Types, Sets and Categories

Abstract

This essay is an attempt to sketch the evolution of type theory from its beginnings early in the last century to the present day. Central to the development of the type concept has been its close relationship with set theory to begin with and later its even more intimate relationship with category theory. Since it is effectively impossible to describe these relationships (especially in regard to the latter) with any pretensions to completeness within the space of a comparatively short article, I have elected to offer detailed technical presentations of just a few important instances

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John L. Bell
University of Western Ontario

Citations of this work

Category theory.Jean-Pierre Marquis - 2008 - Stanford Encyclopedia of Philosophy.
Type theory.Thierry Coquand - 2008 - Stanford Encyclopedia of Philosophy.
On the number of types.Miloš Kosterec - 2017 - Synthese 194 (12):5005-5021.
On gauge symmetries, indiscernibilities, and groupoid-theoretical equalities.Gabriel Catren - 2022 - Studies in History and Philosophy of Science Part A 91 (C):244-261.
The Origin of the Theory of Types.Ryo Ito - 2018 - Annals of the Japan Association for Philosophy of Science 27:27-44.

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References found in this work

Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (3):114-115.
Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
General Theory of Natural Equivalences.Saunders MacLane & Samuel Eilenberg - 1945 - Transactions of the American Mathematical Society:231-294.
Foundations of Constructive Analysis.Errett Bishop - 1967 - New York, NY, USA: Mcgraw-Hill.

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