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

Authors
Bart Van Kerkhove
Vrije Universiteit Brussel
Abstract
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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References found in this work BETA

Mathematics and Plausible Reasoning.George Polya - 1954 - Princeton: Princeton University Press.
The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Reviel Netz - 1999 - Cambridge and New York: Cambridge University Press.

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Citations of this work BETA

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

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