I present a cumulative case for the thesis that we only know propositions that are certain for us. I argue that this thesis can easily explain the truth of eight plausible claims about knowledge: There is a qualitative difference between knowledge and non-knowledge. Knowledge is valuable in a way that non-knowledge is not. Subjects in Gettier cases do not have knowledge. If S knows that P, P is part of S’s evidence. If S knows that P, ~P is epistemically impossible for S. If S knows that P, S can rationally act as if P. If S knows that P, S can rationally stop inquiring whether P. If S knows each of {P1, P2, … P n }, and competently deduces Q from these propositions, S knows that Q. I then argue that the skeptical costs of this the...