直觉分析的潜在主义视角

IF 0.8 1区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Philosophia Mathematica Pub Date : 2025-03-31 DOI:10.1093/philmat/nkae025

Ethan Brauer

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引用次数: 0

摘要

自由选择序列在browwerian连续统中起着关键作用。利用最近对潜在无穷的模态分析，我们可以在不采用布劳尔独特的唯心主义形而上学的情况下，将自由选择序列理解为自然数的潜在无限序列。这为古典主义者提供了一种从他们自己的古典角度理解直觉主义思想的方法。我发展了实数的模态势能理论，足以捕捉到直觉分析的最显著特征，如布劳维尔的连续性定理，存在一个单调的、有界的、非收敛的序列，以及不能非平凡地分解连续体。

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A Potentialist Perspective on Intuitionistic Analysis

Free choice sequences play a key role in the Brouwerian continuum. Using recent modal analysis of potential infinity, we can make sense of free choice sequences as potentially infinite sequences of natural numbers without adopting Brouwer’s distinctive idealistic metaphysics. This provides classicists with a means to make sense of intuitionistic ideas from their own classical perspective. I develop a modal-potentialist theory of real numbers that suffices to capture the most distinctive features of intuitionistic analysis, such as Brouwer’s continuity theorem, the existence of a sequence that is monotone, bounded, and non-convergent, and the inability to decompose the continuum non-trivially.

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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.