Some Fitch-style arguments

Let strong physicalist supervenience (SPS) be the view that necessarily all truths supervene on first-order truth about the spatiotemporal arrangement of physical stuff.

Here is a plausible thesis:

1. Every first-order truth about the spatiotemporal arrangement of physical stuff is possibly known.

Add this premise:

2. If a conjunction is known, so are its conjuncts.

It follows from SPS, 1 and 2 that:

3. Every actual first-order truth about the spatiotemporal arrangement of physical stuff is actually known.

For suppose that p is any actual first-order truth about the spatiotemporal arrangement of physical stuff. Let q be the conjunction of all other actual first-order truths about the spatiotemporal arrangement of physical stuff. Let r be the conjunction of p and q. Then r is a first-order truth about the spatiotemporal arrangement of physical stuff. By 1, there is a possible world w where r is known. Since r contains all actual first-order truths about the spatiotemporal arrangement of physical stuff, w and the actual world have the same first-order truths about the spatiotemporal arrangement of physical stuff. By SPS, it follows that w and the actual world have the same truths. Thus, since it’s true at w that r is known, it’s actually true that r is known. And since r is actually known, so is p by 2. Hence, we have 3.

In exactly the same way, given:

4. Every first-order truth about the spatiotemporal arrangement of physical stuff is possibly explained

5. If a conjunction is explained, so are its conjuncts

and SPS, we get:

6. Every actual first-order truth about the spatiotemporal arrangement of physical stuff actually has an explanation.

But given physicalism, it is clear that 3 and 6 are false. Regarding 3, it is clear that if physicalism is true, nobody knowns how many hairs I have on my head. Regarding 6, given physicalism, there is no explanation of the sum total of physical reality. Thus:

7. Given either 1 and 2, or 4 and 5, at least one of physicalism and SPS is false.

It is tempting to turn this into an argument against physicalism by holding that:

8. If SPS is true, physicalism is true.

But actually I can imagine someone denying 8. Imagine a classical theist who thinks that everything other than God has to be physical. Such a classical theist will actually believe SPS. For on classical theism, facts about God supervene on facts about everything other than God, since classical theism includes divine simplicity according to which there are no contingent facts intrinsically about God, so any two worlds that differ in their facts about God will have to differ in something other than God. And according to our classical theist, everything other than God has to be physical. So any two worlds that differ must differ in facts about the arrangement of physical stuff, which is what SPS says. However, the classical theist is not a physicalist, because God is not physical on classical theism.

Still, I think an argument against the conjunction of physicalism and SPS is still interesting.