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Philosophy of Mathematics

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  1. Oscar João Abdounur, Vecchio Junior & Jacintho Del (2013). Sobre os números transfinitos. Scientiae Studia 11 (2):417-426.
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    Epistemology of Mathematics
     Apriority in Mathematics
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    Set Theory
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    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
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  2. Amir Alexander (1995). The Imperialist Space of Elizabethan Mathematics. Studies in History and Philosophy of Science Part A 26 (4):559-591.
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    Epistemology of Mathematics
     Apriority in Mathematics
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     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
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    Ontology of Mathematics
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     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Truth
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     Axiomatic Truth
     Objectivity Of Mathematics
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    Set Theory
     The Nature of Sets
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  3. Irving H. Anellis (1987). The Conference on the History of Mathematics University of Wisconsin-Lacrosse, April 1, 1986. Philosophia Mathematica 2 (1):123-125.
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    Epistemology of Mathematics
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     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
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    Ontology of Mathematics
     Mathematical Fictionalism
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     Indispensability Arguments in Mathematics
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    Mathematical Truth
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    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
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  4. J. R. Brown (2003). Vladimir Tasic. Mathematics and the Roots of Postmodern Thought. Philosophia Mathematica 11 (2):244-245.
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    Epistemology of Mathematics
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     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
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    Ontology of Mathematics
     Mathematical Fictionalism
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     Objectivity Of Mathematics
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    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
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  5. J. R. Brown (1994). John D. Barrow, Pi in the Sky: Counting, Thinking, and Being. Philosophia Mathematica 2:251-251.
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    Epistemology of Mathematics
     Apriority in Mathematics
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     Mathematical Intuition
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     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
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     Indispensability Arguments in Mathematics
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    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
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     Areas of Mathematics, Misc
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     Predicativism in Mathematics
     Mathematical Naturalism
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    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
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  6. J. P. Burgess & P. Ernest (1997). Philip J. Davis, Reuben Hersh, and Elena Anne Marchisotto. The Mathematical Experience Study Guide and The Companion Guide to the Mathematical Experience Study Edition. [REVIEW] Philosophia Mathematica 5:175-188.
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    Epistemology of Mathematics
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     Mathematical Intuition
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     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
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    Ontology of Mathematics
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     Mathematical Naturalism
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    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
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  7. E. Carson (1998). Maoist Mathematics? Philosophia Mathematica 6 (3):345-350.
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    Epistemology of Mathematics
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     Visualization in Mathematics
     Phenomenology of Mathematics
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    Ontology of Mathematics
     Mathematical Fictionalism
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     Objectivity Of Mathematics
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    Set Theory
     The Nature of Sets
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    Areas of Mathematics
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     Areas of Mathematics, Misc
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     Mathematical Naturalism
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    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
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  8. Emily Carson (2006). Frank Pierobon. Kant Et les Mathématiques: La Conception Kantienne des Mathématiques [Kant and Mathematics: The Kantian Conception of Mathematics]. Bibliothèque d'Histoire de la Philosophie. Paris: J. Vrin. ISBN 2-7116-1645-2. Pp. 240. [REVIEW] Philosophia Mathematica 14 (3):370-378.
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    Epistemology of Mathematics
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     Visualization in Mathematics
     Phenomenology of Mathematics
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    Ontology of Mathematics
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    Mathematical Truth
     Analyticity in Mathematics
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     Objectivity Of Mathematics
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    Set Theory
     The Nature of Sets
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    Areas of Mathematics
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    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
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  9. Jessica Carter (forthcoming). Mathematics Dealing with 'Hypothetical States of Things'. Philosophia Mathematica:nkt040.
    This paper takes as a starting point certain notions from Peirce's writings and uses them to propose a picture of the part of mathematical practice that consists of hypothesis formation. In particular, three processes of hypothesis formation are considered: abstraction, generalisation, and an abductive-like inference. In addition Peirce's pragmatic conception of truth and existence in terms of higher-order concepts are used in order to obtain a kind of pragmatic realist picture of mathematics.
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    Epistemology of Mathematics
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     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
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     Nondeductive Methods in Mathematics
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    Ontology of Mathematics
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     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
     Numbers
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    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
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     Set Theory as a Foundation
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    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
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  10. C. Cellucci (2004). L. Gaeta. Segni Del Cosmo. Logica E Geometria in Whitehead [Signs of the Cosmos. Logic and Geometry in Whitehead]. Philosophia Mathematica 12 (3):289-290.
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    Epistemology of Mathematics
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  11. Stefania Centrone (2014). Mirja Hartimo Ed. Phenomenology and Mathematics. Phaenomenologia; 195. Dordrecht: Springer, 2010. ISBN 978-90-481-3728-2 (Hbk); 978-90-481-3728-2 (E-Book); 978-94-007-3196-7 (Pbk). Pp. Xxv + 222. [REVIEW] Philosophia Mathematica 22 (1):126-129.
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  12. Darcy Cutler (1997). Stewart Shapiro. Foundations Without Foundationalism: A Case for Second-Order Logic. Philosophia Mathematica 5:71-91.
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  13. M. Davis (1998). Review of Dawson [1997]. [REVIEW] Philosophia Mathematica 3 (6).
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  14. W. Dean (2013). Models and Computability. Philosophia Mathematica:nkt035.
    Computationalism holds that our grasp of notions like ‘computable function’ can be used to account for our putative ability to refer to the standard model of arithmetic. Tennenbaum's Theorem has been repeatedly invoked in service of this claim. I will argue that not only do the relevant class of arguments fail, but that the result itself is most naturally understood as having the opposite of a reference-fixing effect — i.e., rather than securing the determinacy of number-theoretic reference, Tennenbaum's Theorem points (...)
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  15. M. Detlefsen (1995). Janet Folina, Poincare and the Philosophy of Mathematics. Philosophia Mathematica 3:208-208.
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  16. Hartry Field (1994). Are Our Logical and Mathematical Concepts Highly Indeterminate? Midwest Studies in Philosophy 19 (1):391-429.
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  17. J. Folina (2003). Mark Greaves. The Philosophical Status of Diagrams. Philosophia Mathematica 11 (3):349-353.
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  18. Joachim Frans & Erik Weber (forthcoming). Mechanistic Explanation and Explanatory Proofs in Mathematics. Philosophia Mathematica:nku003.
    Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics, arguing that using it does not presuppose a Platonist (...)
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  19. Greg Frost-Arnold (2013). Carnap, Tarski, and Quine at Harvard: Conversations on Logic, Mathematics, and Science. Open Court Press.
    During the academic year 1940-1941, several giants of analytic philosophy congregated at Harvard, holding regular private meetings, with Carnap, Tarski, and Quine. Carnap, Tarski, and Quine at Harvard allows the reader to act as a fly on the wall for their conversations. Carnap took detailed notes during his year at Harvard. This book includes both a German transcription of these shorthand notes and an English translation in the appendix section. Carnap’s notes cover a wide range of topics, but surprisingly, the (...)
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  20. Mihai Ganea (forthcoming). Finitistic Arithmetic and Classical Logic. Philosophia Mathematica:nkt042.
    It can be argued that only the equational theories of some sub-elementary function algebras are finitistic or intuitive according to a certain interpretation of Hilbert's conception of intuition. The purpose of this paper is to investigate the relation of those restricted forms of equational reasoning to classical quantifier logic in arithmetic. The conclusion reached is that Edward Nelson's ‘predicative arithmetic’ program, which makes essential use of classical quantifier logic, cannot be justified finitistically and thus requires a different philosophical foundation, possibly (...)
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  21. Intuitionism As Generalization (1990). Fred Richman New Mexico State University. Philosophia Mathematica 5 (124):128.
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  22. D. Gillies (2003). Carlo Cellucci.[Philosophy and Mathematics]. Philosophia Mathematica 11 (2):246-252.
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  23. E. Glas (2004). David Corfield. Towards a Philosophy of Real Mathematics. Philosophia Mathematica 12 (1):65-68.
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  24. N. Griffin (1995). Alejandro R. Garciadiego, Bertrand Russell and the Origins of the Set-theoretic'Paradoxes'. Philosophia Mathematica 3:304-304.
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  25. E. R. Grosholz (2004). Lorenzo Magnani. Philosophy and Geometry: Theoretical and Historical Issues. Philosophia Mathematica 12 (1):79-80.
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  26. Marie Grossi, Montgomery Link, Katalin Makkai & Charles Parsons (1998). A Bibliography of Hao Wang. Philosophia Mathematica 6 (1):25-38.
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  27. G. E. R. Haddock (2003). Anastasio aleman. Logica, matematicas Y realidad. Philosophia Mathematica 11 (1):108-119.
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  28. D. M. Hausman (2003). E. Roy Weintraub. How Economics Became a Mathematical Science. Philosophia Mathematica 11 (3):354-357.
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  29. A. D. Irvine (1995). Bertrand Russell, Philosophical Papers 1896-99. Philosophia Mathematica 3:301-301.
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  30. A. D. Irvine (1995). John Allen Paulos, Beyond Numeracy. Philosophia Mathematica 3:307-307.
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  31. A. D. Irvine (1995). Kurt Goedel, Collected Works. Volumes I and II. Philosophia Mathematica 3:299-299.
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  32. Andrew David Irvine (2014). Mark Colyvan. An Introduction to the Philosophy of Mathematics. Cambridge: Cambridge University Press, 2012. ISBN 978-0-521-82602-0 (Hbk); 978-0-521-53341-6 (Pbk). Pp. Ix + 188. [REVIEW] Philosophia Mathematica 22 (1):124-125.
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  33. J. Kim (2010). Yi on 2. Philosophia Mathematica 18 (3):329-336.
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  34. Ernst Kleinert (2012). Studien Zur Mathematik Und Philosophie. Leipziger Universitätsverlag.
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  35. Gregory Landini (2014). Gregory Landini. Zermelo and Russell's Paradox: Is There a Universal Set? Philosophia Mathematica 22 (1):142-142.
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  36. B. P. Larvor (2004). George Kampis, Ladislav Kvasz, and Michael Stoltzner, Eds. Appraising Lakatos: Mathematics, Methodology, and the Man. Philosophia Mathematica 12 (3):294-300.
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  37. André Lebel (forthcoming). Jean-Michel Salanskis. Philosophie des Mathématiques. Problèmes & Controverses. Paris: Vrin, 2008. ISBN 978-2-7116-1988-7. Pp. 304. [REVIEW] Philosophia Mathematica:nku001.
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  38. M. Lievers (2004). Tomasz Placek. Mathematical Intuitionism and Intersubjectivity. A Critical Exposition of Arguments for Intuitionism. Philosophia Mathematica 12 (2):176-186.
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  39. L. Luna & W. Taylor (forthcoming). Taming the Indefinitely Extensible Definable Universe. Philosophia Mathematica:nkt044.
    In previous work in 2010 we have dealt with the problems arising from Cantor's theorem and the Richard paradox in a definable universe. We proposed indefinite extensibility as a solution. Now we address another definability paradox, the Berry paradox, and explore how Hartogs's cardinality theorem would behave in an indefinitely extensible definable universe where all sets are countable.
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  40. Minxia Luo (2010). Fan Luo Ji Xue Yu Gou Li Lun. Ke Xue Chu Ban She.
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  41. Russell Marcus (forthcoming). How Not to Enhance the Indispensability Argument. Philosophia Mathematica:nku004.
    The new explanatory or enhanced indispensability argument alleges that our mathematical beliefs are justified by their indispensable appearances in scientific explanations. This argument differs from the standard indispensability argument which focuses on the uses of mathematics in scientific theories. I argue that the new argument depends for its plausibility on an equivocation between two senses of explanation. On one sense the new argument is an oblique restatement of the standard argument. On the other sense, it is vulnerable to an instrumentalist (...)
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  42. E. D. Mares (1996). I. Grattan-Guinness, Editor. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Philosophia Mathematica 4:198-201.
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  43. M. Marion (2004). Ludwig Wittgenstein and Friedrich Waismann. The Voices of Wittgenstein. The Vienna Circle. Philosophia Mathematica 12 (3):291-293.
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  44. J. -P. Marquis (1996). D. Vernant. La Philosophie Mathematique de Russell. Philosophia Mathematica 4:202-205.
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  45. V. McGee (2004). Kit Fine. The Limits of Abstraction. Philosophia Mathematica 12 (3):278-283.
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  46. Alex Miller (ed.) (2013). Logic, Language and Mathematics: Essays for Crispin Wright. Oxford University Press.
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  47. A. W. Moore (1995). Shaughan Lavine, Understanding the Infinite. Philosophia Mathematica 3:294-294.
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  48. M. Motterlini (2003). John Kadvany. Imre Lakatos and the Guises of Reason. Philosophia Mathematica 11 (1):120-127.
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  49. M. M. Muntersbjorn (2003). Meir Buzaglo. The Logic of Concept Expansion. Philosophia Mathematica 11 (3):341-348.
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  50. Gianluigi Oliveri (forthcoming). Book Review.'I Fondamenti della Matematica nel Logicismo di Bertrand Russell'. Stefano Donati. Firenze (Firenze Atheneum). 2003. ISBN: 88-7255-204-4. 988 pages.€ 39.00. [REVIEW] Philosophia Mathematica.
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