ORIGIN AND PURPOSE OF THE BOOK

The project of writing this book began in a conversation I had with Gian-Carlo Rota in the spring of 1996. He was then lecturing as visiting professor of mathematics and philosophy at The Catholic University of America.

Rota had often drawn attention to a difference between mathematicians and philosophers. Mathematicians, he said, tend to absorb the writings of their predecessors directly into their own work. They do not comment on the writings of earlier mathematicians, even if they have been very much influenced by them. They simply make use of the material that they find in the authors they read. When advances are made in mathematics, later thinkers condense the findings and move on. Few mathematicians study works from past centuries; compared with contemporary mathematics, such older writings seem to them almost like the work of children.

In philosophy, by contrast, classical works often become enshrined as objects of exegesis rather than resources to be exploited. Philosophers, Rota observed, tend not to ask, “Where do we go from here?” Instead, they inform us about the doctrines of major thinkers. They are prone to comment on earlier works rather than paraphrase them. Rota acknowledged the value of commentaries but thought that philosophers ought to do more. Besides offering exposition, they should abridge earlier writings and directly address issues, speaking in their own voice and incorporating into their own work what their predecessors have done. They should extract as well as annotate.