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  1. P. D. M. A. (1961). The Philosophy of Mathematics: An Introductory Essay. [REVIEW] Review of Metaphysics 14 (4):724-724.
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  2. D. J. Allan (1955). Aristotle's Philosophy of Mathematics. By H. G. Apostle (Cambridge University Press, for the University of Chicago Press. 1953. 45s.). [REVIEW] Philosophy 30 (114):270-.
  3. Alice Ambrose (1957). Wittgenstein's Remarks on the Foundations of Mathematics. [REVIEW] Philosophy and Phenomenological Research 18:262.
  4. Alice Ambrose (1933). A Controversy in the Logic of Mathematics. Philosophical Review 42 (6):594-611.
  5. John Alfred Henry Anderson (1974). Mathematics, the Language Concepts. Stanley Thornes (Publishers).
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  6. Edvard Pavlovich Andreev, Institut Sotsiologicheskikh Issledovanii Sssr) & Sovetskaia Sotsiologicheskaia Assotsiatsiia (1977). Metody Sovremennoi Matematiki I Logiki V Sotsiologicheskikh Issledovaniiakh [Sbornik Statei]. In-T Sotsiol. Issledovanii.
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  7. 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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  8. Irving H. Anellis (2010). Joong Fang (1923–2010). Philosophia Mathematica 18 (2):137-143.
    (No abstract is available for this citation).
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  9. Irving H. Anellis (1993). Letters. Philosophia Mathematica 1 (1):71-73.
  10. Irving H. Anellis (1987). Report on the Thirteenth Annual Meeting of the Canadian Society for History and Philosophy of Mathematics. Philosophia Mathematica (2):211-223.
  11. W. S. Anglin (1997). The Philosophy of Mathematics the Invisible Art.
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  12. 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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  13. W. S. Anglin (1991). Mathematics and Value. Philosophia Mathematica 6 (2):145-173.
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  14. Hippocrates George Apostle (1952). Aristotle's Philosophy of Mathematics. University of Chicago Press.
  15. K. Demis Apostolos (1995). Mathematics and Philosophy in Nicomachus Gerasenus. Neusis 2:117-141.
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  16. Andrew Arana (2008). Review of Ferreiros and Gray's The Architecture of Modern Mathematics. [REVIEW] Mathematical Intelligencer 30 (4).
    This collection of essays explores what makes modern mathematics ‘modern’, where ‘modern mathematics’ is understood as the mathematics done in the West from roughly 1800 to 1970. This is not the trivial matter of exploring what makes recent mathematics recent. The term ‘modern’ (or ‘modernism’) is used widely in the humanities to describe the era since about 1900, exemplified by Picasso or Kandinsky in the visual arts, Rilke or Pound in poetry, or Le Corbusier or Loos in architecture (a building (...)
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  17. Andrew Arana (2007). Review of D. Corfield's Toward A Philosophy Of Real Mathematics. [REVIEW] Mathematical Intelligencer 29 (2).
    When mathematicians think of the philosophy of mathematics, they probably think of endless debates about what numbers are and whether they exist. Since plenty of mathematical progress continues to be made without taking a stance on either of these questions, mathematicians feel confident they can work without much regard for philosophical reflections. In his sharp–toned, sprawling book, David Corfield acknowledges the irrelevance of much contemporary philosophy of mathematics to current mathematical practice, and proposes reforming the subject accordingly.
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  18. William Aspray & Philip Kitcher (1988). History and Philosophy of Modern Mathematics.
  19. Peter Dean Asquith (1970). Alternative Mathematics and Their Status. Dissertation, Indiana University
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  20. David Auerbach (1992). How to Say Things with Formalisms. In Michael Detlefsen (ed.), Proof, logic, and formalization. Routledge. pp. 77--93.
  21. David D. Auerbach (1985). Intensionality and the Gödel Theorems. Philosophical Studies 48 (3):337--51.
  22. Jeremy Avigad, Philosophy of Mathematics.
    The philosophy of mathematics plays an important role in analytic philosophy, both as a subject of inquiry in its own right, and as an important landmark in the broader philosophical landscape. Mathematical knowledge has long been regarded as a paradigm of human knowledge with truths that are both necessary and certain, so giving an account of mathematical knowledge is an important part of epistemology. Mathematical objects like numbers and sets are archetypical examples of abstracta, since we treat such objects in (...)
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  23. Jeremy Avigad (2007). Philosophy of Mathematics: 5 Questions. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
    In 1977, when I was nine years old, Doubleday released Asimov on Numbers, a collection of essays that had first appeared in Isaac Asimov’s Science Fiction and Fantasy column. My mother, recognizing my penchant for science fiction and mathematics, bought me a copy as soon as it hit the bookstores. The essays covered topics such as number systems, combinatorial curiosities, imaginary numbers, and π. I was especially taken, however, by an essay titled “Varieties of the infinite,” which included a photograph (...)
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  24. Steve Awodey & A. W. Carus (2010). Gödel and Carnap. In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.
  25. Jody Azzouni (1999). Comments on Shapiro. Journal of Philosophy 96 (10):541.
  26. R. J. B. (1964). Review of P. Benacerraf and H. Putnam (Eds.), Philosophy of Mathematics: Selected Readings. [REVIEW] Review of Metaphysics 18 (2):390-390.
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  27. Matthias Baaz (ed.) (2011). Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press.
    Machine generated contents note: Part I. Historical Context - Gödel's Contributions and Accomplishments: 1. The impact of Gödel's incompleteness theorems on mathematics Angus Macintyre; 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel; 3. The reception of Gödel's 1931 incompletabilty theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness; 4. 'Dozent Gödel will not lecture' Karl Sigmund; 5. Gödel's thesis: an appreciation Juliette C. Kennedy; 6. Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on (...)
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  28. Kazimierz Badziag (1967). B. Réponses de l'Enquête Sur l'Enseignement de Mathématique Et de Physique B. Replies on the Teaching of Mathematics and Physics Reply to the Questionnaire. Dialectica 21 (1‐4):157-158.
  29. Joan Bagaria (2013). On Turing’s Legacy in Mathematical Logic and the Foundations of Mathematics. Arbor 189 (764):a079.
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  30. Mark Balaguer (2002). Review: Stewart Shapiro, Thinking About Mathematics. The Philosophy of Mathematics. [REVIEW] Bulletin of Symbolic Logic 8 (1):89-91.
  31. Aristides Baltas (1995). Do Mathematics Constitute a Scientific Continent? Neusis 3:97-108.
  32. A. Barabashev (1988). Empiricism as a Historical Phenomenon of Philosophy of Mathematics. Revue Internationale de Philosophie 42 (167):509-517.
  33. A. G. Barabashev (1988). On the Impact of the World Outlook on Mathematical Creativity. Philosophia Mathematica (1):1-20.
  34. A. G. Barabashev, S. S. Demidov & M. I. Panov (1987). Regularities and Modern Tendencies of the Development of Mathematics. Philosophia Mathematica (1):32-47.
  35. Stephen Francis Barker (1964). Philosophy of Mathematics. Englewood Cliffs, N.J., Prentice-Hall.
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  36. Jeffrey A. Barrett (1995). Review of I. Ekeland, The Broken Dice, and Other Mathematical Tales of Chance. [REVIEW] Philosophia Mathematica 3 (3):310-313.
  37. Arnold Beckmann, Costas Dimitracopoulos & Benedikt Löwe (2010). Computability in Europe 2008. Archive for Mathematical Logic 49 (2):119-121.
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  38. John Bell, The Philosophy of Mathematics.
    THE CLOSE CONNECTION BETWEEN mathematics and philosophy has long been recognized by practitioners of both disciplines. The apparent timelessness of mathematical truth, the exactness and objective nature of its concepts, its applicability to the phenomena of the empirical world—explicating such facts presents philosophy with some of its subtlest problems. We shall discuss some of the attempts made by philosophers and mathematicians to explain the nature of mathematics. We begin with a brief presentation of the views of four major classical philosophers: (...)
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  39. John L. Bell (2006). Paul Rusnock. Bolzano's Philosophy and the Emergence of Modern Mathematics. Studien Zur Österreichischen Philosophie [Studies in Austrian Philosophy], Vol. 30. Amsterdam & Atlanta: Editions Rodopi, 2000. Isbn 90-420-1501-2. Pp. 218. [REVIEW] Philosophia Mathematica 14 (3):362-364.
    Bernard Bolzano , one of the leading figures of the Bohemian Enlightenment, made important contributions both to mathematics and philosophy which were virtually unknown in his lifetime and are still largely unacknowledged today. As a mathematician, he was a pioneer in the clarification and rigorization of mathematical analysis; as a philosopher, he may be considered a forerunner of the analytic movement later to emerge with Frege and Russell.Rusnock's account of Bolzano's work is laid out in five chapters and two appendices. (...)
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  40. John L. Bell (2005). Oppositions and Paradoxes in Mathematics and Philosophy. Axiomathes 15 (2):165-180.
    In this paper a number of oppositions which have haunted mathematics and philosophy are described and analyzed. These include the Continuous and the Discrete, the One and the Many, the Finite and the Infinite, the Whole and the Part, and the Constant and the Variable.
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  41. Paul Benacerraf & Hilary Putnam (eds.) (1984). 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, a challenge to 'classical' mathematics from a world-famous mathematician, a new foundational school, 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 with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection (...)
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  42. Paul Benacerraf & Hilary Putnam (1983). Philosophy of Mathematics Selected Readings /Edited by Paul Benacerraf, Hilary Putnam. --. --. Cambridge University Press, 1983.
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  43. Paul Benacerraf & Hilary Putnam (1964). Philosophy of Mathematics Selected Readings. Edited and with an Introd. By Paul Benacerraf and Hilary Putnam. Prentice-Hall.
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  44. Jan Berg (1994). The Ontological Foundations of Bolzano's Philosophy of Mathematics. In Dag Prawitz & Dag Westerståhl (eds.), Logic and Philosophy of Science in Uppsala. Kluwer Academic Publishers. pp. 265--271.
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  45. J. L. Berggren (1996). WS Anglin. Mathematics: A Concise History and Philosophy. Philosophia Mathematica 4 (2):196-197.
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  46. 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 (...)
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  47. 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.
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  48. Evert Willem Beth (1964). The Foundations of Mathematics a Study in the Philosophy of Science. Harper & Row.
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  49. Evert Willem Beth (1959). The Foundations of Mathematics. Amsterdam: North-Holland Pub. Co..
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  50. Abraham Adolf Universitah Ha- Ivrit Bi-Yerushalayim, Yehoshua Fraenkel & Bar-Hillel (1966). Essays on the Foundations of Mathematics Dedicated to A. A. Fraenkel on His Seventieth Anniversary. Magnes Press Hebrew University.
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1 — 50 / 307