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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Computability

Computable Functions, Logic, and the Foundations of Mathematics

Author: Richard L Epstein,Walter A Carnielli

Publisher: Advanced Reasoning Forum

ISBN: 0981550738

Category: Mathematics

Page: 382

View: 9576

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Now in a new edition!--the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics".
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Hahn and Economic Methodology

Author: Thomas Boylan,Paschal O'Gorman

Publisher: Routledge

ISBN: 1136462015

Category: Business & Economics

Page: 160

View: 6882

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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

View: 8699

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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

Author: Joshua M. Epstein

Publisher: Princeton University Press

ISBN: 1400842875

Category: Business & Economics

Page: 384

View: 5729

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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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Interactions in Political Economy

Malvern After Ten Years

Author: Steven Pressman

Publisher: Routledge

ISBN: 1134784104

Category: Business & Economics

Page: 240

View: 2248

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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

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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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Turing Computability

Theory and Applications

Author: Robert I. Soare

Publisher: Springer

ISBN: 3642319335

Category: Computers

Page: 263

View: 3352

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Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author has honed the content over decades according to feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.
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The Annotated Turing

A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine

Author: Charles Petzold

Publisher: John Wiley & Sons

ISBN: 0470229055

Category: Computers

Page: 372

View: 5331

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Provides an expansion of Turing's original paper, a brief look at his life, and information on the Turing machine and computability topics.
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Computability : Computable Functions Logic and the Foundations of Math

Author: Richard L. Epstein

Publisher: Springer

ISBN: 9780534103569

Category: Mathematics

Page: 320

View: 8245

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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
Release