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Gödel '96

Author: Petr Hájek

Publisher: Cambridge University Press

Published: 2017-03-02

Total Pages: 332

ISBN-13: 1316739309

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 sixth publication in the Lecture Notes in Logic series, collects the proceedings of the conference 'Logical Foundations of Mathematics, Computer Science, and Physics - Kurt Gödel's Legacy', held in Brno, Czech Republic, on the 90th anniversary of Gödel's birth. The broad range of speakers who participated in this event affirms the continuing importance of Gödel's work in logic, physics, and the philosophy and foundations of mathematics and computer science. The papers in this volume range over all these topics and contribute to our present understanding of them.

Memoirs of a Proof Theorist

Author: Mariko Yasugi

Publisher: World Scientific

Published: 2003-02-10

Total Pages: 156

ISBN-13: 9814486620

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This volume is a translation of the book Gödel, written in Japanese by Gaisi Takeuti, a distinguished proof theorist. The core of the book comprises a memoir of K Gödel, Takeuti's personal recollections, and his interpretation of Gödel's attitudes towards mathematical logic. It also contains Takeuti's recollection of association with some other famous logicians. Everything in the book is original, as the author adheres to his own experiences and interpretations. There is also an article on Hilbert's second problem as well as on the author's fundamental conjecture about second order logic. Contents:On GödelWork of Paul Bernays and Kurt GödelHilbert and GödelShort Biographies of LogiciansSet Theory and Related TopicsFrom Hilbert to GödelAxioms of Arithmetic and Consistency — The Second Problem of HilbertA Report from Gödel '96Having Read “Gödel Remembered”A Tribute to the Memory of Professor Gödel'Appendices:On Gödel's Continuum HypothesisBirth of Second Order Proof Theory by the Fundamental Conjecture on GLC Readership: Those interested in mathematics, especially logic or the history of mathematics. Keywords:GÃ¶del;Logic;Set Theory

Types, Tableaus, and Gödel’s God

Author: M. Fitting

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 190

ISBN-13: 9401004110

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Gödel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added to produce a modified version of Montague/Gallin intensional logic. Finally, various ontological proofs for the existence of God are discussed informally, and the Gödel argument is fully formalized. Parts of the book are mathematical, parts philosophical.

Gödel's Disjunction

Author: Leon Horsten

Publisher: Oxford University Press

Published: 2016-09-09

Total Pages: 288

ISBN-13: 0191077682

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The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Gödel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.

Kurt Gödel and the Foundations of Mathematics

Author: Matthias Baaz

Publisher: Cambridge University Press

Published: 2011-06-06

Total Pages: 541

ISBN-13: 1139498436

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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.

The Vienna Circle and Religion

Author: Esther Ramharter

Publisher: Springer Nature

Published: 2022-03-08

Total Pages: 280

ISBN-13: 3030761517

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This book is the first systematic and historical account of the Vienna Circle that deals with the relation of logical empiricists with religion as well as theology. Given the standard image of the Vienna Circle as a strong anti-metaphysical group and non-religious philosophical and intellectual movement, this book draws a surprising conclusion, namely, that several members of the famous Moritz Schlick-Circle - e.g., the left wing with Rudolf Carnap, Otto Neurath, Philipp Frank, Edgar Zilsel, but also Schlick himself - dealt with the dualisms of faith/ belief and knowledge, religion and science despite, or because of their non-cognitivist commitment to the values of Enlightenment. One remarkable exception was the philosopher and Rabbi Joseph Schächter, who wrote explicitly on religion and philosophy after the linguistic turn. The book also covers another puzzling figure: the famous logician Kurt Gödel, who wrote on theology and the ontological proof of God in his so far unpublished notebooks. The book opens up new perspectives on the Vienna Circle with its internal philosophical and political pluralism and is of value to philosophers, historians and anybody who is interested in the relation between science and religion.

Petr Hájek on Mathematical Fuzzy Logic

Author: Franco Montagna

Publisher: Springer

Published: 2014-09-23

Total Pages: 318

ISBN-13: 3319062336

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This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.

Dictionary of Modern American Philosophers

Author: John R. Shook

Publisher: A&C Black

Published: 2005-01-01

Total Pages: 2759

ISBN-13: 1843710374

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The Dictionary of Modern American Philosophers includes both academic and non-academic philosophers, anda large number of female and minority thinkers whose work has been neglected. It includes those intellectualsinvolved in the development of psychology, pedagogy, sociology, anthropology, education, theology, politicalscience, and several other fields, before these disciplines came to be considered distinct from philosophy in thelate nineteenth century.Each entry contains a short biography of the writer, an exposition and analysis of his or her doctrines and ideas, abibliography of writings, and suggestions for further reading. While all the major post-Civil War philosophers arepresent, the most valuable feature of this dictionary is its coverage of a huge range of less well-known writers,including hundreds of presently obscure thinkers. In many cases, the Dictionary of Modern AmericanPhilosophers offers the first scholarly treatment of the life and work of certain writers. This book will be anindispensable reference work for scholars working on almost any aspect of modern American thought.

Logic for Programming, Artificial Intelligence, and Reasoning

Author: Robert Nieuwenhuis

Publisher: Springer Science & Business Media

Published: 2001-11-21

Total Pages: 752

ISBN-13: 3540429573

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This volume contains the papers presented at the Eighth International C- ference on Logic for Programming, Arti?cial Intelligence and Reasoning (LPAR 2001), held on December 3-7, 2001, at the University of Havana (Cuba), together with the Second International Workshop on Implementation of Logics. There were 112 submissions, of which 19 belonged to the special subm- sion category of experimental papers, intended to describe implementations or comparisons of systems, or experiments with systems. Each submission was - viewed by at least three program committee members and an electronic program committee meeting was held via the Internet. The high number of submissions caused a large amount of work, and we are very grateful to the other 31 PC members for their e?ciency and for the quality of their reviews and discussions. Finally, the committee decided to accept 40papers in the theoretical ca- gory, and 9 experimental papers. In addition to the refereed papers, this volume contains an extended abstract of the invited talk by Frank Wolter. Two other invited lectures were given by Matthias Baaz and Manuel Hermenegildo. Apart from the program committee, we would also like to thank the other people who made LPAR 2001 possible: the additional referees; the Local Arran- ` gements Chair Luciano Garc ́?a; Andr ́es Navarro and Oscar Guell, ̈ who ran the internet-based submission software and the program committee discussion so- ware at the LSI Department lab in Barcelona; and Bill McCune, whose program committee management software was used.

Beyond Two: Theory and Applications of Multiple-Valued Logic

Author: Melvin Fitting

Publisher: Physica

Published: 2013-06-05

Total Pages: 374

ISBN-13: 3790817694

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This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.