集合论潜在论的分类标准

IF 0.8 1区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Philosophia Mathematica Pub Date : 2024-08-28 DOI:10.1093/philmat/nkae016

Davide Sutto

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引用次数: 0

摘要

集合论势论是数学哲学中最活跃的趋势之一。关于集合的模态论有两种不同的发展方式。第一种是由查尔斯-帕森斯（Charles Parsons）提出的，侧重于作为对象的集合。第二种可追溯到希拉里-普特南（Hilary Putnam）和杰弗里-赫尔曼（Geoffrey Hellman），研究集合论结构。本文确定了技术和概念两方面的开放性问题，以澄清这两种不同但又经常混为一谈的观点，并对当代辩论中出现的潜在论方法进行分类。最后的成果是一个分类法，它应能帮助研究人员浏览模态集合理论的丰富景观。

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A Taxonomy for Set-Theoretic Potentialism

Set-theoretic potentialism is one of the most lively trends in the philosophy of mathematics. Modal accounts of sets have been developed in two different ways. The first, initiated by Charles Parsons, focuses on sets as objects. The second, dating back to Hilary Putnam and Geoffrey Hellman, investigates set-theoretic structures. The paper identifies two strands of open issues, technical and conceptual, to clarify these two different, yet often conflated, views and categorize the potentialist approaches that have emerged in the contemporary debate. The final outcome is a taxonomy that should help researchers navigate the rich landscape of modal set theories.

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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.