Analogical Arguments in Mathematics
This chapter proposes an analysis of analogical arguments in mathematics. Such arguments are used to show that mathematical conjectures are plausible. The core idea of the chapter is that there is a strong link between good analogies and fruitful generalization. Specifically, a good analogical argument in mathematics is one that articulates a clear proof that is ‘fit for imitation’. This idea is first stated as a simple test, and then refined and deepened through a set of models for relationships of similarity that are important in mathematical analogies. The chapter concludes by addressing the philosophical basis for analogical reasoning and the use of analogies in extended mathematical research programs.
Keywordsanalogy analogical arguments heuristics mathematical analogy plausible reasoning.
This chapter is based largely on material in my book (Bartha, 2010), with some additions and clarifications. Sections of that book are reproduced here by kind permission of Oxford University Press. Many issues that are neglected or only briefly mentioned here are discussed in the book. I also wish to acknowledge the helpful contributions of the editors.
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