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Mathematics as a Critical Enterprise

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Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 39))

Abstract

How does mathematics grow? According to tradition, mathematics grows as truths accumulate. Imre Lakatos criticized this traditional answer in a bold and revolutionary way. He said that mathematics grows as conjectures are made and criticized. In Lakatos’ picture of mathematics, truths never get a chance to accumulate because they are always in danger of being refuted by newly discovered counterexamples. In fact, those parts of mathematics which under the traditional view were regarded as truths, that is, theorems, proofs, and so on, are under Lakatos’ view seen as completely conjectural. In fact, according to Lakatos, all mathematics is conjectural. None of it is truth accumulated.

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R. S. Cohen P. K. Feyerabend M. W. Wartofsky

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© 1976 D. Reidel Publishing Company, Dordrecht-Holland

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Marchi, P. (1976). Mathematics as a Critical Enterprise. In: Cohen, R.S., Feyerabend, P.K., Wartofsky, M.W. (eds) Essays in Memory of Imre Lakatos. Boston Studies in the Philosophy of Science, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1451-9_24

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  • DOI: https://doi.org/10.1007/978-94-010-1451-9_24

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-277-0655-3

  • Online ISBN: 978-94-010-1451-9

  • eBook Packages: Springer Book Archive

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