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Argumentation and the Mathematical Process

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Appraising Lakatos

Part of the book series: Vienna Circle Institute Library ((VCIL,volume 1))

Abstract

We have reached a position today from which to evaluate judiciously Lakatos’ contribution to the philosophy of mathematics. We should applaud unreservedly his decision to take the development of mathematics as a topic worthy of philosophical consideration and admire the first steps he took to elucidate patterns of theory change via his identification of certain mechanisms of concept-stretching. We must recognise, however, that the method of proofs and refutations accounts only for the modification of a concept’s definition,1 omitting more fundamental varieties of theory development, and consequently that much remains to be done. The two tasks before us today are to describe an expanded range of varieties of theory production, especially radically innovative mathematical conceptualisations, and to ponder the philosophical issues relating to such a description. Regarding the former, see Corfield (1998a) and Kvasz (1998). Through this paper I shall largely confine myself to the latter, endeavouring to convey a sense of the vast array of possibilities now open to us.

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Author information

Authors and Affiliations

  1. Department of History and Philosophy of Science, University of Cambridge, Free School Lane, Cambridge, CB2 3RH, UK

    David Corfield

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  1. David Corfield
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Editors and Affiliations

  1. Eötvös University, Budapest, Hungary

    George Kampis

  2. Comenius University, Bratislava, Slovakia

    Ladislav Kvasz

  3. Institute Vienna Circle, Vienna, University of Bielefeld, Germany

    Michael Stöltzner

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© 2002 Springer Science+Business Media Dordrecht

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Corfield, D. (2002). Argumentation and the Mathematical Process. In: Kampis, G., Kvasz, L., Stöltzner, M. (eds) Appraising Lakatos. Vienna Circle Institute Library, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0769-5_8

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  • DOI: https://doi.org/10.1007/978-94-017-0769-5_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5922-2

  • Online ISBN: 978-94-017-0769-5

  • eBook Packages: Springer Book Archive

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