To: Leonidas M.
From: Geoffrey Klempner
Subject: Parmenides' argument for 'It is'
Date: 27 March 2002 11:32

Dear Leonidas,

Thank you for your e-mail of 17 March, with your third essay for the Ancient Philosophy program.

Thank you also for your words of encouragement, regarding the International Society for Philosophers. I will be writing to all the members of the new Society later this week. We have a web site in progress (thanks to Pathways student Zeli Y.) and plans for an opt-in database of members and their philosophical interests accessible only to Society members. Only members of the ISFP will be eligible to participate in the Pathways online conferences.

Analyse, and give a commentary on Parmenides' argument for the proposition, 'It is.'

The main challenge for the student trying to make sense of Parmenides' argument, is to present Parmenides as arguing in a sane and rational way, and not falling victim to any blatant fallacy. This is what I try to do in the unit where I discuss Parmenides argument for 'It is'. According to my interpretation, Parmenides is presenting us with a challenge of explaining how there can be 'negative facts'. The problem is that any statement which involves the 'determination of a determinable' entails a negative fact: e.g. 'John is six feet tall' entails that John is not five feet, not four feet etc. etc.

But let's see if there is another approach.

As presented, the assertion, 'There are two alternatives: it is and must be, it is not and cannot be' looks as if it contains an obvious fallacy. It seems incredible that Parmenides would have failed to notice that the logical alternative to 'A is necessarily the case' is not 'Not-A is necessarily the case', but, 'It is not the case that A is necessarily the case'. This leaves open the additional possibilities that A is contingently the case, or A is contingently not the case.

How would Parmenides have ruled out these latter two alternatives? Two unstated premisses that we might plausibly attribute to Parmenides are:

A. Philosophy, the science of the Logos, is only concerned with truths of reason.

B. Every truth of reason is a necessary truth.

I am following your lead here, when you say, 'This Logos...is the only stable Truth. It is also common among all humans, and thus remains as a task for each of us to discover it. It looks as if Parmenides takes really seriously this prompt. He tries with reason alone to find the Truth.'

If we add these two premisses to the argument, then it does indeed follow that the only alternative to 'A is necessarily the case' is 'A is necessarily not the case'.

On this interpretation, Parmenides is asserting that it is impossible to know, indicate or think that which is necessarily not the case. Let's consider, as you do, Plato's philosophy. The Form of the triangle is different from the Form of the square. This implies a statement about what is necessarily not the case: the Form of the triangle is necessarily not the form of the square. So should this be allowed?

This is where we need an additional argument: 'What is necessarily not the case cannot be thought, because every object of thought is something that is.' In thinking, for example that the Form of the triangle is necessarily not the form of the square, I am trying to focus my thought on something that is not, a non-existent object, namely the impossible Form 'square triangle'.

Any attempt to re-formulate this, so that the attempt to think of a non-existent object is not implied, seems doomed to failure. If we say that the distinction between the Form of the triangle and the Form of the square is simply a matter of each having its own 'identity', then in order to explain what we mean by 'identity' we still have to talk about what is necessarily not the case: statements about identity imply statements about non-identity.

As I said above, I am trying to see how a great thinker could have stumbled here. Is there any way in which we can *see* what Parmenides saw? What did Parmenides see?

You suggest that we should look at the way in which one might analyse negative existential statements. Let's see how this would work out in the case of the Forms of the square and the triangle.

In the statement, 'The Form of square triangle does not exist', we appear to have as the object of our thought, an entity which implies a logical contradiction. However, there is no escape here by saying what you said about the example of Pegasus: "'Pegasus does not exist' means 'I have an idea of Pegasus in my mind, but there is no object in reality to which my idea corresponds'." It is impossible to 'have' the idea of the Form of square triangle in one's mind!

Where does one go from here? I don't know.

Apart from the central problem - which neither you nor I have been able to resolve - this is a clear and well constructed essay. I like your emphasis on the point that 'Human logic can not be incoherent with the Logic or Truth of the Universe'. This seems right. It is the peculiar 'way' that Parmenides understood this which remains the sticking point.

All the best,

Geoffrey