Mathematical Arguments in Context

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...

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Bibliographic Details
Published in:Foundations of science Vol. 14; no. 1-2; pp. 45 - 57
Main Authors: Van Bendegem, Jean Paul, Van Kerkhove, Bart
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.03.2009
Springer Nature B.V
Subjects:
Education
Mathematical analysis
Mathematical Logic and Foundations
Methodology of the Social Sciences
Philosophy
Philosophy of Science
Mathematical arguments
Toulmin
Mathematical practice
Contextual knowledge
Rhetoric
ISSN:1233-1821, 1572-8471
Online Access:Get full text
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Summary: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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content type line 14
ISSN:1233-1821
1572-8471
DOI:10.1007/s10699-008-9146-7