Breaking the Tie: Benacerraf's Identification Argument Revisited

IF 0.8 1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Arnon Avron;Balthasar Grabmayr
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引用次数: 1

Abstract

Most philosophers take Benacerraf's argument in ‘What numbers could not be’ to rebut successfully the reductionist view that numbers are sets. This philosophical consensus jars with mathematical practice, in which reductionism continues to thrive. In this note, we develop a new challenge to Benacerraf's argument by contesting a central premise which is almost unanimously accepted in the literature. Namely, we argue that — contra orthodoxy — there are metaphysically relevant reasons to prefer von Neumann ordinals over other set-theoretic reductions of arithmetic. In doing so, we provide set-theoretical facts which, we believe, are crucial for informed assessment of reductionism.
打破平局:对贝纳瑟拉夫身份认同论的再认识
大多数哲学家采用Benacerraf在“数字不可能是什么”中的论点,成功地反驳了简化论者认为数字是集合的观点。这种哲学共识与数学实践不符,在数学实践中,还原论继续蓬勃发展。在这篇文章中,我们通过质疑一个在文献中几乎被一致接受的中心前提,对Benacerraf的论点提出了新的挑战。也就是说,我们认为-反对正统-有形而上学相关的原因,更喜欢冯·诺伊曼序数比其他集合论算术约简。在这样做的过程中,我们提供了集合理论事实,我们相信,这对还原论的知情评估至关重要。
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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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.
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