Godel s Proof

Godel s Proof Author Ernest Nagel
ISBN-10 9781134953998
Year 2012-11-12
Pages 128
Language en
Publisher Routledge

The first book to present a readable explanation of Godel's theorem to both scholars and non-specialists, 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.

Godel s Theorem in Focus

Godel s Theorem in Focus Author S.G. Shanker
ISBN-10 9781134947973
Year 2012-08-21
Pages 272
Language en
Publisher Routledge

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.

S zp Zp

S zp  Zp Author Roy Wagner
ISBN-10 9788876991578
Year 2009
Pages 237
Language en
Publisher Polimetrica s.a.s.

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 logico-mathematical 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 post-structural semiotics into a new form of philosophical fabric, and offers an original way of bridging the gap between the "two cultures".

Godel s Incompleteness Theorems

Godel s Incompleteness Theorems Author Raymond M. Smullyan
ISBN-10 9780195364378
Year 1992-08-20
Pages 160
Language en
Publisher Oxford University Press

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 well-known 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.

An Introduction to G del s Theorems

An Introduction to G  del s Theorems Author Peter Smith
ISBN-10 9781107328488
Year 2013-02-21
Language en
Publisher Cambridge University Press

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.

Principia Mathematica to 56

Principia Mathematica to  56 Author Alfred North Whitehead
ISBN-10 0521626064
Year 1997-09-11
Pages 410
Language en
Publisher Cambridge University Press

The great three-volume 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).

Proof Theory

Proof Theory Author Source Wikipedia
ISBN-10 1230582630
Year 2013-09
Pages 90
Language en
Publisher University-Press.org

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, Curry-Howard correspondence, Mathematical fallacy, Reverse mathematics, Sequent calculus, Large countable ordinal, Hilbert system, Deduction theorem, Fast-growing hierarchy, Ordinal notation, -consistent theory, Decidability, Undecidable problem, Hilbert's program, Metalanguage, Extension by definitions, Ordinal analysis, Veblen function, Dialectica interpretation, Godel-Gentzen negative translation, Pure type system, Herbrand's theorem, Cut-elimination theorem, Bounded quantifier, Slow-growing hierarchy, Gentzen's consistency proof, Elementary function arithmetic, Realizability, Conservative extension, Formal proof, Setoid, Lambda-mu calculus, Primitive recursive functional, Hardy hierarchy, Epsilon calculus, Peano-Russell notation, Independence, Analytic proof, Structural proof theory, Turnstile, Judgment, Proof calculus, Friedman translation, Self-verifying theories, Structural rule, Bachmann-Howard ordinal, Proof-theoretic 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, Feferman-Schutte ordinal, Church-Kleene ordinal, Proof mining, Completeness of atomic initial sequents, Proof net, VIPER microprocessor, NuPRL, Reverse reconstruction.

Godel s theorem simplified

Godel s theorem simplified Author Harry J. Gensler
ISBN-10 UOM:39015049391991
Year 1984-07
Pages 83
Language en
Publisher Univ Pr of Amer

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.

Shadows of the Mind

Shadows of the Mind Author Roger Penrose
ISBN-10 0195106466
Year 1994
Pages 457
Language en
Publisher Oxford University Press, USA

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

Logic and Algebra

Logic and Algebra Author Aldo Ursini
ISBN-10 0824796063
Year 1996-05-30
Pages 728
Language en
Publisher CRC Press

"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."

Kurt G del Collected Works Volume III

Kurt G  del  Collected Works  Volume III Author Kurt Gödel
ISBN-10 0195072553
Year 1995-05-25
Pages 532
Language en
Publisher Oxford University Press

"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.

A World Without Time

A World Without Time Author Palle Yourgrau
ISBN-10 9780786737000
Year 2009-03-04
Pages 224
Language en
Publisher Hachette UK

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.