Computability

Computable Functions Logic and the Foundations of Math

Author: Richard L. Epstein,Walter Alexandr Carnielli

Publisher: Chapman and Hall/CRC

ISBN: 9780534103569

Category: Mathematics

Page: 297

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An introduction to recursion theory and particularly to the theory of computing, including fourteen readings by Hilbert, Godel, Turing, Post, Church, and others along with a discussion of issues such as self-reference and infinite sets. Annotation copyrighted by Book News, Inc., Portland, OR
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Martin Davis on Computability, Computational Logic, and Mathematical Foundations

Author: Eugenio G. Omodeo,Alberto Policriti

Publisher: Springer

ISBN: 3319418424

Category: Philosophy

Page: 438

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This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis’ work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert’s tenth problem. The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’ work. As a whole, this book shows how Davis’ scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic.
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Logic, Foundations of Mathematics, and Computability Theory

Part One of the Proceedings of the Fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada-1975

Author: Robert E. Butts,Jaakko Hintikka

Publisher: Springer Science & Business Media

ISBN: 9401011389

Category: Science

Page: 416

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The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know well, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science.
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Handbook of Computability Theory

Author: E.R. Griffor

Publisher: Elsevier

ISBN: 9780080533049

Category: Mathematics

Page: 724

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The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.
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Hahn and Economic Methodology

Author: Thomas Boylan,Paschal O'Gorman

Publisher: Routledge

ISBN: 1136462015

Category: Business & Economics

Page: 160

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Hahn on Methodology: The Quest for Understanding addresses two fundamental questions: (i) what is distinctive about economic theorising?; (ii) what is the cognitive value of the outcome of this activity of economic theorising, i.e. economic theory. We will argue that for Hahn, economic theorising is distinctive with respect to four dimensions. Firstly, the aim of economic theory is neither to describe nor explain the real economic world, as in the physical sciences. Rather the aim is to achieve objective, but non-scientific, understanding. Secondly, the central question for economic theory remains for Hahn how to understand, but not to predict as in physics for instance, how decentralised choices interact and perhaps get co-ordinated. Thirdly, Hahn identifies ‘three commitments’ without which, he argues, economic theorising for him is not possible. Finally, economic theorising has a distinctive approach, which Hahn calls its ‘grammar of argumentation’ .
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Diagnosing Contemporary Philosophy with the Matrix Movies

Author: O. Bradley Bassler

Publisher: Springer

ISBN: 1137578890

Category: Philosophy

Page: 215

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This book charts the shape of future philosophical investigation by posing the question: “What is the Matrix?” Guided by the example of the Matrix film trilogy, the author examines issues ranging from simulation, proof and action to value, culture and mythology, offering a progressively deeper diagnosis of modern philosophical conditions. In contrast to the contemporary focus upon cognitive science and a commitment to the distinction between appearance and reality, this book helps readers to explore the argument that such abstractions are inevitably displaced by a more concrete distinction between dreaming and waking, with the Matrix as the real and only world we inhabit. Researchers and scholars will find this work an engaging and enlightening examination of reality, via the medium of popular culture and film.
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Generative Social Science: Studies in Agent-Based Computational Modeling

Studies in Agent-Based Computational Modeling

Author: Joshua M. Epstein

Publisher: Princeton University Press

ISBN: 1400842875

Category: Business & Economics

Page: 384

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Agent-based computational modeling is changing the face of social science. In Generative Social Science, Joshua Epstein argues that this powerful, novel technique permits the social sciences to meet a fundamentally new standard of explanation, in which one "grows" the phenomenon of interest in an artificial society of interacting agents: heterogeneous, boundedly rational actors, represented as mathematical or software objects. After elaborating this notion of generative explanation in a pair of overarching foundational chapters, Epstein illustrates it with examples chosen from such far-flung fields as archaeology, civil conflict, the evolution of norms, epidemiology, retirement economics, spatial games, and organizational adaptation. In elegant chapter preludes, he explains how these widely diverse modeling studies support his sweeping case for generative explanation. This book represents a powerful consolidation of Epstein's interdisciplinary research activities in the decade since the publication of his and Robert Axtell's landmark volume, Growing Artificial Societies. Beautifully illustrated, Generative Social Science includes a CD that contains animated movies of core model runs, and programs allowing users to easily change assumptions and explore models, making it an invaluable text for courses in modeling at all levels.
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Computability, Enumerability, Unsolvability

Directions in Recursion Theory

Author: S. B. Cooper,T. A. Slaman,S. S. Wainer

Publisher: Cambridge University Press

ISBN: 9780521557368

Category: Mathematics

Page: 347

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Provides a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory.
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Interactions in Political Economy

Malvern After Ten Years

Author: Steven Pressman

Publisher: Routledge

ISBN: 1134784104

Category: Business & Economics

Page: 240

View: 5865

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In recent years there has been a growing dissatisfaction with standard economic theorising which has fostered the development of alternative ways of understanding how economies actually work. Too often though these approaches have been developed in isolation, or even in opposition to each other. However, Interactions in Political Economy, demonstrates that the different heterodox approaches to economics have much to learn from each other. Economists working within different paradigms, including Post Keynesian, Marxism and Neo-Ricardian economics address a wide range of issues in methodology, the history of economics, theory and policy. The result is a wealth of insight into how economics ought to be done, how various theoretical approaches dovetail, and the efficiency of various approaches to economic theory. The volume reflects the diversity and quality of the annual Great Malvern Political Economy. Contributors include some of the leading names in heterodox economics John Cornwall, Paul Davidson, Kevin Hoover, Philip Mirowski and Ed Nell.
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Computability

Turing, Gödel, Church, and Beyond

Author: B. Jack Copeland,Carl J. Posy,Oron Shagrir

Publisher: MIT Press

ISBN: 0262018993

Category: Computers

Page: 362

View: 8586

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Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments.
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