The Argument of Mathematics

• Corporate Author: SpringerLink (Online service)
• Other Authors: Aberdein, Andrew (Editor), Dove, Ian J. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2013.
• Series: Logic, Epistemology, and the Unity of Science ; 30
• Subjects: Philosophy.; Logic.; Mathematical logic.; Mathematical Logic and Foundations.; Mathematical Logic and Formal Languages.

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,...

Table of Contents:

• Introduction
• Part I. What are Mathematical Arguments?
• Chapter 1. Non-Deductive Logic in Mathematics: The Probability of Conjectures; James Franklin
• Chapter 2. Arguments, Proofs, and Dialogues; Erik C. W. Krabbe
• Chapter 3. Argumentation in Mathematics; Jesús Alcolea Banegas
• Chapter 4. Arguing Around Mathematical Proofs; Michel Dufour
• Part II. Argumentation as a Methodology for Studying Mathematical Practice
• Chapter 5. An Argumentative Approach to Ideal Elements in Mathematics; Paola Cantù
• Chapter 6. How Persuaded Are You? A Typology of Responses; Matthew Inglis and Juan Pablo Mejía-Ramos
• Chapter 7. Revealing Structures of Argumentations in Classroom Proving Processes; Christine Knipping and David Reid
• Chapter 8. Checking Proofs; Jesse Alama and Reinhard Kahle
• Part III. Mathematics as a Testbed for Argumentation Theory
• Chapter 9. Dividing by Zero—and Other Mathematical Fallacies; Lawrence H. Powers
• Chapter 10. Strategic Maneuvering in Mathematical Proofs; Erik C. W. Krabbe
• Chapter. 11 Analogical Arguments in Mathematics; Paul Bartha
• Chapter 12. What Philosophy of Mathematical Practice Can Teach Argumentation Theory about Diagrams and Pictures; Brendan Larvor
• Part IV. An Argumentational Turn in the Philosophy of Mathematics
• Chapter 13. Mathematics as the Art of Abstraction; Richard L. Epstein
• Chapter 14. Towards a Theory of Mathematical Argument; Ian J. Dove
• Chapter 15. Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics; Alison Pease, Alan Smaill, Simon Colton and John Lee
• Chapter 16. Mathematical Arguments and Distributed Knowledge; Patrick Allo, Jean Paul Van Bendegem and Bart Van Kerkhove
• Chapter 17. The Parallel Structure of Mathematical Reasoning; Andrew Aberdein
• Index.