Frege on definitions

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



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Sanford Shieh
Wesleyan University

Citations of this work

Busting a Myth about Leśniewski and Definitions.Rafal Urbaniak & K. Severi Hämäri - 2012 - History and Philosophy of Logic 33 (2):159-189.
Frege’s Unification.Rachel Boddy - 2018 - History and Philosophy of Logic 40 (2):135-151.
A Formal Explication of Blanchette's Conception of Fregean Consequence.Günther Eder - 2023 - History and Philosophy of Logic 44 (3):287-310.

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References found in this work

The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.
Critique of pure reason.Immanuel Kant - 1781/1998 - In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Philosophy and Phenomenological Research. Blackwell. pp. 449-451.
Translations from the philosophical writings of Gottlob Frege.Gottlob Frege - 1952 - Oxford, England: Blackwell. Edited by P. T. Geach & Max Black.

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