Cassou-Noguès, Pierre (Author)
Theoria (0495-4548)
Volume: 21
Pages: 89--104
Publication date: 2006
Language: English
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 al-gebraic or logical signs and the generation of numbers as, for example, described by Brouwer. Cavaillès ar-gues that mathematical practice can indeed be described as constructions in intuition but that these con-structions 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. Key words: sign, symbol, figure, time, intuition, Cavaillès, Hilbert, Brouwer, Kant.
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