ABSTRACT

The mathematical proof is the most important form of justification in mathematics. It is not, however, the only kind of justification for mathematical propositions. The existence of other forms, some of very significant strength, places a question mark over the prominence given to proof within mathematics. This collection of essays, by leading figures working within the philosophy of mathematics, is a response to the challenge of understanding the nature and role of the proof.

chapter |7 pages

PREFACE

chapter 2|33 pages

PROOFS AND EPISTEMIC STRUCTURE

chapter 3|20 pages

WHAT IS A PROOF?

chapter 4|17 pages

HOW TO SAY THINGS WITH FORMALISMS

David Auerbach

chapter 6|23 pages

THE IMPREDICATIVITY OF INDUCTION