数学适用性的内部应用和困惑

IF 0.8 1区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Philosophia Mathematica Pub Date : 2023-10-25 DOI:10.1093/philmat/nkad019

Douglas Bertrand Marshall

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引用次数: 0

摘要

正如数学帮助我们对自然世界进行表征和推理一样，在其内部应用中，数学的一个分支帮助我们对另一个分支的主题进行表征和推理。认识到数学的内部和外部应用之间的密切相似，有助于解决关于数学适用性的两个长期存在的哲学难题:数学对象的抽象性引起的柏拉图主义难题;以及由于数学命题缺乏经验事实内容而产生的经验主义困惑。为了了解这是怎么回事，我们将研究一下什么是内部应用数学并描述一些例子。

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Internal Applications and Puzzles of the Applicability of Mathematics

Abstract Just as mathematics helps us to represent and reason about the natural world, in its internal applications one branch of mathematics helps us to represent and reason about the subject matter of another. Recognition of the close analogy between internal and external applications of mathematics can help resolve two persistent philosophical puzzles concerning its applicability: a platonist puzzle arising from the abstractness of mathematical objects; and an empiricist puzzle arising from mathematical propositions’ lack of empirical factual content. In order to see how this is the case, we will examine what it is to apply mathematics internally and describe examples.

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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.