Mathematical arguments in context

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

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Bart Van Kerkhove
Vrije Universiteit Brussel

Citations of this work

How to think about informal proofs.Brendan Larvor - 2012 - Synthese 187 (2):715-730.
The Argument of Mathematics.Andrew Aberdein & Ian J. Dove (eds.) - 2013 - Dordrecht, Netherland: Springer.
Non-deductive Logic in Mathematics: The Probability of Conjectures.James Franklin - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Springer. pp. 11--29.
Logic, Reasoning, and Rationality.Erik Weber, Joke Meheus & Dietlinde Wouters (eds.) - 2014 - Dordrecht, Netherland: Springer.

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References found in this work

The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Reviel Netz - 1999 - Cambridge and New York: Cambridge University Press.
Mathematics and Plausible Reasoning.George Polya - 1954 - Princeton: Princeton University Press.
Mathematical Thought from Ancient to Modern Times.M. Kline - 1978 - British Journal for the Philosophy of Science 29 (1):68-87.
Analysis and Synthesis in Mathematics,.Michael Otte & Marco Panza (eds.) - 1997 - Kluwer Academic Publishers.

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