Church s Thesis After 70 Years

My task here is to indicate the right terminology that should be employed when ex— amining the Thesis. Although 70 years have passed since Church's Thesis was first presented it would appear that little progress has been made in ...

Author: Adam Olszewski

Publisher: Walter de Gruyter

ISBN: 3110325462

Category: Philosophy

Page: 551

View: 800

Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of a effectively computable function defined in natural numbers with the notion of a recursive function. Despite of the many efforts of prominent scientists, Church's Thesis has never been falsified. There exists a vast literature concerning the thesis. The aim of the book is to provide one volume summary of the state of research on Church's Thesis. These include the following: different formulations of CT, CT and intuitionism, CT and intensional mathematics, CT and physics, the epistemic status of CT, CT and philosophy of mind, provability of CT and CT and functional programming.

Church s Thesis After 70 Years

There exists a vast literature concerning the thesis. The aim of this book is to provide a one volume summary of the state of research on Church's Thesis.

Author: Alonzo Church

Publisher: Ontos Verlag

ISBN: 9783938793091

Category: Mathematics

Page: 551

View: 172

Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of an effectively computable function defined in natural numbers with the notion of a recursive function. Despite the many efforts of prominent scientists, Church's Thesis has never been disproven. There exists a vast literature concerning the thesis. The aim of this book is to provide a one volume summary of the state of research on Church's Thesis. These include the following: different formulations of CT, CT and intuitionism, CT and intensional mathematics, CT and physics, the epistemic status of CT, CT and philosophy of mind, provability of CT and CT and functional programming. Adam Olszewski, is assistant professor of the philosophy of mathematics and mathematical logic at the Department of Philosophy of Pontifical Academy of Theology, Cracow (Poland). Jan Wolenski is professor of philosophy, Institute of Philosphy, Jagiellonian University, Cracow (Poland). He is one of the most distinguished logicians in Poland. Robert Janusz is assistant professor in the Department of Philosophy of Ignatius College, Cracow (Poland).

Ways of Proof Theory

ontos ve 11a 9 ontosMathematicalLogic Volume 1 Adam Olszewski, Jan Woler'lski, Robert Janusz (Eds) Church's Thesis After 70 Years Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two ...

Author: Ralf Schindler

Publisher: Walter de Gruyter

ISBN: 3110324903

Category: Philosophy

Page: 498

View: 115

On the occasion of the retirement of Wolfram Pohlers the Institut für Mathematische Logik und Grundlagenforschung of the University of Münster organized a colloquium and a workshop which took place July 17 – 19, 2008. This event brought together proof theorists from many parts of the world who have been acting as teachers, students and collaborators of Wolfram Pohlers and who have been shaping the field of proof theory over the years. The present volume collects papers by the speakers of the colloquium and workshop; and they produce a documentation of the state of the art of contemporary proof theory.

Computability

On the provability , veracity , and AI - relevance of the Church - Turing thesis . In Church's Thesis after 70 Years , ed . A. Olszewski , J. Wolenski , and R. Janusz , 66-118 . Frankfurt : Ontos - Verlag . Bringsjord , S. , and G. N. ...

Author: B. Jack Copeland

Publisher: MIT Press

ISBN: 0262527480

Category: Computers

Page: 376

View: 816

Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by Turing, Gödel, and Church, including the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics. Contributors Scott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani

Computing and Philosophy

Stanford: Metaphysics Research Lab. http://plato.stanford.edu/archives/ sum2015/entries/church-turing. Accessed 24 Sep 2015. ... Hypercomputation and the physical Church-Turing Thesis. ... Church's thesis after 70 years.

Author: Vincent C. Müller

Publisher: Springer

ISBN: 3319232916

Category: Philosophy

Page: 282

View: 688

This volume offers very selected papers from the 2014 conference of the “International Association for Computing and Philosophy” (IACAP) - a conference tradition of 28 years. The theme of the papers is the two-way relation between computing technologies and philosophical questions: Computing technologies both raise new philosophical questions, and shed light on traditional philosophical problems. The chapters cover: 1) philosophy of computing, 2) philosophy of computer science & discovery, 3) philosophy of cognition & intelligence, 4) computing & society, and 5) ethics of computation.

Introduction to Mathematical Logic

( 2006 ) Church's Thesis after 70 Years . Ontos Verlag Olszewski , A. , J. Wolenski , and R. Janusz ( eds . ) ( 2007 ) Church's Thesis After 70 Years . Ontos Verlag . Orey , S. ( 1956a ) On o - consistency and related properties .

Author: Elliott Mendelson

Publisher: CRC Press

ISBN: 1482237784

Category: Mathematics

Page: 513

View: 602

The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Godel, Church, Kleene, Rosse

The Foundations of Computability Theory

Hodges, A.: Did Church and Turing Have a Thesis about Machines? In: A. Olszewski, J. Wole ́nski, R. Janusz (eds.) Church's Thesis After 70 Years, Ontos Mathematical Logic (Book 1), pp. 242–252. De Gruyter (2006) 109.

Author: Borut Robič

Publisher: Springer Nature

ISBN: 3662624214

Category: Computers

Page: 422

View: 152

This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism. In Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability. In Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. Finally, in the new Part IV the author revisits the computability (Church-Turing) thesis in greater detail. He offers a systematic and detailed account of its origins, evolution, and meaning, he describes more powerful, modern versions of the thesis, and he discusses recent speculative proposals for new computing paradigms such as hypercomputing. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science. This new edition is completely revised, with almost one hundred pages of new material. In particular the author applied more up-to-date, more consistent terminology, and he addressed some notational redundancies and minor errors. He developed a glossary relating to computability theory, expanded the bibliographic references with new entries, and added the new part described above and other new sections.

Computer Science Logic

Church's Thesis After 70 Years, 24–57, Ontos (2006) 7. B ̈orger, E., St ̈ark, R.: Abstract State Machines. Springer, Heidelberg (2003) 8. Boker, U., Dershowitz, N.: The Church-Turing Thesis over arbitrary domains.

Author: Anuj Dawar

Publisher: Springer Science & Business Media

ISBN: 364215204X

Category: Computers

Page: 548

View: 739

This volume constitutes the refereed proceedings of the 24th International Workshop on Computer Science Logic, CSL 2010, held in Brno, Czech Republic, in August 2010. The 33 full papers presented together with 7 invited talks, were carefully reviewed and selected from 103 submissions. Topics covered include automated deduction and interactive theorem proving, constructive mathematics and type theory, equational logic and term rewriting, automata and games, modal and temporal logic, model checking, decision procedures, logical aspects of computational complexity, finite model theory, computational proof theory, logic programming and constraints, lambda calculus and combinatory logic, categorical logic and topological semantics, domain theory, database theory, specification, extraction and transformation of programs, logical foundations of programming paradigms, verification and program analysis, linear logic, higher-order logic, and nonmonotonic reasoning.

G del s Disjunction

Church's Thesis after 70 years. Heusenstamm: Ontos Verlag, 2006. Kreisel, G. Which number theoretic problems can be solved in recursive progressions on 11-paths throughO?Journal of Symbolic Logic37, pp. 311–334, 1972.

Author: Leon Horsten

Publisher: Oxford University Press

ISBN: 0191077682

Category: Mathematics

Page: 288

View: 701

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.

SOFSEM 2012 Theory and Practice of Computer Science

(eds): Church's Thesis after 70 Years, pp. 24–57. Ontos Verlag (2006) 6. Blass, A., Gurevich, Y.: Ordinary interactive small-step algorithms. ACM Trans. Computational Logic (Part I), 7(2), 363–419 (2006); plus 8(3), articles 15 and 16 ...

Author: Mária Bieliková

Publisher: Springer Science & Business Media

ISBN: 3642276598

Category: Computers

Page: 690

View: 794

This book constitutes the refereed proceedings of the 38th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2012, held in Špindlerův Mlýn, Czech Republic, in January 2012. The 43 revised papers presented in this volume were carefully reviewed and selected from 121 submissions. The book also contains 11 invited talks, 10 of which are in full-paper length. The contributions are organized in topical sections named: foundations of computer science; software and Web engineering; cryptography, security, and verification; and artificial intelligence.