Plato’s Parmenides

On my (now defunct) boards, a Hyperborean asked the following:
Do you see it as a critique of Plato’s theory of forms where Plato gives up the theory, or a critique that causes Plato to revise his theory in The Sophist?

I answered: I doubt Plato gave up his theory, and instead he took the more difficult path of self-criticism. Something most philosophers lack the gumption to do: subject their earlier theories to severe critique and getting over the critique as well. 

As two enigmatic and self critical pieces, Parmenides and Theaetetus both belong in the later dialogues. Just as the Theaetetus attacked the epistemology of the middle dialogues, Parmenides attacked the metaphysics of the middle dialogues. If the Timaeus is classified as middle dialogue, then Plato intended the objections in Parmenides to depend upon Forms being both universals and paradigms, and rightaway, Plato stopped thinking of them as paradigms. But if Timaeus is later than Parmenides, which is what stylometric studies appear to claim, then it looks like Plato never made any modification to his theory.

Plato in the Sophist introduces a new metaphysics as well as a far more sophisticated investigation of language within a long discourse on “not being.”

Nevertheless, I’m more intrigued by the new scholarship on Plato, based on the works of Gerald Press, where the thesis that that no character should be taken to be Plato’s mouthpiece is being seriously examined. Rather, it is the entire dialogue that speaks for Plato. 

The Theory of Forms is basically an attempt at explaining predication, and the Third Man Argument is a challenge of that theory. If something participates in a Form, its predicate is explained. And Paradigms are how things participate in forms, that “things participate in Forms by being appropriately related to their paradigms.” But the attempt to explain a predicate by participating in a paradigmatic Form leads to an infinite regress, and turns out to be not much of an explanation at all.

Before we are to ask whether Plato changed his mind, we must pose the question whether Plato intended the  Theory of the Forms (ToF) seriously, as a philosophical theory, that he believed in it. Then the answer depends on whether we are to grant what Timaeus and the Eleatic stranger spoke about the ToF in the Sophist and Statesman as being consistent with what Socrates said in the Phaedo and the Republic. If we cannot find a consistency, then Plato changed his mind about the essence of the Forms. But i think Gerald Press has the right idea: Plato intended the Dialogues as an exercise in philosophy, not a series of a Platonic doctrine. See here for more exposition.

Historians and scholars are prone to the mistaken belief that the ToF contains the entirety of Plato’s philosophy, but it isn’t even present within the elenctic dialogues, and is often ignored in the late dialogues, even subject to criticism. If you observe the actual amount of attention devoted to the ToF during the dialogues between the Symposium and the Timaeus, it is a very small portion. 6 of the 10 books of the Republic do not mention the ToF, nor is it required. Platonism, then, is actually a artifact of scholars, rather than the essence of Plato’s philosophy.

The theory of forms first appears in the Symposium, but gets its full exposition in the Phaedo. The Republic expands and exploits the ToF, and in the Timaeus, although fleeting, it seems to be defended from some unmentioned criticism. The Sophist deploys an altered version of the doctrine, and the ToF is absent from Cratylus and Theaetetus.

Parmenides’ objections to Socrates’ theory of Forms is located in Parmenides 130a3 – 136c5, and the so-called Third Man Argument (TMA), 126a – 135d. Scholars have raged war over the past 24 hundred years over this interesting part. The great scholar Gregory Vlastos in his paper, The Third Man Argument in the Parmenides, with a logical framework, concludes a couple of things: the argument is an ontological regress and yet the premises of the argument are logically inconsistent. Later scholars, T. Penner and S.M. Cohen, reconstruct the argument differently and reject both of Vlastos’ conclusions. They claim that the argument contains an epistemological regress and that the premises aren’t logically inconsistent.

My rendition of the TMA will draw heavily from the Penner-Cohen version of the TMA:

1. There are many perceptible things (a, b, c, …) each of which appear to us to be large, and which we’re able to group all together as large.

2. In order to account why we are capable of grouping together all the a, b, c, …as large, we must postulate the Form of Largeness, L, over and above the many things a, b, c, … we now take to be large.

3. Now, L is added to the group of things we take to be large, so now we must also think there are more large things than initially thought.

4. In order to account why we are capable of grouping together all the a, b, c,…, L as large, we must postulate the Form of Largeness L1, over and above the things a, b, c,…, L we now take to be large.

5. Now, L1 is added to the group of things we take to be large, so now we must also think there are more large things than we thought at step 3.

And so on, ad infinitum…

Ergo, the TMA is intended to challenge the explanatory power of the ToF. If we wish to employ the ToF to account why we can group many things a, b, c, … as large, then we inevitably end up with an infinitely long chain of Forms, then the ToF fails as an explanatory theory.

One-Over-Many Principle (OOM)
The first step from 1 to 2 entails the principle of explanatory necessity:

For any collection of things a, b, c, … which may be grouped together as large, in order to explain why a, b, c,… can be grouped as large, we must postulate the Form of Largeness L over and above the many things a, b, c,… which we currently take to be large.

The Principle of Non-Self Explanation (NSE)The OOM means we always appeal to the Form of Largeness to explain why we can group together all the things we currently take to be large. However, the scholars Penner and Cohen both think Plato escapes the regress by rejecting OOM by maintaining there are some large things, such as the Form of Largeness, which apparent largeness does not itself require explanation.

The step from 3 to 4, or 5 to 6 posits a new Form of Largeness, Lx instead of merely repeating the original Form of Largeness in the grouping of the a, b, c, … , and L. Even though the OOM is the appeal to the Form of Largeness L to account for the capability of grouping together any collection of things as large, we cannot appeal to L itself in order to account why we can group a, b, c,… and L as large. Then it follows that the TMA itself presupposes the principle of non-self-explanation:

Appealing to the Form of Largeness L itself cannot adequately explain the ability to group together a collection of many things, including the Form of Largeness L itself, as large.

Principle of Self-Partaking (SP)The underlying concept of the NSE is that L itself cannot satisfactorily explain why L is large. The common assumption about explanations is that they are supposed to be informative. Yet an explanation like L is large just because L partakes in L seems inadequate, because there is no new information that isn’t already present within the explanandum itself.

The move from 2 to 3 or 4 to 5 compels the addition of L itself to the group of many things that are considered to be large.

The Form of Largeness L is itself large.

Some scholars argue that Plato rejected SP, not OOM. They think Plato thought the way the Form L is large is different from the way things like a, b, c, … are large. Yet Penner and Cohen thought otherwise, that Plato did not and would not have rejected either SP or NSE. Therefore, he must have rejected the OOM in order to escape from the TMA.

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...a philosophisticator who utters heresies, thinks theothanatologically and draws like Kirby on steroids.

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