Andrew Aberdein and Ian J. Dove, eds. The Argument of Mathematics. Logic, Epistemology, and the Unity of Science; 30. Dordrecht: Springer, 2013. ISBN: 978-94-007-6533-7 (hbk); 978-94-007-6534-4 (ebook). Pp. x + 393

Abstract

The premise of this volume, that philosophy of mathematics and argumentation theory ought to have interesting things to tell one another, seems obvious. Mathematical proofs, after all, are the very model of good argumentation — rigorous in ways that other disciplines can only envy, persuasive to anyone competent to understand them, and having to do with matters of unquestionable importance. Only the last of these suggestions seems to me one that only mathematicians are sure to agree with. To date, though, there has been little learning across the divide. Indeed, there is considerable suspicion to be overcome on both sides: argumentation theory is often regarded as the wellspring of the ‘spot the howler’ approach to ‘informal logic’ that consigns philosophy instructors to teaching courses that involve students having the remarkably unchallenging job of finding fallacies on the internet or in the letters to the editor of the local newspaper; and, judging from some of the historical discussion in the articles in this volume, the founders of modern argumentation theory regarded mathematicians and logicians as blind both to obvious facts about the other aspects of mathematical practice besides the production of proofs and to the complicated nature of the relationship between mathematical proofs and derivations in formal systems of proof. Indeed, some argumentation theorists held the view that mathematical proofs are not arguments at all; so one contribution to the volume, Michael Dufour's ‘Arguing around mathematical proofs,’ is primarily an argument that they are.