Frege on definitions

Philosophy Compass 3 (5):992-1012 (2008)

Authors
Sanford Shieh
Wesleyan University
Abstract
This article treats three aspects of Frege's discussions of definitions. First, I survey Frege's main criticisms of definitions in mathematics. Second, I consider Frege's apparent change of mind on the legitimacy of contextual definitions and its significance for recent neo-Fregean logicism. In the remainder of the article I discuss a critical question about the definitions on which Frege's proofs of the laws of arithmetic depend: do the logical structures of the definientia reflect the understanding of arithmetical terms prevailing prior to Frege's analyses? Unless they do, it is unclear how Frege's proofs demonstrate the analyticity of the arithmetic in use before logicism. Yet, especially in late writings, Frege characterizes definitions as arbitrary stipulations of the senses or references of expressions unrelated to pre-definitional understanding. I conclude by examining some options for conceiving of the status of Frege's logicism in light of this apparent tension, and outline a suggestion for a philosophically fruitful way of resolving this tension.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1111/j.1747-9991.2008.00167.x
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 38,992
Through your library

References found in this work BETA

Critique of Pure Reason.Immanuel Kant - 1991 - In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Philosophy and Phenomenological Research. Blackwell. pp. 449-451.
Posthumous Writings.Gottlob Frege - 1991 - Wiley-Blackwell.

View all 30 references / Add more references

Citations of this work BETA

Frege’s Unification.Rachel Boddy - 2018 - History and Philosophy of Logic 40 (2):135-151.
Busting a Myth About Leśniewski and Definitions.Rafal Urbaniak & K. Severi Hämäri - 2012 - History and Philosophy of Logic 33 (2):159 - 189.
Conceptual Analysis and Analytical Definitions in Frege.Gilead Bar‐Elli - 2017 - European Journal of Philosophy 25 (4):963-984.

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
112 ( #61,350 of 2,319,671 )

Recent downloads (6 months)
10 ( #103,613 of 2,319,671 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature