Signs, figures and time : Cavaillès on intuition in mathematics

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,...

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Bibliographic Details
Published in:Theoria (Madrid, Spain) Spain), 2006, Vol.21 (55), p.89-104
Main Author: CASSOU-NOGUES, Pierre
Format: Article
Language:English
Subjects:
Brouwer
Cavaillès
figure
General points
Hilbert
History of science and technology
History of science in relation to other disciplinary fields
intuition
Kant
Philosophy
sign
symbol
time
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Summary: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 critical discussion of both Hilbert¿s and Brouwer¿s foundational programs
ISSN:0495-4548
2171-679X