Kurt Godel Results On Foundations

Download Kurt Godel Results On Foundations full books in PDF, epub, and Kindle. Read online Kurt Godel Results On Foundations ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Kurt Gödel and the Foundations of Mathematics

Author : Matthias Baaz
Publisher : Cambridge University Press
ISBN 13 : 1139498436
Total Pages : 541 pages
Book Rating : 4.1/5 (394 download)

DOWNLOAD NOW!

Book Synopsis Kurt Gödel and the Foundations of Mathematics by : Matthias Baaz

Download or read book Kurt Gödel and the Foundations of Mathematics written by Matthias Baaz and published by Cambridge University Press. This book was released on 2011-06-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

Kurt Gödel: Results on Foundations

Author : Maria Hämeen-Anttila
Publisher :
ISBN 13 : 9783031378775
Total Pages : 0 pages
Book Rating : 4.3/5 (787 download)

DOWNLOAD NOW!

Book Synopsis Kurt Gödel: Results on Foundations by : Maria Hämeen-Anttila

Download or read book Kurt Gödel: Results on Foundations written by Maria Hämeen-Anttila and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel (1906-1978) gained world-wide fame by his incompleteness theorem of 1931. Later, he set as his aim to solve what are known as Hilbert's first and second problems, namely Cantor's continuum hypothesis about the cardinality of real numbers, and secondly the consistency of the theory of real numbers and functions. By 1940, he was halfway through the first problem, in what was his last published result in logic and foundations. His intense attempts thereafter at solving these two problems have remained behind the veil of a forgotten German shorthand he used in all of his writing. Results on Foundations is a set of four shorthand notebooks written in 1940-42 that collect results Gödel considered finished. Its main topic is set theory in which Gödel anticipated several decades of development. Secondly, Gödel completed his 1933 program of establishing the connections between intuitionistic and modal logic, by methods and results that today are at the same time new and 80 years old. The present edition of Gödel's four notebooks encompasses the 368 numbered pages and 126 numbered theorems of the Results on Foundations, together with a list of 74 problems on set theory Gödel prepared in 1946, and a list of an unknown date titled "The grand program of my research in ca. hundred questions.''.

Kurt Gödel: Results on Foundations

Author : Maria Hämeen-Anttila
Publisher : Springer Nature
ISBN 13 : 303137875X
Total Pages : 327 pages
Book Rating : 4.0/5 (313 download)

DOWNLOAD NOW!

Book Synopsis Kurt Gödel: Results on Foundations by : Maria Hämeen-Anttila

Download or read book Kurt Gödel: Results on Foundations written by Maria Hämeen-Anttila and published by Springer Nature. This book was released on 2023-08-18 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel (1906-1978) gained world-wide fame by his incompleteness theorem of 1931. Later, he set as his aim to solve what are known as Hilbert's first and second problems, namely Cantor's continuum hypothesis about the cardinality of real numbers, and secondly the consistency of the theory of real numbers and functions. By 1940, he was halfway through the first problem, in what was his last published result in logic and foundations. His intense attempts thereafter at solving these two problems have remained behind the veil of a forgotten German shorthand he used in all of his writing. Results on Foundations is a set of four shorthand notebooks written in 1940-42 that collect results Gödel considered finished. Its main topic is set theory in which Gödel anticipated several decades of development. Secondly, Gödel completed his 1933 program of establishing the connections between intuitionistic and modal logic, by methods and results that today are at the same time new and 80 years old. The present edition of Gödel's four notebooks encompasses the 368 numbered pages and 126 numbered theorems of the Results on Foundations, together with a list of 74 problems on set theory Gödel prepared in 1946, and a list of an unknown date titled "The grand program of my research in ca. hundred questions.''

Incompleteness

Author : Rebecca Goldstein
Publisher : W. W. Norton & Company
ISBN 13 : 0393327604
Total Pages : 299 pages
Book Rating : 4.3/5 (933 download)

DOWNLOAD NOW!

Book Synopsis Incompleteness by : Rebecca Goldstein

Download or read book Incompleteness written by Rebecca Goldstein and published by W. W. Norton & Company. This book was released on 2006-01-31 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.

Can Mathematics Be Proved Consistent?

Author : Jan von Plato
Publisher : Springer Nature
ISBN 13 : 3030508765
Total Pages : 263 pages
Book Rating : 4.0/5 (35 download)

DOWNLOAD NOW!

Book Synopsis Can Mathematics Be Proved Consistent? by : Jan von Plato

Download or read book Can Mathematics Be Proved Consistent? written by Jan von Plato and published by Springer Nature. This book was released on 2020-07-24 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel (1906–1978) shook the mathematical world in 1931 by a result that has become an icon of 20th century science: The search for rigour in proving mathematical theorems had led to the formalization of mathematical proofs, to the extent that such proving could be reduced to the application of a few mechanical rules. Gödel showed that whenever the part of mathematics under formalization contains elementary arithmetic, there will be arithmetical statements that should be formally provable but aren’t. The result is known as Gödel’s first incompleteness theorem, so called because there is a second incompleteness result, embodied in his answer to the question "Can mathematics be proved consistent?" This book offers the first examination of Gödel’s preserved notebooks from 1930, written in a long-forgotten German shorthand, that show his way to the results: his first ideas, how they evolved, and how the jewel-like final presentation in his famous publication On formally undecidable propositions was composed.The book also contains the original version of Gödel’s incompleteness article, as handed in for publication with no mentioning of the second incompleteness theorem, as well as six contemporary lectures and seminars Gödel gave between 1931 and 1934 in Austria, Germany, and the United States. The lectures are masterpieces of accessible presentations of deep scientific results, readable even for those without special mathematical training, and published here for the first time.

Kurt Gödel: Collected Works: Volume III

Author : Kurt Gödel
Publisher : Oxford University Press, USA
ISBN 13 : 0195072553
Total Pages : 558 pages
Book Rating : 4.1/5 (95 download)

DOWNLOAD NOW!

Book Synopsis Kurt Gödel: Collected Works: Volume III by : Kurt Gödel

Download or read book Kurt Gödel: Collected Works: Volume III written by Kurt Gödel and published by Oxford University Press, USA. This book was released on 1986 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Kurt Gödel

Author : Francisco Rodriguez-Consuegra
Publisher : Springer Science & Business Media
ISBN 13 : 9783764353100
Total Pages : 246 pages
Book Rating : 4.3/5 (531 download)

DOWNLOAD NOW!

Book Synopsis Kurt Gödel by : Francisco Rodriguez-Consuegra

Download or read book Kurt Gödel written by Francisco Rodriguez-Consuegra and published by Springer Science & Business Media. This book was released on 1995-12-01 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel, together with Bertrand Russell, is the most important name in logic, and in the foundations and philosophy of mathematics of this century. However, unlike Russel, Gödel the mathematician published very little apart from his well-known writings in logic, metamathematics and set theory. Fortunately, Gödel the philosopher, who devoted more years of his life to philosophy than to technical investigation, wrote hundreds of pages on the philosophy of mathematics, as well as on other fields of philosophy. It was only possible to learn more about his philosophical works after the opening of his literary estate at Princeton a decade ago. The goal of this book is to make available to the scholarly public solid reconstructions and editions of two of the most important essays which Gödel wrote on the philosophy of mathematics. The book is divided into two parts. The first provides the reader with an incisive historico-philosophical introduction to Gödel's technical results and philosophical ideas. Written by the Editor, this introductory apparatus is not only devoted to the manuscripts themselves but also to the philosophical context in which they were written. The second contains two of Gödel's most important and fascinating unpublished essays: 1) the Gibbs Lecture ("Some basic theorems on the foundations of mathematics and their philosophical implications", 1951); and 2) two of the six versions of the essay which Gödel wrote for the Carnap volume of the Schilpp series The Library of Living Philosophers ("Is mathematics syntax of language?", 1953-1959).

After Gödel

Author : Richard L. Tieszen
Publisher : Oxford University Press
ISBN 13 : 019960620X
Total Pages : 258 pages
Book Rating : 4.1/5 (996 download)

DOWNLOAD NOW!

Book Synopsis After Gödel by : Richard L. Tieszen

Download or read book After Gödel written by Richard L. Tieszen and published by Oxford University Press. This book was released on 2011-05-05 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Tieszen analyzes, develops, and defends the writings of Kurt Gödel (1906-1978) on the philosophy and foundations of mathematics and logic. Gödel's relation to the work of Plato, Leibniz, Husserl, and Kant is examined, and a new type of platonic rationalism that requires rational intuition, called 'constituted platonism', is proposed.

Godel's Theorem in Focus

Author : S.G. Shanker
Publisher : Taylor & Francis
ISBN 13 : 1134947984
Total Pages : 271 pages
Book Rating : 4.1/5 (349 download)

DOWNLOAD NOW!

Book Synopsis Godel's Theorem in Focus by : S.G. Shanker

Download or read book Godel's Theorem in Focus written by S.G. Shanker and published by Taylor & Francis. This book was released on 2012-08-21 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Goedel's Way

Author : Gregory Chaitin
Publisher : CRC Press
ISBN 13 : 1136587640
Total Pages : 160 pages
Book Rating : 4.1/5 (365 download)

DOWNLOAD NOW!

Book Synopsis Goedel's Way by : Gregory Chaitin

Download or read book Goedel's Way written by Gregory Chaitin and published by CRC Press. This book was released on 2011-10-14 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

Principia Mathematica

Author : Alfred North Whitehead
Publisher :
ISBN 13 :
Total Pages : 696 pages
Book Rating : 4.L/5 ( download)

DOWNLOAD NOW!

Book Synopsis Principia Mathematica by : Alfred North Whitehead

Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Gödel, Escher, Bach

Author : Douglas R. Hofstadter
Publisher : Penguin Group(CA)
ISBN 13 : 9780140289206
Total Pages : 832 pages
Book Rating : 4.2/5 (892 download)

DOWNLOAD NOW!

Book Synopsis Gödel, Escher, Bach by : Douglas R. Hofstadter

Download or read book Gödel, Escher, Bach written by Douglas R. Hofstadter and published by Penguin Group(CA). This book was released on 2000 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'What is a self and how can a self come out of inanimate matter?' This is the riddle that drove Douglas Hofstadter to write this extraordinary book. In order to impart his original and personal view on the core mystery of human existence - our intangible sensation of 'I'-ness - Hofstadter defines the playful yet seemingly paradoxical notion of 'strange loop', and explicates this idea using analogies from many disciplines.

An Introduction to Gödel's Theorems

Author : Peter Smith
Publisher : Cambridge University Press
ISBN 13 : 0521857848
Total Pages : 376 pages
Book Rating : 4.5/5 (218 download)

DOWNLOAD NOW!

Book Synopsis An Introduction to Gödel's Theorems by : Peter Smith

Download or read book An Introduction to Gödel's Theorems written by Peter Smith and published by Cambridge University Press. This book was released on 2007-07-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Peter Smith examines Gödel's Theorems, how they were established and why they matter.

Gödel's Proof

Author : Ernest Nagel
Publisher : Psychology Press
ISBN 13 : 041504040X
Total Pages : 118 pages
Book Rating : 4.4/5 (15 download)

DOWNLOAD NOW!

Book Synopsis Gödel's Proof by : Ernest Nagel

Download or read book Gödel's Proof written by Ernest Nagel and published by Psychology Press. This book was released on 1989 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, Godelâ€™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.

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

Author : Kurt Gödel
Publisher : Courier Corporation
ISBN 13 : 0486158403
Total Pages : 82 pages
Book Rating : 4.4/5 (861 download)

DOWNLOAD NOW!

Book Synopsis On Formally Undecidable Propositions of Principia Mathematica and Related Systems by : Kurt Gödel

Download or read book On Formally Undecidable Propositions of Principia Mathematica and Related Systems written by Kurt Gödel and published by Courier Corporation. This book was released on 2012-05-24 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Journey to the Edge of Reason

Author : Stephen Budiansky
Publisher : Oxford University Press
ISBN 13 : 0192636138
Total Pages : 384 pages
Book Rating : 4.1/5 (926 download)

DOWNLOAD NOW!

Book Synopsis Journey to the Edge of Reason by : Stephen Budiansky

Download or read book Journey to the Edge of Reason written by Stephen Budiansky and published by Oxford University Press. This book was released on 2021-05-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A remarkable account of Kurt Gödel, weaving together creative genius, mental illness, political corruption, and idealism in the face of the turmoil of war and upheaval. At age 24, a brilliant Austrian-born mathematician published a mathematical result that shook the world. Nearly a hundred years after Kurt Gödel's famous 1931 paper "On Formally Undecidable Propositions" appeared, his proof that every mathematical system must contain propositions that are true - yet never provable within that system - continues to pose profound questions for mathematics, philosophy, computer science, and artificial intelligence. His close friend Albert Einstein, with whom he would walk home every day from Princeton's famous Institute for Advanced Study, called him "the greatest logician since Aristotle." He was also a man who felt profoundly out of place in his time, rejecting the entire current of 20th century philosophical thought in his belief that mathematical truths existed independent of the human mind, and beset by personal demons of anxiety and paranoid delusions that would ultimately lead to his tragic end from self-starvation. Drawing on previously unpublished letters, diaries, and medical records, Journey to the Edge of Reason offers the most complete portrait yet of the life of one of the 20th century's greatest thinkers. Stephen Budiansky's account brings to life the remarkable world of philosophical and mathematical creativity of pre-war Vienna, and documents how it was barbarically extinguished by the Nazis. He charts Gödel's own hair's-breadth escape from Nazi Germany to the scholarly idyll of Princeton; and the complex, gently humorous, sensitive, and tormented inner life of this iconic but previously enigmatic giant of modern science. Weaving together Gödel's public and private lives, this is a tale of creative genius, mental illness, political corruption, and idealism in the face of the turmoil of war and upheaval.

A Logical Journey

Author : Hao Wang
Publisher : MIT Press
ISBN 13 : 9780262261258
Total Pages : 420 pages
Book Rating : 4.2/5 (612 download)

DOWNLOAD NOW!

Book Synopsis A Logical Journey by : Hao Wang

Download or read book A Logical Journey written by Hao Wang and published by MIT Press. This book was released on 1997-02-03 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gödel. A Logical Journey is a continuation of Wang's Reflections on Gödel and also elaborates on discussions contained in From Mathematics to Philosophy. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook.