11 December 2002, Logic Tea, Ron Rood, Vrije Universiteit

Abstract

There is a growing interest in diagrammatic forms of reasoning these days. Such (apparently) nonlinguistic forms of reasoning have drawn attention from logicians, computer scientists, and cognitive scientists, among others. The questions posed and methods used within the associated fields are extremely diverse. In the light of this, I raise some issues, revolving around interrelated themes like: formality, logicality, language, and epistemology.

I point out that many see some form of (rational) 'intuition' as an important if not indispensable element of mathematical proof (some relevant examples are: Frege (geometry, at least), Hilbert, Klein). In the bulk of my talk, I will attempt to put the issues raised in connection with diagrammatic modes of reasoning in a broader and philosophically informed perspective. Specifically, I will link diagrammatic modes of reasoning to the aforementioned and much broader notion of intuition. In the light of this, I propose a methodological framework for the study of mathematical proof, in which the various issues raised can be given what I deem to be their proper place. In order to show the plausibility and the fruitfulness of this framework, I will illustrate it by offering some representative examples from the history of philosophy and mathematics.

The Logic Tea homepage can be found at http://staff.science.uva.nl/~debruin/logic_tea.html For further information please contact Mark Theunissen at mailto:mtheunis at science.uva.nl, or Boudewijn de Bruin at mailto:debruin at science.uva.nl.