To: David F.
From: Geoffrey Klempner
Subject: Metaphysical atomism of Leucippus and Democritus
Date: 4 May 2005 10:44

Dear David,

Thank you for your email of 24 April, with your fourth essay for the Ancient Philosophy program, in response to the question, 'How much truth is there in the claim that the atomism of Leucippus and Democritus was a 'metaphysical' rather than a 'physical' theory?'.

Thanks also for your email of 26 April with further thoughts about atomism.

Quite a lot has been written on the 'ou mallon' principle (I remember hearing a paper by Stephen Makin one of the lecturers at Sheffield).

I apologize for giving the false impression that the principle of sufficient reason was the 'old' principle and ou mallon the 'new' principle. It is more a case of enthusiastic generalization from a legitimate application of the principle of sufficient reason (in Anaximander) to applications which are rather more dubious. An example of a dubious application is the argument that atoms must be every conceivable shape and size.

Applying the principle of sufficient reason, if an atom has size S, then there is a reason why it has size S and not S', which is larger or smaller than S. That's OK. Maybe we will never know what that reason is, but that's no problem. Whereas the ou mallon argument takes the further step of saying, 'we know there can't be any reason', therefore there must also exist an atom of size S'. The first thing to say about this is that if there can't be a reason why your atom has size S then that violates the PSR. The fact that some other atom somewhere has size S' in no way makes up for this lack. On the other hand if there is a reason why that particular atom has size S - and presumably for the sizes of all the other atoms - then there is absolutely no ground for making any further claims about what the range of sizes must be. Each atom having a sufficient reason for being the size that it is might, for all we know result in atoms having just three sizes, or one, or a million.

What the ou mallon argument does highlight is that the properties of atoms are to be accounted for on strictly logical or metaphysical principles. It is difficult or impossible to think of 'the reason why this particular atom has size S' as being anything other than the physical cause of its having the size that it has. Whereas if we are throwing out that kind of physical explanation on principle, then the ou mallon argument does begin to look plausible.

As I remark in the unit, this makes the atomist theory similar in this respect to Cartesian physics, which attempts to deduce physical properties a priori from the concept of geometrical extension alone.

The difference between the void and the concept of space as I understand it is that space is not inconsistent with physical properties - e.g. the capacity to support fields - whereas the void by definition cannot have any properties. The capacity to support fields is an empirical discovery, which might have been otherwise. Whereas the void by definition cannot support fields or have any physical properties. Again, evidence that atomism is very much a metaphysical rather than a physical theory.

I would say (against Barnes?) that this shows that atoms and the void are equally concrete and equally abstract.

I disagree with you when you say that the atomist account of perception shows its aspect as a physical rather than a metaphysical theory. Sure, the posited explanation of perception, the mechanics of how images are conveyed to the eye, is physical. But there is also a metaphysical claim concerning how these purely mechanical movements in the subject become conscious 'perceptions'. Today, philosophers talk of the 'problem of qualia' or the 'problem of consciousness'. The materialist response is very much a philosophical (metaphysical) claim, as are the various alternatives to materialism.

I am pleased, however, that we agree that atomism is 'essentially and fundamentally metaphysical'.

Further questions

1. Here Frege's account of quantifiers might help. To say that there are no tigers in my room is to say that for all x , if x is in my room then x is not a tiger.

To say that there is nothing between atom A and atom B is to say that for all monadic properties P and all locations y, if y is between A and B then there is no x such that x is located at y and Px. ('Monadic' because if we allowed relational properties this would be trivially false: each location itself has the relational property of being, e.g. closer to A than to B).

To me, that formula comes close to capturing the atomist notion of the void.

2. Your idea of atoms as 'conceptual points' is moving in the direction of Wittgenstein's account of 'simples' in the Tractatus. Have a look at some expositions of Wittgenstein's 'logical atomism'.

All the best,

Geoffrey