Gödel's Proof

Gödel's Proof
Title Gödel's Proof PDF eBook
Author Ernest Nagel
Publisher Psychology Press
Pages 118
Release 1989
Genre Gödel's theorem
ISBN 041504040X

Download Gödel's Proof Book in PDF, Epub and Kindle

In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proofby Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.

Incompleteness

Incompleteness
Title Incompleteness PDF eBook
Author Rebecca Goldstein
Publisher W. W. Norton & Company
Pages 299
Release 2006-01-31
Genre Biography & Autobiography
ISBN 0393327604

Download Incompleteness Book in PDF, Epub and Kindle

"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.

An Introduction to Gödel's Theorems

An Introduction to Gödel's Theorems
Title An Introduction to Gödel's Theorems PDF eBook
Author Peter Smith
Publisher Cambridge University Press
Pages 376
Release 2007-07-26
Genre Mathematics
ISBN 1139465937

Download An Introduction to Gödel's Theorems Book in PDF, Epub and Kindle

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 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.

S(zp, Zp)

S(zp, Zp)
Title S(zp, Zp) PDF eBook
Author Roy Wagner
Publisher Polimetrica s.a.s.
Pages 245
Release 2009
Genre Mathematics
ISBN 8876991573

Download S(zp, Zp) Book in PDF, Epub and Kindle

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".

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

On Formally Undecidable Propositions of Principia Mathematica and Related Systems
Title On Formally Undecidable Propositions of Principia Mathematica and Related Systems PDF eBook
Author Kurt Gödel
Publisher Courier Corporation
Pages 82
Release 2012-05-24
Genre Mathematics
ISBN 0486158403

Download On Formally Undecidable Propositions of Principia Mathematica and Related Systems Book in PDF, Epub and Kindle

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.

Metamathematics, Machines and Gödel's Proof

Metamathematics, Machines and Gödel's Proof
Title Metamathematics, Machines and Gödel's Proof PDF eBook
Author N. Shankar
Publisher Cambridge University Press
Pages 224
Release 1997-01-30
Genre Computers
ISBN 9780521585330

Download Metamathematics, Machines and Gödel's Proof Book in PDF, Epub and Kindle

Describes the use of computer programs to check several proofs in the foundations of mathematics.

Gödel's Theorem

Gödel's Theorem
Title Gödel's Theorem PDF eBook
Author Torkel Franzén
Publisher CRC Press
Pages 184
Release 2005-06-06
Genre Mathematics
ISBN 1439876924

Download Gödel's Theorem Book in PDF, Epub and Kindle

"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel