Object's details: Category Theory and Set Theory as Theories about Complementary Types of Universals

Provider:Akademicka Platforma Czasopism

Description

Title:
Category Theory and Set Theory as Theories about Complementary Types of Universals
Creator:
Ellerman, David
Description:
Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u F = {x | F(x)} for a property F(.) could never be self-predicative in the sense of uF ∈ uF . But the mathematical theory of categories, dating from the mid-twentieth century, includes a theory of always-self-predicative universals – which can be seen as forming the “other bookend” to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato’s Theory of Forms as well as for the idea of a “concrete universal” in Hegel and similar ideas of paradigmatic exemplars in ordinary thought.
Object availability:
free access
Rights:
Prawa autorskie (c) 2017 Logic and Logical Philosophy
Date:
2016.08.05
Type:
info:eu-repo/semantics/article;
info:eu-repo/semantics/publishedVersion
Language:
English
Source:
Logic and Logical Philosophy; Vol. 26 No. 2 (2017): June; 145-162;
Logic and Logical Philosophy; Tom 26 Nr 2 (2017): June; 145-162;
2300-9802;
1425-3305
Format:
application/pdf
Publisher:
Uniwersytet Mikołaja Kopernika w Toruniu
Relation: https://apcz.umk.pl/LLP/article/view/LLP.2016.022/9503
Subject:
universals;
category theory;
Plato’s Theory of Forms;
set theoretic antinomies;
universal mapping properties;
logic
Identifier: https://apcz.umk.pl/LLP/article/view/LLP.2016.022
Data provider:
Akademicka Platforma Czasopism

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