To: Ana B.
From: Geoffrey Klempner
Subject: Anaxagoras: all things have a portion of everything
Date: 23 September 2004 12:34

Dear Ana,

Thank you for your email of 9 September, with your fourth essay for the Ancient Philosophy program, in response to the question, 'All things have a portion of everything.' - Describe the logical steps that led Anaxagoras to assert that paradoxical claim. Is his view coherent?

Your account of the logical steps which lead to the claim that 'all things have a portion of everything' is very clear:

1. Nothing 'can just pop into existence', so every substance that we see - and not just the so-called elements fire, earth, water air - must an indestructible element, there for all time.

2. Observation: the bread that we eat appears to 'generate' flesh and blood.

3. But there can't be any 'generation' because (from 1.) all the elements, all the substances we see, are there for all time.

4. Therefore, when we eat, 'a change in the proportions of the combined substances' causes flesh and blood to 'surface'.

So far, so good. But now you raise an objection:

'If every substance is uniform in its entirety, such that if a piece of paper were torn to shreds, those minuscule, individual shreds would still be paper, and paper alone, how can this paper be made up of everything else (if it's still just paper?)?

I remember a similar objection which occurred to me when I attended lectures on the Presocratic philosophers as a first year undergraduate student.

I couldn't get this out of my head. How can the loaf of bread on my table be: 'bread, blood, flesh bone'? The bread on my table (call this bread1) is surely less bready than the purer bread2 which mixed with blood, flesh, bone produces the resulting loaf.

Now take the bread2, the purer bread, and consider this apart from the blood, flesh and bone that it is mixed with. This substance is also a mixture, containing - guess what! - bread, blood, flesh and bone. So now we have bread3, which produces bread2 when mixed with blood, flesh and bone etc. Logically, this must be purer than bread2. And so on. We never actually meet *bread*, but only bread mixed with other stuff in various proportions.

That raises the question: what *is* bread?

Anaxagoras, I believe, has an answer to this.

Bread is never pure bread, but merely a mixture where the quality of 'breadiness' predominates, and the same applies however finely you divide the mixture.

In fact, 'mixture' is the wrong word, because it implies a notion which we are familiar with, the idea of separate components that are 'mixed' together. But Anaxagoras rejects this. In describing his theory, it would be better to say that every spatial volume exhibits a predominant quality, e.g. breadiness, or fleshiness, or bloodiness. The 'elements' of all things are not stuffs but rather qualities. A rectangular or oval shaped volume of space that exhibits a predominantly bready quality is something we call, 'a loaf of bread'.

Bread is not 'made' or 'created' by mixing blood, flesh bone etc. Breadiness has always existed and will always exist. Certain processes make it 'surface' as the dominant quality and other processes make it 'retreat'.

Similarly, with the paper. What we call 'paper' is a rectangular flat-shaped volume of space which is strongly papery and slightly silvery and bony. When you burn a piece of paper, the quality of being ashy comes to the surface and the paperiness retreats. And so on.

Is this coherent?

Obviously, this is a different question from whether it is coherent with what we 'know', with the benefit of two or three hundred years of scientific inquiry. Suppose you were God and could create any world you liked - and were bound only by the laws of logic - could you create an Anaxagorean world?

One thing which we haven't mentioned is anything to do with measurement or quantity. Take a jar of coloured red liquid and add one drop of bleach: the liquid goes white. This is pretty hard to explain on the Anaxagorean theory. After all, we have changed the proportions only slightly. But the theory doesn't have to explain this.

And that is the point.

There are no rules or laws governing the conditions under which a certain quality surfaces or retreats, nor could there be. It all might as well be by magic.

That is not incoherence, exactly, but it is a serious weakness. In the absence of any quantitative constraints, there cannot be an Anaxagorean 'physics'.

All the best,

Geoffrey