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Philosophy of Mathematics

Edited by Øystein Linnebo (Birkbeck College)
Assistant editor: Sam Roberts (Birkbeck College, University of Oslo)
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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
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     Mathematical Platonism
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     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
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     Geometry
     Logic and Phil of Logic
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     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
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     Mathematical Explanation
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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
     Algebra
     Analysis
     Category Theory
     Geometry
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     Topology
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    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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  3. 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
     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
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     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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  4. Carlo Cellucci (2007). La Filosofia della Matematica del Novecento. Laterza.
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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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     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
     History of Mathematics
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     Phil of Mathematics, General Works
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  5. 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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    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
     Phil of Mathematics, General Works
     Mathematical Explanation
     Phil of Mathematics, Misc
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  6. M. Davis (1998). Review of Dawson [1997]. [REVIEW] Philosophia Mathematica 3 (6).
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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
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     Geometry
     Logic and Phil of Logic
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     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
     History of Mathematics
     Mathematical Practice
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  7. Hartry Field (1994). Are Our Logical and Mathematical Concepts Highly Indeterminate? Midwest Studies in Philosophy 19 (1):391-429.
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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
     Phil of Mathematics, General Works
     Mathematical Explanation
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  8. 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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    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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     Phil of Mathematics, General Works
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  9. 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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    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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     Phil of Mathematics, General Works
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  10. 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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    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
     Phil of Mathematics, General Works
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  11. 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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    Epistemology of Mathematics
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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 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
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     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
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     Topology
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    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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  12. Intuitionism As Generalization (1990). Fred Richman New Mexico State University. Philosophia Mathematica 5 (124):128.
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     Visualization in Mathematics
     Phenomenology of Mathematics
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     Nondeductive Methods in Mathematics
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    Ontology of Mathematics
     Mathematical Fictionalism
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     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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     Geometry
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     Topology
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    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
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  13. 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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  14. E. R. Grosholz (2004). Lorenzo Magnani. Philosophy and Geometry: Theoretical and Historical Issues. Philosophia Mathematica 12 (1):79-80.
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  15. Marie Grossi, Montgomery Link, Katalin Makkai & Charles Parsons (1998). A Bibliography of Hao Wang. Philosophia Mathematica 6 (1):25-38.
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  16. G. E. R. Haddock (2003). Anastasio aleman. Logica, matematicas Y realidad. Philosophia Mathematica 11 (1):108-119.
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  17. D. M. Hausman (2003). E. Roy Weintraub. How Economics Became a Mathematical Science. Philosophia Mathematica 11 (3):354-357.
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  18. 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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  19. 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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  20. A. D. Irvine (1995). Bertrand Russell, Philosophical Papers 1896-99. Philosophia Mathematica 3:301-301.
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  21. A. D. Irvine (1995). John Allen Paulos, Beyond Numeracy. Philosophia Mathematica 3:307-307.
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  22. A. D. Irvine (1995). Kurt Goedel, Collected Works. Volumes I and II. Philosophia Mathematica 3:299-299.
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  23. 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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  24. J. Kim (2010). Yi on 2. Philosophia Mathematica 18 (3):329-336.
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  25. Ernst Kleinert (2012). Studien Zur Mathematik Und Philosophie. Leipziger Universitätsverlag.
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  26. 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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  27. 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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  28. Renren Liu (2010). Duo Zhi Luo Ji Han Shu Jie Gou Li Lun Yan Jiu. Ke Xue Chu Ban She.
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  29. Minxia Luo (2010). Fan Luo Ji Xue Yu Gou Li Lun. Ke Xue Chu Ban She.
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  30. Alex Miller (ed.) (2013). Logic, Language and Mathematics: Essays for Crispin Wright. Oxford University Press.
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  31. M. M. Muntersbjorn (2003). Meir Buzaglo. The Logic of Concept Expansion. Philosophia Mathematica 11 (3):341-348.
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  32. 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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  33. Roland Omnès (2011). Wigner's “Unreasonable Effectiveness of Mathematics”, Revisited. Foundations of Physics 41 (11):1729-1739.
    A famous essay by Wigner is reexamined in view of more recent developments around its topic, together with some remarks on the metaphysical character of its main question about mathematics and natural sciences.
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  34. C. Parsons (1996). Jean Dieudonne. Mathematics-The Music of Reason. Philosophia Mathematica 4:190-195.
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  35. F. Pataut (2004). Michael Potter. Reason's Nearest Kin: Philosophies of Arithmetic From Kant to Carnap. Philosophia Mathematica 12 (3):268-277.
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  36. Christopher Pincock (2005). Torsten Wilholt, Zahl Und Wirklichkeit: Eine Philosophische Untersuchung Über Die Anwendbarkeit der Mathematik [Number and Reality: A Philosophical Investigation of the Applicability of Mathematics]. Paderborn: Mentis, 2004. Pp. 309. ISBN 3-89785-368-X. [REVIEW] Philosophia Mathematica 13 (3):329-337.
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  37. Stephen Pollard (2014). Reuben Hersh. Experiencing Mathematics: What Do We Do, When We Do Mathematics?. Providence, Rhode Island: American Mathematical Society, 2014. ISBN 978-0-8218-9420-0. Pp. Xvii + 291. [REVIEW] Philosophia Mathematica 22 (2):271-274.
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  38. Marie La Palme Reyes, John Macnamara, Gonzalo E. Reyes & Houman Zolfaghari (1994). The Non-Boolean Logic of Natural Language Negation. Philosophia Mathematica 2 (1):45-68.
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  39. F. Richman (1997). Christopher Ormell. Some Criteria for Sets in Mathematics. Philosophia Mathematica 5:92-96.
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  40. A. Riskin (1997). Jen Hoeyrup, In Measure, Number, and Weight. Philosophia Mathematica 5:276-277.
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  41. S. Shapiro & G. Svensson (1996). Special Issue Of. Philosophia Mathematica 3 (4).
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  42. Barry Smith (1976). Historicity, Value and Mathematics. In. In A. T. Tymieniecka (ed.), Ingardeniana. 219--239.
    At the beginning of the present century, a series of paradoxes were discovered within mathematics which suggested a fundamental unclarity in traditional mathemati­cal methods. These methods rested on the assumption of a realm of mathematical idealities existing independently of our thinking activity, and in order to arrive at a firmly grounded mathematics different attempts were made to formulate a conception of mathematical objects as purely human constructions. It was, however, realised that such formulations necessarily result in a mathematics which lacks (...)
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  43. M. Steiner (1995). Shlomo Sternberg, Group Theory and Physics. Philosophia Mathematica 3:313-313.
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  44. Daniël F. M. Strauss (forthcoming). The On to Log I Cal Sta Tus of the Prin Ci Ple of the Ex Cluded Mid Dle. Philosophia Mathematica.
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  45. Göran Sundholm (1998). Inference, Consequence, Implication: A Constructivist's Perspective. Philosophia Mathematica 6 (2):178-194.
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  46. R. Teiszen (1996). Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness. Philosophia Mathematica 4:281-289.
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  47. N. Tennant (1995). Keith Devlin, Logic and Information. Philosophia Mathematica 3:179-179.
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  48. Neil Tennant (forthcoming). Logic, Mathematics, and the A Priori, Part I: A Problem for Realism. Philosophia Mathematica:nku006.
    This is Part I of a two-part study of the foundations of mathematics through the lenses of (i) apriority and analyticity, and (ii) the resources supplied by Core Logic. Here we explain what is meant by apriority, as the notion applies to knowledge and possibly also to truths in general. We distinguish grounds for knowledge from grounds of truth, in light of our recent work on truthmakers. We then examine the role of apriority in the realism/anti-realism debate. We raise a (...)
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  49. Neil Tennant (forthcoming). Logic, Mathematics, and the A Priori, Part II: Core Logic as Analytic, and as the Basis for Natural Logicism. Philosophia Mathematica:nku009.
    We examine the sense in which logic is a priori, and explain how mathematical theories can be dichotomized non-trivially into analytic and synthetic portions. We argue that Core Logic contains exactly the a-priori-because-analytically-valid deductive principles. We introduce the reader to Core Logic by explaining its relationship to other logical systems, and stating its rules of inference. Important metatheorems about Core Logic are reported, and its important features noted. Core Logic can serve as the basis for a foundational program that could (...)
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  50. Neil Tennant (2003). Bob Hale and Crispin Wright. The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. Philosophia Mathematica 11 (2):226-240.
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     Phil of Mathematics, General Works
     Mathematical Explanation
     Phil of Mathematics, Misc
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