Third Man Critique

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Adam Brewer

PHIL 3463 February 2006

The Third Man: Paradigm of a Paradigm?

The famed Third Man Argument (TMA)1 against the Platonic Theory of Forms has been the

subject of much attention and revision in the second half of the 20 th century. The analysis of

TMA by G. Vlastos claimed to tease out some of the arguments implicit assumptions, which he

used as grounds for rejecting it because he thought the assumptions to be contradictory. 2 Vlastos

objections were contested by some scholars, particularly S. Marc Cohen,3 as they felt the

assumptions he held to underlie TMA were incorrect. I shall follow the arguments progression

and reformulation as it has been presented by Cohen,4 showing how Vlastos interpretation was

flawed, and how TMA could be strengthened to avoid the problems of Vlastos formulation. I

shall then proceed to suggest how the problems for the Theory of Forms raised by the

strengthened TMA could be avoided by Plato.

In order to fully understand TMA we should first lay out some basic tenets of the Theory of

Forms which bear directly upon the argument. A Form is considered a one-over-many. That is

to say, if we have two or more things which share in common a single name or quality, then

there exists a single Form which is the cause of those things having the same name or quality. A

Form is considered a cause because it is the perfect paradigm of a thing such as beauty and

1 Plato.Parmenides. 132a-b.2 Vlastos, G. 1954. The Third Man Argument in theParmenides, The Philosophical Review 63:3 319-349.3 There have been many more T. Penner and W. Sellars, to name a couple but in this paper I shall follow the

arguments and interpretations of Cohen as I think he has developed the relevant issues most thoroughly for the

arguments I wish to raise.4 Cohen, S. M. 1971. The Logic of the Third Man, The Philosophical Review 80:4 448-475. The main

observations made in his paper can also be found at: Cohen, S. M. 2002. Criticism of Theory of Forms.

http://faculty.washington.edu/smcohen/320/tmalect.htm (accessed 20 Jan 2006).

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it is through participation5 in the Form that a material particular is said to have the quality of the

Form e.g. it is by participating in the Form of Beauty that all particulars we call beautiful

derive their beauty. The Theory of Forms can be seen as an epistemological theory which

attempts to explain predication: ifx is Fthen the Theory of Forms would offer the explanation

thatx isFbecausex participates inF-ness e.g. if Bob is Tall it is because Bob participates in

the Form of Tallness.

TMA attempts to show that the Theory of Forms will lead one into an infinite regress when

trying to explain predication in the manner mentioned above. I shall outline the general flow of

the argument6:

1. There are many things (a, b, c, ) each of

which seem to us to be large (we are able to

group them all together as large).

a, b, c,

2. Because we can group these things

together as all being large, we infer that there

must be one single Form (Largeness) by

virtue of which each thing seems large (as

they all participate in Largeness). So we have

a one-over-many.

L1

a, b, c,

3. Now consider all the large things (a, b, c,

5 Though the details surrounding participation are fairly ambiguous and the notion of participation may lead the

Theory of Forms into certain difficulties I am not concerned in this paper with such things but I shall refer to

participation as a central tenet of the Theory of Forms without offering a close analysis of how it might operate.6 This outline is based on the argument in theParmenides as well as outlines given by both Cohen and Vlastos.

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) along with Largeness (the Form by virtue

of which the things seem large)

a, b, c, , L1

4. These large things (a, b, c, ) and

Largeness (L) must have a Form they

participate in by virtue of which they all have

being large in common (this is the same as in

2 above). There must be a one-over-many.

some Form of Largeness

a, b, c, , L1

5. The Form introduced in 4 and the Form

introduced in 2 (L1) cannot be the same

Form. So the Form in 4 must be a separate

Form of Largeness (L2), the Form by virtue

of which L1 and all of its participants seem

large.

L2

a, b, c, , L1

6. Now consider all the large things (a, b, c,

) and L1 along with L2 (same step as 3

above only with an additional Form

considered).

a, b, c, , L1, L2

7. So on, ad infinitum.

Under this formulation of TMA the argument rests on three premises pointed out by Vlastos,

who went on to attack them. These premises can be teased out of the argument by examining

how the argument moves from one step to the next. The principle of One-Over-Many (OM) is

implicit in the move from 1 to 2. A Form (one) is posited for any group of things (many) which

all appear to share something in common. In moving from 2 to 3 TMA has added the Form into

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the group of its participants and in so doing assumes the Form can also be predicated in the same

way as its participants that is to say, the Form of Largeness can have large as its predicate.

This is known as the principle of Self-Predication(SP). From 3 to 4 One-Over-Many is used

again. Now the crucial step in generating the infinite regress comes in moving from 4 to 5. It is

this move where the additional Form is posited allowing for an infinite number of Forms by

repeating the steps of the argument. What is it that makes the Form of step 2 different than the

Form of step 4? In moving from 4 to 5 there is an implicit assumption that a Form cannot

participate in itself, otherwise 5 could have been rendered:

L1

a, b, c, , L1

If 5 were rendered this way, then no new Form would be created and the infinite regress could

not occur. Vlastos claims the assumption of the argument is what he calls the Nonidentity

Assumption (NI) and it states that something with a certain character (e.g. largeness) cannot be

identical with the Form of that character (e.g. the Form of Largeness). This would require there

to be two separate and distinct Forms in TMA step 5 and justify the move from 4 to 5.

With the three assumptions extracted from TMA we can better assess the validity of the

argument. Vlastos believes that the argument fails on the grounds that two of the premises are

contradictory. The three premises again are:

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(OM) Any set of things which have a predicate in common have one Form in which

they all participate.

If a set of things x, y, z, etc., are allF, there is a single F-ness (Form) by virtue of

participating in which they are allF.

(SP) Any Form can be predicated of itself.

F-ness is itselfF.7

(NI) If anything has a certain character, it cannot be identical with the Form in virtue

of which we apprehend that character.

Ifx isF,x cannot be identical withF-ness.8

Vlastos claims that, of these three, SP and NI are contradictory. Vlastos explains that ifF-ness is

substituted forx we would get: IfF-ness isF,F-ness cannot be identical withF-ness.9 Because

this turns out to be self-contradictory Vlastos believes that SP, NI, or both, must be wrong. So

his main attack on TMA is that it rests on contradictory premises.

It seems that there is definitely a problem with NI. As Cohen and others have correctly pointed

out, Vlastos formulation of NI is what creates the contradiction with SP. In examining the move

from 4 to 5 we could render a different premise from NI which would not contradict SP. Keeping

in mind that participation is supposed to explain predication, we can render the implicit premise

7 Vlastos, p. 3248 Vlastos, p. 3259 Vlastos, p. 326

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behind 4 and 5 as a premise which states that a Form cannot participate in itself; if it participated

in itself then it would be used as an explanation for itself, which would be circular and vacuous

and hence not much of an explanation at all. So we could dismiss Vlastos NI in favor of a

premise we might call Non-Self-Participation (NSP) which would state that: we cannot explain

xs being Fby appealing to x. This would avoid the contradiction with SP and offer a stronger

TMA, more challenging to the Theory of Forms.

So how is Plato to respond? If the notion of Forms as paradigms is upheld strongly we may be

able to undermine TMA. If Forms are always held to be paradigms, then it is their nature that

they explain somethings being F and that nothing explains their being F. If TMA were

successful, we would have Forms over Forms and there would be no paradigm, or we would

have paradigms of paradigms, and that would be absurd. The principle of One-Over-Many,

therefore, does not apply to the Forms. Plato could reject TMAs formulation of OM and

maintain that there are some things that are F(e.g. the Forms themselves) whose being Fitself

does not require explanation. Rejecting OM could end the explanatory regress generated by

TMA.

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Third Man Critique