Section 31 Revisited

Abstract

Abstract In Section 31 of his Grundgesetze der Arithmetik, Frege argues that all the simple names in his logical notation have Bedeutung. Most contemporary philosophers have found Frege's argument deeply mysterious. While the argument is certainly difficult to interpret, I argue that its apparent fallaciousness and circularity are largely artifacts of the standard interpretation. On that interpretation, the early sections of Grundgesetze are meant to set out a metatheoretic (proto‐soundness) proof, and Section 31's burden is to establish the basic case of an inductive proof that all Begriffsschrift expressions have Bedeutung. But there are compelling reasons for rejecting the metatheoretic proofreading; for it conflicts with many of Frege's actual statements in these sections. I offer a reading that fits Frege's statements, and one upshot is a new understanding of Section 31 on which its argument is neither fallacious nor circular.