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The British Journal for the Philosophy of Science 1990 41(3):351-375; doi:10.1093/bjps/41.3.351
© 1990 by British Society for the Philosophy of Science
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The Uses and Abuses of the History of Topos Theory

COLIN McLARTY

Case Western Reserve University Cleveland, Ohio, U.S.A.

The view that toposes originated as generalized set theory is a figment of set theoretically educated common sense. This false history obstructs understanding of category theory and especially of categorical foundations for mathematics. Problems in geometry, topology, and related algebra led to categories and toposes. Elementary toposes arose when Lawvere's interest in the foundations of physics and Tierney's in the foundations of topology led both to study Grothendieck's foundations for algebraic geometry. I end with remarks on a categorical view of the history of set theory, including a false history plausible from that point of view that would make it helpful to introduce toposes as a generalization from set theory.


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 Philosophia MathematicaHome page
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