Frege, Kant, and the logic in logicism

Philosophical Review 111 (1):25-65 (2002)
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Abstract

Let me start with a well-known story. Kant held that logic and conceptual analysis alone cannot account for our knowledge of arithmetic: “however we might turn and twist our concepts, we could never, by the mere analysis of them, and without the aid of intuition, discover what is the sum [7+5]” (KrV, B16). Frege took himself to have shown that Kant was wrong about this. According to Frege’s logicist thesis, every arithmetical concept can be defined in purely logical terms, and every theorem of arithmetic can be proved using only the basic laws of logic. Hence, Kant was wrong to think that our grasp of arithmetical concepts and our knowledge of arithmetical truth depend on an extralogical source—the pure intuition of time (Frege 1884, §89, §109). Arithmetic, properly understood, is just a part of logic.

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John MacFarlane
University of California, Berkeley

Citations of this work

On the Transcendental Freedom of the Intellect.Colin McLear - 2020 - Ergo: An Open Access Journal of Philosophy 7:35-104.
The Kantian (Non)‐conceptualism Debate.Colin McLear - 2014 - Philosophy Compass 9 (11):769-790.
Kant: constitutivism as capacities-first philosophy.Karl Schafer - 2019 - Philosophical Explorations 22 (2):177-193.

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Critique of Pure Reason.Immanuel Kant - 1998 - Cambridge: Cambridge University Press. Edited by J. M. D. Meiklejohn. Translated by Paul Guyer & Allen W. Wood.

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