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The third man argument in Plato's 'Parmenides'


To: Chris M.
From: Geoffrey Klempner
Subject: The third man argument in Plato's 'Parmenides'
Date: 29th July 2009 12:18

Dear Christian,

Thank you for your email of 19 July, with your one hour timed essay for the University of London Plato and the Presocratics module, in response to the question, 'The Third man Argument does not undermine Plato's theory of Forms because it relies on assumptions that are themselves contradictory.' Discuss.

Your answer is very much on the right track: the question is whether the theory that Parmenides 'refutes' contains essence of any interesting or worthwhile version of Plato's theory of Forms, or whether, on the contrary, the theory which Parmenides attacks is a straw man which Plato would have no difficulty in giving up, assuming that he ever held it.

Within this question, is the issue of how we should regard the key assumption in Parmenides' attack, which Vlastos calls, 'self-predication'.

In a previous email I expressed the view that Plato never held self-predication, or at least a literal version of that doctrine according to which every Form F is F, and indeed that the doctrine is prima facie absurd. The form of Large (your example) is not large because Forms don't have a particular size. There are not larger or smaller forms, nor does it make any sense to compare the size of a Form with the size of something that is not a Form.

You cite Meinwald as an example of an interpretation which offers an alternative to self-predication, taken in the 'normal' way. Largeness, or The Large, just is what it is to be large. This looks like a good solution (all the more so, because her interpretation helps make sense of the baffling part II of Plato's dialogue 'Parmenides'). However, I have problems with this as a solution to the challenge of the Third Man argument.

There is no doubt that *knowledge* of the Form of Largeness, is knowledge of what it is to be large, just as knowledge of the Form of Justice is knowledge of what it is to be just. There is a difference between these two examples: Knowledge of what it is to be just is knowledge that the philosopher seeks; I don't think any plausible case could be made that the philosopher seeks knowledge of what it is to be large, or a table, or a horse.

However, it is logically invalid to infer from, 'knowledge of the Form of Largeness is knowledge of what it is to be large' to 'the Form of Largeness is what it is to be large'. Knowledge of the London A-Z is knowledge of how to find your way around London; it doesn't follow (in fact, it doesn't make any sense to say) that the London A-Z *is* how to find your way around London. The London A-Z is a map of all the London streets, and you can use this map to find your way around London.

Knowing the form of Justice (whatever that is) is knowledge we can apply to the world, in deciding whether a particular act is just or unjust. The deep question, which the Third Man argument raises, is what kind of thing a Form (or this particular Form) can be in order to perform this role.

You suggest at one point that 'Plato's Forms have certainly the function to provide causal explanation (why the beautiful things are beautiful etc.)'. If we put aside the interpretation of Plato's cosmology (Timaeus) I don't think there is any evidence in the dialogues for this view. Alice is beautiful because she had plastic surgery for her cross eyes and crooked nose. That's a causal explanation. If you don't agree that Alice is beautiful as a result of her surgery then you don't know what beauty is. That's a *formal* explanation.

However, the example of beauty leads to the second problem which I have with the idea that we can discard self-predication (as understood 'pros ta alla' according to Meinwald's distinction) as one of the characteristics of Forms. Mathematicians will sometimes talk of a particular mathematical proof being 'beautiful'. The philosopher who joyously contemplates the Forms, might find them beautiful too. The form of Justice is beautiful; so is the form of Temperance; so is the form of Beauty.

You can see where this is leading: if Forms have ANY properties at all, then a situation will inevitably arise where we want to say that the form of F is F ('pros ta alla'), and moreover shares the property of F-ness with forms G, H and I.

So it looks as though all Parmenides has to do in order to sharpen his argument is to particularize it. Instead of making the general claim that the Form of F-ness is always F, it suffices that, for some F, it is true that the Form of F-ness is F.

Overall, you have written a very good, knowledgeable essay. You are right to cite scholarly debate. However, I think that an examiner might be a little disappointed that apart from offering a clear exposition, you haven't really contributed anything of your own. Why is this issue gripping? What ARE the Forms? Do you have a view on this?

All the best,