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  1. Naturalism in mathematics.Penelope Maddy - 1997 - New York: Oxford University Press.
    Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
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  • Introduction to mathematical philosophy.Bertrand Russell - 1919 - New York: Dover Publications.
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  • On the Question ‘Do Numbers Exist?’.Arthur W. Collins - 1998 - Philosophical Quarterly 48 (190):23-36.
    Since we know that there are four prime numbers less than 8 we know that there are numbers. This ‘short argument’ is correct but it is not an ontological claim or part of philosophy of mathematics. Both realists and nominalists reject the short argument and adopt the idea that the existence of numbers might be posited to explain known mathematical truths. Philosophers operate with a negative conception of what numbers are: they are not in space and time, not related causally (...)
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  • On the question 'do numbers exist?'.Arthur W. Collins - 1998 - Philosophical Quarterly 48 (190):23-36.
    Since we know that there are four prime numbers less than 8 we know that there are numbers. This ‘short argument’ is correct but it is not an ontological claim or part of philosophy of mathematics. Both realists (Quine) and nominalists (Field) reject the short argument and adopt the idea that the existence of numbers might be posited to explain known mathematical truths. Philosophers operate with a negative conception of what numbers are: they are not in space and time, not (...)
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  • What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
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  • Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
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  • Translations from the philosophical writings of Gottlob Frege.Gottlob Frege - 1952 - Oxford, England: Blackwell. Edited by P. T. Geach & Max Black.
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  • Set Theory and its Philosophy: A Critical Introduction.Michael D. Potter - 2004 - Oxford, England: Oxford University Press.
    Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set (...)
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  • The Provocations of Alain Badiou.Benjamin Noys - 2003 - Theory, Culture and Society 20 (1):123-132.
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  • Realistic Rationalism.Jerrold J. Katz - 1998 - Bradford.
    In _Realistic Rationalism_, Jerrold J. Katz develops a new philosophical position integrating realism and rationalism. Realism here means that the objects of study in mathematics and other formal sciences are abstract; rationalism means that our knowledge of them is not empirical. Katz uses this position to meet the principal challenges to realism. In exposing the flaws in criticisms of the antirealists, he shows that realists can explain knowledge of abstract objects without supposing we have causal contact with them, that numbers (...)
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  • Realistic Rationalism. [REVIEW]Mark Eli Kalderon - 2000 - Philosophical Review 109 (3):456.
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  • Realistic Rationalism.Jerrold J. Katz - 1998 - MIT Press.
    Jerrold Katz develops a new philosophical position integrating realism and rationalism.
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  • Ethics: an essay on the understanding of evil.Alain Badiou - 1998 - New York: Verso.
    Alain Badiou, one of the most powerful voices in contemporary French philosophy, shows how our prevailing ethical principles serve ultimately to reinforce an ...
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  • ssays on the Theory of Numbers. [REVIEW]R. Dedekind - 1903 - Ancient Philosophy (Misc) 13:314.
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  • Introduction to mathematical philosophy.Bertrand Russell - 1920 - Revue de Métaphysique et de Morale 27 (2):4-5.
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  • Introduction to Mathematical Philosophy.Bertrand Russell - 1919 - Revue Philosophique de la France Et de l'Etranger 89:465-466.
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  • [Liminaire sur l'ouvrage d'Alain Badiou “L'etre et l'evenement”].Philippe Lacoue-Labarthe, Jacques RanciÈre, Jean-franÇois Lyotard & Alain Badiou - 1989 - le Cahier (Collège International de Philosophie) 8:201-268.
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  • Essays on the Theory of Numbers.R. Dedekind - 1903 - The Monist 13:314.
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