Foundations of Science 14 (1-2):45-57 (2009)

Bart Van Kerkhove
Vrije Universiteit Brussel
Except in very poor mathematical contexts, mathematical arguments do not stand in isolation of other mathematical arguments. Rather, they form trains of formal and informal arguments, adding up to interconnected theorems, theories and eventually entire fields. This paper critically comments on some common views on the relation between formal and informal mathematical arguments, most particularly applications of Toulmin’s argumentation model, and launches a number of alternative ideas of presentation inviting the contextualization of pieces of mathematical reasoning within encompassing bodies of explicit and implicit, formal and informal background knowledge.
Keywords Contextual knowledge  Mathematical arguments  Mathematical practice  Toulmin  Rhetoric
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DOI 10.1007/s10699-008-9146-7
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Mathematical Thought From Ancient to Modern Times.M. Kline - 1978 - British Journal for the Philosophy of Science 29 (1):68-87.
Mathematics and Plausible Reasoning.George Pólya - 1954 - Princeton: Princeton University Press.
Mathematics and Plausible Reasoning.George Polya - 1954 - Princeton University Press.
Analysis and Synthesis in Mathematics,.Michael Otte & Marco Panza (eds.) - 1997 - Kluwer Academic Publishers.

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How to Think About Informal Proofs.Brendan Larvor - 2012 - Synthese 187 (2):715-730.

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