Gödel Without (Too Many) Tears
Author: Peter Smith
Publisher:
Published: 2022-12
Total Pages: 0
ISBN-13: 9781916906341
DOWNLOAD EBOOK →Author: Peter Smith
Publisher:
Published: 2022-12
Total Pages: 0
ISBN-13: 9781916906341
DOWNLOAD EBOOK →Author: Peter Smith
Publisher:
Published: 2021-06-15
Total Pages: 146
ISBN-13: 9781916906303
DOWNLOAD EBOOK →Kurt Gödel's famous First Incompleteness Theorem shows that for any sufficiently rich theory that contains enough arithmetic, there are some arithmetical truths the theory cannot prove. How is this remarkable result proved? This short book explains. It also discusses Gödel's Second Incompleteness Theorem. Based on lecture notes for a course given in Cambridge for many years, the aim is to make the Theorems available, clearly and accessibly, even to those with a quite limited formal background.
Author: Kurt Gödel
Publisher: Courier Corporation
Published: 2012-05-24
Total Pages: 82
ISBN-13: 0486158403
DOWNLOAD EBOOK →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
Publisher: Cambridge University Press
Published: 2007-07-26
Total Pages: 376
ISBN-13: 0521857848
DOWNLOAD EBOOK →Peter Smith examines Gödel's Theorems, how they were established and why they matter.
Author: Torkel Franzén
Publisher: CRC Press
Published: 2005-06-06
Total Pages: 182
ISBN-13: 1439876924
DOWNLOAD EBOOK →"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
Author: Raymond M. Smullyan
Publisher: Knopf
Published: 2012-07-04
Total Pages: 286
ISBN-13: 0307962466
DOWNLOAD EBOOK →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: James R. Meyer
Publisher:
Published: 2008
Total Pages: 346
ISBN-13: 9781906706005
DOWNLOAD EBOOK →Author: Mark C. Chu-Carroll
Publisher: Pragmatic Bookshelf
Published: 2013-07-18
Total Pages: 269
ISBN-13: 168050360X
DOWNLOAD EBOOK →Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you. Why do Roman numerals persist? How do we know that some infinities are larger than others? And how can we know for certain a program will ever finish? In this fast-paced tour of modern and not-so-modern math, computer scientist Mark Chu-Carroll explores some of the greatest breakthroughs and disappointments of more than two thousand years of mathematical thought. There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular "Good Math" blog, you'll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird. Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing. If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark's book will both entertain and enlighten you.
Author: George Boolos
Publisher: Harvard University Press
Published: 1998
Total Pages: 458
ISBN-13: 9780674537675
DOWNLOAD EBOOK →George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.
Author: L. S. Pontryagin
Publisher: Courier Corporation
Published: 2015-05-20
Total Pages: 112
ISBN-13: 0486406857
DOWNLOAD EBOOK →Concise, rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Lucid coverage of the field includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete and careful manner. A beneficial text for a graduate-level course, "this little book is an extremely valuable addition to the literature of algebraic topology." — The Mathematical Gazette.