To: Nikolaos B.
From: Geoffrey Klempner
Subject: Third man argument in Plato's Parmenides
Date: 14 October 2005 12:03

Dear Nikos,

Thank you for your email of 3 October, with your Essay, 'The Third man Argument in Plato's Parmenides'.

This is for the most part a careful and informative exposition of Plato's argument, drawing largely from the analysis of Vlastos. However, I was not sure about what conclusions you would draw from this. How, in your view, did the mature Plato conceive of the Forms, and what role is played by the Third Man argument in developing this conception?

According to Vlastos, a vicious regress is generated if one adheres to three key assumptions: Self-Predication, One over Many, and Non-Identity. Reject any one of these assumptions, and there is no regress.

The question which the scholars argue over is which of the three assumptions Plato was prepared, or might have been prepared, to reject. Is there any way that one could preserve the spirit of the Forms theory if one rejects either self-predication, or one over many, or non-identity?

Before we get on to this, I would like to point out an inaccuracy in your introduction. Socrates does not distinguish the Forms of fire, water, just, beautiful etc from 'hair, mud and dirt' as such. What he says is that there are no *Forms* of hair, mud and dirt. Upon which Parmenides wisely replies, 'That is because you are still young, and philosophy has not yet enthralled you as I think she will do some day. When that time comes you will lay aside all this indifference; but at the present, because of your age, you keep an eye on popular opinion'!

We can smile at that. But there is a serious question here, which in a way gets to the heart of the nature of the Forms. Why is there not a Form of dirt, for example? Is it perhaps because the concept 'dirt' implies negation?

For example, my tea mug is 'dirty' because there is a thick layer of tannin round the inside. Tannin is a substance which, in itself one would not regard as 'dirty'. Or perhaps Plato would say (if he learned more about modern chemistry) that as a chemical compound there is no Form of tannin but only Forms for the component atoms which make up a molecule of tannin. Mud, on the other hand, is clearly a mixture of stuffs, so we only require Forms of the individual stuffs (water, earth, etc.).

But why hair? I leave you to guess.

What does this show? We do not need Forms for everything. All the things we perceive, including mud, hair and dirt ultimately derive their properties from the Forms, but not in the simplistic way of a 'Form for every general term'. Where Socrates goes wrong, in Parmenides' eyes, is not in failing to recognize that there can be a Form of mud, but rather in failing (through distaste?) to consider the question of how the Forms explain why mud is the way it is.

This should be sufficient to at least put into question the naive idea that the Form of a horse just is a 'horse' or that the Form of a tree is a 'tree' and so on. We are not to think of Plato's heaven as a kind of museum where every possible object that one might encounter is exhibited, in all its 'perfection'. ('Here is the exhibit for 'horse', here is the exhibit for 'horse hair', here is the exhibit for 'horse dung' etc.)

The question we are considering, in other words, is just what it takes for a non-physical entity such as Forms are conceived to be, to be a 'paradigm'.

In ordinary usage, a paradigm is a member of the class of things which it is a paradigm of. Let's say this morning one of my students sent me a 'paradigm' essay on Descartes First Meditation, the perfect essay which in my opinion could not be bettered and against which all other essays on Descartes First Meditation are measured.

But Forms are not like this. Indeed, there could never be a perfect essay on Descartes, any more than there could be a perfect horse. In the physical world everything is relative. Paradigms have their place, but it is ultimately a practical question whether this or that example serves as a paradigm.

The Form of horse embodies the essence of what it is to be a horse. It is the ultimate explanation of horseness.

It is indeed a remarkable fact that we find the world 'chunked' in the way that we do, with the class of horses marked off from other animals. (In another possible world, there might be infinite variability, with no recognizable 'species' or natural kinds of organisms or substances.)

Plato believed that it required a timeless metaphysical principle to do this. Let's give him that assumption. So we have one over many. We also have non-identity. We also have paradigms. What we do not have is *literal* self-predication.

Personally, I find it absurd that philosophers have even considered that self-predication might be literally true. Knowing (or recollecting) the Form of a horse, I know what a horse essentially is. But there are other ways of 'knowing' besides looking at a picture or a model. Mental perception (perception of a Form) is certainly analogous to sense perception. However, I would argue that the point of the analogy is simply the 'direct relation' between the percipient and the object. The precise nature of this direct relation is different in the case of sense perception and mental perception. That is all Plato needs to say in order to resist the conclusion of the Third Man argument.

All the best,

Geoffrey