Brian Loar believes he has refuted all those antiphysicalist arguments that take as their point of departure observations about what is or isn’t conceivable. I argue that there remains an important, popular and plausible-looking form of conceivability argument that Loar has entirely overlooked. Though he may not have realized it, Saul Kripke presents, or comes close to presenting, two fundamentally different forms of conceivability argument. I distinguish the two arguments and point out that while Loar has succeeded in refuting one of Kripke's arguments he has not refuted the other. Loar is mistaken: physicalism still faces an apparently insurmountable conceptual obstacle.