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  1. Dr Afsar Abbas, Mathematics as an Exact and Precise Language of Nature.
    One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is offered here. This will allow us to appreciate the manner in which mathematics acts as an exact and precise language of nature. This has significant implications for Artificial Intelligence.
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  2. Andrew Aberdein, Commentary On: Michel Dufour's "Argument and Explanation in Mathematics.
  3. Bahareh Afshari & Michael Rathjen (2010). A Note on the Theory of Positive Induction, {{Rm ID}^*_1}. Archive for Mathematical Logic 49 (2):275-281.
    The article shows a simple way of calibrating the strength of the theory of positive induction, ${{\rm ID}^{*}_{1}}$ . Crucially the proof exploits the equivalence of ${\Sigma^{1}_{1}}$ dependent choice and ω-model reflection for ${\Pi^{1}_{2}}$ formulae over ACA 0. Unbeknown to the authors, D. Probst had already determined the proof-theoretic strength of ${{\rm ID}^{*}_{1}}$ in Probst, J Symb Log, 71, 721–746, 2006.
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  4. Jon Agar (2003). Rockefeller and the Internationalization of Mathematics Between the Two World Wars: Documents and Studies for the Social History of Mathematics in the 20th Century. [REVIEW] British Journal for the History of Science 36 (1):87-127.
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  5. Evandro Agazzi (1997). The Relation of Mathematics to the Other Sciences. In Evandro Agazzi & György Darvas (eds.), Philosophy of Mathematics Today. Kluwer. 235--259.
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  6. M. S. Akperov (1992). Filosofskie Problemy Matematiki.
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  7. Albert Albertus & Fries (1981). Ausgewählte Texte Lateinisch-Deutsch.
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  8. Amir Alexander (2011). How to Read Historical Mathematics. [REVIEW] British Journal for the History of Science 44 (3):456-458.
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  9. Dennis Almeida & Paul Ernest (1996). Editorial: Teaching and the Nature of Mathematics. Philosophy of Mathematics Education Journal 9.
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  10. Alice Ambrose (1933). A Controversy in the Logic of Mathematics. Philosophical Review 42 (6):594-611.
  11. John Alfred Henry Anderson (1974). Mathematics, the Language Concepts. Stanley Thornes (Publishers) Ltd..
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  12. 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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  13. Irving H. Anellis (1993). Letters. Philosophia Mathematica 1 (1):71-73.
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  14. Irving H. Anellis (1987). Book-Review. Philosophia Mathematica (1):110-116.
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  15. 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.
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  16. Irving H. Anellis (1987). The Conference on the History of Mathematics. Philosophia Mathematica (1):123-125.
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  17. W. S. Anglin (1997). The Philosophy of Mathematics the Invisible Art. Monograph Collection (Matt - Pseudo).
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  18. 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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  19. W. S. Anglin (1991). Mathematics and Value. Philosophia Mathematica 6 (2):145-173.
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  20. Hippocrates George Apostle (1952). Aristotle's Philosophy of Mathematics. [Chicago]University of Chicago Press.
  21. K. Demis Apostolos (1995). Mathematics and Philosophy in Nicomachus Gerasenus. Neusis 2:117-141.
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  22. William Aspray & Philip Kitcher (1988). History and Philosophy of Modern Mathematics. Monograph Collection (Matt - Pseudo).
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  23. Peter Dean Asquith (1970). Alternative Mathematics and Their Status. Dissertation, Indiana University
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  24. David Auerbach (1992). How to Say Things with Formalisms. In Michael Detlefsen (ed.), Proof, logic, and formalization. Routledge. 77--93.
  25. David D. Auerbach (1985). Intensionality and the Gödel Theorems. Philosophical Studies 48 (3):337--51.
  26. 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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  27. Jeremy Avigad, Philosophy of Mathematics: 5 Questions.
    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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  28. 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.
  29. Jody Azzouni (1999). Comments on Shapiro. Journal of Philosophy 96 (10):541 - 544.
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  30. L. K. B. (1957). Physics and Metaphysics of Music and Essays on the Philosophy of Mathematics. Review of Metaphysics 11 (2):352-352.
  31. R. J. B. (1964). Philosophy of Mathematics. Review of Metaphysics 18 (2):390-390.
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  32. 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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  33. 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.
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  34. Mark Balaguer (2002). Review: Stewart Shapiro, Thinking About Mathematics. The Philosophy of Mathematics. [REVIEW] Bulletin of Symbolic Logic 8 (1):89-91.
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  35. Aristides Baltas (1995). Do Mathematics Constitute a Scientific Continent? Neusis 3:97-108.
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  36. A. Barabashev (1988). Empiricism as a Historical Phenomenon of Philosophy of Mathematics. Revue Internationale de Philosophie 42 (167):509-517.
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  37. A. G. Barabashev (1988). On the Impact of the World Outlook on Mathematical Creativity. Philosophia Mathematica (1):1-20.
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  38. A. G. Barabashev, S. S. Demidov & M. I. Panov (1987). Regularities and Modern Tendencies of the Development of Mathematics. Philosophia Mathematica (1):32-47.
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  39. Alexei G. Barabashev (1986). The Philosophy of Mathematics in U.S.S.R. Philosophia Mathematica (1-2):15-25.
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  40. Stephen Francis Barker (1964). Philosophy of Mathematics. Englewood Cliffs, N.J.,Prentice-Hall.
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  41. Emmanuel Barot (2009). Lautman. Les Belles Lettres.
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  42. Jeffrey A. Barrett (1995). Review of I. Ekeland, The Broken Dice, and Other Mathematical Tales of Chance. [REVIEW] Philosophia Mathematica 3 (3):310-313.
  43. John D. Barrow (2004). Mathematical Explanation. In John Cornwell (ed.), Explanations: Styles of Explanation in Science. Oxford University Press. 81--109.
  44. Marvin Barsky (1969). Two General Methods of Extending Mathematical Theory Creative Process in Mathematics. Philosophia Mathematica (1-2):22-27.
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  45. Jon Barwise (1999). Critical Studies / Book Reviews. Philosophia Mathematica 7 (2):238-240.
  46. Jon Barwise (ed.) (1977). Handbook of Mathematical Logic. North-Holland.
  47. O. Bradley Bassler (1997). The Principles of Mathematics Revisited. [REVIEW] Review of Metaphysics 51 (2):424-425.
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  48. Robert J. Baum (1973). Philosophy and Mathematics, From Plato to the Present. San Francisco,Freeman, Cooper.
  49. Edward Beach (2006). Hegel's Misunderstood Treatment of Gauss in the Science of Logic: Its Implications for His Philosophy of Mathematics. Idealistic Studies 36 (3):191-218.
    This essay explores Hegel’s treatment of Carl Friedrich Gauss’s mathematical discoveries as examples of “Analytic Cognition.” Unfortunately, Hegel’s main point has been virtually lost due to an editorial blunder tracing back almost a century, an error that has been perpetuated in many subsequent editions and translations.The paper accordingly has three sections. In the first, I expose the mistake and trace its pervasive influence in multiple languages and editions of the Wissenschaftder Logik. In the second section, I undertake to explain the (...)
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  50. JC Beall (2005). Review of Stewart Shapiro (Ed.), The Oxford Handbook of Philosophy of Mathematics and Logic. [REVIEW] Notre Dame Philosophical Reviews 2005 (9).
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