On the number of types

Miloš Kosterec

pp. 5005-5021

in: Matteo Colombo, Raoul Gervais, Jan Sprenger (eds), Objectivity in science, Synthese 194 (12), 2017.

Abstract

In this paper, I investigate type theories (TTs) 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.