Recursion Theory for Metamathematics

Author: Raymond M. Smullyan

Publisher: Oxford University Press on Demand

ISBN: 019508232X

Category: Social Science

Page: 163

View: 3359

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This work is a sequel to the author's G�del's Incompleteness Theorems, though it can be read independently by anyone familiar with G�del's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
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Physical (A)Causality

Determinism, Randomness and Uncaused Events

Author: Karl Svozil

Publisher: Springer

ISBN: 3319708155

Category: Science

Page: 219

View: 6796

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This book is open access under a CC BY 4.0 license. This book addresses the physical phenomenon of events that seem to occur spontaneously and without any known cause. These are to be contrasted with events that happen in a (pre-)determined, predictable, lawful, and causal way. All our knowledge is based on self-reflexive theorizing, as well as on operational means of empirical perception. Some of the questions that arise are the following: are these limitations reflected by our models? Under what circumstances does chance kick in? Is chance in physics merely epistemic? In other words, do we simply not know enough, or use too crude levels of description for our predictions? Or are certain events "truly", that is, irreducibly, random? The book tries to answer some of these questions by introducing intrinsic, embedded observers and provable unknowns; that is, observables and procedures which are certified (relative to the assumptions) to be unknowable or undoable. A (somewhat iconoclastic) review of quantum mechanics is presented which is inspired by quantum logic. Postulated quantum (un-)knowables are reviewed. More exotic unknowns originate in the assumption of classical continua, and in finite automata and generalized urn models, which mimic complementarity and yet maintain value definiteness. Traditional conceptions of free will, miracles and dualistic interfaces are based on gaps in an otherwise deterministic universe.
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Choice

Publication of the Association of College and Research Libraries, a Division of the American Library Association

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Best books

Page: N.A

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A Beginner's Further Guide to Mathematical Logic

Principles and Applications (with Companion Media Pack)Fourth Edition of Rapid Prototyping Fourth Edition

Author: Raymond Smullyan

Publisher: World Scientific Publishing Company

ISBN: 9814733016

Category:

Page: 288

View: 2836

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This is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan. This book is a sequel to my Beginner's Guide to Mathematical Logic. The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results. The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a "fein" chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a "decision machine." Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic. This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics. Request Inspection Copy
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Revenge of the Liar

New Essays on the Paradox

Author: J. C. Beall

Publisher: OUP Oxford

ISBN: N.A

Category: Philosophy

Page: 374

View: 9902

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Fourteen new essays by some of the world's leading experts, together with an extensive introduction, examine the nature of the Liar paradox and its resistance to any attempt to solve it.
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Handbook of Logic and Proof Techniques for Computer Science

Author: Steven G. Krantz

Publisher: Springer Science & Business Media

ISBN: 9780817642204

Category: Computers

Page: 245

View: 1121

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Logic plays a central conceptual role in modern mathematics. However, mathematical logic has grown into one of the most recondite areas of mathematics. As a result, most of modern logic is inaccessible to all but the specialist. This new book is a resource that provides a quick introduction and review of the key topics in logic for the computer scientist, engineer, or mathematician.Handbook of Logic and Proof Techniques for Computer Science presents the elements of modern logic, including many current topics, to the reader having only basic mathematical literacy. Computer scientists will find specific examples and important ideas such as axiomatics, recursion theory, decidability, independence, completeness, consistency, model theory, and P/NP completeness. The book contains definitions, examples and discussion of all of the key ideas in basic logic, but also makes a special effort to cut through the mathematical formalism, difficult notation, and esoteric terminology that is typical of modern mathematical logic. TThis handbook delivers cogent and self-contained introductions to critical advanced topics, including:* Godel`s completeness and incompleteness theorems* Methods of proof, cardinal and ordinal numbers, the continuum hypothesis, the axiom of choice, model theory, and number systems and their construction* Extensive treatment of complexity theory and programming applications* Applications to algorithms in Boolean algebra* Discussion of set theory and applications of logicThe book is an excellent resource for the working mathematical scientist. The graduate student or professional in computer science and engineering or the systems scientist who needs to have a quick sketch of a key idea from logic will find it here in this self-contained, accessible, and easy-to-use reference.
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Books in Print

Author: R.R. Bowker Company

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.
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Diagonalization and Self-reference

Author: Raymond M. Smullyan

Publisher: Oxford University Press on Demand

ISBN: 9780198534501

Category: Mathematics

Page: 396

View: 853

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The main purpose of this book is to present a unified treatment of fixed points as they occur in Godel's incompleteness proofs, recursion theory, combinatory logic, semantics and metamathematics. It provides a survey of introductory material and a summary of recent research. The first chapters are of an introductory nature, and consist mainly of exercises with solutions given to most of them. The book should be of interest to researchers and graduate students in mathematical logic.
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