Category theory and the search for universals

a very short guide for philosophers

Alberto Peruzzi

pp. 159-182

in: Francine F. Abeles, Mark E. Fuller (eds), Modern logic 1850-1950, East and West, Basel, Birkhäuser, 2016

Abstract

The aim of the paper is to present the categorical notion of an adjoint functor as a key to formally capturing the philosophical notion of "universal" especially as it figures in relation to semantics and epistemology. In the first part (first section to seventh section) the relevance of category theory for the main topics of analytic philosophy is suggested, in opposition to a widespread conservative attitude towards the entrenched conjunction of logic and ∈-based set theory. In the second part (8th section to 16th section) the concept of an adjunction is introduced and shown to provide the framework of some fundamental examples of universality. The paper is of an introductory character, because it is addressed to a broad philosophical audience, in particular to philosophically-oriented logicians and logically-educated philosophers with no previous knowledge of category theory.