
Author 
Ernest Nagel 
ISBN10 
9781134953998 
Year 
20121112 
Pages 
128 
Language 
en 
Publisher 
Routledge 
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The first book to present a readable explanation of Godel's theorem to both scholars and nonspecialists, this is a gripping combination of science and accessibility, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.

Author 
Rebecca Goldstein 
ISBN10 
9780393327601 
Year 
20060217 
Pages 
296 
Language 
en 
Publisher 
W. W. Norton & Company 
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A portrait of the eminent twentiethcentury mathematician discusses his theorem of incompleteness, relationships with such contemporaries as Albert Einstein, and untimely death as a result of mental instability and selfstarvation.

Author 
S.G. Shanker 
ISBN10 
9781134947973 
Year 
20120821 
Pages 
272 
Language 
en 
Publisher 
Routledge 
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A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.

Author 
Roy Wagner 
ISBN10 
9788876991578 
Year 
2009 
Pages 
237 
Language 
en 
Publisher 
Polimetrica s.a.s. 
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S(zp,zp) performs an innovative analysis of one of modern logic's most celebrated cornerstones: the proof of Gödel's first incompleteness theorem. The book applies the semiotic theories of French post structuralists such as Julia Kristeva, Jacques Derrida and Gilles Deleuze to shed new light on a fundamental question: how do mathematical signs produce meaning and make sense? S(zp,zp) analyses the text of the proof of Gödel's result, and shows that mathematical language, like other forms of language, enjoys the full complexity of language as a process, with its embodied genesis, constitutive paradoxical forces and unbounded shifts of meaning. These effects do not infringe on the logicomathematical validity of Gödel's proof. Rather, they belong to a mathematical unconscious that enables the successful function of mathematical texts for a variety of different readers. S(zp,zp) breaks new ground by synthesising mathematical logic and poststructural semiotics into a new form of philosophical fabric, and offers an original way of bridging the gap between the "two cultures".

Author 
Raymond M. Smullyan 
ISBN10 
9780195364378 
Year 
19920820 
Pages 
160 
Language 
en 
Publisher 
Oxford University Press 
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Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a wellknown logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.

Author 
N. Shankar 
ISBN10 
0521585333 
Year 
19970130 
Pages 
202 
Language 
en 
Publisher 
Cambridge University Press 
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Describes the use of computer programs to check several proofs in the foundations of mathematics.

Author 
Kurt Gödel 
ISBN10 
9780486158402 
Year 
20120524 
Pages 
80 
Language 
en 
Publisher 
Courier Corporation 
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First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.

Author 
Peter Smith 
ISBN10 
9781107328488 
Year 
20130221 
Pages 

Language 
en 
Publisher 
Cambridge University Press 
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In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book  extensively rewritten for its second edition  will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

Author 
Alfred North Whitehead 
ISBN10 
0521626064 
Year 
19970911 
Pages 
410 
Language 
en 
Publisher 
Cambridge University Press 
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The great threevolume Principia Mathematica (CUP 1927) is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part I (in which the logical properties of propositions, propositional functions, classes and relations are established); section A of Part II (dealing with unit classes and couples); and Appendices A and C (which give further developments of the argument on the theory of deduction and truth functions).

Author 
Source Wikipedia 
ISBN10 
1230582630 
Year 
201309 
Pages 
90 
Language 
en 
Publisher 
UniversityPress.org 
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 88. Chapters: Mathematical induction, Presburger arithmetic, Godel's completeness theorem, Soundness, Natural deduction, Original proof of Godel's completeness theorem, Consistency, Godel's incompleteness theorems, CurryHoward correspondence, Mathematical fallacy, Reverse mathematics, Sequent calculus, Large countable ordinal, Hilbert system, Deduction theorem, Fastgrowing hierarchy, Ordinal notation, consistent theory, Decidability, Undecidable problem, Hilbert's program, Metalanguage, Extension by definitions, Ordinal analysis, Veblen function, Dialectica interpretation, GodelGentzen negative translation, Pure type system, Herbrand's theorem, Cutelimination theorem, Bounded quantifier, Slowgrowing hierarchy, Gentzen's consistency proof, Elementary function arithmetic, Realizability, Conservative extension, Formal proof, Setoid, Lambdamu calculus, Primitive recursive functional, Hardy hierarchy, Epsilon calculus, PeanoRussell notation, Independence, Analytic proof, Structural proof theory, Turnstile, Judgment, Proof calculus, Friedman translation, Selfverifying theories, Structural rule, BachmannHoward ordinal, Prooftheoretic semantics, Provability logic, Disjunction and existence properties, Conservativity theorem, Paraconsistent mathematics, Deep inference, Psi0(Omega omega), Takeuti's conjecture, Deductive system, Geometry of interaction, Tolerant sequence, Weak interpretability, Proof procedure, Decidable sublanguages of set theory, FefermanSchutte ordinal, ChurchKleene ordinal, Proof mining, Completeness of atomic initial sequents, Proof net, VIPER microprocessor, NuPRL, Reverse reconstruction.

Author 
Harry J. Gensler 
ISBN10 
UOM:39015049391991 
Year 
198407 
Pages 
83 
Language 
en 
Publisher 
Univ Pr of Amer 
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This helpful volume explains and proves Godel's theorem, which states that arithmetic cannot be reduced to any axiomatic system. Written simply and directly, this book is intended for the student and general reader and presumes no specialized knowledge of mathematics or logic.

Author 
Roger Penrose 
ISBN10 
0195106466 
Year 
1994 
Pages 
457 
Language 
en 
Publisher 
Oxford University Press, USA 
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Presenting a look at the human mind's capacity while criticizing artificial intelligence, the author makes suggestions about classical and quantum physics and the role of microtubules

Author 
Aldo Ursini 
ISBN10 
0824796063 
Year 
19960530 
Pages 
728 
Language 
en 
Publisher 
CRC Press 
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"Attempts to unite the fields of mathematical logic and general algebra. Presents a collection of refereed papers inspired by the International Conference on Logic and Algebra held in Siena, Italy, in honor of the late Italian mathematician Roberto Magari, a leading force in the blossoming of research in mathematical logic in Italy since the 1960s."

Author 
Kurt Gödel 
ISBN10 
0195072553 
Year 
19950525 
Pages 
532 
Language 
en 
Publisher 
Oxford University Press 
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"Anyone interested in the life and work of Kurt Gödel, or in the history of mathematical logic in this century, is indebted to all of the contributors to this volume for the care with which they have presented Gödel's work. They have succeeded in using their own expertise to elucidate both the nature and significance of what Gödel and, in turn, mathematical logic have accomplished." Isis (on volume I). The third volume brings togetherGödels unpublished essays and lectures.

Author 
Palle Yourgrau 
ISBN10 
9780786737000 
Year 
20090304 
Pages 
224 
Language 
en 
Publisher 
Hachette UK 
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In 1942, the logician Kurt Godel and Albert Einstein became close friends; they walked to and from their offices every day, exchanging ideas about science, philosophy, politics, and the lost world of German science. By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.