Brendan Larvor

This article canvasses five senses in which one might introduce an historical element into the philosophy of mathematics: 1. The temporal dimension of logic; 2. Explanatory Appeal to Context rather than to General Principles; 3. Heraclitean Flux; 4. All history is the History of Thought; and 5. History is Non-Judgmental. It concludes by adapting Bernard Williams’ distinction between ‘history of philosophy’ and ‘history of ideas’ to argue that the philosophy of mathematics is unavoidably historical, but need not and must not merge with historiography.

It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the field

Dans cet article, j’explore dans un premier temps la conception que se fait Lautman de la dialectique en examinant ses références à Platon et Heidegger. Je compare ensuite les structures dialectiques identifiées par Lautman dans les mathématiques contemporaines avec celles qui émergent de ses sources philosophiques. Enfin, je soutiens que les structures qu’il a découvertes dans les mathématiques sont plus riches que le suggère son modèle platonicien, et que la distinction « ontologique » de Heidegger est moins utile que semblait le penser Lautman. In this paper, I first explore Lautman’s conception of dialectics by a consideration of his references to Plato and Heidegger. I then compare the dialectical structures that he found in contemporary mathematics with the model that emerges from his philosophical sources. Finally, I argue that the structures that he discovered in mathematics are richer than his Platonist model suggests, and that Heidegger’s “ontological” distinction is less useful than Lautman seemed to believe

The Chances of Explanation: Causal Explanation in the Social, Medical, and Physical Sciences Paul Humphreys, 1989 Princeton University Press x+170 pp., £12.95 (paperback) ISBN 0 691 020286 8; £25.00 (hardback) ISBN 0 69107353 8In Search of a Better World: Lectures and Essays from Thirty Years Karl Popper London, Routledge £25.00 (hardback)Artificial Morality: Virtuous Robots for Virtual Games Peter Danielson, 1992 London, Routledge £35.00 (hardback) ISBN 0 415 034841; £10.99 (paperback) ISBN 0 415 07691 9A System of Pragmatic Idealism Nicholas Rescher, 1992 Princeton, Princeton University Press 335pp., $37.50 (hardback)