What Is Categorical Structuralism?

Geoffrey Hellman

doi:10.1017/9781108657419.003

2 - What Is Categorical Structuralism?

from Part I - Structuralism, Extendability, and Nominalism

Published online by Cambridge University Press: 26 January 2021

Geoffrey Hellman

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Geoffrey Hellman: Affiliation:
University of Minnesota

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Summary

In a recent paper Hellman [2003], we examined to what extent category theory (CT) provides an autonomous framework for mathematical structuralism. The upshot of that investigation was that, as it stands, while CT provides many valuable insights into mathematical structure – specific structures and structure in general – it does not sufficiently address certain key questions of logic and ontology that, in our view, any structuralist framework needs to address. On the positive side, however, a theory of large domains was sketched as a way of supplying answers to those key questions, answers intended to be friendly to CT both in demonstrating its autonomy vis-à-vis set theory and in preserving its “arrows only” methods of describing and interrelating structures and the insights that those methods provide.

Type: Chapter
Information: Mathematics and Its Logics
Philosophical Essays
, pp. 43 - 53

DOI: https://doi.org/10.1017/9781108657419.003 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2021

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