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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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     Mathematical Intuition
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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
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     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
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    Set Theory
     The Nature of Sets
     Axioms of Set Theory
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     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
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  2. Ross T. Brady (2012). The Consistency of Arithmetic, Based on a Logic of Meaning Containment. Logique Et Analyse 55 (219).
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    Epistemology of Mathematics
     Apriority in Mathematics
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     Mathematical Intuition
     Mathematical Proof
     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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     Mathematical Neo-Fregeanism
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     Indispensability Arguments in Mathematics
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     The Nature of Sets
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
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    Set Theory
     The Nature of Sets
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     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
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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
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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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  4. F. K. C. (1974). Meaning and Existence in Mathematics. Review of Metaphysics 27 (4):790-791.
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    Epistemology of Mathematics
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     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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     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
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  5. J. D. C. (1971). Philosophie der Arithmetik. Review of Metaphysics 25 (1):127-128.
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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
     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
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  6. L. C. (1967). Mathematics and Logic in History and in Contemporary Thought. Review of Metaphysics 21 (1):154-154.
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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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     Mathematical Platonism
     Mathematical Psychologism
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     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
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    Mathematical Truth
     Analyticity in 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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  7. Carlo Cellucci (2007). La Filosofia della Matematica del Novecento. Laterza.
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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
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     Indeterminacy in Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Truth
     Analyticity in 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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     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
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  8. Stefania Centrone (2014). Mirja Hartimo Ed. Phenomenology and Mathematics. Phaenomenologia; 195. Dordrecht: Springer, 2010. ISBN 978-90-481-3728-2 ; 978-90-481-3728-2 ; 978-94-007-3196-7 . 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
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     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
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    Areas of Mathematics
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    Theories of Mathematics
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     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
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    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
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  9. M. Davis (1998). Review of Dawson [1997]. [REVIEW] Philosophia Mathematica 3 (6).
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    Epistemology of Mathematics
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     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
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    Ontology of Mathematics
     Mathematical Fictionalism
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     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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     Predicativism in Mathematics
     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. 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
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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
     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
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     Geometry
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     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
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     History of Mathematics
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  11. 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 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 ordinals. However, that set has an ordinal in turn which is not a member of the set constructed; so no (...)
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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
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    Ontology of Mathematics
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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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     Analysis
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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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  12. 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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     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of 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
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     Axiomatic Truth
     Objectivity Of Mathematics
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    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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    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
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  13. Gottlob Frege (2013). Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & Ii. Oxford University Press.
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  14. 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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  15. 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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  16. Intuitionism As Generalization (1990). Fred Richman New Mexico State University. Philosophia Mathematica 5 (124):128.
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  17. Eduard Glas (2014). A Role for Quasi-Empiricism in Mathematics Education. In Michael R. Matthews (ed.), International Handbook of Research in History, Philosophy and Science Teaching. Springer. 731-753.
    Although there are quite a few directions in modern philosophy of mathematics that invoke some essential role for (quasi-)empirical material, this chapter will be devoted exclusively to what may be considered the seminal tradition. This enabled me to present the subject as one coherent whole and to forestall the discussion getting scattered in a diversity of directions without doing justice to any one of them. -/- Quasi-empiricism in this tradition is the view that the logic of mathematical inquiry is based, (...)
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  18. 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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  19. E. R. Grosholz (2004). Lorenzo Magnani. Philosophy and Geometry: Theoretical and Historical Issues. Philosophia Mathematica 12 (1):79-80.
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  20. Marie Grossi, Montgomery Link, Katalin Makkai & Charles Parsons (1998). A Bibliography of Hao Wang. Philosophia Mathematica 6 (1):25-38.
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  21. G. E. R. Haddock (2003). Anastasio aleman. Logica, matematicas Y realidad. Philosophia Mathematica 11 (1):108-119.
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  22. D. M. Hausman (2003). E. Roy Weintraub. How Economics Became a Mathematical Science. Philosophia Mathematica 11 (3):354-357.
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  23. James Higginbotham (1993). McGinn's Logicisms. Philosophical Issues 4:119-127.
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  24. 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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  25. 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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  26. A. D. Irvine (1995). Bertrand Russell, Philosophical Papers 1896-99. Philosophia Mathematica 3:301-301.
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  27. A. D. Irvine (1995). John Allen Paulos, Beyond Numeracy. Philosophia Mathematica 3:307-307.
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  28. A. D. Irvine (1995). Kurt Goedel, Collected Works. Volumes I and II. Philosophia Mathematica 3:299-299.
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  29. 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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  30. J. Kim (2010). Yi on 2. Philosophia Mathematica 18 (3):329-336.
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  31. Ernst Kleinert (2012). Studien Zur Mathematik Und Philosophie. Leipziger Universitätsverlag.
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  32. Israel Krakowski (1980). The Four Color Problem Reconsidered. Philosophical Studies 38 (1):91 - 96.
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  33. 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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  34. 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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  35. Renren Liu (2010). Duo Zhi Luo Ji Han Shu Jie Gou Li Lun Yan Jiu. Ke Xue Chu Ban She.
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  36. Giuseppe Longo (1999). Mathematical Intelligence, Infinity and Machines: Beyond Godelitis. Journal of Consciousness Studies 6 (11-12):11-12.
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  37. Minxia Luo (2010). Fan Luo Ji Xue Yu Gou Li Lun. Ke Xue Chu Ban She.
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  38. William Marias Malisoff (1935). An Examination of the Quantum Theories. IV. Philosophy of Science 2 (3):334-343.
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  39. William Marias Malisoff (1934). An Examination of the Quantum Theories. I. Philosophy of Science 1 (1):71-77.
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  40. William Marias Malisoff (1934). An Examination of the Quantum Theories. II. Philosophy of Science 1 (2):170-175.
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  41. William Marias Malisoff (1934). An Examination of the Quantum Theories III. Philosophy of Science 1 (4):398-408.
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  42. Paolo Mancosu (forthcoming). William Ewald and Wilfried Sieg, Eds, David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1917–1933. Heidelberg: Springer, 2013. ISBN: 978-3-540-69444-1 ; 978-3-540-20578-4 . Pp. Xxv + 1062. [REVIEW] Philosophia Mathematica:nku031.
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  43. Alex Miller (ed.) (2013). Logic, Language and Mathematics: Essays for Crispin Wright. Oxford University Press.
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  44. M. M. Muntersbjorn (2003). Meir Buzaglo. The Logic of Concept Expansion. Philosophia Mathematica 11 (3):341-348.
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  45. 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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  46. 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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  47. C. Parsons (1996). Jean Dieudonne. Mathematics-The Music of Reason. Philosophia Mathematica 4:190-195.
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  48. 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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  49. 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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  50. Arkady Plotnitsky (2011). On the Reasonable and Unreasonable Effectiveness of Mathematics in Classical and Quantum Physics. Foundations of Physics 41 (3):466-491.
    The point of departure for this article is Werner Heisenberg’s remark, made in 1929: “It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which seems entirely (...)
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