Jonathan Vogel

Are there Counterexamples to the Closure Principle

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 recognizes as such. Putting it differently, we might say that knowledge is closed under known logical implication.1