Foundations of Science 14 (1-2):111-135 (2009)
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Abstract |
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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Keywords | Lakatos Argumentation Philosophy of mathematics Computational model Theory refinement |
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DOI | 10.1007/s10699-008-9150-y |
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References found in this work BETA
The Logic of Scientific Discovery.K. Popper - 1959 - British Journal for the Philosophy of Science 10 (37):55-57.
Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos (ed.) - 1976 - Cambridge and London: Cambridge University Press.
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Citations of this work BETA
Proof, Explanation, and Justification in Mathematical Practice.Moti Mizrahi - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (4):551-568.
Five Theories of Reasoning: Interconnections and Applications to Mathematics.Alison Pease & Andrew Aberdein - 2011 - Logic and Logical Philosophy 20 (1-2):7-57.
Argumentation Theory for Mathematical Argument.Joseph Corneli, Ursula Martin, Dave Murray-Rust, Gabriela Rino Nesin & Alison Pease - 2019 - Argumentation 33 (2):173-214.
Reasoning About Representations in Autonomous Systems: What Pόlya and Lakatos Have to Say.Alan Bundy - 2012 - In David McFarland, Keith Stenning & Maggie McGonigle (eds.), The Complex Mind. Palgrave-Macmillan. pp. 167.
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