David Chalmers' conceivability argument against physicalism relies on the entailment from a priori conceivability to metaphysical possibility. The a posteriori physicalist rejects this premise, but is consequently committed to psychophysical strong necessities. These don't fit into the Kripkean model of the necessary a posteriori, and they are therefore, according to Chalmers, problematic. But given semantic assumptions that are essential to the conceivability argument, there is reason to believe in microphysical strong necessities. This means that some of Chalmers' criticism is unwarranted, and the rest equally afflicts the dualist. Moreover, given that these assumptions are independently plausible, there's a general case to be made for the existence of strong necessities outside the psychophysical domain.