波法集合论中的同一性和扩展性

IF 0.8 1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Philosophia Mathematica Pub Date : 2024-02-08 DOI:10.1093/philmat/nkad025
Nuno Maia, Matteo Nizzardo
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引用次数: 0

摘要

波法非完备集合论允许几个不同的集合等于各自的单子,即所谓的 "奎因原子"。里格认为,这一理论不能忠实地描述集合论的现实。他认为,即使承认存在非完备集合,"集合的扩展性 "也排除了在数量上截然不同的奎因原子。在本文中,我们揭示了里格的论证与数学结构主义如何构想非刚性结构之间的重要相似之处。这为反对里格的观点开辟了道路,同时也为博法集合论作为集合论现实的忠实描述进行辩护提供了理论资源。
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Identity and Extensionality in Boffa Set Theory
Boffa non-well-founded set theory allows for several distinct sets equal to their respective singletons, the so-called ‘Quine atoms’. Rieger contends that this theory cannot be a faithful description of set-theoretic reality. He argues that, even after granting that there are non-well-founded sets, ‘the extensional nature of sets’ precludes numerically distinct Quine atoms. In this paper we uncover important similarities between Rieger’s argument and how non-rigid structures are conceived within mathematical structuralism. This opens the way for an objection against Rieger, whilst affording the theoretical resources for a defence of Boffa set theory as a faithful description of set-theoretic reality.
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来源期刊
Philosophia Mathematica
Philosophia Mathematica HISTORY & PHILOSOPHY OF SCIENCE-
CiteScore
1.70
自引率
9.10%
发文量
26
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.
期刊最新文献
Predicative Classes and Strict Potentialism Is Iteration an Object of Intuition? A Taxonomy for Set-Theoretic Potentialism Up with Categories, Down with Sets; Out with Categories, In with Sets! Identity and Extensionality in Boffa Set Theory
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