Aspects of Incompleteness

DOWNLOAD NOW »

Author: Per Lindström

Publisher: Cambridge University Press

ISBN: 1107167922

Category: Mathematics

Page: 142

View: 5602

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the tenth publication in the Lecture Notes in Logic series, Per Lindström presents some of the main topics and results in general metamathematics. In addition to standard results of Gödel et al. on incompleteness, (non-)finite axiomatizability, and interpretability, this book contains a thorough treatment of partial conservativity and degrees of interpretability. It comes complete with exercises, and will be useful as a textbook for graduate students with a background in logic, as well as a valuable resource for researchers.

Logic in Tehran

DOWNLOAD NOW »

Author: Ali Enayat,Iraj Kalantari,Mojtaba Moniri

Publisher: Cambridge University Press

ISBN: 1108670008

Category: Mathematics

Page: N.A

View: 3536

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-sixth publication in the Lecture Notes in Logic series, contains the proceedings of the 'Workshop and Conference on Logic, Algebra and Arithmetic' held at the Institute for Studies in Theoretical Physics and Mathematics (IPM) in Tehran, Iran in October, 2003. These papers are mostly revised and expanded versions of those that were originally presented at the meeting and address all areas of mathematical logic. The book also includes a short history of mathematical logic in Iran.

Handbook of Proof Theory

DOWNLOAD NOW »

Author: S.R. Buss

Publisher: Elsevier

ISBN: 9780080533186

Category: Mathematics

Page: 810

View: 3916

This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

The Logic of Provability

DOWNLOAD NOW »

Author: George Boolos

Publisher: Cambridge University Press

ISBN: 9780521483254

Category: Philosophy

Page: 275

View: 7918

Boolos, a pre-eminent philosopher of mathematics, investigates the relationship between provability and modal logic.

Aspects of Philosophical Logic

Some Logical Forays into Central Notions of Linguistics and Philosophy

DOWNLOAD NOW »

Author: Uwe Mönnich

Publisher: Springer Science & Business Media

ISBN: 9400983840

Category: Philosophy

Page: 290

View: 4963

This volume constitutes the Proceedings of a workshop on formal seman tics of natural languages which was held in Tiibingen from the 1st to the 3rd of December 1977. Its main body consists of revised versions of most of the papers presented on that occasion. Three supplementary papers (those by Gabbay and Sma by) are included because they seem to be of particular interest in their respective fields. The area covered by the work of scholars engaged in philosophical logic and the formal analysis of natural languages testifies to the live liness in those disciplines. It would have been impossible to aim at a complete documentation of relevant research within the limits imposed by a short conference whereas concentration on a single topic would have conveyed the false impression of uniformity foreign to a young and active field. It is hoped that the essays collected in this volume strike a reasonable balance between the two extremes. The topics discussed here certainly belong to the most important ones enjoying the attention of linguists and philosophers alike: the analysis of tense in formal and natural languages (van Benthem, Gabbay), the quickly expanding domain of generalized quantifiers (Goldblatt), the problem of vagueness (Kamp), the connected areas of pronominal reference (Smaby) and presupposition (von Stechow) and, last but not least, modal logic as a sort of all-embracing theoretical framework (Bressan). The workshop which led to this collection formed part of the activities celebrating the 500th anniversary of Tiibingen University.

Philosophy of Mathematics

5 Questions

DOWNLOAD NOW »

Author: Vincent F. Hendricks,Hannes Leitgeb

Publisher: Automatic Press Publishing

ISBN: 9788799101351

Category: Mathematics

Page: 342

View: 2241

Philosophy of Mathematics: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in this field. We hear their views aim, scope, use, the future direction and how their work fits in these respects.

Kurt Gödel

Essays for his Centennial

DOWNLOAD NOW »

Author: Solomon Feferman,Charles Parsons,Stephen G. Simpson

Publisher: Cambridge University Press

ISBN: 1139487752

Category: Mathematics

Page: N.A

View: 5209

Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible sets.

Kurt Gödel: Collected Works:

DOWNLOAD NOW »

Author: Kurt Gödel

Publisher: Clarendon Press

ISBN: 0191003778

Category: Mathematics

Page: 692

View: 1226

Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass. These long-awaited final two volumes contain Gödel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gödel's Nachlass. All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Gödel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gödel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.

Correspondence H-Z

DOWNLOAD NOW »

Author: Kurt Gödel,S. Feferman

Publisher: Oxford University Press

ISBN: 9780198500759

Category: Computers

Page: 690

View: 5172

Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass. These long-awaited final two volumes contain Gödel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gödel's Nachlass. L All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Gödel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gödel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.

Goedel's Way

Exploits into an undecidable world

DOWNLOAD NOW »

Author: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

Publisher: CRC Press

ISBN: 0415690854

Category: Mathematics

Page: 160

View: 8620

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

Logic Colloquium 2006

DOWNLOAD NOW »

Author: S. Barry Cooper

Publisher: Cambridge University Press

ISBN: 0521110815

Category: Mathematics

Page: 373

View: 5622

The 2006 proceedings from the Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium.

Introduction to Mathematical Logic, Fourth Edition

DOWNLOAD NOW »

Author: Elliott Mendelson

Publisher: CRC Press

ISBN: 9780412808302

Category: Mathematics

Page: 440

View: 4004

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.

Incompleteness: The Proof and Paradox of Kurt Gödel (Great Discoveries)

DOWNLOAD NOW »

Author: Rebecca Goldstein

Publisher: W. W. Norton & Company

ISBN: 0393327604

Category: Biography & Autobiography

Page: 296

View: 2893

A portrait of the eminent twentieth-century mathematician discusses his theorem of incompleteness, relationships with such contemporaries as Albert Einstein, and untimely death as a result of mental instability and self-starvation.

Perception-Based Data Processing in Acoustics

Applications to Music Information Retrieval and Psychophysiology of Hearing

DOWNLOAD NOW »

Author: Bozena Kostek

Publisher: Springer Science & Business Media

ISBN: 9783540257295

Category: Computers

Page: 420

View: 5060

This monograph provides novel insights into cognitive mechanisms underlying the processing of sound and music in different environments. A solid understanding of these mechanisms is vital for numerous technological applications such as for example information retrieval from distributed musical databases or building expert systems. In order to investigate the cognitive mechanisms of music perception fundamentals of hearing psychophysiology and principles of music perception are presented. In addition, some computational intelligence methods are reviewed, such as rough sets, fuzzy logic, artificial neural networks, decision trees and genetic algorithms. The applications of hybrid decision systems to problem solving in music and acoustics are exemplified and discussed on the basis of obtained experimental results.

Proceedings of the International Congress of Mathematicians

Madrid, August 22-30, 2006

DOWNLOAD NOW »

Author: Marta Sanz Solé

Publisher: Amer Mathematical Society

ISBN: 9783037190227

Category: Mathematics

Page: 4500

View: 1850

The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject. Information for our distributors: Distributed within the Americas by the American Mathematical Society. All commerical channel discounts apply.

Principia Mathematica.

DOWNLOAD NOW »

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 690