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  1. Evandro Agazzi (1974). The Rise of the Foundational Research in Mathematics. Synthese 27 (1-2):7 - 26.
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  2. Evandro Agazzi & György Darvas (eds.) (1997). Philosophy of Mathematics Today. Kluwer.
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  3. Murad D. Akhundov (2005). Social Influence on Physics and Mathematics: Local or Attributive? [REVIEW] Journal for General Philosophy of Science 36 (1):135 - 149.
    The article is devoted to the nature of science. To what extent are science and mathematics affected by the society in which they are developed? Philosophy of science has accepted the social influence on science, but limits it only to the context of discovery (a "locational" approach). An opposite "attributive" approach states that any part of science may be so influenced. L. Graham is sure that even the mathematical equations at the core of fundamental physical theories may display social attributes. (...)
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  4. Jamin Asay (2012). Review of Truth, Reference and Realism. [REVIEW] International Studies in the Philosophy of Science 26 (3):345-348.
    International Studies in the Philosophy of Science, Volume 26, Issue 3, Page 345-348, September 2012.
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  5. Ignacio Ayestaran Uriz (1995). Il International Simposium Galdeano (ZARAGOZA'94): Paradigms and Mathematics, Zaragoza, septiembre de 1994. Theoria 10 (1):233-237.
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  6. Fahiem Bacchus & Toby Walsh (eds.) (2005). Theory and Applications of Satisfiability Testing: 8th International Conference, Sat 2005, St Andrews, Uk, June 19-23, 2005: Proceedings. [REVIEW] Springer.
    This book constitutes the refereed proceedings of the 8th International Conference on Theory and Applications of Satisfiability Testing, SAT 2005, held in St Andrews, Scotland in June 2005. The 26 revised full papers presented together with 16 revised short papers presented as posters during the technical programme were carefully selected from 73 submissions. The whole spectrum of research in propositional and quantified Boolean formula satisfiability testing is covered including proof systems, search techniques, probabilistic analysis of algorithms and their properties, problem (...)
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  7. Alan Baker, Non-Deductive Methods in Mathematics. Stanford Encyclopedia of Philosophy.
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  8. Alan Baker (2008). Experimental Mathematics. Erkenntnis 68 (3):331 - 344.
    The rise of the field of “<span class='Hi'>experimental</span> mathematics” poses an apparent challenge to traditional philosophical accounts of mathematics as an a priori, non-empirical endeavor. This paper surveys different attempts to characterize <span class='Hi'>experimental</span> mathematics. One suggestion is that <span class='Hi'>experimental</span> mathematics makes essential use of electronic computers. A second suggestion is that <span class='Hi'>experimental</span> mathematics involves support being gathered for an hypothesis which is inductive rather than deductive. Each of these options turns out to be inadequate, and instead a (...)
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  9. Mark Balaguer (1999). Critical Studies / Book Reviews. Philosophia Mathematica 7 (1):108-126.
  10. Edward G. Ballard (1961). Kant and Whitehead, and the Philosophy of Mathematics. Tulane Studies in Philosophy 10:3-29.
  11. A. G. Barabashev (1997). In Support of Significant Modernization of Original Mathematical Texts (in Defense of Presentism). Philosophia Mathematica 5 (1):21-41.
    At their extremes, the modernization of ancient mathematical texts (absolute presentism) leaves nothing of the source and the refusal to modernize (absolute antiquarism) changes nothing. The extremes exist only as tendencies. This paper attempts to justify the admissibility of broad modernization of mathematical sources (presentism) in the context of a socio-cultural (non-fundamentalist) philosophy of mathematics.
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  12. Jon Barwise (1999). Critical Studies / Book Reviews. Philosophia Mathematica 7 (2):238-240.
  13. O. Bradley Bassler (1997). Review of J. Hintikka, The Principles of Mathematics Revisited. [REVIEW] Review of Metaphysics 51 (2):424-425.
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  14. Robert J. Baum (1972). The Instrumentalist and Formalist Elements of Berkeley's Philosophy of Mathematics. Studies in History and Philosophy of Science Part A 3 (2):119-134.
    The main thesis of this paper is that, Contrary to general belief, George berkeley did in fact express a coherent philosophy of mathematics in his major published works. He treated arithmetic and geometry separately and differently, And this paper focuses on his philosophy of arithmetic, Which is shown to be strikingly similar to the 19th and 20th century philosophies of mathematics known as 'formalism' and 'instrumentalism'. A major portion of the paper is devoted to showing how this philosophy of mathematics (...)
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  15. André Bazzoni (forthcoming). Hintikka on the Foundations of Mathematics: IF Logic and Uniformity Concepts. Journal of Philosophical Logic:1-10.
    The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic (IFL) is the real logic of mathematics is supported in that article by an argument relying on uniformity concepts taken from real analysis. I show that the central point of his argument is a simple logical mistake. Second and more generally, I conclude, based on the previous remarks and on another standard (...)
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  16. J. L. Bell (1995). Review of B. Rotman, Ad Infinitum - The Ghost In Turing's Machine: Taking God Out of Mathematics and Putting the Body Back In: An Essay in Corporeal Semiotics. [REVIEW] Philosophia Mathematica 3 (2):218-221.
  17. John Bell, Contribution to “Philosophy of Mathematics: 5 Questions”.
    V. Hendricks and H. Leitgeb, eds., Automatic Press, 2007.
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  18. Jose Benardete (1985). Review of C. Parsons, Mathematics and Philosophy: Selected Essays. [REVIEW] Review of Metaphysics 38 (3):674-676.
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  19. Jean Paul Van Bendegem (2000). Alternative Mathematics: The Vague Way. Synthese 125 (1/2):19 - 31.
    Is alternative mathematics possible? More specifically, is it possible to imagine that mathematics could have developed in any other than the actual direction? The answer defended in this paper is yes, and the proof consists of a direct demonstration. An alternative mathematics that uses vague concepts and predicates is outlined, leading up to theorems such as "Small numbers have few prime factors".
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  20. Jean-Yves Béziau (ed.) (2005). Logica Universalis: Towards a General Theory of Logic. Birkhäuser.
    Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the last (...)
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  21. Erwin Biser (1957). Book Review:The Philosophy of Mathematics Edward A. Maziarz. [REVIEW] Philosophy of Science 24 (4):357-.
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  22. Virginia Black, Stephen L. Darwall & L. Baronovitch (1981). Book Reviews and Critical Studies. [REVIEW] Philosophia 9 (3-4):339-373.
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  23. Patricia Blanchette (2003). Review of A. George and D. J. Velleman, Philosophies of Mathematics. Philosophia Mathematica 11 (3):358-362.
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  24. Susanne Bobzien (2011). The Combinatorics of Stoic Conjunction. Oxford Studies in Ancient Philosophy 40 (1):157-188.
    ABSTRACT: The 3rd BCE Stoic logician "Chrysippus says that the number of conjunctions constructible from ten propositions exceeds one million. Hipparchus refuted this, demonstrating that the affirmative encompasses 103,049 conjunctions and the negative 310,952." After laying dormant for over 2000 years, the numbers in this Plutarch passage were recently identified as the 10th (and a derivative of the 11th) Schröder number, and F. Acerbi showed how the 2nd BCE astronomer Hipparchus could have calculated them. What remained unexplained is why Hipparchus’ (...)
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  25. Boccuni (2011). On the Consistency of a Plural Theory of Frege’s Grundgesetze. Studia Logica 97 (3):329-345.
    PG (Plural Grundgesetze) is a predicative monadic second-order system which is aimed to derive second-order Peano arithmetic. It exploits the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. In this paper, a model-theoretical consistency proof for the system PG is provided.
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  26. David Boersema (2002). Philosophy of Mathematics. Teaching Philosophy 25 (3):261-265.
  27. Ljiljana Brankovic, Yuqing Lin & Bill Smyth (eds.) (2008). Proceedings of the International Workshop on Combinatorial Algorithms, 2007. College Publications.
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  28. Manuel Bremer, Frege's Basic Law V and Cantor's Theorem.
    The following essay reconsiders the ontological and logical issues around Frege’s Basic Law (V). If focuses less on Russell’s Paradox, as most treatments of Frege’s Grundgesetze der Arithmetik (GGA)1 do, but rather on the relation between Frege’s Basic Law (V) and Cantor’s Theorem (CT). So for the most part the inconsistency of Naïve Comprehension (in the context of standard Second Order Logic) will not concern us, but rather the ontological issues central to the conflict between (BLV) and (CT). These ontological (...)
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  29. J. Richard Buchi (1957). Review of K. Menger, The Basic Concepts of Mathematics. [REVIEW] Philosophy of Science 24 (4):366-.
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  30. Otavio Bueno, Second-Order Logic Revisited.
    In this paper, I shall provide a defence of second-order logic in the context of its use in the philosophy of mathematics. This shall be done by considering three problems that have been recently posed against this logic: (1) According to Resnik [1988], by adopting second-order quantifiers, we become ontologically committed to classes. (2) As opposed to what is claimed by defenders of second-order logic (such as Shapiro [1985]), the existence of non-standard models of first-order theories does not establish the (...)
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  31. Bernd Buldt, Gödel, Kurt.
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  32. John P. Burgess (2000). Critical Studies / Book Reviews. Philosophia Mathematica 8 (1):84-91.
  33. Piotr Błaszczyk, Mikhail G. Katz & David Sherry (2013). Ten Misconceptions From the History of Analysis and Their Debunking. Foundations of Science 18 (1):43-74.
    The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...)
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  34. F. K. C. (1974). Meaning and Existence in Mathematics. Review of Metaphysics 27 (4):790-791.
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  35. J. D. C. (1971). Philosophie der Arithmetik. Review of Metaphysics 25 (1):127-128.
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  36. L. C. (1967). Mathematics and Logic in History and in Contemporary Thought. Review of Metaphysics 21 (1):154-154.
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  37. Florian Cajori (1915). Oughtred's Ideas and Influence on the Teaching of Mathematics. The Monist 25 (4):495-530.
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  38. Paola Cantù, Bolzano Versus Kant: Mathematics as a Scientia Universalis. Philosophical Papers Dedicated to Kevin Mulligan.
    The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence of the overcome of Kant's (...)
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  39. Leonard S. Carrier (1981). Book Reviews and Critical Studies. [REVIEW] Philosophia 9 (3-4):379-389.
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  40. E. Carson (1998). Review of J. Belna, La Notion de Nombre Chez Dedekind, Cantor, Frege. Theories, Conceptions, Et Philosophie. [REVIEW] Philosophia Mathematica 6 (3):345-350.
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  41. Gregory J. Chaitin (2011). Gödel's Way: Exploits Into an Undecidable World. Crc Press.
    This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no ...
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  42. Gilles Châtelet (2006). Interlacing the Singularity, the Diagram and the Metaphor. Translated by Simon B. Duffy. In Simon B. Duffy (ed.), Virtual Mathematics: the logic of difference. Clinamen.
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  43. Daniele Chiffi (2012). Kurt Gödel: Philosophical Explorations: History and Theory. Aracne.
  44. Nino Cocchiarella (1982). Introduction to the Philosophy of Mathematics. [REVIEW] Teaching Philosophy 5 (1):69-72.
  45. Hermann Cohen (2013). The Platonic Doctrine of Ideas and Mathematics. Rivista di Storia Della Filosofia 68:81-101.
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  46. Mark Colyvan (2012). An Introduction to the Philosophy of Mathematics. Cambridge University Press.
    Machine generated contents note: 1. Mathematics and its philosophy; 2. The limits of mathematics; 3. Plato's heaven; 4. Fiction, metaphor, and partial truths; 5. Mathematical explanation; 6. The applicability of mathematics; 7. Who's afraid of inconsistent mathematics?; 8. A rose by any other name; 9. Epilogue: desert island theorems.
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  47. Roy Cook & Stewart Shpiro (1998). Hintikka's Revolution: Review of J. Hintikka, The Principles of Mathematics Revisited. [REVIEW] British Journal for the Philosophy of Science 49 (2):309 - 316.
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  48. John Corcoran (1991). REVIEW OF Alfred Tarski, Collected Papers, Vols. 1-4 (1986) Edited by Steven Givant and Ralph McKenzie. [REVIEW] MATHEMATICAL REVIEWS 91 (h):01101-4.
    Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but most of the Aristotelian corpus is not about logic, whereas (...)
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  49. D. Corfield (1998). Hintikka, J.-The Principles of Mathematics Revisited. Philosophical Books 39:150-155.
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  50. Gabriella Crocco & Eva-Maria Engelen (forthcoming). Kurt Gödel's Philosophical Remarks (Max Phil). In Gabriella Crocco & Eva-Maria Engelen (eds.), Kurt Gödel: Philosopher-Scientist. Presses Universitaires de Provence.
    Kurt Gödel left Philosophical Remarks in his Nachlass that he himself entitled Max Phil (Maximen Philosophie). The opus originally comprised 16 notebooks but one has been lost. The content is on the whole the outline of a rational metaphysics able to relate the different domains of knowledge and of moral investigations to each other. The notebooks were at first started as an intellectual diary in which Gödel writes an account of what he does and especially about what he should do (...)
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