Metamathematics, Machines and Gödel's Proof PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Metamathematics, Machines and Gödel's Proof PDF full book. Access full book title Metamathematics, Machines and Gödel's Proof by N. Shankar. Download full books in PDF and EPUB format.
Author: N. Shankar
Publisher: Cambridge University Press
ISBN: 9780521585330
Category : Computers
Languages : en
Pages : 224
Get Book
Book Description
Describes the use of computer programs to check several proofs in the foundations of mathematics.
Author: N. Shankar
Publisher: Cambridge University Press
ISBN: 9780521585330
Category : Computers
Languages : en
Pages : 224
Get Book
Book Description
Describes the use of computer programs to check several proofs in the foundations of mathematics.
Author: Ernest Nagel
Publisher:
ISBN:
Category :
Languages : en
Pages : 118
Get Book
Book Description
Author: Ernest Nagel
Publisher: Lulu.com
ISBN: 0359079261
Category : Gödel's theorem
Languages : en
Pages : 132
Get Book
Book Description
In 1931 Kurt Gödel published his paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." Gödel’s paper challenged certain basic assumptions underlying much research in mathematics and logic. However, few scholars were unable to understand Gödel’s ideas. Ernest Nagel and James Newman provide a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery.
Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 0393327604
Category : Biography & Autobiography
Languages : en
Pages : 299
Get Book
Book Description
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Author: Gregory J. Chaitin
Publisher: Springer Science & Business Media
ISBN: 9789814021722
Category : Mathematics
Languages : en
Pages : 148
Get Book
Book Description
This essential companion to Chaitins highly successful The Limits of Mathematics, gives a brilliant historical survey of important work on the foundations of mathematics. The Unknowable is a very readable introduction to Chaitins ideas, and includes software (on the authors website) that will enable users to interact with the authors proofs. "Chaitins new book, The Unknowable, is a welcome addition to his oeuvre. In it he manages to bring his amazingly seminal insights to the attention of a much larger audience His work has deserved such treatment for a long time." JOHN ALLEN PAULOS, AUTHOR OF ONCE UPON A NUMBER
Author: Roman Murawski
Publisher: Springer Science & Business Media
ISBN: 9401728666
Category : Philosophy
Languages : en
Pages : 395
Get Book
Book Description
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.
Author: Bernd Finkbeiner
Publisher: Springer
ISBN: 3319249533
Category : Computers
Languages : en
Pages : 520
Get Book
Book Description
This book constitutes the proceedings of the 13th International Symposium on Automated Technology for Verification and Analysis, ATVA 2015, held in Shanghai, China, in October 2015. The 27 revised papers presented together with 6 tool papers in this volume were carefully reviewed and selected from 95 submissions. They show current research on theoretical and practical aspects of automated analysis, verification and synthesis by providing an international forum for interaction among the researchers in academia and industry.
Author: Raymond M. Smullyan
Publisher: Oxford University Press
ISBN: 0195364376
Category : Mathematics
Languages : en
Pages : 156
Get Book
Book Description
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.
Author: Pascal Fontaine
Publisher: Springer Nature
ISBN: 3030294366
Category : Computers
Languages : en
Pages : 603
Get Book
Book Description
This book constitutes the proceeding of the 27th International Conference on Automated Deduction, CADE 27, held in Natal, Brazil, in August 2019. The 27 full papers and 7 system descriptions presented were carefully reviewed and selected from 65 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience.
Author: Rossella Lupacchini
Publisher: Springer Science & Business Media
ISBN: 8847007844
Category : Philosophy
Languages : en
Pages : 285
Get Book
Book Description
This volume is located in a cross-disciplinary ?eld bringing together mat- matics, logic, natural science and philosophy. Re?ection on the e?ectiveness of proof brings out a number of questions that have always been latent in the informal understanding of the subject. What makes a symbolic constr- tion signi?cant? What makes an assumption reasonable? What makes a proof reliable? G ̈ odel, Church and Turing, in di?erent ways, achieve a deep und- standing of the notion of e?ective calculability involved in the nature of proof. Turing’s work in particular provides a “precise and unquestionably adequate” de?nition of the general notion of a formal system in terms of a machine with a ?nite number of parts. On the other hand, Eugene Wigner refers to the - reasonable e?ectiveness of mathematics in the natural sciences as a miracle. Where should the boundary be traced between mathematical procedures and physical processes? What is the characteristic use of a proof as a com- tation, as opposed to its use as an experiment? What does natural science tell us about the e?ectiveness of proof? What is the role of mathematical proofs in the discovery and validation of empirical theories? The papers collected in this book are intended to search for some answers, to discuss conceptual and logical issues underlying such questions and, perhaps, to call attention to other relevant questions.
