On the number of types

Synthese 194 (12):5005-5021 (2017)
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Abstract

In this paper, I investigate type theories from several perspectives. First, I present and elaborate the philosophical and technical motivations for these theories. I then offer a formal analysis of various TTs, focusing on the cardinality of the set of types contained in each. I argue that these TTs can be divided into four formal categories, which are derived from the cardinality of the set of their basic elementary types and the finiteness of the lengths of their molecular types. The paper provides proofs of the cardinality of the universe of types for each of the specified theories.

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10.1007/s11229-016-1190-1

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Citations of this work

Hyperintensionality and Normativity.Federico L. G. Faroldi - 2019 - Cham, Switzerland: Springer Verlag.

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References found in this work

Introduction to mathematical logic..Alonzo Church - 1944 - Princeton,: Princeton university press: London, H. Milford, Oxford university press. Edited by C. Truesdell.
The Impossible: An Essay on Hyperintensionality.Mark Jago - 2014 - Oxford, United Kingdom: Oxford University Press.
Principia Mathematica.A. N. Whitehead & B. Russell - 1927 - Annalen der Philosophie Und Philosophischen Kritik 2 (1):73-75.
Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.

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