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detlefsen m proof logic formalization 1992

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Textbook in PDF format 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

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detlefsen m proof logic formalization 1992

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