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  1. Constructive Models.I͡Uriĭ Leonidovich Ershov - 2000 - Consultants Bureau.
  2. The Language of Logic.Morton L. Schagrin - 1968 - New York: Random House.
  3. The Logic of History.Charles Morazé - 1976 - Mouton.
  4. Non-Standard Logics for Automated Reasoning.Philippe Smets (ed.) - 1988 - Academic Press.
  5. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences.I. Grattan-Guinness (ed.) - 1994 - Routledge.
    The Companion Encyclopedia is the first comprehensive work to cover all the principal lines and themes of the history and philosophy of mathematics from ancient times up to the twentieth century. In 176 articles contributed by 160 authors of 18 nationalities, the work describes and analyzes the variety of theories, proofs, techniques, and cultural and practical applications of mathematics. The work's aim is to recover our mathematical heritage and show the importance of mathematics today by treating its interactions with the (...)
  6. Philosophy of Science, Logic, and Mathematics in the Twentieth Century.Stuart Shanker (ed.) - 1996 - Routledge.
    Volume 9 of the Routledge History of Philosophy surveys ten key topics in the Philosophy of Science, Logic and Mathematics in the Twentieth Century. Each article is written by one of the world's leading experts in that field. The papers provide a comprehensive introduction to the subject in question, and are written in a way that is accessible to philosophy undergraduates and to those outside of philosophy who are interested in these subjects. Each chapter contains an extensive bibliography of the (...)
  7. 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 ...
  8. The Philosophy of Mathematics Education.Paul Ernest - 1991 - Falmer Press.
  9. A Bridge to Advanced Mathematics.Dennis Sentilles - 1975 - Baltimore: Williams & Wilkins.
  10. 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 ...
  11. Mathematical Knowledge.Mark Steiner - 1975 - Cornell University Press.
  12. 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 ...
  13. Tracking Reason: Proof, Consequence, and Truth.Jody Azzouni - 2006 - Oup Usa.
    When ordinary people - mathematicians among them - take something to follow from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, despite our apparent intuitive grasp of consequence, we do not introspect rules by which we reason, nor do we grasp the scope and range of the domain, as it were, (...)
  14. The Foundations of Mathematics.Ian Stewart & David Tall - 1977 - Oxford University Press.
    The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books.
  15. 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 (...)
  16. Philosophy of Mathematics: An Introduction to a World of Proofs and Pictures.James Robert Brown - 1999 - Routledge.
    _Philosophy of Mathematics_ is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.
  17. The Usefulness of Mathematical Learning Explained and Demonstrated: Being Mathematical Lectures Read in the Publick Schools at the University of Cambridge.Isaac Barrow - 1734 - London: Cass.
    (I) MATHEMATICAL LECTURES. LECTURE I. Of the Name and general Division of the Mathematical Sciences. BEING about to treat upon the Mathematical Sciences, ...
  18. Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century.Paolo Mancosu - 1996 - Oxford University Press.
    The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...)
  19. 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. (...)
  20. The Principles of Mathematics Revisited.Jaakko Hintikka - 1996 - Cambridge University Press.
    This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous (...)
  21. Proofs and Fundamentals: A First Course in Abstract Mathematics.Ethan D. Bloch - 2000 - Birkhäuser.
  22. Degrees of Unsolvability: Structure and Theory.Richard L. Epstein - 1979 - Springer Verlag.
    The contributions in the book examine the historical and contemporary manifestations of organized crime, the symbiotic relationship between legitimate and ...
  23. Proceedings of the Second Scandinavian Logic Symposium.Jens Erik Fenstad (ed.) - 1971 - Amsterdam: North-Holland Pub. Co..
    Provability, Computability and Reflection.
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  24. Conversations on Mind, Matter, and Mathematics.Jean-Pierre Changeux & Alain Connes - 1998 - Princeton University Press.
    "This wonderfully eloquent and playful colloquy of two brilliant minds gives new life to the old notion of Dialogue, a sadly forgotten form now.... I "love" this book!
  25. 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 (...)
  26. 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 ...
  27. Meaning and Existence in Mathematics.Charles Castonguay - 1972 - New York: Springer Verlag.
  28. Understanding the Infinite.Shaughan Lavine - 1994 - Harvard University Press.
    An engaging account of the origins of the modern mathematical theory of the infinite, his book is also a spirited defense against the attacks and misconceptions ...
  29. 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, (...)
  30. Ontological Economy: Substitutional Quantification and Mathematics.Dale Gottlieb - 1980 - Oxford University Press.
  31. The Origin of Concepts.Susan Carey - 2009 - Oxford University Press.
    Only human beings have a rich conceptual repertoire with concepts like tort, entropy, Abelian group, mannerism, icon and deconstruction. How have humans constructed these concepts? And once they have been constructed by adults, how do children acquire them? While primarily focusing on the second question, in The Origin of Concepts , Susan Carey shows that the answers to both overlap substantially. Carey begins by characterizing the innate starting point for conceptual development, namely systems of core cognition. Representations of core cognition (...)
  32. Mathematics, Science, and Epistemology.Imre Lakatos - 1978 - Cambridge University Press.
    Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics (much of it unpublished), together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues.
  33. Geometrical Investigations: Illustrating the Art of Discovery in the Mathematical Field.John Pottage - 1983 - Addison-Wesley.
  34. 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 (...)
  35. The Combinatory Programme.Erwin Engeler (ed.) - 1995 - Birkhäuser.
  36. 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 (...)
  37. Structuralism: Moscow, Prague, Paris.Jan M. Broekman - 1974 - D. Reidel Pub. Co..
    THE STRUCTURALISTIC ENDEAVOUR. THE WORLD AS MUSICAL SCORE The recent decades of this century have witnessed unusually rapid and far- reaching changes in the ...
  38. The Moment of Proof: Mathematical Epiphanies.Donald C. Benson - 1999 - Oxford University Press.
    When Archimedes, while bathing, suddenly hit upon the principle of buoyancy, he ran wildly through the streets of Syracuse, stark naked, crying "eureka!" In The Moment of Proof, Donald Benson attempts to convey to general readers the feeling of eureka--the joy of discovery--that mathematicians feel when they first encounter an elegant proof. This is not an introduction to mathematics so much as an introduction to the pleasures of mathematical thinking. And indeed the delights of this book are many and varied. (...)
  39. Deflating Existential Commitment: A Case for Nominalism.Jody Azzouni - 2004 - Oup Usa.
    If we take mathematical statements to be true, then must we also believe in the existence of invisible mathematical objects, accessible only by the power of thought? Jody Azzouni says we do not have to, and claims that the way to escape such a commitment is to accept - as an essential part of scientific doctrine - true statements which are 'about' objects which don't exist in any real sense.
  40. Philosophical Logic.J. W. Davis - 1969 - Dordrecht: D. Reidel.
  41. 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, (...)
  42. The Philosophy of Mathematics.Jaakko Hintikka (ed.) - 1969 - London: Oxford University Press.
  43. 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 ...
  44. Mathematical Analysis and Proof.David S. G. Stirling - 2009 - Horwood.
    This fundamental and straightforward text addresses a weakness observed among present-day students, namely a lack of familiarity with formal proof. Beginning with the idea of mathematical proof and the need for it, associated technical and logical skills are developed with care and then brought to bear on the core material of analysis in such a lucid presentation that the development reads naturally and in a straightforward progression. Retaining the core text, the second edition has additional worked examples which users have (...)
  45. 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 (...)
  46. A Metaphysics of Elementary Mathematics.J. Sicha - 1974 - Amherst, University of Massachusetts Press.
  47. 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.
  48. 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 (...)
  49. Deductive Logic in Natural Language.Douglas Cannon - 2002 - Broadview Press.
    This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.
  50. 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.
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