Gödel, Wittgenstein and the Nature of Mathematical Knowledge

Abstract

“And so, if I understand you correctly, you act and you know why act, but you don't know why you know that you know what you do?”The problem that I want to discuss can be stated simply. For the sake of argument, I assume that knowledge is a relation between people and propositions, and that mathematical knowledge is a subspecies of this. Ordinarily, we are inclined to assume that we can account for one mathematician's knowledge without reference to any other mathematician. So in epistemology we assume that there is but a single ideal mathematician or that, at least as far as knowledge goes, an individual mathematician can be considered in isolation from all others. In so far as a community of mathematicians enters epistemology at all, it is after the already established fact of individual knowledge. The community typically serves as a device for the efficient distribution of knowledge.