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    What is a proof?

    Bundy, A. and Jamnik, M. and Fugard, Andrew J.B. (2005) What is a proof? Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363 (1835), pp. 2377-2391. ISSN 1364-503X.

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    Abstract

    To those brought up in a logic-based tradition there seems to be a simple and clear definition of proof. But this is largely a twentieth century invention; many earlier proofs had a different nature. We will look particularly at the faulty proof of Euler's Theorem and Lakatos' rational reconstruction of the history of this proof. We will ask: how is it possible for the errors in a faulty proof to remain undetected for several years—even when counter-examples to it are known? How is it possible to have a proof about concepts that are only partially defined? And can we give a logic-based account of such phenomena? We introduce the concept of schematic proofs and argue that they offer a possible cognitive model for the human construction of proofs in mathematics. In particular, we show how they can account for persistent errors in proofs.

    Metadata

    Item Type: Article
    School: Birkbeck Schools and Departments > School of Social Sciences, History and Philosophy > Psychosocial Studies
    Depositing User: Sarah Hall
    Date Deposited: 14 Aug 2017 14:58
    Last Modified: 23 Feb 2018 10:12
    URI: http://eprints.bbk.ac.uk/id/eprint/19391

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