Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. awhether a plane really did strike the Pentagon on September 11 2001 (Birdsell and Groarke, 2007, 109a110). ... In a given case of visual argumentation, we should seek answers to questions 2 and 3 (and a good part of the answer to 1) not in the ... The proofs in Euclidean geometry are reliable because the practice of geometry has suitable answers to these three ... New York: Holt, Rinehart aamp; Winston.
|Title||:||The Argument of Mathematics|
|Author||:||Andrew Aberdein, Ian J Dove|
|Publisher||:||Springer Science & Business Media - 2013-07-01|