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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.
Notes on contributors
Preface
Proofs about proofs: a defense of classical logic. Part I: The aims of classical logic
John P. Burgess
Proofs and epistemic structure
Glen Helman
What is a proof?
Richard Tieszen
How to say things with formalisms
David Auerbach
Some considerations on arithmetical truth and the ω-rule
Daniel Isaacson
The impredicativity of induction
Charles Parsons
Three insufficiently attended to aspects of most mathematical proofs: phenomenological studies
Robert S. Tragesser
On an alleged refutation of Hilbert’s program using Gödel’s first incompleteness theorem
Michael Detlefsen
Index