Mathematical arguments in context
Foundations of Science 14 (1-2):45-57 (2009)
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.Author's Profile
DOI
10.1007/s10699-008-9146-7
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Citations of this work
The Argument of Mathematics.Andrew Aberdein & Ian J. Dove (eds.) - 2013 - Dordrecht, Netherland: Springer.
Proofs, Mathematical Practice and Argumentation.Begoña Carrascal - 2015 - Argumentation 29 (3):305-324.
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.
References found in this work
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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.
Analysis and Synthesis in Mathematics,.Michael Otte & Marco Panza (eds.) - 1997 - Kluwer Academic Publishers.