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  1. Erwin Engeler (ed.) (1995). The Combinatory Programme. Birkhäuser.
  2. 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.
  3. 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.
  4. Austin Marsden Farrer (1979). Finite and Infinite: A Philosophical Essay. Seabury Press.
  5. Dennis Sentilles (1975). A Bridge to Advanced Mathematics. Baltimore,Williams & Wilkins.
  6. 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.
  7. 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 ...
  8. John Pottage (1983). Geometrical Investigations: Illustrating the Art of Discovery in the Mathematical Field. Addison-Wesley.
  9. 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, (...)
  10. 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 (...)
  11. Ian Stewart & David Tall (1977). The Foundations of Mathematics. 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.
  12. Charles Castonguay (1972). Meaning and Existence in Mathematics. New York,Springer-Verlag.
  13. J. W. Davis (1969). Philosophical Logic. Dordrecht, D. Reidel.
  14. 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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  15. C. Foster (1990). Algorithms, Abstraction and Implementation. Academic Press.
  16. 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 (...)
  17. 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.
  18. 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.
  19. 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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  20. 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.
  21. Ludwig Wittgenstein (1978). Remarks on the Foundations of Mathematics. B. Blackwell.
  22. J. Sicha (1974). A Metaphysics of Elementary Mathematics. Amherst, University of Massachusetts Press.
  23. Charles S. Chihara (1973). Ontology and the Vicious-Circle Principle. Ithaca [N.Y.]Cornell University Press.
  24. 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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  25. 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.
  26. 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 (...)
  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. 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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  29. 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. (...)
  30. 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 (...)
  31. Philip J. Davis (1995). The Companion Guide to the Mathematical Experience, Study Edition. Birkhäuser.
  32. 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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  33. 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 ...
  34. Mark Steiner (1975). Mathematical Knowledge. Cornell University Press.
  35. Costas Dimitracopoulos (ed.) (2008). Logic Colloquium 2005: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Athens, Greece, July 28-August 3, 2005. [REVIEW] Cambridge University Press.
    The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of recent developments. Highlights of this volume from the 2005 meeting include three papers on different aspects of connections between model theory and algebra; a survey of recent major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's (...)
  36. 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 (...)
  37. 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 (...)
  38. Penelope Maddy (2007). Second Philosophy: A Naturalistic Method. Oxford University Press.
    Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In Second Philosophy, Penelope Maddy describes and practices a particularly austere form of naturalism called "Second Philosophy". Without a definitive criterion for what counts as "science" and what doesn't, Second Philosophy can't be specified directly ("trust only the methods of science" for example), so Maddy proceeds instead by illustrating the behaviors of an idealized inquirer she calls the "Second Philosopher". (...)
  39. 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 (...)
  40. 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.
  41. 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.
  42. 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. (...)
  43. Philippe Smets (ed.) (1988). Non-Standard Logics for Automated Reasoning. Academic Press.
  44. Edward Nelson (1986). Predicative Arithmetic. Princeton University Press.
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  45. 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 (...)
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  46. 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, (...)
  47. 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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  48. Clare Boucher (2000). The Six Blind Men and the Elephant: A Traditional Indian Story. Candlewick Press.
  49. 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 (...)
  50. Fred Richman (ed.) (1981). Constructive Mathematics: Proceedings of the New Mexico State University Conference Held at Las Cruces, New Mexico, August 11-15, 1980. [REVIEW] Springer-Verlag.
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