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Signs, figures and time: Cavaillès on “intuition” in mathematics

Cassou-Noguès, Pierre (2006) Signs, figures and time: Cavaillès on “intuition” in mathematics. THEORIA. An International Journal for Theory, History and Foundations of Science, 21 (1). pp. 89-104. ISSN 2171-679X

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This paper is concerned with Cavaillès’ account of “intuition” in mathematics. Cavaillès starts from Kant’s theory of constructions in intuition and then relies on various remarks by Hilbert to apply it to modern mathematics. In this context, “intuition” includes the drawing of geometrical figures, the use of algebraic or logical signs and the generation of numbers as, for example, described by Brouwer. Cavaillès argues that mathematical practice can indeed be described as “constructions in intuition” but that these constructions are not imbedded in the space and in the time of our Sensibility, as Kant believed: They take place in other structures which are engendered in the history of mathematics. This leads Cavaillès to a criti-cal discussion of both Hilbert’s and Brouwer’s foundational programs.

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Item Type: Published Article or Volume
Cassou-Noguès, Pierre
Additional Information: ISSN: 0495-4548 (print)
Keywords: sign, symbol, figure, time, intuition, Cavaillès, Hilbert, Brouwer, Kant
Depositing User: Users 15304 not found.
Date Deposited: 11 Mar 2014 17:25
Last Modified: 11 Mar 2014 17:25
Item ID: 10464
Journal or Publication Title: THEORIA. An International Journal for Theory, History and Foundations of Science
Publisher: Euskal Herriko Unibertsitatea / Universidad del País Vasco
Official URL:
DOI or Unique Handle:
Date: January 2006
Page Range: pp. 89-104
Volume: 21
Number: 1
ISSN: 2171-679X

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