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  1. 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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  2. 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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  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. 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 ...
  5. 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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  6. Frederic B. Fitch (1974). Elements of Combinatory Logic. New Haven,Yale University Press.
  7. Charles Castonguay (1972). Meaning and Existence in Mathematics. New York,Springer-Verlag.
  8. Erwin Engeler (ed.) (1995). The Combinatory Programme. Birkhäuser.
  9. Austin Marsden Farrer (1979). Finite and Infinite: A Philosophical Essay. Seabury Press.
  10. 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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  11. 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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  12. Alfred North Whitehead & Bertrand Russell (1962). 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. Roman Murawski (ed.) (2010). Essays in the Philosophy and History of Logic and Mathematics. Rodopi.
    The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the (...)
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  14. John Pottage (1983). Geometrical Investigations: Illustrating the Art of Discovery in the Mathematical Field. Addison-Wesley.
  15. 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 (...)
  16. Jody Azzouni (2005). 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, (...)
  17. T. K. Seung (1982). Structuralism and Hermeneutics. Columbia University Press.
  18. Dale Gottlieb (1980). Ontological Economy: Substitutional Quantification and Mathematics. Oxford University Press.
  19. 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.
  20. 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 ...
  21. Mark Steiner (1975). Mathematical Knowledge. Cornell University Press.
  22. 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. (...)
  23. Penelope Maddy (1997). Naturalism in Mathematics. Oxford University Press.
    Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
  24. 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 (...)
  25. Robert J. Baum (1973). Philosophy and Mathematics, From Plato to the Present. San Francisco,Freeman, Cooper.
  26. Mike Prest (2009). Purity, Spectra and Localisation. Cambridge University Press.
    The central aim of this book is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories.
  27. J. Sicha (1974). A Metaphysics of Elementary Mathematics. Amherst, University of Massachusetts Press.
  28. 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, (...)
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  29. Douglas Cannon (2002). Deductive Logic in Natural Language. 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.
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  30. Imre Lakatos (ed.) (1976). Proofs and Refutations: The Logic of Mathematical Discovery. 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 (...)
  31. Gila Sher & Richard L. Tieszen (eds.) (2000). Between Logic and Intuition: Essays in Honor of Charles Parsons. 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.
  32. 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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  33. Evert Willem Beth (1965). Mathematical Thought. Dordrecht, Holland, D. Reidel Pub. Co..
    Another striking deviation with regard to philosophical tradition consists in the fact that contemporary schools in the philosophy of mathematics, with the exception again of Brouwer's intuitionism, hardly ever refer to mathematical thought.
  34. 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.
  35. 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.
  36. J. W. Davis (1969). Philosophical Logic. Dordrecht, D. Reidel.
  37. Raymond M. Smullyan (1987). Forever Undecided: A Puzzle Guide to Gödel. Oxford University Press.
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  38. 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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  39. 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 ...
  40. Chin-Liang Chang (1973). Symbolic Logic and Mechanical Theorem Proving. 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.
  41. Philip J. Davis (1995). The Companion Guide to the Mathematical Experience, Study Edition. Birkhäuser.
  42. 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 (...)
  43. Charles Chihara (2003). A Structural Account of Mathematics. Clarendon Press.
    A Structural Account of Mathematics will be required reading for anyone working in this field.
  44. Friederike Moltmann (2013). Abstract Objects and the Semantics of Natural Language. Oxford University Press.
    This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, numbers, propositions, and degrees (...)
  45. 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.
  46. Dominic J. O'Meara (1989). Pythagoras Revived: Mathematics and Philosophy in Late Antiquity. Oxford University Press.
    The Pythagorean idea that numbers are the key to understanding reality inspired philosophers in late Antiquity (4th and 5th centuries A.D.) to develop theories in physics and metaphysics based on mathematical models. This book draws on some newly discovered evidence, including fragments of Iamblichus's On Pythagoreanism, to examine these early theories and trace their influence on later Neoplatonists (particularly Proclus and Syrianus) and on medieval and early modern philosophy.
  47. Moshe Machover (1996). Set Theory, Logic and Their Limitations. Cambridge University Press.
    This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations.
  48. Eli Maor (1987). 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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  49. 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.
  50. Jaakko Hintikka (ed.) (1969). The Philosophy of Mathematics. London, Oxford U.P..
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