Frege, Kant, and the logic in logicism

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

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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References found in this work

Philosophical Investigations.Ludwig Josef Johann Wittgenstein - 1953 - New York, NY, USA: Wiley-Blackwell.
Individualism and the Mental.Tyler Burge - 1979 - Midwest Studies in Philosophy 4 (1):73-122.
Philosophical investigations.Ludwig Wittgenstein & G. E. M. Anscombe - 1953 - Revue Philosophique de la France Et de l'Etranger 161:124-124.
Critique of Pure Reason.Immanuel Kant - 1998 - Cambridge: Cambridge University Press.

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Citations of this work

On the Transcendental Freedom of the Intellect.Colin McLear - 2020 - Ergo: An Open Access Journal of Philosophy 7:35-104.
Kant: Constitutivism as Capacities-First Philosophy.Karl Schafer - 2019 - Philosophical Explorations 22 (2):177-193.
The Kantian (Non)‐Conceptualism Debate.Colin McLear - 2014 - Philosophy Compass 9 (11):769-790.
Logical Pluralism and Normativity.Stewart Shapiro & Teresa Kouri Kissel - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (3-4):389-410.

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