The Argument of Mathematics

1. Introduction
Andrew Aberdein, Ian J. Dove

Part I. What are Mathematical Arguments?

2. Non-deductive Logic in Mathematics: The Probability of Conjectures
James Franklin

3. Arguments, Proofs, and Dialogues
Erik C. W. Krabbe

4. Argumentation in Mathematics
Jesús Alcolea Banegas

5. Arguing Around Mathematical Proofs
Michel Dufour

Part II. Argumentation as a Methodology for Studying Mathematical Practice

6. An Argumentative Approach to Ideal Elements in Mathematics
Paola Cantù

7. How Persuaded Are You? A Typology of Responses
Matthew Inglis, Juan Pablo Mejía-Ramos

8. Revealing Structures of Argumentations in Classroom Proving Processes
Christine Knipping, David Reid

9. Checking Proofs
Jesse Alama, Reinhard Kahle

Part III. Mathematics as a Testbed for Argumentation Theory

10. Dividing by Zero—and Other Mathematical Fallacies
Lawrence H. Powers

11. Strategic Maneuvering in Mathematical Proofs
Erik C. W. Krabbe

12. Analogical Arguments in Mathematics
Paul Bartha

13. 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

14. Mathematics as the Art of Abstraction
Richard L. Epstein

15. Towards a Theory of Mathematical Argument
Ian J. Dove

16. Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics
Alison Pease, Alan Smaill, Simon Colton, John Lee

17. Mathematical Arguments and Distributed Knowledge
Patrick Allo, Jean Paul Bendegem, Bart Kerkhove

18. The Parallel Structure of Mathematical Reasoning
Andrew Aberdein

Keywords: Philosophy, Logic, Mathematical Logic and Foundations, Mathematical Logic and Formal Languages