Frege, Kant, and the logic in logicism

J MacFarlane - The philosophical review, 2002 - JSTOR
The philosophical review, 2002JSTOR
Let me start with a well-known story. Kant held that logic and concep-tual 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 …
Let me start with a well-known story. Kant held that logic and concep-tual 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. Never mind whether Frege was right about this. I want to address a different question: Does Frege's position on arithmetic really contradict Kant's? I do not deny that Frege endorsed
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