What has come to be known as “a priori physicalism” is the thesis, roughly, that the non-physical truths in the actual world can be deduced a priori from a complete physical description of the actual world. To many contemporary philosophers, a priori physicalism seems extremely implausible. In this paper I distinguish two kinds of a priori physicalism. One sort – strict a priori physicalism – I reject as both unmotivated and implausible. The other sort – liberal a priori physicalism – (...) I argue is both motivated and plausible. This variety of a priori physicalism insists that the necessitation of non-physical truths by the physical facts must be underwritten in a certain fashion by a priori knowledge, but the a priori knowledge need not amount to a simple deduction of the non-physical truths from a complete physical description of the world. Further, this sort of liberal a priori physicalism has the advantage that it offers hope for a genuinely satisfying account of how the physical facts manage to necessitate the facts about phenomenal consciousness – thereby in effect solving the “hard problem” of consciousness. The first half of the paper sets out the motivation for liberal a priori physicalism and its superiority to the strict version; the second half presents one strategy available to the liberal a priori physicalist for showing how consciousness can be accommodated in a purely physical world. (shrink)