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  1. Philippe Smets (ed.) (1988). Non-Standard Logics for Automated Reasoning. Academic Press.
  2. Alessandro Andretta, Keith Kearnes & Domenico Zambella (eds.) (2008). Logic Colloquium 2004: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Torino, Italy, July 25-31, 2004. [REVIEW] Cambridge University Press.
    Highlights of this volume from the 2004 Annual European Meeting of the Association for Symbolic Logic (ASL) include a tutorial survey of the recent highpoints of universal algebra, written by a leading expert; explorations of foundational questions; a quartet of model theory papers giving an excellent reflection of current work in model theory, from the most abstract aspect "abstract elementary classes" to issues around p-adic integration.
  3. Mary Tiles (1991). Mathematics and the Image of Reason. Routledge.
    A thorough account of the philosophy of mathematics. In a cogent account the author argues against the view that mathematics is solely logic.
  4. Dennis Sentilles (1975). A Bridge to Advanced Mathematics. Baltimore,Williams & Wilkins.
  5. Yehoshua Bar-Hillel (ed.) (1970). Mathematical Logic and Foundations of Set Theory. 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 ...
  6. Jody Azzouni (2010). Talking About Nothing: Numbers, Hallucinations, and Fictions. Oxford University Press.
    Numbers -- Hallucinations -- Fictions -- Scientific languages, ontology, and truth -- Truth conditions and semantics.
  7. H. Kirchner & Christophe Ringeissen (eds.) (2000). Frontiers of Combining Systems: Third International Workshop, Frocos 2000, Nancy, France, March 22-24, 2000: Proceedings. [REVIEW] 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.
  8. John Pottage (1983). Geometrical Investigations: Illustrating the Art of Discovery in the Mathematical Field. Addison-Wesley.
  9. Donald Gillies (ed.) (1992). Revolutions in Mathematics. Oxford University Press.
    Social revolutions--that is critical periods of decisive, qualitative change--are a commonly acknowledged historical fact. But can the idea of revolutionary upheaval be extended to the world of ideas and theoretical debate? The publication of Kuhn's The Structure of Scientific Revolutions in 1962 led to an exciting discussion of revolutions in the natural sciences. A fascinating, but little known, off-shoot of this was a debate which began in the United States in the mid-1970's as to whether the concept of revolution could (...)
  10. Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.
    Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...)
  11. Thomas J. Jech (1971). Lectures in Set Theory. New York,Springer-Verlag.
  12. Charles Castonguay (1972). Meaning and Existence in Mathematics. New York,Springer-Verlag.
  13. Stephen David Ross (1994). Locality and Practical Judgment: Charity and Sacrifice. Fordham University Press.
    This work completes Ross's trilogy examining the inexhaustible complexity of the world and our relation to our surroundings.
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  14. Dale Gottlieb (1980). Ontological Economy: Substitutional Quantification and Mathematics. Oxford University Press.
  15. Hilary Putnam (1979). Mathematics, Matter, and Method. Cambridge University Press.
    Professor Hilary Putnam has been one of the most influential and sharply original of recent American philosophers in a whole range of fields. His most important published work is collected here, together with several new and substantial studies, in two volumes. The first deals with the philosophy of mathematics and of science and the nature of philosophical and scientific enquiry; the second deals with the philosophy of language and mind. Volume one is now issued in a new edition, including an (...)
  16. Michael D. Resnik (1980). Frege and the Philosophy of Mathematics. Cornell University Press.
  17. W. S. Anglin (1996). Mathematics, a Concise History and Philosophy. 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 (...)
  18. George Polya (1990). Mathematics and Plausible Reasoning. 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.
  19. Jody Azzouni (2004). Deflating Existential Commitment: A Case for Nominalism. 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.
  20. Ludwig Wittgenstein (1978). Remarks on the Foundations of Mathematics. B. Blackwell.
  21. Michał Heller & W. H. Woodin (eds.) (2011). Infinity: New Research Frontiers. 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. (...)
  22. Philip Kitcher (1983). The Nature of Mathematical Knowledge. 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 ...
  23. Charles S. Chihara (1973). Ontology and the Vicious-Circle Principle. Ithaca [N.Y.]Cornell University Press.
  24. Michael Detlefsen (ed.) (1992). Proof and Knowledge in Mathematics. Routledge.
    Proof and Knowledge in Mathematics tackles the main problem that arises when considering an epistemology for mathematics, the nature and sources of mathematical justification. Focusing both on particular and general issues, these essays from leading philosophers of mathematics raise important issues for our current understanding of mathematics. Is mathematical justification a priori or a posteriori? What role, if any, does logic play in mathematical reasoning or inference? And how epistemologically important is the formalizability of proof? Michael Detlefsen has brought together (...)
  25. J. Sicha (1974). A Metaphysics of Elementary Mathematics. Amherst, University of Massachusetts Press.
  26. Imre Lakatos (1978). Mathematics, Science, and Epistemology. 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.
  27. Eli Maor (1987/1991). To Infinity and Beyond: A Cultural History of the Infinite. 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 (...)
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  28. Alfred North Whitehead & Bertrand Russell (1962/1997). Principia Mathematica, to *56. 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 (...)
  29. Amir D. Aczel (2000). The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity. 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 (...)
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  30. Bryan H. Bunch (1982/1997). Mathematical Fallacies and Paradoxes. Dover Publications.
    Stimulating, thought-provoking analysis of a number of the most interesting intellectual inconsistencies in mathematics, physics and language. Delightful elucidations of methods for misunderstanding the real world of experiment (Aristotle’s Circle paradox), being led astray by algebra (De Morgan’s paradox) and other mind-benders. Some high school algebra and geometry is assumed; any other math needed is developed in text. Reprint of 1982 ed.
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  31. Shaughan Lavine (1994). Understanding the Infinite. 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 ...
  32. Thomas J. McKay (2006). Plural Predication. Oxford University Press.
    Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. However, the apparatus of modern logic does not allow a place for them. Thomas McKay here explores the enrichment of logic with non-distributive plural predication and quantification. His book will be (...)
  33. C. S. Jenkins (2008). Grounding Concepts: An Empirical Basis for Arithmetical Knowledge. Oup Oxford.
    Carrie Jenkins presents a new account of arithmetical knowledge, which manages to respect three key intuitions: a priorism, mind-independence realism, and empiricism. Jenkins argues that arithmetic can be known through the examination of empirically grounded concepts, non-accidentally accurate representations of the mind-independent world.
  34. Charles S. Chihara (1990). Constructibility and Mathematical Existence. Oxford University Press.
    Chihara here develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. He utilizes this system in the analysis of the nature of mathematics, and discusses many recent works in the philosophy of mathematics from the viewpoint of the constructibility theory developed. This innovative analysis will appeal to mathematicians and philosophers of logic, mathematics, and science.
  35. Paul Benacerraf & Hilary Putnam (eds.) (1983). Philosophy of Mathematics: Selected Readings. Cambridge University Press.
    The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, (...)
  36. Charles Chihara (2004). A Structural Account of Mathematics. Clarendon Press.
    A Structural Account of Mathematics will be required reading for anyone working in this field.
  37. Philip J. Davis (1995/1982). The Mathematical Experience. Birkhäuser.
    Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...
  38. Paolo Mancosu (1996). Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century. 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 (...)
  39. Clare Boucher (2000). The Six Blind Men and the Elephant: A Traditional Indian Story. Candlewick Press.
  40. Joseph Mazur (2005). Euclid in the Rainforest: Discovering Universal Truth in Logic and Math. Pi Press.
  41. Geoffrey Hellman (1989). Mathematics Without Numbers: Towards a Modal-Structural Interpretation. Oxford University Press.
    Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while ...
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  42. Jody Azzouni (2006). Deflating Existential Consequence: A Case for Nominalism. Oup Usa.
    If we must take mathematical statements to be true, must we also believe in the existence of abstract eternal invisible mathematical objects accessible only by the power of pure thought? Jody Azzouni says no, and he claims that the way to escape such commitments is to accept (as an essential part of scientific doctrine) true statements which are about objects that don't exist in any sense at all. Azzouni illustrates what the metaphysical landscape looks like once we avoid a militant (...)
  43. Ulrich Felgner (1971). Models of Zf-Set Theory. New York,Springer-Verlag.
  44. William Demopoulos (ed.) (1995). Frege's Philosophy of Mathematics. Harvard University Press.
  45. George R. Exner (1997). An Accompaniment to Higher Mathematics. 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, (...)
  46. Steven M. Rosen (1994). Science, Paradox, and the Moebius Principle: The Evolution of a "Transcultural" Approach to Wholeness. 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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  47. Roberto Casati & Achille C. Varzi (1999). Parts and Places. The Structures of Spatial Representation. The Mit Press.
    Thinking about space is thinking about spatial things. The table is on the carpet; hence the carpet is under the table. The vase is in the box; hence the box is not in the vase. But what does it mean for an object to be somewhere? How are objects tied to the space they occupy? This book is concerned with these and other fundamental issues in the philosophy of spatial representation. Our starting point is an analysis of the interplay between (...)
  48. Daniel O. Dahlstrom, David T. Ozar & Leo Sweeney (eds.) (1981). Infinity. National Office of the American Catholic Philosophical Association, Catholic University of America.
  49. P. T. Johnstone (1987). Notes on Logic and Set Theory. Cambridge University Press.
    A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed (...)
  50. Mario Livio (2009). Is God a Mathematician? 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, (...)
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