Formal Analyticity

Abstract

This dissertation consists of three papers that together serve to defend a notion of analyticity for formal languages: A sentence (or rule of inference) of a formal language is formally analytic if understanding the sentence (or rule of inference) is sufficient for being in a position to know it. This is a way of reviving a traditional method of explaining our knowledge of mathematics. I first defend the claim that certain basic axioms of set theory are formally analytic by using a notion of unfolding, inspired by Kurt Gödel's influential remarks that some axioms of set theory "only unfold the content of the concept of set" (in "Unfolding the Content of the Concept of Set"). I then argue that Timothy Williamson's famous argument template against analyticity doesn't work against the claim that there are formally analytic sentences (in "Defending Formal Analyticity"). Finally, I argue that recognizing formal analyticity in set theory can help answer some philosophical questions concerning the nature and extent of the universe of sets (in "Why Is the Universe of Sets Not a Set?").