Preface

Summary

Reflections, a symposium on the foundations of mathematics, was held at Stanford University on December 11–13, 1998. The symposium was organized to honor Solomon Feferman who has played an enormous role in shaping the field over the last 40 years. It was timed so that its last day would coincide with Feferman's 70-th birthday; this provided a very special occasion to celebrate him and his career-long dedication to foundational research.

Jon Barwise and Wilfried Sieg, both doctoral students of Feferman, took the initiative in early 1996 of planning what became playfully called the Feferfest; Carolyn Talcott and Rick Sommer soon joined as the local Stanford organizers. Jon was instrumental in our subsequent venture to shape a program; he opened the symposium and gave a lecture on his latest work; he helped with the initial steps towards this volume, even after he had been diagnosed with cancer. Wemiss him.

The symposium was structured around proof-theoretically inspired themes. True to their origin in the work of David Hilbert and Paul Bernays, prooftheoretic investigations have sustained a special emphasis on or, at least a genuine connection to, broad philosophical issues. Stanford University has had an important role in fostering such work through actively engaged faculty, doctoral students, and visitors. Feferman has been at the very center of these activities.

This was an opportune moment to reflect broadly on such investigations, but also to connect them systematically with topics in Feferman's work. His primary contributions have been to proof theory, recursion theory and, in more recent years, to an analysis of the development of mathematical logic in the twentieth century. Indeed, all of thesematters are of intense interest in the current discussion concerning modern mathematical thought.

The symposium had six sessions. The details of the program - with the names of contributors and chairs - can be found at the very back of the book. The papers in this volume were submitted by symposium participants, as well as by some of Feferman's students and former collaborators, as a tribute to Feferman. They are grouped, somewhat differently from the symposium program, into four parts: Proof-theoretic analysis, Logic and computation,Applicative and self-applicative theories, and Philosophy of modern mathematical and logical thought.