Induction and Analogy in Mathematics

Comprehensivism is an emerging practice that takes seriously Buckminster Fuller’s observation that we want “to understand all and put everything together”. In this practice, we value learning from other traditions of inquiry and action, all our communicated experiences, and the Ethnosphere, our all-encompassing cultural zone. To assess this learning, we value accumulating and comparing many working hypotheses, conjectures, guesses, theories, and explanations so we can evaluate our vast inventory of knowledge comprehensively.

With these aspirations and values in mind, this resource will consider inductive reasoning as a moral basis for science as examined by George Pólya (1887–1985) in his 1954 public domain book “Mathematics and Plausible Reasoning: Volume I: Induction and Analogy in Mathematics”. We will also explore the implications of Pólya’s ideas for our comprehensivity, our efforts at learning that are broad in scope and deeply incisive or cutting. For diligent readers who want to assess the relevant parts of Pólya’s book on their own, at the end there is a section with links to its most important and most accessible sections on inductive reasoning.