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.
Author(s): Andrew Aberdein, Ian J Dove (eds.)
Series: Logic, Epistemology, and the Unity of Science 30
Publisher: Springer
Year: 2013
Language: English
Pages: 391
Tags: Logic; Mathematical Logic and Foundations; Mathematical Logic and Formal Languages
Front Matter....Pages i-x
Introduction....Pages 1-8
Front Matter....Pages 9-9
Non-deductive Logic in Mathematics: The Probability of Conjectures....Pages 11-29
Arguments, Proofs, and Dialogues....Pages 31-45
Argumentation in Mathematics....Pages 47-60
Arguing Around Mathematical Proofs....Pages 61-76
Front Matter....Pages 77-77
An Argumentative Approach to Ideal Elements in Mathematics....Pages 79-99
How Persuaded Are You? A Typology of Responses....Pages 101-117
Revealing Structures of Argumentations in Classroom Proving Processes....Pages 119-146
Checking Proofs....Pages 147-170
Front Matter....Pages 171-171
Dividing by Zero—and Other Mathematical Fallacies....Pages 173-179
Strategic Maneuvering in Mathematical Proofs....Pages 181-197
Analogical Arguments in Mathematics....Pages 199-237
What Philosophy of Mathematical Practice Can Teach Argumentation Theory About Diagrams and Pictures....Pages 239-253
Front Matter....Pages 255-255
Mathematics as the Art of Abstraction....Pages 257-289
Towards a Theory of Mathematical Argument....Pages 291-308
Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics....Pages 309-338
Mathematical Arguments and Distributed Knowledge....Pages 339-360
The Parallel Structure of Mathematical Reasoning....Pages 361-380
Back Matter....Pages 381-393
