An Introduction to Gödel's Theorems

Author: Peter Smith

Publisher: Cambridge University Press

ISBN: 1107022843

Category: Mathematics

Page: 406

View: 7428

A clear and accessible treatment of Gödel's famous, intriguing, but much misunderstood incompleteness theorems, extensively revised in a second edition.
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An Introduction to Non-Classical Logic

From If to Is

Author: Graham Priest

Publisher: Cambridge University Press

ISBN: 9781139469678

Category: Science

Page: N.A

View: 9451

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.
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An Introduction to Metalogic

Author: Aladdin M. Yaqub

Publisher: Broadview Press

ISBN: 1554811716

Category: Philosophy

Page: 344

View: 1290

An Introduction to Metalogic is a uniquely accessible introduction to the metatheory of first-order predicate logic. No background knowledge of logic is presupposed, as the book is entirely self-contained and clearly defines all of the technical terms it employs. Yaqub begins with an introduction to predicate logic and ends with detailed outlines of the proofs of the incompleteness, undecidability, and indefinability theorems, covering many related topics in between.
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An Introduction to Decision Theory

Author: Martin Peterson

Publisher: Cambridge University Press

ISBN: 1107151597

Category: Business & Economics

Page: 348

View: 8089

Now revised and updated, this introduction to decision theory is both accessible and comprehensive, covering topics including decision making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice theory. No mathematical skills are assumed, with all concepts and results explained in non-technical and intuitive as well as more formal ways. There are now over 140 exercises with solutions, along with a glossary of key terms and concepts. This second edition includes a new chapter on risk aversion as well as updated discussions of numerous central ideas, including Newcomb's problem, prisoner's dilemmas, and Arrow's impossibility theorem. The book will appeal particularly to philosophy students but also to readers in a range of disciplines, from computer science and psychology to economics and political science.
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Modal Logic

An Introduction

Author: Brian F. Chellas

Publisher: Cambridge University Press

ISBN: 9780521295154

Category: Mathematics

Page: 295

View: 6535

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an up-to-date and reliable guide essential for the student.
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Computability and Logic

Author: George S. Boolos,John P. Burgess,Richard C. Jeffrey

Publisher: Cambridge University Press

ISBN: 110704927X

Category: Philosophy

Page: N.A

View: 4060

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual.
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An Introduction to Harmonic Analysis

Author: Yitzhak Katznelson

Publisher: Cambridge University Press

ISBN: 9780521543590

Category: Mathematics

Page: 314

View: 4792

First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.
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Scientific Method in Brief

Author: Hugh G. Gauch, Jr

Publisher: Cambridge University Press

ISBN: 1107311527

Category: Science

Page: N.A

View: 4611

The fundamental principles of the scientific method are essential for enhancing perspective, increasing productivity, and stimulating innovation. These principles include deductive and inductive logic, probability, parsimony and hypothesis testing, as well as science's presuppositions, limitations, ethics and bold claims of rationality and truth. The examples and case studies drawn upon in this book span the physical, biological and social sciences; include applications in agriculture, engineering and medicine; and also explore science's interrelationships with disciplines in the humanities such as philosophy and law. Informed by position papers on science from the American Association for the Advancement of Science, National Academy of Sciences and National Science Foundation, this book aligns with a distinctively mainstream vision of science. It is an ideal resource for anyone undertaking a systematic study of scientific method for the first time, from undergraduates to professionals in both the sciences and the humanities.
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The Cambridge Companion to Utilitarianism

Author: Ben Eggleston,Dale E. Miller

Publisher: Cambridge University Press

ISBN: 1139867482

Category: Philosophy

Page: N.A

View: 9288

Utilitarianism, the approach to ethics based on the maximization of overall well-being, continues to have great traction in moral philosophy and political thought. This Companion offers a systematic exploration of its history, themes, and applications. First, it traces the origins and development of utilitarianism via the work of Jeremy Bentham, John Stuart Mill, Henry Sidgwick, and others. The volume then explores issues in the formulation of utilitarianism, including act versus rule utilitarianism, actual versus expected consequences, and objective versus subjective theories of well-being. Next, utilitarianism is positioned in relation to Kantianism and virtue ethics, and the possibility of conflict between utilitarianism and fairness is considered. Finally, the volume explores the modern relevance of utilitarianism by considering its practical implications for contemporary controversies such as military conflict and global warming. The volume will be an important resource for all those studying moral philosophy, political philosophy, political theory, and history of ideas.
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There's Something About Gdel

The Complete Guide to the Incompleteness Theorem

Author: Francesco Berto

Publisher: John Wiley & Sons

ISBN: 1444357611

Category: Philosophy

Page: 256

View: 1515

Berto’s highly readable and lucid guide introduces students and the interested reader to Gödel’s celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments. Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chapters Discusses interpretations of the Theorem made by celebrated contemporary thinkers Sheds light on the wider extra-mathematical and philosophical implications of Gödel’s theories Written in an accessible, non-technical style
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Gödel's Theorem

An Incomplete Guide to Its Use and Abuse

Author: Torkel Franzén

Publisher: A K Peters/CRC Press

ISBN: 9781568812380

Category: Mathematics

Page: 182

View: 5365

"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel
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Intermediate Logic

Author: David Bostock

Publisher: Clarendon Press

ISBN: 9780191567070

Category: Mathematics

Page: 404

View: 6084

Intermediate Logic fills a serious gap in the range of university logic texts by offering a clear, reliable, general guide for students taking a second course in logic after completing a basic introduction. It will serve as an ideal follow-up to any of the standard introductory texts, and will give excellent preparation for advanced work in logical theory or applications of logic in philosophy, mathematics, or computing theory. - ;Intermediate Logic is an ideal text for anyone who has taken a first course in logic and is progressing to further study. It examines logical theory, rather than the applications of logic, and does not assume any specific technological grounding. The author introduces and explains each concept and term, ensuring that readers have a firm foundation for study. He provides a broad, deep understanding of logic by adopting and comparing a variety of different methods and approaches. In the first section, Bostock covers such fundamental notions as truth, validity, entailment, quantification, and decision procedures. Part two lays out a definitive introduction to four key logical tools or procedures: semantic tableaux, axiomatic proofs, natural deduction, and sequent calculi. The final section opens up new areas of existence and identity, concluding by moving from orthodox logic to examination of `free logic'. Intermediate Logic provides an ideal secondary course in logic for university students, and a bridge to advanced study of such subjects as model theory, proof theory, and other specialized areas of mathematical logic. -
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The Principles of Quantum Theory, From Planck's Quanta to the Higgs Boson

The Nature of Quantum Reality and the Spirit of Copenhagen

Author: Arkady Plotnitsky

Publisher: Springer

ISBN: 3319320688

Category: Science

Page: 313

View: 8934

The book considers foundational thinking in quantum theory, focusing on the role the fundamental principles and principle thinking there, including thinking that leads to the invention of new principles, which is, the book contends, one of the ultimate achievements of theoretical thinking in physics and beyond. The focus on principles, prominent during the rise and in the immediate aftermath of quantum theory, has been uncommon in more recent discussions and debates concerning it. The book argues, however, that exploring the fundamental principles and principle thinking is exceptionally helpful in addressing the key issues at stake in quantum foundations and the seemingly interminable debates concerning them. Principle thinking led to major breakthroughs throughout the history of quantum theory, beginning with the old quantum theory and quantum mechanics, the first definitive quantum theory, which it remains within its proper (nonrelativistic) scope. It has, the book also argues, been equally important in quantum field theory, which has been the frontier of quantum theory for quite a while now, and more recently, in quantum information theory, where principle thinking was given new prominence. The approach allows the book to develop a new understanding of both the history and philosophy of quantum theory, from Planck’s quantum to the Higgs boson, and beyond, and of the thinking the key founding figures, such as Einstein, Bohr, Heisenberg, Schrödinger, and Dirac, as well as some among more recent theorists. The book also extensively considers the nature of quantum probability, and contains a new interpretation of quantum mechanics, “the statistical Copenhagen interpretation.” Overall, the book’s argument is guided by what Heisenberg called “the spirit of Copenhagen,” which is defined by three great divorces from the preceding foundational thinking in physics—reality from realism, probability from causality, and locality from relativity—and defined the fundamental principles of quantum theory accordingly.
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An Introduction to Kolmogorov Complexity and Its Applications

Author: Ming Li,Paul Vitányi

Publisher: Springer Science & Business Media

ISBN: 9780387498201

Category: Mathematics

Page: 792

View: 8802

“The book is outstanding and admirable in many respects. ... is necessary reading for all kinds of readers from undergraduate students to top authorities in the field.” Journal of Symbolic Logic Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and applications of Kolmogorov complexity. The book presents a thorough treatment of the subject with a wide range of illustrative applications. Such applications include the randomness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computational learning theory, the complexity of algorithms, and the thermodynamics of computing. It will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. The book is self-contained in that it contains the basic requirements from mathematics and computer science. Included are also numerous problem sets, comments, source references, and hints to solutions of problems. New topics in this edition include Omega numbers, Kolmogorov–Loveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information and others.
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An Introduction to Rights

Author: William A. Edmundson

Publisher: Cambridge University Press

ISBN: 1107378621

Category: Political Science

Page: N.A

View: 778

An Introduction to Rights is a readable and accessible introduction to the history, logic, moral implications and political tendencies of the idea of rights. It is organized chronologically and discusses important historical events such as the French and American Revolutions. It treats a range of historical figures, including Grotius, Paley, Hobbes, Locke, Bentham, Burke, Godwin, Douglass, Mill and Hohfeld and relates the concept of rights to contemporary debates such as consequentialism versus contractualism. This thoroughly updated second edition includes a new preface and expands the discussion of the surprising role that slavery has played in the history of rights. It includes new material on egalitarianism, distributive justice and what the demand for equal rights means.
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Principia Mathematica

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: N.A

View: 6624

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An Introduction to Formal Logic

Author: Peter Smith

Publisher: Cambridge University Press

ISBN: 9780521008044

Category: Mathematics

Page: 357

View: 6449

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
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Quantum Information and Consciousness

A Gentle Introduction

Author: Danko D. Georgiev

Publisher: CRC Press

ISBN: 1351401777

Category: Science

Page: 344

View: 8623

"I loved the book! This book is not just interesting, it is exciting. I have probably read every significant book in the field, and this is the strongest and most convincing one yet. It is also one of the most comprehensive in its explanations. I shall most certainly recommend the book to colleagues." –Richard G. Petty, MD "a very good introduction to the basic theory of quantum systems.... Dr. Georgiev’s book aptly prepares the reader to confront whatever might be in store later." –from the Foreword by Prof. James F. Glazebrook, Eastern Illinois University This book addresses the fascinating cross-disciplinary field of quantum information theory applied to the study of brain function. It offers a self-study guide to probe the problems of consciousness, including a concise but rigorous introduction to classical and quantum information theory, theoretical neuroscience, and philosophy of the mind. It aims to address long-standing problems related to consciousness within the framework of modern theoretical physics in a comprehensible manner that elucidates the nature of the mind-body relationship. The reader also gains an overview of methods for constructing and testing quantum informational theories of consciousness.
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McDowell and His Critics

Author: Cynthia Macdonald,Graham MacDonald

Publisher: John Wiley & Sons

ISBN: 0470777079

Category: Philosophy

Page: 264

View: 4802

The most comprehensive discussion available of the work of philosopher, John McDowell. Contains newly commissioned papers by distinguished philosophers on McDowell’s work, along with substantial replies to each by McDowell himself. The contributors are philosophers with international reputations for their work in the areas in which they are contributing. Covers the whole of McDowell’s philosophy, including his contributions in ancient philosophy, moral philosophy, philosophy of mind, philosophy of language, metaphysics and epistemology. McDowell’s replies to the contributions in this volume contribute to the body of his work.
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An Introduction to the Formalism of Quantum Information with Continuous Variables

Author: Carlos Navarrete-Benlloch

Publisher: Morgan & Claypool Publishers

ISBN: 1681744066

Category: Science

Page: 115

View: 3459

Quantum information is an emerging field which has attracted a lot of attention in the last couple of decades. It is a broad subject which extends from the most applied questions (e.g. how to build quantum computers or secure cryptographic systems) to the most theoretical problems concerning the formalism and interpretation of quantum mechanics, its complexity, and its potential to go beyond classical physics. This book is an introduction to quantum information with special emphasis on continuous-variable systems (such as light) which can be described as collections of harmonic oscillators. It covers a selection of basic concepts, focusing on their physical meaning and mathematical treatment. It starts from the very first principles of quantum mechanics, and builds up the concepts and techniques following a logical progression. This is an excellent reference for students with a full semester of standard quantum mechanics and researchers in closely related fields.
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