In this paper, I will make the case that an associative account of predication in Hume seems to allow for impossible predicative conceptions—that is, the conceiving of impossible states of affairs involving subjects instantiating properties or qualities—which violate his Conceivability Principle. The natural response is to argue that such conceptions are not clear and distinct, but substantive worries are raised about a number of attempted solutions along these lines. This poses a predicament for Hume scholars: either we must modify or (...) abandon the Conceivability Principle, or reject an associative account of predication, or concede that Hume faces a difficulty he cannot solve. (shrink)