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Deduction, Computation, Experiment : Exploring the Effectiveness of Proof - G. Corsi

Deduction, Computation, Experiment

Exploring the Effectiveness of Proof

By: G. Corsi, Rossella Lupacchini

eText | 25 September 2008 | Edition Number 1

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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.
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Non-FictionComputing & I.T.Computer ScienceMathematicsMathematical FoundationMathematical LogicPhilosophyEpistemology & The Theory of KnowledgePhilosophy & LogicSciencePhysicsScience in General
Philosophy of ScienceNature & The Natural World

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