Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics

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Pease, Alison; Smaill, Alan; Colton, Simon and Lee, John. 2009. Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics. Foundations of Science, 14(1/2), pp. 111-135. ISSN 1233-1821 [Article]

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We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Proofs and Refutations, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, in which we use work by Haggith on argumentation structures, and identify connections between these structures and Lakatos’s methods.

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Article

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https://doi.org/10.1007/s10699-008-9150-y