论文标题
通过类比确认数学猜想
Confirming Mathematical Conjectures by Analogy
论文作者
论文摘要
类比已作为经验科学中的一种归纳推理形式受到关注。但是，其在纯数学中的作用较少。本文介绍了与更熟悉的数学领域的类比如何有助于确认数学猜想。通过参考案例研究，我们提出了通过数学类比的增量和非习得形式的确认形式的区别。我们在贝叶斯确认理论的流行框架内提供了前者的描述。至于非注册概念，我们在没有引入新的数学证据的情况下，捍卫其在合理地告知数学家先前的信誉中的作用。由此产生的“混合”框架捕获了在纯数学领域中使用类比推断的许多重要方面。
Analogy has received attention as a form of inductive reasoning in the empirical sciences. However, its role in pure mathematics has received less consideration. This paper provides an account of how an analogy with a more familiar mathematical domain can contribute to the confirmation of a mathematical conjecture. By reference to case-studies, we propose a distinction between an incremental and a non-incremental form of confirmation by mathematical analogy. We offer an account of the former within the popular framework of Bayesian confirmation theory. As for the non-incremental notion, we defend its role in rationally informing the prior credences of mathematicians in those circumstances in which no new mathematical evidence is introduced. The resulting 'hybrid' framework captures many important aspects of the use of analogical inference in the realm of pure mathematics.
