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  1. Marian Przelecki (1969). The Logic of Empirical Theories. London, Routledge & K. Paul.
    Chapter One INTRODUCTORY REMARKS The title of this monograph needs explanation. It certainly sounds too promising. A more adequate, though more cumbersome ...
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  2. 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 ...
  3. 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.
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  4. Charles Castonguay (1972). Meaning and Existence in Mathematics. New York,Springer-Verlag.
  5. O. B. Lupanov (ed.) (2005). Stochastic Algorithms: Foundations and Applications: Third International Symposium, Saga 2005, Moscow, Russia, October 20-22, 2005: Proceedings. [REVIEW] 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 (...)
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  6. Austin Marsden Farrer (1979). Finite and Infinite: A Philosophical Essay. Seabury Press.
  7. John Pottage (1983). Geometrical Investigations: Illustrating the Art of Discovery in the Mathematical Field. Addison-Wesley.
  8. 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 (...)
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  9. V. Di Gesù, F. Masulli & Alfredo Petrosino (eds.) (2006). Fuzzy Logic and Applications: 5th International Workshop, Wilf 2003, Naples, Italy, October 9-11, 2003: Revised Selected Papers. [REVIEW] Springer.
    This volume constitutes the thoroughly refereed post-workshop proceedings of the 5th International Workshop on Fuzzy Logic and Applications held in Naples, Italy, in October 2003. The 40 revised full papers presented have gone through two rounds of reviewing and revision. All current issues of theoretical, experimental and applied fuzzy logic and related techniques are addressed with special attention to rough set theory, neural networks, genetic algorithms and soft computing. The papers are organized in topical section on fuzzy sets and systems, (...)
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  10. Jody Azzouni (2006). Tracking Reason: Proof, Consequence, and Truth. 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, (...)
  11. Ethan D. Bloch (2000). Proofs and Fundamentals: A First Course in Abstract Mathematics. Birkhäuser.
  12. 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 (...)
  13. Nelson Goodman (1983). Fact, Fiction, and Forecast. Harvard University Press.
    In his new foreword to this edition, Hilary Putnam forcefully rejects these nativist claims.
  14. Erwin Engeler (ed.) (1995). The Combinatory Programme. Birkhäuser.
  15. 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. (...)
  16. Francesco Berto (2009). There's Something About Gödel: The Complete Guide to the Incompleteness Theorem. Wiley-Blackwell.
    The Gödelian symphony -- Foundations and paradoxes -- This sentence is false -- The liar and Gödel -- Language and metalanguage -- The axiomatic method or how to get the non-obvious out of the obvious -- Peano's axioms -- And the unsatisfied logicists, Frege and Russell -- Bits of set theory -- The abstraction principle -- Bytes of set theory -- Properties, relations, functions, that is, sets again -- Calculating, computing, enumerating, that is, the notion of algorithm -- Taking numbers (...)
  17. D. S. Bridges (1987). Varieties of Constructive Mathematics. Cambridge University Press.
    This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.
  18. Frederic B. Fitch (1974). Elements of Combinatory Logic. New Haven,Yale University Press.
  19. T. K. Seung (1982). Structuralism and Hermeneutics. Columbia University Press.
  20. Paul C. Rosenbloom (1950/2005). The Elements of Mathematical Logic. 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 (...)
  21. 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.
  22. A. S. Troelstra (1977). Choice Sequences: A Chapter of Intuitionistic Mathematics. Clarendon Press.
  23. Stewart Shapiro (ed.) (1985). Intentional Mathematics. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
    Among the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics. - The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise classical contexts and represents the formalization of important intensional aspects of mathematical practice. - The direct formalization of intensional concepts (such as computability) in a mixed constructive/classical context.
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  24. Ludwig Wittgenstein (1978). Remarks on the Foundations of Mathematics. B. Blackwell.
  25. Raymond M. Smullyan (1987/1988). Forever Undecided: A Puzzle Guide to Gödel. Oxford University Press.
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  26. J. W. Davis (1969). Philosophical Logic. Dordrecht, D. Reidel.
  27. 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.
  28. 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 (...)
  29. Lyn D. English (ed.) (1997). Mathematical Reasoning: Analogies, Metaphors, and Images. L. Erlbaum Associates.
    Presents the latest research on how reasoning with analogies, metaphors, metonymies, and images can facilitate mathematical understanding. For math education, educational psychology, and cognitive science scholars.
  30. Jaakko Hintikka (1996). The Principles of Mathematics Revisited. 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 (...)
  31. 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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  32. 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.
  33. Hilary Putnam (ed.) (1979). Philosophical Papers, Volume 1: 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 (...)
  34. Alexander George (ed.) (1994). Mathematics and Mind. 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 (...)
  35. David S. G. Stirling (2009). Mathematical Analysis and Proof. Horwood Pub..
    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 (...)
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  36. 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.
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  37. Roland Omnès (2004). Converging Realities: Toward a Common Philosophy of Physics and Mathematics. 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.
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  38. Thomas Tymoczko (ed.) (1998). New Directions in the Philosophy of Mathematics: An Anthology. Princeton University Press.
    This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.
  39. Dale Gottlieb (1980). Ontological Economy: Substitutional Quantification and Mathematics. Oxford University Press.
  40. Charles S. Chihara (1973). Ontology and the Vicious-Circle Principle. Ithaca [N.Y.]Cornell University Press.
  41. 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 ...
  42. W. D. Hart (ed.) (1996). The Philosophy of Mathematics. 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, (...)
  43. Hao Wang (1990). Reflections on Kurt Gödel. A Bradford Book.
    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. 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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  45. Edward Nelson (1986). Predicative Arithmetic. Princeton University Press.
  46. Bob Hale (ed.) (2001). The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. Oxford University 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 (...)
  47. C. Foster (1990). Algorithms, Abstraction and Implementation. Academic Press.
  48. Alonzo Church (1956). Introduction to Mathematical Logic. Princeton, Princeton University Press.
    This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.
  49. Elliott Mendelson (1964). Introduction to Mathematical Logic. Princeton, N.J.,Van Nostrand.
    The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in ...
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  50. Philip J. Davis (1995). The Companion Guide to the Mathematical Experience, Study Edition. Birkhäuser.
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