Nearly everybody nowadays accepts the 'causal completeness of physics' - every physical event (or at least its probability) has a full physical cause. This leaves no room for non-physical things to make a causal difference to physical effects. But it would be absurd to deny that thoughts and feelings (and population movements and economic depressions . . .) cause physical effects. So they must be physical things.
If there is such a simple argument for physicalism, how come everybody hasn't always been a physicalist? That's a good question, and there is a good answer. The 'causal completeness of physics' wasn't widely accepted until recently.
A certain kind of methodologically-minded philosopher of science is quick to read off metaphysical conclusions from features of scientific practice. Chemists don't derive their laws from fundamental physics, so reductive physicalism must be false. Biologists refer to natural numbers in some of their explanations, so numbers must exist. I think that this kind of thing makes for bad philosophy.
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