To: Sean K.
From: Geoffrey Klempner
Subject: Parmenides: what is not cannot be thought
Date: 11th February 2009 11:37
Thank you for your email of 2 February, with your essay for the University of London Plato and the Presocratics module, entitled, 'Parmenides, 'what is not' cannot be thought.'
You describe Parmenides as a bold (in fact 'brazen') thinker. This is a very bold essay on Parmenides. You deserve credit for offering an original take on Parmenides' argument for the impossibility of thinking or speaking 'what is not' and the deductions he makes from this, a take which is not that implausible, at least not more so than other interpretations which have been given.
The principle operating here (as I may have mentioned before) is the interpretative 'principle of charity': you give the best interpretation of a philosopher's arguments, consistent with what they actually said, on the assumption that the arguments are worth taking seriously.
However, it is also important to anchor what you say on behalf of Parmenides in the evidence -- in this case quoted fragments from his work, together with reports of commentators who had the opportunity to see the complete text. You only quote from Parmenides once, and give no argument in favour of interpreting the statement, 'it is' as referring to the universal set, or 'it is not' as referring to the null set.
What you say about the vague and woolly way in which we form the concept of 'everything' is instructive -- indeed, this would make a very good introduction to a discussion of Russell's paradox and the solution which he offers (the theory of types), or indeed other solutions such as the cumulative hierarchy in Zermelo-Fraenkel set theory.
Your version of Parmenides deduction that all of Being must be the same quality, is highly ingenious but implausible given what Parmenides actually says. In terms of the mathematics of real numbers we would now say that the reasoning (there must be some point x which is not contained in any subvolume because it is on the borderline between subvolumes) is fallacious (although this takes some showing). One wouldn't expect Parmenides to see this, but then there is no evidence that he did consider this argument in the first place. It is pointless to wonder what he would have said if he had considered it.
In other words, what I'm saying is that you are straying far from the text. There is no evidence that Parmenides had any concept of a set as such. What he says is that 'it is' can be thought and 'it is not' cannot. What is 'it'? What is 'is'?
Here there has been much scholarly debate: my own view (for what it's worth) is that Parmenides isn't too fussed about this, indeed the whole strength of the argument resides in the fact that however you interpret 'it' and 'is' the result is the same. Take any x. Either x 'exists' or x doesn't exist. Or, take any x, either x is F (for some F) or x is not F.
An examiner would expect you to show knowledge of the different interpretations ('it' is reality, 'it' is the One of the Milesians, 'it' is any x; 'is' is 'exists', 'is' is 'is F' etc.). Once again, we are in the area of the principle of charity, looking for a way in which Parmenides' argument for 'it is' can be made to look anything but crazy.
There is a philosophical problem about 'not', illustrated by the continuing debate over 'negative facts' (which exercised Russell, for one) and also turns up in discussions of the correspondence theory of truth (e.g. in the famous Aristotelian Society debate between P.F. Strawson and J.L. Austin).
When I say that my desk is not blue, my statement is true by virtue of some fact or facts which account for its not-blueness. We don't think that not-blueness is itself a feature of reality. The desk is brown, and an a priori necessary truth about colours is that the same point on the same surface seen from the same point of view cannot be two different colours at one and the same time.
This observation, generalized, parallels to some extent what you say about the different ways of 'being'. Sherlock Holmes does not exist, there is no detective past or present of that name (and description etc.) but he 'is' a character of fiction. Whatever we talk about has some kind of 'being' (but then, what do you say about 'round squares' etc. -- that was Russell's problem with Meinong). So I can see a way in which the point about being could be seen as an illustration, or an example, of the more general point about 'not'.
Even if we stick to the text, there is plenty of room for philosophical analysis, or metaphysical speculation. The important thing (as I have iterated previously) is that you answer the question, whatever the question may be. (In the case of this essay, you don't give the question!)
With regard to the deductions from 'it is', it does not require such ingenious argument to see that any differentiation implies 'is not' as does any change or any variation in density.
At one point in his argument, as you indicate, Parmenides does resort to another principle, the 'no more reason' or 'ou mallon' argument which appears in a number of Presocratic philosophers (e.g. Anaximander). There is no more reason for the cosmos to have begun at one time rather than another, therefore it cannot have begun. Here, I would say that Parmenides is icing the cake. He doesn't need this argument, indeed he ought not to need it if his original reasoning is sound. It is a weakness of your interpretation that you have Parmenides offering (or being prepared to offer) the same 'no more reason' argument against the hypothesis of differences in density.
All the best,