Arb There Counterexamples to the Cu)sure Principle? Arb Timrb Counterexamples to Tim Closure Principlb7

Very often, a person can't know a proposition without knowing various logical consequences of that proposition. So, for instance, if you know that your friend is wearing a yellow tie, you can't fail to know that your friend is wearing a tie. period. In this case, the relation of logical consequence is obvious. When the relation isn't obvious, a proposition you know may have a logical consequence you don't know for example, a suitably obscure mathematical theorem. In light of these considerations. it seems plausible to hold that if a person knows a given proposition, that person must also know any logical consequence of that proposition which he or she nxognizts as such. Putting it differently, we might say that knowledge is closed under known logical implication.' The problem of skepticism about the external world gives this epistemic principle (hereafter, the "Closure Principle") a special interest. When the skeptic argues that we have no knowledge of the world because we don't know that we aren't massively deceived in some way, he or she appears to assume that knowledge has the closure property. But if it is possible to find clear examples demonstrating that closure sometims fails. a crucial piece of support for skepticism will be removed. The purpose of this paper is to show that even the strongest apparent counterexamples to closure don't hold up under scrutiny. To that extent. the problem of skepticism is still with us.