Section 31 Revisited

Joan Weiner

in From Frege to Wittgenstein

Published in print January 2002 | ISBN: 9780195133264
Published online November 2003 | e-ISBN: 9780199833580 | DOI:
Section 31 Revisited

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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.

Keywords: Bedeutung; elucidation; Frege; Grundgesetze; inductive proof; logic; metatheory; soundness

Chapter.  20711 words. 

Subjects: History of Western Philosophy

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