论文标题
数学实践中的类比推理
Reasoning by Analogy in Mathematical Practice
论文作者
论文摘要
著名数学家的证词和实践表明，数学的表面和深层类比之间存在重要的现象学和认识论差异。在本文中，我们提供了数学中类比推理的描述性理论，并指出了一般条件，在这种情况下，类比可以为数学猜想提供真正的感应支持（超过和更高履行了“在心理意义上提出”猜想的启发式启发式作用）。拟议的条件推广了Hesse（1963）在经验科学中对类比推理的有影响力的工作中提出的标准。通过参考几个案例研究，我们认为本文提出的帐户在辩护数学中的使用比Bartha（2009）捍卫的明显替代方案方面做得更好。此外，我们的建议还提供了对扩展到已知在有限域中已知的无限案例数学特性的实践的新见解。
The testimony and practice of notable mathematicians indicate that there is an important phenomenological and epistemological difference between superficial and deep analogies in mathematics. 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 put forward by Hesse (1963) 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 (2009). Moreover, our proposal offers novel insights into the practice of extending to the infinite case mathematical properties known to hold in finite domains.
