Van Bendegem J. P. & Van Kerkhove B. (2009) Mathematical arguments in context. Foundations of Science 14(1/2): 45–57. Fulltext at https://cepa.info/321
Mathematical arguments in context.
Foundations of Science 14(1/2): 45–57.
Fulltext at https://cepa.info/321
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.