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

Sanford Shieh
Wesleyan University
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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DOI 10.1111/j.1747-9991.2008.00167.x
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References found in this work BETA

The Foundations of Arithmetic.Gottlob Frege - 1953 - Evanston: Ill., Northwestern University Press.
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.

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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.
Frege's Definition of Number: No Ontological Agenda?Edward Kanterian - 2010 - Hungarian Philosophical Review 54 (4):76-92.
What is in a Definition? Understanding Frege’s Account.Edward Kanterian - 2018 - Siegener Beiträge Zur Geschichte Und Philosophie der Mathematik 9:7-46.
Conceptual Analysis and Analytical Definitions in Frege.Gilead Bar‐Elli - 2017 - European Journal of Philosophy 25 (4):963-984.

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