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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
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
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     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of 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
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
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     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
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  3. Bruno Almeida (2012). On the Origins of Dee's Mathematical Programme: The John Dee–Pedro Nunes Connection. Studies in History and Philosophy of Science Part A 43 (3):460-469.
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
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     Set Theory
     Topology
     Areas of Mathematics, Misc
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     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
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  4. Shigeyuki Atarashi (forthcoming). Alison Walsh. Relations Between Logic and Mathematics in the Work of Benjamin and Charles S. Peirce. Boston: Docent Press, 2012. ISBN 978-098370046-3 (Pbk). Pp. X + 314. [REVIEW] Philosophia Mathematica:nku028.
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
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     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
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  5. L. K. B. (1957). Physics and Metaphysics of Music and Essays on the Philosophy of Mathematics. Review of Metaphysics 11 (2):352-352.
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
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  6. R. J. B. (1964). Philosophy of Mathematics. Review of Metaphysics 18 (2):390-390.
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     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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     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
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     Numbers
     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
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     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
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     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
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  7. R. J. B. (1964). Philosophy of Mathematics. Review of Metaphysics 18 (2):390-390.
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
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  8. O. Bradley Bassler (1997). The Principles of Mathematics Revisited. Review of Metaphysics 51 (2):424-425.
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    Epistemology of Mathematics
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     Mathematics and the Causal Theory of Knowledge
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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
     Mathematical Nominalism
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     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
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     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
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  9. Jose Benardete (1985). Mathematics and Philosophy. Review of Metaphysics 38 (3):674-676.
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    Epistemology of Mathematics
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     Visualization in Mathematics
     Phenomenology of Mathematics
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     Nondeductive Methods in Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
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     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
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     Mathematical Naturalism
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     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
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  10. Sandy Berkovski (2002). Surprising User-Friendliness. Logique Et Analyse 45 (179-180):283-297.
    Some theorists are bewildered by the effectiveness of mathematical concepts. For example, Steiner attempts to show that there can be no rational explanation of mathematical applicability in physics. Others (notably Penrose) are concerned primarily with the unexpected effectiveness within mathematics. Both views consist of two parts: a puzzle and a positive solution. I defend their paradoxical parts against the sceptics who do not believe that the very problem of effectiveness is a genuine one. Utilising Horwich’s theory of surprise, I argue (...)
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    Epistemology of 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
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    Ontology of Mathematics
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     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
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     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
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     Objectivity Of Mathematics
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    Set Theory
     The Nature of Sets
     Axioms of Set Theory
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     Set Theory as a Foundation
    Areas of Mathematics
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     Predicativism in Mathematics
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     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
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  11. Izabela Bondecka-Krzykowska & Roman Murawski (2008). Structuralism and Category Theory in the Contemporary Philosophy of Mathematics. Logique Et Analyse 51 (204):365.
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  12. Ross T. Brady (2012). The Consistency of Arithmetic, Based on a Logic of Meaning Containment. Logique Et Analyse 55 (219).
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  13. 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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  14. F. K. C. (1974). Meaning and Existence in Mathematics. Review of Metaphysics 27 (4):790-791.
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  15. J. D. C. (1971). Philosophie der Arithmetik. Review of Metaphysics 25 (1):127-128.
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  16. L. C. (1967). Mathematics and Logic in History and in Contemporary Thought. Review of Metaphysics 21 (1):154-154.
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  17. Carlo Cellucci (2007). La Filosofia della Matematica del Novecento. Laterza.
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  18. 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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  19. Roy T. Cook (2013). Appendix: How to Read Grundgesetze. In Gottlob Frege (ed.), Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & Ii. Oxford University Press.
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  20. M. Davis (1998). Review of Dawson [1997]. [REVIEW] Philosophia Mathematica 3 (6).
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  21. Igor Douven (2011). Similarity After Goodman. Review of Philosophy and Psychology 2 (1):61-75.
    In a famous critique, Goodman dismissed similarity as a slippery and both philosophically and scientifically useless notion. We revisit his critique in the light of important recent work on similarity in psychology and cognitive science. Specifically, we use Tversky’s influential set-theoretic account of similarity as well as Gärdenfors’s more recent resuscitation of the geometrical account to show that, while Goodman’s critique contained valuable insights, it does not warrant a dismissal of similarity.
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  22. Philip A. Ebert & Marcus Rossberg (2013). Translator's Introduction. In Gottlob Frege (ed.), Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & Ii. Oxford University Press.
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  23. Hartry Field (1994). Are Our Logical and Mathematical Concepts Highly Indeterminate? Midwest Studies in Philosophy 19 (1):391-429.
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  24. Thomas Forster (forthcoming). Mathematical Objects Arising From Equivalence Relations and Their Implementation in Quine's NF. Philosophia Mathematica:nku005.
    Many mathematical objects arise from equivalence classes and invite implementation as those classes. Set-existence principles that would enable this are incompatible with ZFC's unrestricted aussonderung but there are set theories (e.g., NF and Church's CUS) which admit more instances than does ZF. NF provides equivalence classes for stratified relations only. Church's construction provides equivalence classes for “low” sets, and thus, for example, a set of all (low) ordinals. However, that set has an ordinal in turn which is not a member (...)
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  25. Joachim Frans & Erik Weber (2014). Mechanistic Explanation and Explanatory Proofs in Mathematics. Philosophia Mathematica 22 (2):231-248.
    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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  26. Gottlob Frege (2013). Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & Ii. Oxford University Press.
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  27. 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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  28. Mihai Ganea (2014). Finitistic Arithmetic and Classical Logic. Philosophia Mathematica 22 (2):167-197.
    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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  29. Intuitionism As Generalization (1990). Fred Richman New Mexico State University. Philosophia Mathematica 5 (124):128.
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  30. 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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  31. E. R. Grosholz (2004). Lorenzo Magnani. Philosophy and Geometry: Theoretical and Historical Issues. Philosophia Mathematica 12 (1):79-80.
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  32. Marie Grossi, Montgomery Link, Katalin Makkai & Charles Parsons (1998). A Bibliography of Hao Wang. Philosophia Mathematica 6 (1):25-38.
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  33. G. E. R. Haddock (2003). Anastasio aleman. Logica, matematicas Y realidad. Philosophia Mathematica 11 (1):108-119.
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  34. D. M. Hausman (2003). E. Roy Weintraub. How Economics Became a Mathematical Science. Philosophia Mathematica 11 (3):354-357.
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  35. David Hilbert (1996). On the Concept of Number. In William Bragg Ewald (ed.), From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Oxford University Press. 2--1089.
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  36. Carlo Ierna (2014). Burt C. Hopkins. The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein. Studies in Continental Thought. Bloomington: University of Indiana Press, 2011. ISBN 978-0-253-35671-0 (Hbk). Pp. Xxxi + 559. [REVIEW] Philosophia Mathematica 22 (2):249-262.
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  37. A. D. Irvine (1995). Bertrand Russell, Philosophical Papers 1896-99. Philosophia Mathematica 3:301-301.
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  38. A. D. Irvine (1995). John Allen Paulos, Beyond Numeracy. Philosophia Mathematica 3:307-307.
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  39. A. D. Irvine (1995). Kurt Goedel, Collected Works. Volumes I and II. Philosophia Mathematica 3:299-299.
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  40. 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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  41. J. Kim (2010). Yi on 2. Philosophia Mathematica 18 (3):329-336.
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  42. Ernst Kleinert (2012). Studien Zur Mathematik Und Philosophie. Leipziger Universitätsverlag.
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  43. G. Landini (2014). Gregory Landini. Zermelo and Russell's Paradox: Is There a Universal Set? Philosophia Mathematica 22 (1):142-142.
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  44. André Lebel (2014). Jean-Michel Salanskis. Philosophie des Mathématiques. Problèmes & Controverses. Paris: Vrin, 2008. ISBN 978-2-7116-1988-7. Pp. 304. [REVIEW] Philosophia Mathematica 22 (2):262-270.
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  45. Renren Liu (2010). Duo Zhi Luo Ji Han Shu Jie Gou Li Lun Yan Jiu. Ke Xue Chu Ban She.
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  46. Minxia Luo (2010). Fan Luo Ji Xue Yu Gou Li Lun. Ke Xue Chu Ban She.
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  47. William Marias Malisoff (1935). An Examination of the Quantum Theories. IV. Philosophy of Science 2 (3):334-343.
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  48. William Marias Malisoff (1934). An Examination of the Quantum Theories. I. Philosophy of Science 1 (1):71-77.
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  49. William Marias Malisoff (1934). An Examination of the Quantum Theories. II. Philosophy of Science 1 (2):170-175.
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  50. William Marias Malisoff (1934). An Examination of the Quantum Theories III. Philosophy of Science 1 (4):398-408.
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