Mathematical reasoning: induction, deduction and beyond

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Abstract

Mathematics used to be portrayed as a deductive science. Stemming from Polya (1954), however, is a philosophical movement which broadens the concept of mathematical reasoning to include inductive or quasi-empirical methods. Interest in inductive methods is a welcome turn from foundationalism toward a philosophy grounded in mathematical practice. Regrettably, though, the conception of mathematical reasoning embraced by quasi-empiricists is still too narrow to include the sort of thought-experiment which Mueller describes as traditional mathematical proof (Mueller, 1969, p. 295) and which Lakatos examines in Proofs and refutations (Lakatos, 1976). This paper extends the concept of mathematical reasoning along two further dimensions to accommodate thought-experiment.

Original languageEnglish (US)
Pages (from-to)489-504
Number of pages16
JournalStudies in History and Philosophy of Science Part A
Volume37
Issue number3
DOIs
StatePublished - Sep 2006

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Keywords

  • Informal proof
  • Mathematical reasoning
  • Thought-experiment

ASJC Scopus subject areas

  • History

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