Proofs and Refutations: A Reassessment

Abstract

Since the appearance in print of Lakatos’ Proofs and Refutations, much lively discussion has taken place between philosophers and mathematicians. It is by now generally accepted that it was a fine piece of work which, though it did not by any means settle all of the issues it raised, helped us to redirect our attention toward the dynamics of mathematical discovery. We came to realize that the study of the dynamics of mathematical discovery is equally important for both the historian and the philosopher, as well as for the mathematician. Such a study, though, is extremely difficult to carry out, and models which are meant to be rational reconstructions (or “distilled” histories¹) of the process of mathematical discovery can only be partially successful. This is mainly due to the enormous difficulties stemming from the complexity of the issues one is faced with when one attempts both to describe such a process and to provide us with explanatory schemata about it. This is, I think, the problem Lakatos’ Proofs and Refutations suffers from. My aim in this paper is to discuss or — at least — indicate what I consider to be some of the weak points of the work.