To: Andrew W.
From: Geoffrey Klempner
Subject: Plato and the form of Beauty
Date: 2 September 2004 10:30

Dear Andrew,

Thank you for your email of 24 August, with your essay for the Associate Award in response to the question, 'The philosopher thinks ‘that there is such a thing as beauty itself, and has the ability to see it as well as the things that partake in it’ (476c). Explain the contrast Plato makes in the Republic between examples of visible beauty and the beautiful itself. Why does he believe that true knowledge must relate to the latter and not to the former?'

This is a very good essay. You have really got to grips with Plato's arguments in the Republic, highlighting the seemingly incompatible things which Plato says about the nature of the Forms, and in particular the Form of Beauty, and concluding with a fascinating theory of beauty - or suggestion of a theory - which looks very much like something to which Plato the mathematician might have nodded his assent.

The attack on the sightseers is very much in the Socratic tradition of, 'You have given me lots of examples of F, but I am asking about F-ness itself.' The sightseers are not incapable of recognizing beautiful things. On the contrary: the fact that the unreflective person is able, at least sometimes, to successfully recognize F when it occurs is the 'explanandum', the thing to be explained. Where the sightseers go wrong is in their inchoate theorizing about the nature of F-ness. For example, the naive idea that 'black is beauty in painted figures' - a theory which can be practically refuted by showing the sightseer a grotesque example of a black painted figure and asking them if they find it 'beautiful'.

What this calls for is a theory of F-ness. Or, in the case of beauty, a theory of aesthetics. In the same way, our ability to discriminate between just and unjust acts calls for a theory of justice.

A theory of F-ness is a philosophical definition of F. That is what the sightseers are unable to provide. Moreover, lacking such a definition, their ability to discriminate Fs, even when successfully exercised, cannot be described as knowledge. You might be right that the car that sped by was a Jag, but if you were ignorant of the fact that some 'Jags' are made by Daimler then your true belief isn't knowledge.

There is a story to be told - which only the theorist about Fs is in a position to tell - about how the F-ness in an object gives rise to the true belief, 'this is an F'. The story, the theory, also explains why things which are not F but G can give rise to the false belief 'this is an F'. The theorist knows when something is F. The one who lacks a theory cannot know but can only believe.

However, this does not yet bring out what is characteristic about Plato's theory.

The transition to a full-blown metaphysical theory occurs when Plato lumps together the relativity of the judgements made by sightseers or non-theorists ('a beautiful object is not beautiful in every context... a beautiful object seems beautiful to one observer but not beautiful to another') with the observation that over time beautiful things lose their beauty, because nothing in the physical world is permanent.

That's the point when we seemingly have no choice but to go along with Plato's idea that some *object* is exempted from all the flux, something remains beautiful no matter what - the form of Beauty itself.

I don't see the example of the three fingers as showing any discrepancy in Plato's account. From the point of view of the theory of Forms, every successful perception of an example of F is explained by the theory. In some cases, ratiocination, or an act of comparison is involved, but this can be successfully done by someone who lacks the philosopher's knowledge of what F-ness is in itself.

Again, I don't think that the example of the pipe-player shows that Plato is inconsistent in his account of knowledge and belief. The distinction between knowledge and belief can be explained using examples from the sensible world (like the Jag and Daimler example above). Arguments for scepticism typically start of by explaining the distinction between 'knowledge' and 'belief' so-called as these terms are applied in everyday life, then demonstrating how, in the light of the implicit principle behind the distinction - which only the philosopher with the theory is in a position to give - no-one in fact 'knows' anything.

The 'Third Man' is significant, because here Plato explicitly recognizes the inconsistency of combining self-predication with the one-over-many assumption. And this relates to the issue which you raise at the end, concerning the tension between the idea that Beauty itself, like the form of the Good, cannot ultimately be explained discursively but can only be seen by the philosopher who has perfected the art of Plato's dialectic - and the idea that there may, in fact, be a deep mathematical explanation of our sense of beauty.

Suppose we succeeded in persuading Plato that the fractal theory is true. The form of Beauty in some sense *is* the fractal theory. To a mathematician, the fractal theory of beauty might indeed appear 'beautiful', but only in the way that all deep mathematical theories are. It is not literally 'beautiful', not in the sense in which Pollock's painting is beautiful. In other words we have abandoned the assumption of self-predication, defusing the Third Man argument.

This would not necessarily be a comfort to Plato, however. With the idea that *theory* is the all-important thing, Plato's notion of Forms as metaphysical 'objects' which we perceive with the eye of the intellect recedes into the background. That is why I suspect that, contrary to the previous paragraph, Plato would never accept an explicit, cut-and-dried theory. And in this, he is in agreement with the Socrates of the Socratic dialogues. The dialectic trains us to *see* the Forms, but it cannot, ultimately, define them.

All the best,

Geoffrey