David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Theoria 21 (1):89-104 (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 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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Gila Sher & Richard L. Tieszen (eds.) (2000). Between Logic and Intuition: Essays in Honor of Charles Parsons. Cambridge University Press.
Paul Cortois (1996). The Structure of Mathematical Experience According to Jean Cavaillèst. Philosophia Mathematica 4 (1):18-41.
Paul Anthony Wilson, Constructing Numbers Through Moments in Time: Kant's Philosophy of Mathematics.
Paolo Mancosu (ed.) (1998). From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s. Oxford University Press.
Colin Mclarty (1997). Poincaré: Mathematics & Logic & Intuition. Philosophia Mathematica 5 (2):97-115.
Michael Friedman (2012). Kant on Geometry and Spatial Intuition. Synthese 186 (1):231-255.
Colin Cheyne (1997). Getting in Touch with Numbers: Intuition and Mathematical Platonism. Philosophy and Phenomenological Research 57 (1):111-125.
Thomas Mormann (2009). Completions, Constructions, and Corollaries. In H. Pulte, G. Hanna & H.-J. Jahnke (eds.), Explanation and Proof in Mathematics: Philosophical and Educational Perspectives. Springer.
Richard Tieszen (2002). Gödel and the Intuition of Concepts. Synthese 133 (3):363 - 391.
Frode Kjosavik (2009). Kant on Geometrical Intuition and the Foundations of Mathematics. Kant-Studien 100 (1):1-27.
Added to index2009-01-28
Total downloads16 ( #116,729 of 1,410,540 )
Recent downloads (6 months)3 ( #76,382 of 1,410,540 )
How can I increase my downloads?