## Friday, June 1, 2012

### A moderately smart being that knows all necessary truths can know everything

Suppose Fred knows all necessary truths and is at least as smart as the author of this post. Fred wants to know whether a proposition p is true. So Fred says: "I stipulate that P is the singleton set {p} and that S is the subset of all the members of P that are true." But sets have their members essentially. So S is necessarily empty or necessarily non-empty. If S is necessarily empty, then Fred knows that, and if S is necessarily non-empty, then Fred knows that, too. Since Fred is at least as smart as the author of this post, if Fred knows that S is necessarily empty, he can figure out that therefore S is empty, and hence that all the propositions in P are false, and hence that p is not true. And if Fred knows that S is necessarily non-empty, then Fred can figure out that therefore S is non-empty, and hence that p is true. In either case, then, Fred can figure out whether p is true.