数学：没有形而上学的方法

IF 0.8 1区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Philosophia Mathematica Pub Date : 2022-04-01 DOI:10.1093/philmat/nkac027

Elaine Landry

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引用次数: 0

摘要

我利用对柏拉图的阅读来发展我所说的ifism，即在数学中，我们把假设当作第一原则来对待，我们这样做的目的是解决数学问题。然后，我将这一观点扩展到现代数学，表明当我们将重点从哲学方法转移到数学方法时，我们看到，对数学结构主义的方法论解释可以用来描述数学的实践和适用性，同时避免将形而上学的考虑与数学的考虑混为一谈。

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Mathematics: Method Without Metaphysics

I use my reading of Plato to develop what I call as-ifism, the view that, in mathematics, we treat our hypotheses as if they were first principles and we do this with the purpose of solving mathematical problems. I then extend this view to modern mathematics showing that when we shift our focus from the method of philosophy to the method of mathematics, we see that an as-if methodological interpretation of mathematical structuralism can be used to provide an account of the practice and the applicability of mathematics while avoiding the conflation of metaphysical considerations with mathematical ones.

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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.