分类向上，集合向下；分类向外，集合向内！

IF 0.8 1区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Philosophia Mathematica Pub Date : 2024-04-13 DOI:10.1093/philmat/nkae010

Jonathan Kirby

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引用次数: 0

摘要

本文比较了来自广义集合论和范畴论数学传统的子集和外延集概念的实用方法。我认为，对于 "向下 "或 "向内 "看子集，集合论方法是最实用的；而对于 "向上 "或 "向外 "看扩展集，范畴论方法是最实用的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Up with Categories, Down with Sets; Out with Categories, In with Sets!

Practical approaches to the notions of subsets and extension sets are compared, coming from broadly set-theoretic and category-theoretic traditions of mathematics. I argue that the set-theoretic approach is the most practical for ‘looking down’ or ‘in’ at subsets and the category-theoretic approach is the most practical for ‘looking up’ or ‘out’ at extensions, and suggest some guiding principles for using these approaches without recourse to either category theory or axiomatic set theory.

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来源期刊

Philosophia Mathematica HISTORY & PHILOSOPHY OF SCIENCE-

CiteScore

1.70

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Philosophia Mathematica is the only journal in the world devoted specifically to philosophy of mathematics. The journal publishes peer-reviewed new work in philosophy of mathematics, the application of mathematics, and computing. In addition to main articles, sometimes grouped on a single theme, there are shorter discussion notes, letters, and book reviews. The journal is published online-only, with three issues published per year.