Overview
- Editors:
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Rossella Lupacchini
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Dipartimento di Filosofia, Università degli Studi di Bologna, Italia
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Giovanna Corsi
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Dipartimento di Filosofia, Università degli Studi di Bologna, Italia
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Table of contents (13 chapters)
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- Wilfried Sieg, Clinton Field
Pages 117-140
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- Ugo Dal Lago, Simone Martini
Pages 141-157
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- Francis Bailly, Giuseppe Longo
Pages 243-271
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Back Matter
Pages 273-279
About this book
This volume is located in a cross-disciplinary ?eld bringing together mat- matics, logic, natural science and philosophy. Re?ection on the e?ectiveness of proof brings out a number of questions that have always been latent in the informal understanding of the subject. What makes a symbolic constr- tion signi?cant? What makes an assumption reasonable? What makes a proof reliable? G¨ odel, Church and Turing, in di?erent ways, achieve a deep und- standing of the notion of e?ective calculability involved in the nature of proof. Turing’s work in particular provides a “precise and unquestionably adequate” de?nition of the general notion of a formal system in terms of a machine with a ?nite number of parts. On the other hand, Eugene Wigner refers to the - reasonable e?ectiveness of mathematics in the natural sciences as a miracle. Where should the boundary be traced between mathematical procedures and physical processes? What is the characteristic use of a proof as a com- tation, as opposed to its use as an experiment? What does natural science tell us about the e?ectiveness of proof? What is the role of mathematical proofs in the discovery and validation of empirical theories? The papers collected in this book are intended to search for some answers, to discuss conceptual and logical issues underlying such questions and, perhaps, to call attention to other relevant questions.
