Suppose I asserted that the difference of the positions of B and G# in the A major scale was identical with, supervened upon, or was in some other way explicable in terms of, the greater than relation that the number 23 bears to the number 18. You would no doubt wonder what the hell I was talking about. Just as notes in a scale are one thing and numbers are another, so too are positions in the scale and positions in the sequence of numbers different things, and that’s that. Relations of identity, supervenience, explanation, etc. simply don’t hold between the two. (Of course, there are mathematical relationships between notes in a scale; the point is that the relationships between notes are clearly not reducible to or entirely explicable in terms of mathematical relationships.)
Note that this has nothing to do with the lack of a law-like correlation between the two – whatever that could mean in this context, since we’re talking about abstractions rather than concrete objects or events. And even if we reverted to speaking of concrete objects and events, we don’t think that the reason talk of identity, supervenience, etc. makes no sense in this context is that we find no regular correlation in nature between (for example) the playing of B on a musical instrument and there being 23 of something in the vicinity. Correlation or lack thereof just has nothing to do with it. Even if we found that some such bizarre correlation held, we wouldn’t think “Aha! B in the A major scale must be identical to or supervenient upon the number 23!” Such a claim would be just as unintelligible in the presence of the correlation as in the absence of it.
I propose that the same thing is true of claims like this: “Having a thought with the content that P is identical to, supervenient upon, or otherwise explicable in terms of having a sentence with the meaning that P encoded in the brain”; “The semantic-cum-logical relations between thoughts are identical to, supervenient upon, or otherwise explicable in terms of the causal relations between brain events”; and other claims of this sort. Such claims are simply nonsensical. Logical relations are one thing, causal relations are another, and that’s that. If you don’t see this, either you don’t understand what a logical relation is or you don’t understand what a causal relation is – or, more likely, you are in the grip of some ideology that leads you to speak nonsense. Similarly with the claim that having a thought involves having a sentence in the head. Having the thought that 2 + 2 + 4 – that is to say, grasping the proposition that 2 + 2 = 4 – is one thing, and having some sentence instantiated somewhere (whether on a chalkboard, in a notebook, in a computer, in a brain, or wherever) is another, and that’s that. If you don’t see this, then, again, either you don’t understand what a proposition is, or you don’t understand what a sentence is, or you are in the grip of some ideology.
The ideology in question is, of course, materialism (or physicalism or naturalism, if you prefer). If you start with the assumption that thinking simply must be identical to, supervenient upon, or otherwise explicable in terms of brain activity, then it will seem to you at least plausible that logical relations might be reducible to causal relations, thoughts identifiable with the having of brain sentences, etc. But no one would think these things plausible even for a moment if they were not already seeing the world through materialist glasses – indeed, they would take the evident absurdity of such proposals as prima facie evidence of the falsity of materialism. (And that is, I propose, part of the reason why most philosophers historically have not been materialists.)
“But what about the correlations holding between certain mental events and certain brain events?” Well, what about them? Again, no one would think for a moment that a correlation between (say) the playing of B on a musical instrument and there being 23 of something in the vicinity is even prima facie evidence for the plausibility of the claim that the difference of the positions of B and G# in the A major scale was identical with, supervened upon, or was in some other way explicable in terms of, the greater than relation that the number 23 bears to the number 18. Or if he did think so, it could only be because he is already in the grip of some bizarre ideology (Pythagoreanism?) which independently insists already on there being some deep metaphysical connection between musical relationships and mathematical ones – and which has deadened thereby his ability to spot clear category mistakes.
From an Aristotelian point of view, such correlations are in any event not the least bit surprising despite the falsity of materialism. Since soul and body are related as form and matter, mental and physiological correlations are no more surprising than the “correlation” that exists between the form of some particular tree and the matter than composes it. But in neither case is there any question of identity, supervenience, etc., since form and matter in general are simply irreducible.
Peter Geach said it well: “When we hear of some new attempt to explain reasoning or language or choice naturalistically, we ought to react as if we were told that someone had squared the circle or proved the square root of 2 to be rational. Only the mildest curiosity is in order – how well has the fallacy been concealed?” (The Virtues, p. 52) Like Pythagoreanism, materialism is philosophically interesting, often defended by thinkers of genius – and ultimately simply and clearly wrong.