In spite of the intuitiveness of epistemic closure, there has been a stubborn stalemate regarding whether it is true, largely because some of the “Moorean” things we seem to know easily (like that I’m sitting on a green chair) seem clearly to entail “heavyweight” philosophical things that we apparently cannot know easily—or perhaps even at all (like that I’m not actually lying in bed dreaming). In this paper, I will show that two widely accepted facts about what we do and don’t know—facts with which any minimally acceptable understanding of knowledge must comport—are jointly inconsistent with the truth of CLR. The proof works by supposing the truth of “Categorialism,” a thesis about the relation between basic categories and common nouns and predicates, which is itself a heavyweight claim that cannot be easily known to be either true or false.