Philosophy of mathematics Books
Taylor & Francis Nondeductive Inference 2 Routledge Library
Book SynopsisOriginally published in 1966. An introduction to current studies of kinds of inference in which validity cannot be determined by ordinary deductive models. In particular, inductive inference, predictive inference, statistical inference, and decision making are examined in some detail. The last chapter discusses the relationship of these forms of inference to philosophical notions of rationality. Special features of the monograph include a discussion of the legitimacy of various criteria for successful predictive inference, the development of an intuitive model which exhibits the difficulties of choosing probability measures over infinite sets, and a comparison of rival views on the foundations of probability in terms of the amount of information which the members of these schools believe suitable for fruitful formalization. The bibliographies include articles by statisticians accessible to students of symbolic logic. Table of Contents1. Inductive and Predictive Inference 2. Hypothesis and Predictive Inference 3. Probability and Predictive Inference 4. Statistical Inference 5. Bayesian Statistical Inference 6. Statistical Decision and Utility 7. Theories and Rationality 8. Bibliography
£87.39
Taylor & Francis Topics in Modern Logic
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Taylor & Francis The Logic of Commands
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Taylor & Francis The Logic of Commands
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Taylor & Francis Ltd The Equation of Knowledge
Book SynopsisThe Equation of Knowledge: From Bayes'' Rule to a Unified Philosophy of Science introduces readers to the Bayesian approach to science: teasing out the link between probability and knowledge. The author strives to make this book accessible to a very broad audience, suitable for professionals, students, and academics, as well as the enthusiastic amateur scientist/mathematician. This book also shows how Bayesianism sheds new light on nearly all areas of knowledge, from philosophy to mathematics, science and engineering, but also law, politics and everyday decision-making.Bayesian thinking is an important topic for research, which has seen dramatic progress in the recent years, and has a significant role to play in the understanding and development of AI and Machine Learning, among many other things. This book seeks to act as a tool for proselytising the benefits and limits of Bayesianism to a wider public. Features Trade ReviewLê Nguyên Hoang takes us on a fascinating intellectual journey into Bayesianism, cutting across many social and natural sciences. The Equation of Knowledge: From Bayes' Rule to a Unified Philosophy of Science is a real page turner.—George Zaccour, HEC Montréal and co-author of Handbook of Dynamic Game Theory"Each chapter is opened with a fascinating epigraph quoting famous persons, and is completed by the most recent references. There are multiple illustrations, and the Bayes’ formulae are many times presented via various funny symbols of emoji kind. The book is addressed to a wide audience of students, professionals, and actually any reader interested to be better acquainted with modern ideas in various sciences and philosophy of science, and their Bayesian statistical description and interpretation."— Stan Lipovetsky, Technometrics (Volume 63, 2021 - Issue 1)"[. . . ] Trained in the hard school of online videos, Le Nguyen Hoang has found a new tone to talk about science, a tone that is both rigorous and narrative, where examples illuminate the most abstract questions."— From the Foreword by Gilles Dowek, Professor at École Polytechnique and researcher at the Laboratoire d'Informatique de l'École Polytechnique and the Institut National de Recherche en Informatique et en Automatique (INRIA).Lê Nguyên Hoang takes us on a fascinating intellectual journey into Bayesianism, cutting across many social and natural sciences. The Equation of Knowledge: From Bayes' Rule to a Unified Philosophy of Science is a real page turner.— George Zaccour, HEC Montréal and co-author of Handbook of Dynamic Game Theory"Making math accessible to everyone, showing its connections with dozens of different domains, narrating scientific discovery as a personal human adventure, and sharing impressive enthusiasm: there is definitely something of Greg Chaitin's Meta Math! in Lê Nguyên Hoang's book!" — Rémi Peyre, École des Mines de Nancy"A remarkable piece of work, broad and insightful at the same time. This book is unique in that it gives an accessible journey from subtle probabilistic puzzles to the most advanced concepts at the heart of the machine learning revolution; with unrivalled clarity, it exposes deep ideas that have remained very confidential outside of specialized circles, and that yet are becoming fundamental in the way we understand our world."— Clément Hongler, Associate Professor and Chair of Statistical Field Theory, EPFL "As someone who practices research and publishes academic papers, it is frustrating to note how little we, scientists, are trained in epistemology. ‘How do we know that we know?’ This question is often neglected or taken for granted. The recent controversies about reproducibility of scientific publishing might be one of the tips of a larger iceberg. This book will, in my opinion, be remembered as one of those that helped melt the iceberg." — El Mahdi El Mhamdi, École Polytechnique Fédérale de Lausanne."The book has a lively writing style, rather like you are listening to an inspiring lecturer. Indeed the author has a French YouTube channel and is clearly enthusiastic about exposition. It is overtly an account of what the author personally finds interesting. [. . .] In teaching a basic college course, focused on the mathematical setup and on the analysis of data, I often find there is one student who comes to office hours and is interested in seeing connections with broad scientific fields, or in conceptual issues of the philosophy of science. I could certainly recommend this book to such a student. Similarly, for the MAA community it could be an innovative basis for an undergraduate seminar course, in which students would choose a topic from the book and delve deeper into it."— David Aldous, Mathematical Association of AmericaTable of ContentsSction I. Pure Bayesianism. 1. On A Transformative Journey. 2. Bayes Theorem. 3. Logically Speaking... 4. Let’s Generalize! 5. All Hail Prejudices. 6. The Bayesian Prophets. 7. Solomonoff’s Demon. Section II. Applied Bayesianism. 8. Can You Keep A Secret? 9. Game, Set and Math. 10. Will Darwin Select Bayes? 11. Exponentially Counter-Intuitive. 12. Ockham Cuts to the Chase. 13. Facts Are Misleading. Section III. Pragmatic Bayesianism. 14. Quick And Not Too Dirty. 15. Wish Me Luck. 16. Down Memory Lane. 17. Let’s Sleep On It. 18. The Unreasonable Effectiveness of Abstraction. 19. The Bayesian Brain. Section IV. Beyond Bayesianism. 20. It’s All Fiction. 21. Exploring The Origins Of Beliefs. 22. Beyond Bayesianism.
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Taylor & Francis Ltd The Equation of Knowledge
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Taylor & Francis The Spherics of Theodosios
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Taylor & Francis Incomparable Values
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Taylor & Francis Ltd Science and Mathematics
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Taylor & Francis The Reform of the International System of Units SI
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Taylor & Francis The Routledge Handbook of the Philosophy and Psychology of Luck
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Taylor & Francis Ltd Monthly Problem Gems
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Taylor & Francis Ltd Monthly Problem Gems
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Taylor & Francis Ibn alHaythams Geometrical Methods and the Philosophy of Mathematics
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Taylor & Francis The Logical Foundations of Scientific Theories
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Taylor & Francis Principles of Mathematics
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Taylor & Francis The Collected Papers of Bertrand Russell Volume 3
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Taylor & Francis Philosophical Theories of Probability Philosophical Issues in Science
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Taylor & Francis Philosophical Theories of Probability Philosophical Issues in Science
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Taylor & Francis The Limits of Thought Discussions between J Krishnamurti and David Bohm
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Taylor & Francis The Price Index and its Extension
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Taylor & Francis Ltd Wittgenstein and the Turning Point in the Philosophy of Mathematics Routledge Library Editions Wittgenstein
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£285.00
Taylor & Francis The Analysis of Linear Economic Systems Father Maurice Potrons Pioneering Works 117 Routledge Studies in the History of Economics
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Taylor & Francis Philosophy of Probability Contemporary Readings
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Taylor & Francis Philosophy of Probability Contemporary Readings
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Taylor & Francis Conceptual Roots of Mathematics International Library of Philosophy
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Taylor & Francis Ltd Wittgenstein and the TurningPoint in the Philosophy of Mathematics
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Taylor & Francis The Textual Genesis of Wittgensteins Philosophical Investigations
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Taylor & Francis The Price Index and its Extension
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Taylor & Francis The Meaning of the Concept of Probability in Application to Finite Sequences Routledge Revivals
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Taylor & Francis The Meaning of the Concept of Probability in Application to Finite Sequences Routledge Revivals
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Taylor & Francis The Analysis of Linear Economic Systems Father Maurice Potrons Pioneering Works
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Taylor & Francis Mathematics and the Image of Reason
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Taylor & Francis Fiction and Fictionalism New Problems of Philosophy
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Taylor & Francis The Force of Argument
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Taylor & Francis Ltd Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences
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Taylor & Francis Properties Powers and Structures Issues in the Metaphysics of Realism 05 Routledge Studies in Metaphysics
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Taylor & Francis The Routledge Handbook of the Philosophy and Psychology of Luck
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Taylor & Francis Ltd Philosophy of Mathematics
Book SynopsisThe philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge.With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic.Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, conTrade Review"The philosophically minded mathematician will find every penny and every second engaged with this book well spent." - Firdous Ahmad Mala, The Mathematical IntelligencerTable of Contents1. Introduction 2. Mathematical Preliminaries 3. Platonism 4. Intuitionism 5. Logicism 6. Formalism 7. Gödel’s Incompleteness Theorem and Computability 8. The Church-Turing Thesis 9. Infinity 10. Supertasks 11. Models, Completeness, and Skolem’s Paradox 12. Axiom of Choice 13. Naturalism 14. Structuralism 15. Yablo’s Paradox 16. Mathematical Pluralism 17. Does Mathematics Need More Axioms? 18. Mathematical Nominalism
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Taylor & Francis Ltd Miracles Mystics Mathematicians
Book SynopsisMiracles, Mystics, Mathematicians: Searching for Deep Reality focuses on the lives and writings of some of historyâs most influential mathematicians and the impact that their mystical beliefs had on their lives and on their mathematical work. Modern biographers often cleanse the lives of renowned scientists of any hint of mysticism or occultism. Such threads are sometimes regarded as relics of the superstitious past; flaws that need to be hushed up, marginalized, or reinterpreted. This book represents a minor attempt to push back against this tendency and to examine these aspects of the history of mathematics with seriousness and intellectual curiosity.Features A breadth of scope covering many centuries Suitable for anyone interested in mathematics, history, philosophy, paranormal phenomena, psi-research, mysticism, or in any combination of the above An almost unique account of known histories, examined from a new vantage point Sasho Kalajdzievski is a Senior Scholar in the Department of Mathematics at the University of Manitoba.Table of ContentsChapter 1. On Defining Mystics, Miracles, and Mathematicians. Chapter 2. From Mathematics to Mysticism and Back. Chapter 3. Alexander Grothendieck: the Man Who Searched. Chapter 3. Kurt Gödel: The Man Who Proved. Chapter 4. Alan Turing and the ‘Joke’. Chapter 5. A Gallery of Mystics and Mathematicians: First Digest. Chapter 6. The Many Lives of Bertus Brouwer. Chapter 7. Srinivasa Ramanujan. Chapter 8. Augustus De Morgan and His Wife Sophia. Chapter 9. Leibniz and Newton. Chapter 10. The Multitalented Blaise Pascal. Chapter 11. René Descartes: The Philosopher and the Warrior. Chapter 12. Cardano: The Psychic Mystic. Chapter 13. A Gallery of Mystics and Mathematicians: First Digest. Chapter 14. The Great Pythagoras.
£45.99
Taylor & Francis Ltd An Essay on the Foundations of Geometry
Book SynopsisAn Essay on the Foundations of Geometry was first published in 1897 when Bertrand Russell was 25 years old. It marks his first major foray into analytic philosophy, a movement in which Russell is one of the founding members and figurehead. It provides a brilliant insight into Russell''s early philosophical thought and an engaging and authoritative introduction to the philosophical and logical foundations of geometry - a version of which was fundamental to Einstein''s theory of relativity.Russell explores and introduces the concepts of geometry and their philosophical implications, including a historical overview of geometrical theory, making it an invaluable resource not only for students of philosophy but anyone interested in the origins of the thought of one of the twentieth century''s most important and widely-read philosophers.This Routledge Classics edition includes a new Foreword by Michael Potter.Table of ContentsForeword to the Routledge Classics Edition Michael Potter, Preface, Introduction: Our Problem Defined by its Relations to Logic, Psychology and Mathematics, 1. A Short History of Metageometry, 2. Critical Account of Some Previous Philosophical Theories of Geometry, 3. The Axioms of Projective Geometry and The Axioms of Metrical Geometry, 4. Philosophical Consequences, Index
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Taylor & Francis Ltd On Constructive Interpretation of Predictive
Book SynopsisFirst published in 1990, this book consists of a detailed exposition of results of the theory of interpretation developed by G. Kreisel the relative impenetrability of which gives the elucidation contained here great value for anyone seeking to understand his work. It contains more complex versions of the information obtained by Kreisel for number theory and clustering around the no-counter-example interpretation, for number-theorectic forumulae provide in ramified analysis. It also proves the omega-consistency of ramified analysis. The author also presents proofs of Schütte's cut-elimination theorems which are based on his consistency proofs and essentially contain them these went further than any published work up to that point, helping to squeeze the maximum amount of information from these proofs.Table of ContentsPreface; Chapter I. Introduction; 1. Statement of the Problem 2. Systems Considered 3. Metamathematical Methods of Proof; Chapter II. Over-Simple Interpretations; 1. Trivial Interpretation 2. Failure of Interpretation by Recursive Satisfaction 3. Dependence of the Proof of the Verifiable Formula corresponding to a Theorem; Chapter III. Herbrand Interpretation; 1. The Concept of Herbrand Interpretation 2. Herbrand Interpretation of Elementary Number Theory without Induction 3. Properties of the Interpretation 4. Impossibility of an Herbrand Interpretation of Number Theory with Induction; Chapter IV. The No-Counter-Example Interpretation of Number Theory; 1. Non-constructive Considerations 2. No-Counter-Example Interpretation of Number Theory without Induction 3. No-Counter-Example Interpretation, 1*-Consistency, and External Consistency 4. Ordinal Recursive Functionals, 1*-Consistency of Number Theory with Induction 5. Representation of Ordinal Recursive Functionals in Elementary Number Theory; Chapter V. Ramified Analysis; 1. Description of Systems 2. Ramified Analysis without Induction 3. Recursive Well-orderings and Ordinal Recursive Functionals 4. Ramified Analysis with Induction 5. Representation of Ordinal Recursive Functionals in Ramified Analysis; Chapter VI. Ω-Consistency; 1. Critique of the Concept of ω-Consistency 2. Ω-Consistency, External Consistency, and 1*-Consistency 3. Ω-Consistency of Ramified Analysis; Appendix I. Arithmetization of Schütte’s Cut-elimination theorems; Appendix II. Ordinal Functions; Bibliography; Index of Definitions
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Taylor & Francis Ltd Introduction to Abstract Algebra Third Edition
Book SynopsisThe first and second editions of this successful textbook have been highly praised for their lucid and detailed coverage of abstract algebra. In this third edition, the author has carefully revised and extended his treatment, particularly the material on rings and fields, to provide an even more satisfying first course in abstract algebra.Table of ContentsChapter One SETS AND LOGIC -- 1. Some very general remarks -- 2. Introductory remarks on sets -- 3. Statements and conditions; quantifiers -- 4. The implies sign () -- 5. Proof by contradiction -- 6. Subsets -- 7. Unions and intersections -- 8. Cartesian product of sets -- EXERCISES -- Chapter Two SOME PROPERTIES OF -- 9. Introduction -- 10. The well-ordering principle -- I I. The division algorithm -- 12. Highest common factors and Euclid’s algorithm -- 13. The fundamental theorem of arithmetic -- 14. Congruence modulo m (mE f4J) -- EXERCISES -- Chapter Three EQUIVALENCE RELATIONS AND EQUIVALENCE CLASSES -- 15. Relations in general -- 16. Equivalence relations -- 17. Equivalence classes -- 18. Congruence classes -- 19. Properties of l,, as an algebraic system -- EXERCISES -- Chapter Four MAPPINGS -- 20. Introduction -- 21. The image of a subset of the domain; surjcctions -- 22. Injections; bijections; inverse of a bijection -- 23. Restriction of a mapping -- 24. Composition of mappings -- 25. Some further results and examples on mappings -- EXERCISES -- Chapter Five SEMIGROUPS -- 26. Introduction -- 27. Binary operations -- 28. Associativity and commutativity -- 29. Semigroups: definition and examples -- 30. Powers of an element in a semigroup -- 31. Identity elements and inverses -- 32. Subsemigroups -- EXERCISES -- Chapter Six AN INTRODUCTION TO GROUPS -- 33. The definition of a group -- 34. Examples of groups -- 35. Elementary consequences of the group axioms -- 36. Subgroups -- 37. Some important general examples of subgroups -- 38. Period of an element -- 39. Cyclic groups -- EXERCISES -- Chapter Seven COSETS AND LAGRANGE’S THEOREM ON FINITE GROUPS -- 40. Introduction -- 41. Multiplication of subsets of a group -- 42. Another approach to cosets -- 43. Lagrange’s theorem -- 44. Some consequences of Lagrange’s theorem -- EXERCISES -- Chapter Eight HOMOMORPHISMS, NORMAL SUBGROUPS, AND QUOTIENT GROUPS -- 45. Introduction -- 46. Isomorphic groups -- 47. Homomorphisms and their elementary properties -- 48. Conjugacy -- 49. Normal subgroups -- 50. Quotient groups -- 51. The quotient group G/Z -- 52. The first isomorphism theorem -- EXERCISES -- Chapter Nine THE SYMMETRIC GROUP S -- 53. Introduction -- 54. Cycles -- 55. Products of disjoint cycles -- 56. Periods of elements of Sft -- 57. Conjugacy in S1 -- 58. Arrangement of the objects 1,2,...,n -- 59. The alternating character, and alternating groups -- 60. The simplicity of A5 -- EXERCISES -- Chapter Ten THE FUNDAMENTALS OF RING THEORY -- 61. Introduction -- 62. The definition of a ring and its elementary consequences -- 63. Special types of ring and ring elements -- 64. Subrings and subtIelds -- 65. Ring homomorphisms -- 66. Ideals -- 67. Principal ideals in a commutative ring with a one -- 68. Factor rings -- 69. Characteristic of an integral domain or field -- 70. The field of fractions of an integral domain -- EXERCISES -- Chapter Eleven POLYNOMIALS AND FIELDS -- 71. Introduction -- 72. Polynomial rings -- 73. Some properties of F[X], where F is a field -- 74 Generalities on factorization -- 75. Further properties of F[XJ, where F is a field -- 76. Some matters of notation -- 77. Minimal polynomials and the structure of F(c) -- 78. Some elementary properties of finite fields -- 79. Construction of fields by root adjunction -- 80. Degrees of field extensions -- 81. Epilogue -- EXERCISES -- BIBLIOGRAPHY -- APPENDIX TO EXERCISES -- INDEX.
£171.00
Taylor & Francis The Infinite
Book SynopsisWe are all captivated and puzzled by the infinite, in its many varied guises; by the endlessness of space and time; by the thought that between any two points in space, however close, there is always another; by the fact that numbers go on forever; and by the idea of an all-knowing, all-powerful God. In this acclaimed introduction to the infinite, A. W. Moore takes us on a journey back to early Greek thought about the infinite, from its inception to Aristotle. He then examines medieval and early modern conceptions of the infinite, including a brief history of the calculus, before turning to Kant and post-Kantian ideas. He also gives an account of Cantorâs remarkable discovery that some infinities are bigger than others. In the second part of the book, Moore develops his own views, drawing on technical advances in the mathematics of the infinite, including the celebrated theorems of Skolem and GÃdel, and deriving inspiration from Wittgenstein. He concludes this part with a disTrade ReviewPraise for previous editions'Moore provides a splendid guide through the intellectual history of this powerful and far-reaching idea ... [He] offers a fascinating consideration of the mystical aspects of infinity and the issues of human finitude and death ... very highly recommended for all readers.' - CHOICE'Moore's book provides us with an instructive and authoritative overview of a topic of considerable philosophical importance.' - Roger Penrose, Times Literary Supplement'Moore's book points to deep and unresolved issues in the philosophy of mathematics, and even deeper issues in general philosophy ... It deserves serious study by both mathematicians and philosophers.' - Thomas Tymoczko, Philosophia Mathematica'Moore's treatment of] the problems with which the history of thought about the infinite confronts us today ... shows that questions concerning the nature and existence of the infinite are still very much alive. [A] highly stimulating account of the nature of infinity and its bold defence of finitism.' - W. L. Craig, International Philosophical Quarterly'In the last three thought-provoking chapters of his book Moore draws heavily, but creatively on Kant and Wittgenstein. Moore presents an analysis and proposed resolution of the issues that are both stimulating and accessible.' - Mary Tiles, Times Higher Education SupplementPraise for previous editions'Moore provides a splendid guide through the intellectual history of this powerful and far-reaching idea ... [He] offers a fascinating consideration of the mystical aspects of infinity and the issues of human finitude and death ... very highly recommended for all readers.' - CHOICE'Moore's book provides us with an instructive and authoritative overview of a topic of considerable philosophical importance.' - Roger Penrose, Times Literary Supplement'Moore's book points to deep and unresolved issues in the philosophy of mathematics, and even deeper issues in general philosophy ... It deserves serious study by both mathematicians and philosophers.' - Thomas Tymoczko, Philosophia Mathematica'[Moore's treatment of] the problems with which the history of thought about the infinite confronts us today ... shows that questions concerning the nature and existence of the infinite are still very much alive. [A] highly stimulating account of the nature of infinity and its bold defence of finitism.' - W. L. Craig, International Philosophical Quarterly'In the last three thought-provoking chapters of his book Moore draws heavily, but creatively, on Kant and Wittgenstein. Moore presents an analysis and proposed resolution of the issues that are both stimulating and accessible.' - Mary Tiles, Times Higher Education SupplementTable of ContentsPart I: The History 1. Early Greek Thought 2. Aristotle 3. Medieval and Renaissance Thought 4. The Calculus 5. The Rationalists and the Empiricists 6. Kant 7. Post-Kantian Metaphysics of the Infinite 8. The Mathematics of the Infinite, and the Impact of Cantor 9. Reactions Part II: Infinity Assessed 10. Transfinite Mathematics 11. The Lowenheim–Skolem Theorem 12. Gödel’s Theorem 13. Saying and Showing 14. Infinity Assessed. The History Reassessed 15. Human Finitude Part III: Infinity Superseded 16. Infinity Reassessed. The History Reassessed Anew 17. Learning How to be Finite
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Cambridge University Press Between Logic and Intuition
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Cambridge University Press The Logic of Concept Expansion
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Cambridge University Press Information Flow The Logic of Distributed Systems 44 Cambridge Tracts in Theoretical Computer Science Series Number 44
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Cambridge University Press The Dynamics of Norms
Book SynopsisThis 'state-of-the-art' collection of essays presents some of the best contemporary research into the dynamical processes underlying the formation, maintenance, metamorphosis and dissolution of norms. The volume combines formal modelling with more traditional analysis.Table of Contents1. The evolution of strategies in the iterated prisoner's dilemma Robert Axelrod; 2. Learning to co-operate Cristina Bicchieri; 3. On the dynamics of social norms Pier Luigi Sacco; 4. Learning and efficiency in common interest signalling games David Canning; 5. Learning on a Torus Luca Anderlini and Antonella Ianni; 6. Evolutive vs. naive Bayesian learning Immanuel M. Bomze and Jurgen Eichberger; 7. Learning and mixed strategy equilibria in evolutionary games Vincent P. Crawford; 8. Bayesian learning in games: a non-Bayesian perspective J. S. Jordan; 9. Savage-Bayesian agents play a repeated game Yaw Nyarko; 10. Chaos and the explanatory significance of equilibrium: strange attractors in evolutionary game theory Brian Skyrms.
£29.44