Bayesian Induction and Statistical Inference

Abstract

For more than two thousand years the question of how to achieve valid knowledge of the world has concerned Western epistemologists. From Aristotle, in the 4th Century B.C., until the contemporary theoreticians of induction, including both frequentist and Bayesian statisticians, the belief in the inductive character of the scientific method has been embodied in Western culture, with very few exceptions. Therefore Karl Popper (1979), one of the rare philosophers of science who, as David Hume in the first half of the Eighteenth Century, did not believe in induction as the ‘glory of science’, rightly called the problem of induction one of the two fundamental problems of epistemology; the other one being the problem of demarcation between genuine science and pseudoscience.

This paper was written during tenure of research grant 92–169 of the DGICYT; I very much thank the Spanish Ministry of Education and Science for this award. I also am very indebted to Prof. Colin Howson, LSE, for having given to me the opportunity to present many of the ideas of this article in a staff/graduate seminar of the Philosophy Department of the LSE.