In this paper, we offer a descriptive theory of analogical reasoning in mathematics, stating general conditions under which an analogy may provide genuine inductive support to a mathematical conjecture (over and above fulfilling the merely heuristic role of ‘suggesting’ a conjecture in the psychological sense). The proposed conditions generalize the criteria of Hesse in her influential work on analogical reasoning in the empirical sciences. By reference to several case studies, we argue that the account proposed in this paper does a better job in vindicating the use of analogical inference in mathematics than the prominent alternative defended by Bartha.

中文翻译：

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数学实践中的类比推理

在这篇论文中，我们提供了数学中类比推理的描述性理论，陈述了类比可以为数学猜想提供真正归纳支持的一般条件). 所提出的条件概括了黑塞在她关于经验科学中类比推理的有影响力的工作中的标准。通过参考几个案例研究，我们认为本文提出的解释在证明类比推理在数学中的使用方面比 Bartha 所捍卫的著名替代方案做得更好。