作为数学非演绎推理形式的最佳解释推理

IF 0.8 1区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Philosophia Mathematica Pub Date : 2025-04-02 DOI:10.1093/philmat/nkae024

Marc Lange

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引用次数: 0

摘要

本文提出数学家通常使用最佳解释推理（IBE）来证实他们的猜想。数学家可以合理地推断，他们所拥有的某些数学证据的“最佳解释”将是对它的证明，同样证明了一个给定的猜想。通过IBE，证据因此证实了这样一个尚未被发现的证据的存在，并且该猜想成立。一旦贝叶斯主义的逻辑全知性被规避，这种推理就可以用贝叶斯术语来表达。贝叶斯分析确定影响数学IBE强度的因素，并有助于将数学IBE与科学IBE统一起来。

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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Inference to the Best Explanation as a Form of Non-Deductive Reasoning in Mathematics

This paper proposes that mathematicians routinely use inference to the best explanation (IBE) to confirm their conjectures. Mathematicians can justly reason that the ‘best explanation’ of some mathematical evidence they possess would be a proof of it that likewise proves a given conjecture. By IBE, the evidence thereby confirms that such an as-yet-undiscovered proof exists and that the conjecture holds. This reasoning can be expressed in Bayesian terms once Bayesianism’s logical omniscience has been circumvented. A Bayesian analysis identifies considerations affecting a mathematical IBE’s strength and helps to unify mathematical IBEs with scientific IBEs.

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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.