Author : Peter Smith
Publisher : Unknown
Page : 0 pages
File Size : 44,6 Mb
Release : 2022-12
Category : Electronic
ISBN : 1916906346
Gödel Without (Too Many) Tears
Peter Smith
Gödel Without Too Many Tears
Gödel Without Too Many Tears Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Gödel Without Too Many Tears book. This book definitely worth reading, it is an incredibly well-written.
An Introduction to Gödel's Theorems
Peter Smith
Author : Peter Smith
Publisher : Cambridge University Press
Page : 376 pages
File Size : 51,9 Mb
Release : 2007-07-26
Category : Mathematics
ISBN : 9780521857840
An Introduction to Gödel's Theorems by Peter Smith Pdf
Peter Smith examines Gödel's Theorems, how they were established and why they matter.
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
Kurt Gödel
Author : Kurt Gödel
Publisher : Courier Corporation
Page : 82 pages
File Size : 41,9 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780486158402
On Formally Undecidable Propositions of Principia Mathematica and Related Systems by Kurt Gödel Pdf
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.
Forever Undecided
Raymond M. Smullyan
Author : Raymond M. Smullyan
Publisher : Knopf
Page : 286 pages
File Size : 53,7 Mb
Release : 2012-07-04
Category : Mathematics
ISBN : 9780307962461
Forever Undecided by Raymond M. Smullyan Pdf
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!
Explaining Chaos
Peter Smith
Author : Peter Smith
Publisher : Cambridge University Press
Page : 198 pages
File Size : 41,8 Mb
Release : 1998-09-24
Category : Philosophy
ISBN : 0521477476
Explaining Chaos by Peter Smith Pdf
A clear and accessible discussion of the ideas and issues behind chaotic dynamics.
Gödel's Theorem
Torkel Franzén
Author : Torkel Franzén
Publisher : CRC Press
Page : 182 pages
File Size : 41,9 Mb
Release : 2005-06-06
Category : Mathematics
ISBN : 9781439876923
Gödel's Theorem by Torkel Franzén Pdf
"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
Kurt Gödel
William D. Brewer
Author : William D. Brewer
Publisher : Springer Nature
Page : 502 pages
File Size : 51,8 Mb
Release : 2022-09-08
Category : Mathematics
ISBN : 9783031113093
Kurt Gödel by William D. Brewer Pdf
During his lifetime, Kurt Gödel was not well known outside the professional world of mathematicians, philosophers and theoretical physicists. Early in his career, for his doctoral thesis and then for his Habilitation (Dr.Sci.), he wrote earthshaking articles on the completeness and provability of mathematical-logical systems, upsetting the hypotheses of the most famous mathematicians/philosophers of the time. He later delved into theoretical physics, finding a unique solution to Einstein’s equations for gravity, the ‘Gödel Universe’, and made contributions to philosophy, the guiding theme of his life. This book includes more details about the context of Gödel’s life than are found in earlier biographies, while avoiding an elaborate treatment of his mathematical/scientific/philosophical works, which have been described in great detail in other books. In this way, it makes him and his times more accessible to general readers, and will allow them to appreciate the lasting effects of Gödel’s contributions (the latter in a more up-to-date context than in previous biographies, many of which were written 15–25 years ago). His work spans or is relevant to a wide spectrum of intellectual endeavor, and this is emphasized in the book, with recent examples. This biography also examines possible sources of his unusual personality, which combined mathematical genius with an almost childlike naiveté concerning everyday life, and striking scientific innovations with timidity and hesitancy in practical matters. How he nevertheless had a long and successful career, inspiring many younger scholars along the way, with the help of his loyal wife Adele and some of his friends, is a fascinating story in human nature.
Logic, Logic, and Logic
George Boolos
Author : George Boolos
Publisher : Harvard University Press
Page : 458 pages
File Size : 55,5 Mb
Release : 1998
Category : Mathematics
ISBN : 067453767X
Logic, Logic, and Logic by George Boolos Pdf
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.
Good Math
Mark C. Chu-Carroll
Author : Mark C. Chu-Carroll
Publisher : Pragmatic Bookshelf
Page : 269 pages
File Size : 51,9 Mb
Release : 2013-07-18
Category : Computers
ISBN : 9781680503609
Good Math by Mark C. Chu-Carroll Pdf
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.
Laws and Lawmakers
Marc Lange
Author : Marc Lange
Publisher : Oxford University Press
Page : 277 pages
File Size : 49,6 Mb
Release : 2009-07-09
Category : Philosophy
ISBN : 9780199745036
Laws and Lawmakers by Marc Lange Pdf
What distinguishes laws of nature from ordinary facts? What are the "lawmakers": the facts in virtue of which the laws are laws? How can laws be necessary, yet contingent? Lange provocatively argues that laws are distinguished by their necessity, which is grounded in primitive subjunctive facts, while also providing a non-technical and accessible survey of the field.
The shackles of conviction
James R. Meyer
Author : James R. Meyer
Publisher : Unknown
Page : 346 pages
File Size : 54,9 Mb
Release : 2008
Category : Fiction
ISBN : 190670600X
The shackles of conviction by James R. Meyer Pdf
Incompleteness and Computability
Richard Zach
Author : Richard Zach
Publisher : Createspace Independent Publishing Platform
Page : 228 pages
File Size : 53,5 Mb
Release : 2017-06-15
Category : Electronic
ISBN : 1548138088
Incompleteness and Computability by Richard Zach Pdf
A textbook on recursive function theory and G�del's incompleteness theorems. Also covers models of arithmetic and second-order logic.
A World Without Time
Palle Yourgrau
Author : Palle Yourgrau
Publisher : Basic Books
Page : 226 pages
File Size : 45,5 Mb
Release : 2009-03-04
Category : Science
ISBN : 9780786737000
A World Without Time by Palle Yourgrau Pdf
It is a widely known but little considered fact that Albert Einstein and Kurt Godel were best friends for the last decade and a half of Einstein's life. The two walked home together from Princeton's Institute for Advanced Study every day; they shared ideas about physics, philosophy, politics, and the lost world of German science in which they had grown up. 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, since it decisively overthrew the classical world-view to which he was committed. But he could find no way to refute it, and in the half-century since then, neither has anyone else. Even more remarkable than this stunning discovery, however, was what happened afterward: nothing. Cosmologists and philosophers alike have proceeded with their work as if Godel's proof never existed -one of the greatest scandals of modern intellectual history. A World Without Time is a sweeping, ambitious book, and yet poignant and intimate. It tells the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue from undeserved obscurity the brilliant work they did together.
Logic Matters
P. T. Geach,B. Geach
Author : P. T. Geach,B. Geach
Publisher : Univ of California Press
Page : 356 pages
File Size : 43,5 Mb
Release : 1980-04-30
Category : Philosophy
ISBN : 0520038479
Logic Matters by P. T. Geach,B. Geach Pdf
"This is a significant and ofren rather demanding collection of essays. It is an anthology purring together the uncollected works of an important twentieth-century philosopher. Many of the articles treat one or another of the more important issues considered by analytic philosophers during the last quarter-century. Of significant importance to philosophers interested in researching the many topics contained in Logic Matters is the inclusion in this anthology of a rather extensive eight-page name-topic index."--Thomist "The papers are arranged by topic: Historical Essays, Traditional Logic, Theory of Reference and Syntax, Intentionality, Quotation and Semantics, Set Theory, Identity Theory, Assertion, Imperatives and Practical Reasoning, Logic in Metaphysics and Theology. The broad range of issues that have engaged Geach's complex and systematic reasoning is impressive. In addition to classical logic, topics in ethics, ontology, and even the logic of religious dogmas are tackled .... the work in this collection is more brilliant and ingenious than it is difficult and demanding."--Philosophy of Science "Geach displays his mastery of applying logical techniques and concepts to philosophical questions. Compared with most works in philosophical logic this book is remarkable for its range of topics. Plato, Aristotle, Aquinas, Russell, Wittgenstein, and Quine all figure prominently. Geach's style is remarkably lively considering the rightly argued matter. Although some of the articles treat rather technical questions in mathematical logic, most are accessible to philosophers with modest backgrounds in logic." --Choice
Math with Bad Drawings
Ben Orlin
Author : Ben Orlin
Publisher : Black Dog & Leventhal
Page : 556 pages
File Size : 40,9 Mb
Release : 2018-09-18
Category : Mathematics
ISBN : 9780316509022
Math with Bad Drawings by Ben Orlin Pdf
A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark "bad drawings," which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike.