Eliezer confirmed (at a meetup) that he had "leanings" in the direction of constructivism/intuitionism -- apparently not quite aware of the discredited status of such views in mathematics.

Can you elaborate on constructivism, intuitionism, and their discrediting? And what that has to do with the law of the excluded middle? I thought constructivism and intuitionism were epistemological theories, and it isn't immediately obvious how they apply to mathematics. Does a constructivist mathematician not believe in proof by contradiction?

Also, I don't know what you mean by "the standard proof of infinite sets".