To: Matthew M.
From: Geoffrey Klempner
Subject: Does Heraclitus deny the principle of non-contradiction?
Date: 11th October 2010 13:42

Dear Matthew,

Thank you for your email of 30 September, with your essay for the University of London Plato and the Presocratics module, in response to the question, 'Does Heraclitus deny the Principle of Non-Contradiction?'

This is a good essay, so far as it goes, which largely succeeds in its aim of defending Heraclitus from the charge of denying the Principle of Non-Contradiction (PNC).

I also think, however, that the doubts which you express in your email, specifically your question about the link between Heraclitus' 'theory of opposites and his theory of change', suggest that maybe your deflationary interpretation of Heraclitus' views of PNC doesn't give the whole story.

In order to be convicted of violating PNC, Heraclitus must show the same thing has contradictory properties at the same time, in the same respect, from the same point of view etc. When analysed closely, none of the examples he gives casts the least doubt on PNC. On the contrary, the very process of analysing them requires us to apply PNC in order not to end up talking nonsense.

But that leaves a huge question unanswered: what on earth was Heraclitus driving at? What is he trying to get us to see, by means of all these examples?

One possibility, the least attractive in my view, would be to say that Heraclitus was genuinely confused, that he really thought he was giving valid counterexamples to PNC, which puts him on a par with second- or third-rate sophists of the 'This is your dog, this dog is a father, therefore this dog is your father' variety.

There are two other possibilities.

The second possibility is that Heraclitus is arguing against a logical/ metaphysical view about the nature of 'the opposites' as they were so-called, a view which we have considerable difficulty in even conceiving, but which in his time was the prevailing philosophy. That view was that there are such things as 'the hot', 'the cold', 'the dense', 'the rare', 'the wet', 'the dry' etc. It is part of common sense now that heat and cold, density and rarity, degrees of wetness are on a scale (you could argue that in the case of water, there is this difference: that either there is water present, or there isn't). But it wasn't common sense when Anaximander put forward his theory of 'the opposites'.

The problem with this interpretation is that Anaximenes was there before Heraclitus: in his theory of condensation-rarefaction as the basic principle accounting for degrees of heat or cold, as well as the differentiation of substances, he had already made the decisive move which rejects the naive view of 'the opposites'. -- Well, maybe, Heraclitus is merely generalizing on Anaximenes, taking his philosophy one step further.

But then we still have to reckon with the fact that Heraclitus saw his philosophy as a radical alternative to a universe made of substance or substances, in the manner of Thales, Anaximander or Anaximenes. Fire is not a substance, it is a process, the very process of war, tension between opposites, simultaneous creation-destruction that he talks so much about in his aphorisms.

The third possibility, then, relates to the very nature of 'substance' of what it is to 'exist'. Here, your intuition is correct, that Heraclitus has something to tell us about existence. It isn't exactly that the same thing can 'exist and not exist' (at the same time, in the same respect, from the same point of view etc.). It is arguably more radical even than that. Nothing exists, that is to say, no 'things'. There is good evidence that this is how Plato and Aristotle understand Heraclitus (an interpretation of Heraclitus which seems to be out of favour amongst contemporary scholars). You say the river 'exists', but you forget that it isn't 'the same' from one moment to the next. Something can't 'exist' and not be 'the same' not even in two successive moments of time.

On the Platonic interpretation of Heraclitus, the things we call 'objects' are like rivers. There's no substance in them. They are merely the stable images created by incessant change. The only constant, in Heraclitus' view, is the law of change, the Logos. Plato was so impressed that he took Heraclitus description and applied it to the 'world of phenomena' (while the logos becomes the template for the 'world of forms').

What better way to say that nothing 'exists' as a substance than to assert that 'to be' and 'not to be' are one and the same? Is that a contradiction? If you tell me that there are witches, then one way to deny your claim is to state that every object (or every person) both is a witch and isn't a witch. That is to say, the concept of 'witch' is self-contradictory. If you tell me that something exists, that there are 'things' or 'substances' which make up the world of our experience, then one way to contradict your claim is to state that every alleged 'object of experience' both exists and doesn't exist.

All the best,

Geoffrey