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  1. Mathematical Logic and Foundations of Set Theory.Yehoshua Bar-Hillel (ed.) - 1970 - Amsterdam: North-Holland Pub. Co..
    LN , so f lies in the elementary submodel M'. Clearly co 9 M' . It follows that 6 = {f(n): n em} is included in M'. Hence the ordinals of M' form an initial ...
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  2. The Mathematical Experience.Philip J. Davis - 1981 - Birkhäuser.
    Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...
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  3. Infinity: New Research Frontiers.Michał Heller & W. H. Woodin (eds.) - 2011 - Cambridge University Press.
    Machine generated contents note: Introduction Rudy Rucker; Part I. Perspectives on Infinity from History: 1. Infinity as a transformative concept in science and theology Wolfgang Achtner; Part II. Perspectives on Infinity from Mathematics: 2. The mathematical infinity Enrico Bombieri; 3. Warning signs of a possible collapse of contemporary mathematics Edward Nelson; Part III. Technical Perspectives on Infinity from Advanced Mathematics: 4. The realm of the infinite W. Hugh Woodin; 5. A potential subtlety concerning the distinction between determinism and nondeterminism W. (...)
  4. Mathematics and Plausible Reasoning.George Polya - 1954 - Princeton University Press.
    Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.
  5. Discrete Mathematics and Theoretical Computer Science 4th International Conference, Dmtcs 2003, Dijon, France, July 2003, Proceedings. [REVIEW]Cristian Calude, M. J. Dinneen & Vincent Vajnovszki - 2003
  6. The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity.Amir D. Aczel - 2000 - Four Walls Eight Windows.
    From the end of the 19th century until his death, one of history's most brilliant mathematicians languished in an asylum. The Mystery of the Aleph tells the story of Georg Cantor (1845-1918), a Russian-born German who created set theory, the concept of infinite numbers, and the "continuum hypothesis," which challenged the very foundations of mathematics. His ideas brought expected denunciation from established corners - he was called a "corruptor of youth" not only for his work in mathematics, but for his (...)
  7. Stochastic Algorithms: Foundations and Applications: Third International Symposium, Saga 2005, Moscow, Russia, October 20-22, 2005: Proceedings. [REVIEW]O. B. Lupanov (ed.) - 2005 - Springer.
    This book constitutes the refereed proceedings of the Third International Symposium on Stochastic Algorithms: Foundations and Applications, SAGA 2005, held in Moscow, Russia in October 2005. The 14 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The contributed papers included in this volume cover both theoretical as well as applied aspects of stochastic computations whith a special focus on new algorithmic ideas involving stochastic decisions and the design and evaluation (...)
  8. An Accompaniment to Higher Mathematics.George R. Exner - 1997 - Springer.
    This text prepares undergraduate mathematics students to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs. The book begins by teaching how to read mathematics actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a technique famililar to any mathematician, but rarely taught); it provides practice by indicating explicitly where work with pencil and paper must interrupt reading. The book then turns to proofs, (...)
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  9. Uncertainty in Knowledge Bases.B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.) - 1991 - Springer.
    One out of every two men over eigthy suffers from carcinoma of the prostate.It is discovered incidentally in many patients with an alleged benign prostatic ...
  10. Non-Standard Logics for Automated Reasoning.Philippe Smets (ed.) - 1988 - Academic Press.
  11. The Philosophy of Mathematics Today.Matthias Schirn (ed.) - 1998 - Clarendon Press.
    This comprehensive volume gives a panorama of the best current work in this lively field, through twenty specially written essays by the leading figures in the field. All essays deal with foundational issues, from the nature of mathematical knowledge and mathematical existence to logical consequence, abstraction, and the notions of set and natural number. The contributors also represent and criticize a variety of prominent approaches to the philosophy of mathematics, including platonism, realism, nomalism, constructivism, and formalism.
  12. Berkeley's Philosophy of Mathematics.Douglas M. Jesseph - 1993 - University of Chicago Press.
    In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work.
  13. Between Logic and Intuition: Essays in Honor of Charles Parsons.Gila Sher & Richard Tieszen (eds.) - 2000 - Cambridge University Press.
    This collection of new essays offers a 'state-of-the-art' conspectus of major trends in the philosophy of logic and philosophy of mathematics. A distinguished group of philosophers addresses issues at the centre of contemporary debate: semantic and set-theoretic paradoxes, the set/class distinction, foundations of set theory, mathematical intuition and many others. The volume includes Hilary Putnam's 1995 Alfred Tarski lectures, published here for the first time.
  14. Mathematics and Mind.Alexander George (ed.) - 1994 - Oxford University Press.
    Those inquiring into the nature of mind have long been interested in the foundations of mathematics, and conversely this branch of knowledge is distinctive in that our access to it is purely through thought. A better understanding of mathematical thought should clarify the conceptual foundations of mathematics, and a deeper grasp of the latter should in turn illuminate the powers of mind through which mathematics is made available to us. The link between conceptions of mind and of mathematics has been (...)
  15. Science, Paradox, and the Moebius Principle: The Evolution of a "Transcultural" Approach to Wholeness.Steven M. Rosen - 1994 - State University of New York Press; Series in Science, Technology, and Society.
    This book confronts basic anomalies in the foundations of contemporary science and philosophy. It deals with paradoxes that call into question our conventional way of thinking about space, time, and the nature of human experience.
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  16. Philosophical Logic.J. W. Davis - 1969 - Dordrecht: D. Reidel.
  17. Encounters with Infinity: A Metamathematical Dissertation.Michael Van Laanen - 2004 - New Age Book.
    This thesis is presented in the hope that it will resonate with mathematicians and others who are interested in analysis concepts and pure number theory.
  18. Science in the Looking Glass: What Do Scientists Really Know?E. Brian Davies - 2003 - Oxford University Press UK.
    How do scientific conjectures become laws? Why does proof mean different things in different sciences? Do numbers exist, or were they invented? Why do some laws turn out to be wrong? In this wide-ranging book, Brian Davies discusses the basis for scientists' claims to knowledge about the world. He looks at science historically, emphasizing not only the achievements of scientists from Galileo onwards, but also their mistakes. He rejects the claim that all scientific knowledge is provisional, by citing examples from (...)
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  19. Is God a Mathematician?Mario Livio - 2009 - Simon & Schuster.
    Nobel Laureate Eugene Wigner once wondered about "the unreasonable effectiveness of mathematics" in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that -- mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, (...)
  20. Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos (ed.) - 1976 - Cambridge University Press.
    Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre (...)
  21. The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford University Press.
    This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...
  22. Godel's Theorem in Focus.S. G. Shanker (ed.) - 1990 - Routledge.
    A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
  23. Descartes' Dream: The World According to Mathematics.Philip J. Davis - 1986 - Dover Publications.
    Philosopher Rene Descartes visualized a world unified by mathematics, in which all intellectual issues could be resolved rationally by local computation. This series of provocative essays takes a modern look at the seventeenth-century thinker’s dream, examining the physical and intellectual influences of mathematics on society, particularly in light of technological advances. They survey the conditions that elicit the application of mathematic principles; the effectiveness of these applications; and how applied mathematics constrain lives and transform perceptions of reality. Highly suitable for (...)
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  24. Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education.Sal Restivo, Jean Paul Van Bendegem & Roland Fischer (eds.) - 1993 - State University of New York Press.
    An international group of distinguished scholars brings a variety of resources to bear on the major issues in the study and teaching of mathematics, and on the problem of understanding mathematics as a cultural and social phenomenon. All are guided by the notion that our understanding of mathematical knowledge must be grounded in and reflect the realities of mathematical practice. Chapters on the philosophy of mathematics illustrate the growing influence of a pragmatic view in a field traditionally dominated by platonic (...)
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  25. Twenty-Five Years of Constructive Type Theory: Proceedings of a Congress Held in Venice, October 1995.Giovanni Sambin & Jan M. Smith (eds.) - 1998 - Oxford University Press.
    This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Lof over the last twenty-five years.
  26. Meta-Logics and Logic Programming.Krzysztof R. Apt & Franco Turini - 1995
  27. No Matter, Never Mind.Kunio Yasue, Marj Jibu & Tarcisio Della Senta (eds.) - 2002 - John Benjamins.
  28. Frontiers of Combining Systems: Third International Workshop, Frocos 2000, Nancy, France, March 22-24, 2000: Proceedings. [REVIEW]H. Kirchner & Christophe Ringeissen (eds.) - 2000 - Springer.
    This book constitutes the refereed proceedings of the Third International Workshop on Frontiers of Combining Systems, FroCoS 2000, held in Nancy, France, in March 2000.The 14 revised full papers presented together with four invited papers were carefully reviewed and selected from a total of 31 submissions. Among the topics covered are constraint processing, interval narrowing, rewriting systems, proof planning, sequent calculus, type systems, model checking, theorem proving, declarative programming, logic programming, and equational theories.
  29. To Infinity and Beyond: A Cultural History of the Infinite.Eli Maor - 1987 - Princeton University Press.
    Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes (...)
  30. The Foundations of Arithmetic: A Logico-Mathematical Enquiry Into the Concept of Number.Gottlob Frege - 1950 - Northwestern University Press.
    § i. After deserting for a time the old Euclidean standards of rigour, mathematics is now returning to them, and even making efforts to go beyond them. ...
  31. Nonmonotonic and Inductive Logic Second International Workshop, Reinhardsbrunn Castle, Germany, December 2-6, 1991 : Proceedings. [REVIEW]Gerhard Brewka, K. P. Jantke, P. H. Schmitt & International Workshop on Nonmonotonic and Inductive Logic - 1993
  32. Logic From a to Z: The Routledge Encyclopedia of Philosophy Glossary of Logical and Mathematical Terms.John B. Bacon, Michael Detlefsen & David Charles McCarty - 1999 - Routledge.
    First published in the most ambitious international philosophy project for a generation; the _Routledge Encyclopedia of Philosophy_. _Logic from A to Z_ is a unique glossary of terms used in formal logic and the philosophy of mathematics. Over 500 entries include key terms found in the study of: * Logic: Argument, Turing Machine, Variable * Set and model theory: Isomorphism, Function * Computability theory: Algorithm, Turing Machine * Plus a table of logical symbols. Extensively cross-referenced to help comprehension and add (...)
  33. Mathematics, a Concise History and Philosophy.W. S. Anglin - 1996 - Springer.
    This is a concise introductory textbook for a one semester course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. It is shorter than the standard textbooks in that area and thus more accessible to students who have trouble coping with vast amounts of reading. Furthermore, there are many detailed explanations of the important mathematical procedures (...)
  34. Meaning and Existence in Mathematics.Charles Castonguay - 1972 - New York: Springer Verlag.
  35. Philosophy of Mathematics.Paul Benacerraf - 1964 - Englewood Cliffs, N.J., Prentice-Hall.
    The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers.
  36. Principia Mathematica, to *56.Alfred North Whitehead & Bertrand Russell - 1962 - Cambridge University Press.
    The great three-volume Principia Mathematica is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premisses and primitive ideas, and so to prove that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will wish (...)
  37. Euclid in the Rainforest: Discovering Universal Truth in Logic and Math.Joseph Mazur - 2005 - Pi Press.
  38. Symbolic Logic and Mechanical Theorem Proving.Chin-Liang Chang - 1973 - Academic Press.
    This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4–9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
  39. Reflections on Kurt Gödel.Hao Wang - 1990 - Bradford.
    In this first extended treatment of his life and work, Hao Wang, who was in close contact with Godel in his last years, brings out the full subtlety of Godel's ideas and their connection with grand themes in the history of mathematics and ...
  40. What is Mathematics, Really?Reuben Hersh - 1997 - Oxford University Press.
    Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist (...)
  41. The Theory of Models Proceedings of the 1963 International Symposium at Berkeley.J. W. Addison, Leon Henkin & Alfred Tarski - 1965
  42. Infinity: Beyond the Beyond the Beyond.Lillian R. Lieber - 1953 - Paul Dry Books.
    This elegant, accessible artfully illuminates the concept of infinity with its striking drawings.
  43. Converging Realities: Toward a Common Philosophy of Physics and Mathematics.Roland Omnès - 2004 - Princeton University Press.
    The philosophical relationship between mathematics and the natural sciences is the subject of Converging Realities, the latest work by one of the leading thinkers on the subject.
  44. Philosophy of Mathematics and Natural Science.Hermann Weyl - 1949 - Princeton University Press.
    This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.
  45. Logic and Philosophy an Integrated Introduction.William H. Brenner - 1993
  46. Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics.Friedrich Waismann - 1951 - Dover Publications.
    "With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics."--Carl B. Boyer, Brooklyn College. This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition. Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; and the rigorous construction of elementary arithmetic. Advanced (...)
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  47. The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics.Crispin Wright & Bob Hale - 2001 - Oxford: Clarendon Press.
    Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized as the (...)
  48. Structuralism: The Art of the Intelligible.Peter CAWS - 1988 - Humanities Press.
  49. The Philosophy of Mathematics.W. D. Hart (ed.) - 1996 - Oxford University Press.
    This volume offers a selection of the most interesting and important work from recent years in the philosophy of mathematics, which has always been closely linked to, and has exerted a significant influence upon, the main stream of analytical philosophy. The issues discussed are of interest throughout philosophy, and no mathematical expertise is required of the reader. Contributors include W.V. Quine, W.D. Hart, Michael Dummett, Charles Parsons, Paul Benacerraf, Penelope Maddy, W.W. Tait, Hilary Putnam, George Boolos, Daniel Isaacson, Stewart Shapiro, (...)
  50. The Elements of Mathematical Logic.Paul C. Rosenbloom - 1950 - New York]Dover Publications.
    An excellent introduction to mathematical logic, this book provides readers with a sound knowledge of the most important approaches to the subject, stressing the use of logical methods in attacking nontrivial problems. It covers the logic of classes, of propositions, of propositional functions, and the general syntax of language, with a brief introduction that also illustrates applications to so-called undecidability and incompleteness theorems. Other topics include the simple proof of the completeness of the theory of combinations, Church's theorem on the (...)
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