Arbitrary combination and the use of signs in mathematics: Kant’s 1763 Prize Essay and its Wolffian background

Canadian Journal of Philosophy 44 (5-6):658-685 (2014)
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Abstract

In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant's 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional applicability of mathematical concepts

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10.1080/00455091.2014.967738

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Katherine Dunlop
University of Texas at Austin

Citations of this work

Conceptual Analysis and the Analytic Method in Kant’s Prize Essay.Gabriele Gava - forthcoming - Hopos: The Journal of the International Society for the History of Philosophy of Science.
Definitions and Empirical Justification in Christian Wolff’s Theory of Science.Katherine Dunlop - 2018 - History of Philosophy & Logical Analysis 21 (1):149-176.
The Roles of Kant’s Doctrines of Method.Gabriele Gava & Andrew Chignell - 2023 - Journal of Transcendental Philosophy 4 (2):73-79.

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References found in this work

Mathematical Thought and its Objects.Charles Parsons - 2007 - New York: Cambridge University Press.
Philosophical papers and letters.Gottfried Wilhelm Leibniz & Leroy E. Loemker - 1956 - Chicago,: University of Chicago Press. Edited by Leroy E. Loemker.
Philosophical Papers and Letters.Martha Kneale - 1957 - Philosophical Review 66 (4):574.
Kant on the Mathematical Method.Jaakko Hintikka - 1967 - The Monist 51 (3):352-375.

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