Mathematical reasoning: induction, deduction and beyond |
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Authors: | David Sherry |
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Affiliation: | aDepartment of Philosophy, Northern Arizona University, PO Box 6011, Flagstaff, AZ 86011-6011, USA |
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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. |
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Keywords: | Thought-experiment Informal proof Mathematical reasoning |
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