Article ID: CBB000933621

Signs, Figures and Time: Cavaillès on “Intuition” in Mathematics (2006)


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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Authors & Contributors
Rowe, David E.
Sieg, Wilfried
Gauthier, Yvon
Di, Li
Corry, Leo
Cerroni, Cinzia
Perspectives on Science
Historia Mathematica
Science in Context
Nei Menggu Shifan Daxue Xuebao (Ziran Kexue Ban)
Revue d'Histoire des Mathématiques
Archive for History of Exact Sciences
Kluwer Academic
de Gruyter
Springer International
Formalization (philosophy)
Hilbert, David
Enriques, Federigo
Gödel, Kurt
Kronecker, Leopold
Klein, Felix
Dedekind, Richard
Time Periods
20th century, early
19th century
20th century
Paris (France)
Universität Göttingen
Göttingen. Universität

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