数学中反事实解释面临的挑战

IF 0.8 1区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Philosophia Mathematica Pub Date : 2021-09-21 DOI:10.1093/philmat/nkab023

Lange M.

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引用次数: 0

摘要

一些数学证明解释了为什么它们所证明的定理成立。本文确定了数学中任何反事实解释的几个挑战(也就是说，任何根据解释性证明揭示解释如何不同的解释，如果解释中的事实不同)。这篇论文假定反数学可以是非平凡的。它认为，尽管如此，反事实的解释将解释力描绘得太容易实现，没有捕捉到解释的不对称性，也没有说明为什么某些证据是解释性的，而其他证据不是。关于反事实依赖的更多信息甚至可能产生更少的解释力。

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Challenges Facing Counterfactual Accounts of Explanation in Mathematics

ABSTRACT

Some mathematical proofs explain why the theorems they prove hold. This paper identifies several challenges for any counterfactual account of explanation in mathematics (that is, any account according to which an explanatory proof reveals how the explanandum would have been different, had facts in the explanans been different). The paper presumes that countermathematicals can be nontrivial. It argues that nevertheless, a counterfactual account portrays explanatory power as too easy to achieve, does not capture explanatory asymmetry, and fails to specify why certain proofs are explanatory and others are not. Greater informativeness about counterfactual dependence can even yield less explanatory power.

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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.

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