Yesterday I wrote, "And yet if particular a reduces to particular b, then a is nothing other than b, and is therefore identical to b." This was part of an argument that reduction collapses into elimination. A reader objects: "I am not sure that this is an accurate definition of reduction."
He gives an argument having to do with material composition. I'll put the argument in my own way, so as to strengthen it and make it even more of a challenge for me.
1. Whether or not minds are physically reducible, physical reductionism is surely true of some things, statues for example. A statue is reducible to the matter that composes it, a hunk of bronze, say. No one is a statue-hunk dualist. It is not as if there are two things in the same place, the statue and the hunk of bronze. Nor is anyone an eliminativist when it comes to statues.There are such things, but what they are is just hunks of matter. We avoid both dualism and eliminativism by adopting reductionism.
2. But surely the matter of the statue might have been configured or worked in some other way to make a different statue or a non-statue. Before the sculptor went to work on it, the hunk of bronze was just a hunk, and after it became a statue it could have reverted back to being a mere hunk if it were melted down.
3. The statue and the hunk differ property-wise: the hunk, but not the statue, has the property of existing at times at which the statue does not exist. And at every time at which both hunk and statue exist, the hunk, but not the statue, has the modal property of being possibly such as to be a non-statue.
4. By the indiscernibility of Identicals, statue and hunk are not identical.
5. The statue is reducible to its constituent matter but not identical to it. (By 1, 4)
6. It is not the case that if particular a reduces to particular b, then a is identical to b.
This is an impressive argument, but I don't see that it shows that one can have reduction without identity of the reduced to the reducer. I take the argument as further evidence of the incoherence of the notion of the reduction of one particular to another. The first premise, though plausible, is not obviously true. What's more, it seems inconsistent with the second premise. I have argued many times before that in cases like these, statue and lump, fist and hand, brick house and bricks, the thing and its matter differ property-wise and so cannot be identical. They are both temporally and modally discernible. If fist and hand cannot be numerically identical, then they must be numerically distinct. When I take my hand and make a fist of it, the hand does not cease to exist, but something new comes into existence, a fist. Hand and fist, as long as both exist, are two numerically different things occupying exactly the same spatiotemporal position. Admittedly, that sounds strange. Nevertheless, I claim here is just as much reason to be a hand-fist dualist as there is to be a fist-to-hand reductionist.
One could also be an eliminativist. Amazingly, Peter van Inwagen -- no slouch of a philosopher; you don't get a chair if you slouch -- is an eliminativist about artifacts such as the house built by the Wise Pig. See here.
Perhaps I can drive the reductionist onto the horns of a dilemma. Either fist and hand are identical or they are not. They cannot be identical because they differ property-wise. If two things are not numerically identical, however, then they are numerically different. But if fist and hand are numerically different, then the fist does not reduce to the hand.
So I persist in my view that reduction is an incoherent notion. There is no viable via media between dualism and eliminativism.