Abstract
Kant maintains that mathematical judgments are synthetic — that we cannot ground them merely through reflection on their constituent concepts. Instead, he argues, we must construct those concepts, i.e., “exhibit a priori the intuition which corresponds to” them, grounding our judgments on what can be made evident only through such construction. (A 713/B 741)1 I first sketch an interpretation of Kant’s doctrine, focusing on the construction of arithmetical concepts. I then go on to indicate how an understanding of Kant’s view concerning arithmetical construction can shed light on his views concerning imagination.
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Notes
Quotations are from Kemp Smiths translation of the Critique of Pure Reason, 2nd impression with corrections, Macmillan, London, 1963.
Arithmetik und Kombinatorik hei Kant (dissertation done at Freiburg, 1934), Itzehoe, 1938.
Kant on the Mathematical Method, Monist 51 (1967); reprinted in this volume pp. 21-42.
Kants Philosophy of Arithmetic, in Philosophy, Science, and Method: Essays in Honor of Ernest Nagel, ed. by S. Morgenbesser, P. Suppes, and M. White, St. Martins, New York, 1969; reprinted in this volume pp. 43-79.
Kant introduces the notion of symbolic construction only in his discussion of algebra. Like Parsons, however, I believe that it is legitimate to extend the notion and to describe both the use of numerals in calculation and the use of formulae in logic as involving symbolic construction. For fuller discussion of this point, see my Kant on the Construction of Arithmetical Concepts, Kant-Studien 73 (1982), 17-46.
As Parsons notes, analogous points can be made for proofs of the sort that Leibniz proposed, as well as for proofs of quantificational schemata that are closely related to the arithmetical identities. bid.,pp. 66-67. 9 Parsons views on this matter are developed further in Mathematical Intuition, Proceedings of the Aristotelian Society,Vol. 80 (1979-80), pp. 145-68.
The ideas sketched here are developed a bit more fully in my Kants View of Imagination, Kant-Studien 79 (1988), pp. 140-164.
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© 1992 Springer Science+Business Media Dordrecht
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Young, J.M. (1992). Construction, Schematism, and Imagination. In: Posy, C.J. (eds) Kant’s Philosophy of Mathematics. Synthese Library, vol 219. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8046-5_7
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