I defend physicalism about phenomenal consciousness against recent epistemic arguments for dualism. First I argue (as against Kripke) that psychophysical identities can be a posteriori (and apparently contingent, and conceivably false). Their epistemic status is due to the analytic independence of phenomenal and physical-functional terms. Unlike Kripke’s own explanation of a posteriori necessity, analytic independence is consistent with—indeed explained by—the direct reference of phenomenal terms, so Kripke’s argument against psychophysical identities fails. I then argue (as against White and Chalmers) that direct reference does not itself make identities a priori. Next I endorse the “a priori entailment thesis”: if physicalism is true, phenomenal truths follow a priori from a complete statement of the facts of physics. I argue that physicalists must accept a priori entailment if we are to avoid brute or “strong” a posteriori necessities. I show that a priori entailment is consistent with analytic independence, and so make room for what Chalmers calls “type-C” physicalism. Jackson’s “Mary”, who knows all the physical facts, would be able to deduce the physical-functional reference of phenomenal terms, and so the truth of psychophysical identities, without appealing to analytic connections. The “knowledge” argument for dualism therefore fails. The lack of such connections does, however, help explain why Mary’s deduction seems intuitively impossible. A priori entailment makes zombie scenarios inconceivable, so Chalmers’s “conceivability” argument fails. It also closes Levine’s “explanatory gap” between physical and phenomenal truths. Though it may not satisfy all demands for explanation, any remainder poses no threat to physicalism. I then defend type-C physicalism against some recent objections to the “phenomenal-concept strategy”. I close by observing that while the view I defend can rebut epistemic arguments for dualism, it leaves the question of whether consciousness has a physical basis as a matter for empirical investigation.