From absolute to local mathematics

Synthese 69 (3):409 - 426 (1986)
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Abstract

In this paper (a sequel to [4]) I put forward a "local" interpretation of mathematical concepts based on notions derived from category theory. The fundamental idea is to abandon the unique absolute universe of sets central to the orthodox set-theoretic account of the foundations of mathematics, replacing it by a plurality of local mathematical frameworks - elementary toposes - defined in category-theoretic terms.

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10.1007/bf00413980

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John L. Bell
University of Western Ontario

Citations of this work

Studies in logical theory.John Dewey - 1903 - New York: AMS Press.
Exploring Categorical Structuralism.C. Mclarty - 2004 - Philosophia Mathematica 12 (1):37-53.
The uses and abuses of the history of topos theory.Colin Mclarty - 1990 - British Journal for the Philosophy of Science 41 (3):351-375.

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References found in this work

The unreasonable effectiveness of mathematics in the natural sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.
A course in mathematical logic.J. L. Bell - 1977 - New York: sole distributors for the U.S.A. and Canada American Elsevier Pub. Co.. Edited by Moshé Machover.
Two applications of logic to mathematics.Gaisi Takeuti - 1978 - [Princeton, N.J.]: Princeton University Press.
[Omnibus Review].Robert Goldblatt - 1986 - Journal of Symbolic Logic 51 (1):225-227.

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