Idea of F was not sometimes F and sometimes not F, nor

was it F in one respect and not F in another respect. What is now said about

the One marks a very signiWcant departure from the original Theory of

Ideas.

In the case of the sensible particulars, we could specify the times,

respects, relations, and so forth that made them—without any violation

of the principle of non-contradiction—both F and not F. What we now

have to do is to draw appropriate distinctions to see how both a predicate

and its opposite can be true in diVerent respects, of the One, and by

implication, of other Forms. It is to be noted that the subjects of all

Parmenides’ predications are Ideas, or at least they are all items referred

to by universal terms, not individual names: the expressions for them are

things like ‘the same’, ‘the other’, not ‘Callias’, or ‘Dio’.

In order to resolve some of the problems about Ideas, Plato introduces a

distinction between two types of predication. Using a terminology which

belongs to a later period, we can say that he makes a distinction between

predication per se and predication per accidens. The diVerence between the

two can be brought out thus: S is P per se if being P is part of what it is to be

S. Thus, an oak is a tree per se. (If we allow improper as well as proper parts

of what it is to be S, then an oak is oak per se.) S is P per accidens, on the other

hand, if S is as a matter of fact P, but it is no part of being S to be P. Thus, if

oaks are as a matter of fact plentiful in a certain area, ‘plentiful’ is

predicated only per accidens.2

We have seen that Plato, in the Parmenides, abandoned the Principles of

Purity and Uniqueness. With respect to the Principle of Self-predication he

makes use of his distinction between types of predicate. The Large is indeed

2 The Latin terms are meant to correspond to, though they are not translations of, Plato’s

Greek terms pros heauto (with respect to itself) and pros alla (with respect to others).

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large: being large is an improper part of what it is to be large. But other

things are not large per se. If my house is large, that is not because being

large is part of what it is to be a house. Hence ‘large’ is not predicated in the

same way of large things and of the Large; and hence the Large and

the other large things cannot be grouped together to form a set as they

have to be in order to generate the regress nicknamed the Third Man.

Similarly, the Slave belongs per se to the Owner: for belonging to an

owner is part of what it is to be a slave. But the relations between human

slaves and human owners, and the relations between both and the Ideal

Slave and the Ideal Owner are not per se but per accidens. Both sets of

relationship, relationships between individuals and between forms, can

function side by side without conXict.

Finally, we can revisit the notion of participation. A major diYculty in

understanding how many things can share in a single Idea was that this

seemed to divide an Idea into parts. We can now say that a Form is one per

se if it is part of what it is to be a Form that it should be single and unique:

otherwise it will not achieve the purpose for which it was invented, to

mark what is common to things bearing the same name. But if there are

many individuals instantiating the Form, then it will be many per accidens.

The common thread that runs through the dialectical arguments and

the suggested solutions to the Parmenidean diYculties about the Theory of

Forms is this: nothing can be predicated in the same way of individuals and

of the Forms in which the individuals partake. One modern analogue of

the Platonic notion of participation is that of class membership: if x

participates in the Form of F, x is a member of the class of Fs. Equally, a

modern analogue of the message of the Parmenides is that one cannot simply

predicate of classes what one predicates of individuals. The paradox that

results if we talk of the class of all classes that are not members of

themselves is the lineal descendant of the paradoxes of the Parmenides.

The adaptation of the Theory of Ideas into a Theory of Forms is carried

out further in the dialogue the Sophist. The oYcial purpose of the dialogue is

to Wnd a deWnition of a sophist. The deWnition eventually oVered is clearly

intended as a joke. What the search for the deWnition is meant to illustrate

is a method of deWnition that is still popular in parlour games. In such

games the respondent thinks of an object that it is the questioner’s task to

identify by putting a series of questions oVering a dichotomy. Is it living or

non-living? If living, is it an animal or a plant? If an animal, is it human

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or non-human? And so on. In the course of the dialogue Plato examines

the metaphysical presuppositions of such a style of deWnition.

What the pursuit of a deWnition by division will reveal, if it is carried out

in a serious manner, is a tree structure in which species will appear under

genera, and narrower genera under broader genera: human under animal,

animal under living being, and so on. This tree structure is related to the

predication per se which we found an important feature of the Parmenides.

For anything that appears above F in a genus–species tree structure will be

something that is predicated per se. Thus, being an animal is part of what it

is to be human; being a living thing is part of what it is to be an animal.

On the way to the deWnition of the sophist we have to address the

problem of false thought and false discourse. One cannot distinguish

the fraudulent sophist from the true philosopher without discussing the

nature of falsehood. But how can we talk about falsehood without falling

into the traps set out by the historical Parmenides in his poem (237a)? To

say what is false is to say what is not. But what is not is surely Unbeing, and

Unbeing is nonsense for reasons that Parmenides gave (238e). It seems to be

impossible, therefore, to say what is false without talking nonsense. Shall

we revise our account, then, and maintain that to say what is false is to say

that what is, is not, or that what is not, is? Will this avoid Parmenides’

censure?

To deal with this problem we have to disarm Parmenides by forcing him

to agree that what is not, in some respect is, and what is, in a manner is not

(241d). Motion, for instance, is not rest, but that does not mean that

motion is not anything at all (250b). There are many things that even

Being is not: for instance, Being is not motion and Being is not rest

(250c–e).

In the Sophist as in the Parmenides Plato is interested in the relationships

between diVerent Forms. Here, he describes this topic as ‘the interweaving

of Forms’, which he says is what underpins language (259e). We dig a pit for

ourselves if we assume either that no Forms can combine with each other

or that all can (251e–252e). Clearly, some can and some cannot, and we

need to inqu ire which Forms can combine with which other Forms. Being

(to on) here occupies the central role in this inquiry that the One (to hen)

occupied in the Parmenides. But in addition to Being four other forms—

motion, rest, sameness, and diVerence—are considered and their interrela-

tions explored.

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DiVerence turns out to have a crucial relationship to Being (256d–e).

When we speak of what is not, we are not talking of Unbeing, the contrary

of Being: we are speaking simply of something that is diVerent from one of

the things there are (257b). The non-beautiful diVers from the beautiful

and the unjust diVers from the just; but the non-beautiful and the unjust

are no less real than the beautiful and the just (257e–258a). If we lump

together all the things that are non-something, or unsomething, then we

get the category of non-being, which is just as real as the category of Being.

So we have blown open the prison into which Parmenides had conWned us

(258c).

We are now in a position to give an account of falsehood in thought and

speech. The problem was that it was not possible to think or say what was

not, because Unbeing was nonsense. But now that we have found that

non-being is perfectly real, we can use this to explain false thoughts and

false sentences.

A typical sentence consists of a noun and a verb, and it says something

about something (262a–e). ‘Theaetetus is sitting’ and ‘Theaetetus is Xying’

are both sentences about Theaetetu s, but one of them is true and one false

(263b). They say diVerent things about Theaetetus, and the true one says a

thing about him that is among the things that he is, while the false one says

a thing about him that is among the things that he is not. Flying is not

Unbeing, it is a thing that is—there is quite a lot of it about—but it is a

thing that is diVerent from the things that Theaetetus is, the things that

can truly be said of Theaetetus (263b).

From time to time in the Sophist Plato describes the controversy over the

nature of Being in terms of a battle between groups of philosophical

adversaries. In one place it is a battle between giants and gods, giants

being materialists who think there is nothing but bodies, and gods being

idealists who accept non-bodily Forms as described in the Theory of Ideas

(246a V.). Elsewhere the materialists appear, under the leadership of Hera-

clitus, as the proponents of universal Xux (since all bodies are constantly

changing) while the chief of the friends of Forms appears to be Parmenides,

with his doctrine that all reality is changeless. Finally we are told that the

true philosopher must turn a deaf ear to Heraclitus, and also reject the

doctrine that all true reality is changeless, whether put forward by the

champion of a single Form (Parmenides) or the champion of many Forms

(the Plato of the theory).

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The Sophist shows us the way to have our cake and eat it and say that

Being encompasses all that is unchangeable and all that is in change (271d).

Aristotelian Forms

Aristotle was a severe critic of the Theory of Ideas. Sometimes he criticizes

it respectfully (e.g. NE 1. 6. 1096a11 V.: Plato is my friend, but truth is a

greater one), and sometimes contemptuously (e.g. APo. 1. 22. 83 a28: farewell

to such tarradiddle). His critique, whether rude or civil, always seem

directed to the theory as presented in the middle dialog ues, and not to

Whether or not Aristotle refuted Platonism, Filippino Lippi was in no doubt that

Aquinas had done so (Caraffa Chapel, S. Maria sopra Minerva, Rome)

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the developments of the Theory of Forms in the Parmenides and the Sophist.

He does, however, often tacitly make use of Plato’s later thoughts in his

own writings, in particular when developing his own theory of forms in

Metaphysics F. There, he treats on equal terms problems with Plato’s theory

and diYculties in his own. The book is dense and diYcult, and the account

of it I now give can only claim to be one possible thread to guide us

through its labyrinth.

The diVerence between Aristotelian forms and Platonic Forms is that for

Aristotle forms are not separate (chorista ): any form is the form of some

actual individual. As we have seen in our account of Aristotelian physics,

form is paired with matter, and the paradigm examples of forms are the

substantial or accidental forms of material substances. Aristotle cannot

avoid, however, the questions for which Plato sought a solution in his

theory. He must, for instance, provide his own answer to someone who

asks what is common to the many things that are called by the same name

or fall under the same predicate. He must, that is, oVer an account of

universal terms.

In Metaphysics F Aristotle discusses the relationships between being,

substance, matter, and form. He there works to relate the teaching of

the Categories on substance and predication with the teaching of the Physics

on matter and form, and he combines the two together, with modiWcation

and ampliWcation, into a treatise on Being. ‘The question that was asked of

old, and is asked now, and always will be asked and always will be a

problem is ‘‘what is Being?’’ And this is the question; ‘‘what is substance?’’ ’

(F 1. 1028b2–4).

The reason he gives for eliding the two questions recalls the Categories.

Whatever there is must be either a substance or something that belongs to

a substance, such as a quantity or a quality of it. When we are listing the

things that there are, we may count, if you like, health and goodness; but

any actual health is someone’s health, and any actual goodness is the

goodness of something or other. If we ask, in such cases, what really and

truly is, the answer will be: this healthy person, this good dog (F 1.

1028a24–30).

So Aristotle can regard it as obvious that material entities like animals

and plants and earth and water and the sun and the stars are substances (D

8. 1017b8; F 3. 1028b8). He puts on one side, for later treatment that we have

no space to follow, a number of further questions. Are surfaces, lines, and

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