Heuristics and Mathematical Discovery: the Case of Bayesian Networks by Donald Gillies, University College London (
[email protected]) This is the final author version of a paper published in C.Cellucci & D.Gillies (eds.) Mathematical Reasoning and Heuristics, King’s College Publications, 2005, pp. 87-118. Contents 1. Introduction 2. The Development of Artificial Intelligence and the Discovery of Bayesian Networks 3. Heuristics Involved: (a) the Use of Philosophical Ideas 4. Heuristics Involved: (b) New Practical Problems 5. Heuristics Involved: (c) Domain Interaction 6. Heuristics of Mathematical Discovery versus Logic of Mathematical Discovery 1. Introduction I will begin this paper by discussing some ideas to be found in two recent books on the philosophy of mathematics. These are (i) Carlo Cellucci’s Filosofia e matematica, published by La Terza in 2002, and (ii) David Corfield’s Towards a Philosophy of Real Mathematics, published by Oxford University Press in 2003. I will start with Cellucci’s book. In his book, Cellucci is highly critical of the traditional or foundational approach to the philosophy of mathematics, based on the attempt to justify mathematics. Instead he advocates what he calls the heuristic approach to the philosophy of mathematics. As he says (2002, p. viii): ‘According to the dominant point of view the principal problem in the philosophy of mathematics is that of the justification of mathematics. … In this book I maintain instead that the principal problem of reflection on mathematics is that of mathematical discovery. This problem includes the problem of justification …’ I partly agree and partly disagree with this. It is certainly true that traditional philosophy of mathematics focussed exclusively on the problem of the justification of mathematics and neglected the problem of mathematical discovery.