 As for lottery propositions: several theorists suggest that we do not in fact know that they are true because knowing them requires believing them because of something that establishes their truth, and we (normally) cannot establish the truth of lottery propositions. There are various ways to understand what is meant by “establishing” the truth of a claim. Dretske, as we have seen, thinks that knowledge entails having a conclusive reason for thinking as we do. David Armstrong (1973, p. 187) said that knowledge entails having a belief state that “ensures” truth. Safe indication theorists suggest that we know things when we believe them because of something that safely indicates their truth. And Harman and Sherman (2004, p. 492) say that knowledge requires believing as we do because of something “that settles the truth of that belief.” On all four views, we fail to know that a claim is true when our only grounds for believing it is that it is highly likely. However, the unknowability of lottery propositions is not a substantial threat to closure, since it is not obvious that there are propositions that are both known to be true and that entail lottery propositions. Consider the example discussed earlier: the conditional if win then buy together with not-buy. If I know these, then, by GK, I know not-win, a lottery proposition. But it is quite plausible to deny that I do know these. After all, I might win the lottery.