Raymond Smullyan On Self Reference

Author : Melvin Fitting
Publisher : Springer
ISBN 13 : 3319687328
Total Pages : 195 pages
Book Rating : 4.22/5 ( download)

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Download or read book Raymond Smullyan on Self Reference written by Melvin Fitting and published by Springer. This book was released on 2018-01-11 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects, for the first time in one volume, contributions honoring Professor Raymond Smullyan’s work on self-reference. It serves not only as a tribute to one of the great thinkers in logic, but also as a celebration of self-reference in general, to be enjoyed by all lovers of this field. Raymond Smullyan, mathematician, philosopher, musician and inventor of logic puzzles, made a lasting impact on the study of mathematical logic; accordingly, this book spans the many personalities through which Professor Smullyan operated, offering extensions and re-evaluations of his academic work on self-reference, applying self-referential logic to art and nature, and lastly, offering new puzzles designed to communicate otherwise esoteric concepts in mathematical logic, in the manner for which Professor Smullyan was so well known. This book is suitable for students, scholars and logicians who are interested in learning more about Raymond Smullyan's work and life.

Author : Raymond M. Smullyan
Publisher : Oxford Logic Guides
ISBN 13 : 9780198534501
Total Pages : 0 pages
Book Rating : 4.07/5 ( download)

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Download or read book Diagonalization and Self-reference written by Raymond M. Smullyan and published by Oxford Logic Guides. This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The book provides a survey of introductory material and a summary of recent research. The firstchapters are of an introductory nature and consist mainly of exercises with solutions given to most of them.

Author : S.J. Bartlett
Publisher : Springer Science & Business Media
ISBN 13 : 940093551X
Total Pages : 365 pages
Book Rating : 4.18/5 ( download)

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Download or read book Self-Reference written by S.J. Bartlett and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-reference, although a topic studied by some philosophers and known to a number of other disciplines, has received comparatively little explicit attention. For the most part the focus of studies of self-reference has been on its logical and linguistic aspects, with perhaps disproportionate emphasis placed on the reflexive paradoxes. The eight-volume Macmillan Encyclopedia of Philosophy, for example, does not contain a single entry in its index under "self-reference", and in connection with "reflexivity" mentions only "relations", "classes", and "sets". Yet, in this volume, the introductory essay identifies some 75 varieties and occurrences of self-reference in a wide range of disciplines, and the bibliography contains more than 1,200 citations to English language works about reflexivity. The contributed papers investigate a number of forms and applications of self-reference, and examine some of the challenges posed by its difficult temperament. The editors hope that readers of this volume will gain a richer sense of the sti11largely unexplored frontiers of reflexivity, and of the indispensability of reflexive concepts and methods to foundational inquiries in philosophy, logic, language, and into the freedom, personality and intelligence of persons.

Author : Raymond M. Smullyan
Publisher : Knopf
ISBN 13 : 0307819825
Total Pages : 281 pages
Book Rating : 4.26/5 ( download)

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Download or read book Satan, Cantor, And Infinity And Other Mind-bogglin written by Raymond M. Smullyan and published by Knopf. This book was released on 2012-05-30 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than two hundred new and challenging logic puzzles—the simplest brainteaser to the most complex paradoxes in contemporary mathematical thinking—from our topmost puzzlemaster (“the most entertaining logician who ever lived,” Martin Gardner has called him). Our guide to the puzzles is the Sorcerer, who resides on the Island of Knights and Knaves, where knights always tell the truth and knaves always lie, and he introduces us to the amazing magic—logic—that enables to discover which inhabitants are which. Then, in a picaresque adventure in logic, he takes us to the planet Og, to the Island of Partial Silence, and to a land where metallic robots wearing strings of capital letters are noisily duplicating and dismantling themselves and others. The reader’s job is to figure out how it all works. Finally, we accompany the Sorcerer on an alluring tour of Infinity which includes George Cantor’s amazing mathematical insights. The tour (and the book) ends with Satan devising a diabolical puzzle for one of Cantor’s prize students—who outwits him! In sum: a devilish magician’s cornucopia of puzzles—a delight for every age and level of ability.

Author : Raymond M. Smullyan
Publisher : Oxford University Press on Demand
ISBN 13 : 019508232X
Total Pages : 180 pages
Book Rating : 4.26/5 ( download)

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Download or read book Recursion Theory for Metamathematics written by Raymond M. Smullyan and published by Oxford University Press on Demand. This book was released on 1993 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Raymond M. Smullyan
Publisher : Courier Corporation
ISBN 13 : 0486315770
Total Pages : 240 pages
Book Rating : 4.75/5 ( download)

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Download or read book The Gödelian Puzzle Book written by Raymond M. Smullyan and published by Courier Corporation. This book was released on 2013-08-21 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: These logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. No background in formal logic necessary.

Author : Raymond M. Smullyan
Publisher : Knopf
ISBN 13 : 0307962466
Total Pages : 286 pages
Book Rating : 4.61/5 ( download)

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Download or read book Forever Undecided written by Raymond M. Smullyan and published by Knopf. This book was released on 2012-07-04 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!

Author : René Woudenberg
Publisher : Walter de Gruyter
ISBN 13 : 3110327511
Total Pages : 294 pages
Book Rating : 4.19/5 ( download)

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Download or read book Basic Belief and Basic Knowledge written by René Woudenberg and published by Walter de Gruyter. This book was released on 2013-05-02 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last two decades foundationalism has been severely criticized. In response to this various alternatives to it have been advanced, notably coherentism. At the same time new versions of foundationalism were crafted, that were claimed to be immune to the earlier criticisms. This volume contains 12 papers in which various aspects of this dialectic are covered. A number of papers continue the trend to defend foundationalism, and foundationalism's commitment to basic beliefs and basic knowledge, against various attacks. Others aim to show that one important objection against coherentism, viz. that the notion of 'coherence' is too vague to be useful, can be countered.

Author : Raymond M. Smullyan
Publisher : Harper Collins
ISBN 13 : 0062281410
Total Pages : 303 pages
Book Rating : 4.18/5 ( download)

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Download or read book The Tao Is Silent written by Raymond M. Smullyan and published by Harper Collins. This book was released on 2013-03-05 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Tao Is Silent Is Raymond Smullyan's beguiling and whimsical guide to the meaning and value of eastern philosophy to westerners. "To me," Writes Smullyan, "Taoism means a state of inner serenity combined with an intense aesthetic awareness. Neither alone is adequate; a purely passive serenity is kind of dull, and an anxiety-ridden awareness is not very appealing." This is more than a book on Chinese philosophy. It is a series of ideas inspired by Taoism that treats a wide variety of subjects about life in general. Smullyan sees the Taoist as "one who is not so much in search of something he hasn't, but who is enjoying what he has." Readers will be charmed and inspired by this witty, sophisticated, yet deeply religious author, whether he is discussing gardening, dogs, the art of napping, or computers who dream that they're human.

Author : Raymond R. Smullyan
Publisher : Springer Science & Business Media
ISBN 13 : 3642867189
Total Pages : 167 pages
Book Rating : 4.87/5 ( download)

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Download or read book First-Order Logic written by Raymond R. Smullyan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Except for this preface, this study is completely self-contained. It is intended to serve both as an introduction to Quantification Theory and as an exposition of new results and techniques in "analytic" or "cut-free" methods. We use the term "analytic" to apply to any proof procedure which obeys the subformula principle (we think of such a procedure as "analysing" the formula into its successive components). Gentzen cut-free systems are perhaps the best known example of ana lytic proof procedures. Natural deduction systems, though not usually analytic, can be made so (as we demonstrated in [3]). In this study, we emphasize the tableau point of view, since we are struck by its simplicity and mathematical elegance. Chapter I is completely introductory. We begin with preliminary material on trees (necessary for the tableau method), and then treat the basic syntactic and semantic fundamentals of propositional logic. We use the term "Boolean valuation" to mean any assignment of truth values to all formulas which satisfies the usual truth-table conditions for the logical connectives. Given an assignment of truth-values to all propositional variables, the truth-values of all other formulas under this assignment is usually defined by an inductive procedure. We indicate in Chapter I how this inductive definition can be made explicit-to this end we find useful the notion of a formation tree (which we discuss earlier).