ABSTRACT
The form of this discussion is taken directly from Lakatos (1961, 1976). Although many discussions of scientific ideas have been presented as dialogues, Lakatos’ book (1976) uses a quasi-historical format both to clarify and to enrich the relationships between ideas in the development of work on mathematical problems. By acknowledging my debt to Lakatos’ very important book, I do not mean to pretend to anything like the degree of his achievement. Lakatos gave a thorough exploration of some fundamental issues concerning the nature of mathematical knowledge. My task is much more modest, of course. However, I do hope that this form may provide a useful context for identifying some of the interesting issues raised in the papers on which I was privileged to comment.
