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Observations on category theory

Axiomathes 12 (1-2):151-155 (2001)

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  1. Mathematics is megethology.David K. Lewis - 1993 - Philosophia Mathematica 1 (1):3-23.
    is the second-order theory of the part-whole relation. It can express such hypotheses about the size of Reality as that there are inaccessibly many atoms. Take a non-empty class to have exactly its non-empty subclasses as parts; hence, its singleton subclasses as atomic parts. Then standard set theory becomes the theory of the member-singleton function—better, the theory of all singleton functions—within the framework of megethology. Given inaccessibly many atoms and a specification of which atoms are urelements, a singleton function exists, (...)
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  • The Ghost of Modality.Hermann Weyl - 1940 - In Marvin Farber (ed.), Philosophical essays in memory of Edmund Husserl. New York,: Greenwood Press. pp. 278-304.
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  • From absolute to local mathematics.J. L. Bell - 1986 - Synthese 69 (3):409 - 426.
    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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  • A Primer of Infinitesimal Analysis.John Lane Bell - 1998 - Cambridge University Press.
    This is the first elementary book to employ the concept of infinitesimals.
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