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  1. Science Without Numbers.Hartry Field - 1980 - Princeton University Press.
    Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.
     
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  • Naturalism in Mathematics.Penelope Maddy - 1997 - 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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  • A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics.John P. Burgess & Gideon Rosen - 1997 - Oxford University Press.
    Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...)
  • Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
  • Mathematics, Indispensability and Scientific Progress.Alan Baker - 2001 - Erkenntnis 55 (1):85-116.
  • What's Wrong with Indispensability?Mary Leng - 2002 - Synthese 131 (3):395 - 417.
    For many philosophers not automatically inclined to Platonism, the indispensability argument for the existence of mathematical objectshas provided the best (and perhaps only) evidence for mathematicalrealism. Recently, however, this argument has been subject to attack, most notably by Penelope Maddy (1992, 1997),on the grounds that its conclusions do not sit well with mathematical practice. I offer a diagnosis of what has gone wrong with the indispensability argument (I claim that mathematics is indispensable in the wrong way), and, taking my cue (...)
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  • Where Mathematics Comes From How the Embodied Mind Brings Mathematics Into Being.George Lakoff & Rafael E. Núñez - 2000
  • Confirmation Theory and Indispensability.Mark Colyvan - 1999 - Philosophical Studies 96 (1):1-19.
    In this paper I examine Quine''s indispensability argument, with particular emphasis on what is meant by ''indispensable''. I show that confirmation theory plays a crucial role in answering this question and that once indispensability is understood in this light, Quine''s argument is seen to be a serious stumbling block for any scientific realist wishing to maintain an anti-realist position with regard to mathematical entities.
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  • Mathematics and Indispensability.Elliott Sober - 1993 - Philosophical Review 102 (1):35-57.
    Realists persuaded by indispensability arguments af- firm the existence of numbers, genes, and quarks. Van Fraassen's empiricism remains agnostic with respect to all three. The point of agreement is that the posits of mathematics and the posits of biology and physics stand orfall together. The mathematical Platonist can take heart from this consensus; even if the existence of num- bers is still problematic, it seems no more problematic than the existence of genes or quarks. If the two positions just described (...)
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  • Go Figure: A Path Through Fictionalism.Stephen Yablo - 2001 - Midwest Studies in Philosophy 25 (1):72–102.
  • Mathematics and Aesthetic Considerations in Science.Mark Colyvan - 2002 - Mind 111 (441):69-74.
  • Weaseling Away the Indispensability Argument.J. Melia - 2000 - Mind 109 (435):455-480.
    According to the indispensability argument, the fact that we quantify over numbers, sets and functions in our best scientific theories gives us reason for believing that such objects exist. I examine a strategy to dispense with such quantification by simply replacing any given platonistic theory by the set of sentences in the nominalist vocabulary it logically entails. I argue that, as a strategy, this response fails: for there is no guarantee that the nominalist world that go beyond the set of (...)
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  • Kitcher, Ideal Agents, and Fictionalism.Sarah Hoffman - 2004 - Philosophia Mathematica 12 (1):3-17.
    Kitcher urges us to think of mathematics as an idealized science of human operations, rather than a theory describing abstract mathematical objects. I argue that Kitcher's invocation of idealization cannot save mathematical truth and avoid platonism. Nevertheless, what is left of Kitcher's view is worth holding onto. I propose that Kitcher's account should be fictionalized, making use of Walton's and Currie's make-believe theory of fiction, and argue that the resulting ideal-agent fictionalism has advantages over mathematical-object fictionalism.
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  • Mathematics and Bleak House.John P. Burgess - 2004 - Philosophia Mathematica 12 (1):18-36.
    The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.
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  • Philosophical Naturalism. Philosophical Naturalism.David Papineau - 1993 - Blackwell.
  • Steps Toward a Constructive Nominalism.Nelson Goodman & W. V. Quine - 1947 - Journal of Symbolic Logic 12 (4):105-122.
  • Nominalism.Charles Chihara - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 483--514.
    Nominalism is the view that abstract mathematical objects like numbers, functions, and sets do not exist. The chapter articulates and defends a variety of nominalism, based on a reading of mathematical statements in terms of possible linguistic constructions. The chapter responds directly to a recent study of nominalism by Gideon Rosen and John Burgess, and develops a reply to the Quine-Putnam indispensability argument for the existence of mathematical objects.
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  • Three Forms of Naturalism.Penelope Maddy - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press.
    This chapter compares and contrasts Quine’s naturalism with the versions of two post-Quineans on the nature of science, logic, and mathematics. The role of indispensability in the philosophy of mathematics is treated in detail.
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  • Naturalism and Abstract Entities.Feng Ye - 2010 - International Studies in the Philosophy of Science 24 (2):129-146.
    I argue that the most popular versions of naturalism imply nominalism in philosophy of mathematics. In particular, there is a conflict in Quine's philosophy between naturalism and realism in mathematics. The argument starts from a consequence of naturalism on the nature of human cognitive subjects, physicalism about cognitive subjects, and concludes that this implies a version of nominalism, which I will carefully characterize. The indispensability of classical mathematics for the sciences and semantic/confirmation holism does not affect the argument. The disquotational (...)
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  • Revolutionary Fictionalism: A Call to Arms.Mary Leng - 2005 - Philosophia Mathematica 13 (3):277-293.
    This paper responds to John Burgess's ‘Mathematics and _Bleak House_’. While Burgess's rejection of hermeneutic fictionalism is accepted, it is argued that his two main attacks on revolutionary fictionalism fail to meet their target. Firstly, ‘philosophical modesty’ should not prevent philosophers from questioning the truth of claims made within successful practices, provided that the utility of those practices as they stand can be explained. Secondly, Carnapian scepticism concerning the meaningfulness of _metaphysical_ existence claims has no force against a _naturalized_ version (...)
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  • The Applicability of Mathematics as a Scientific and a Logical Problem.Feng Ye - 2010 - Philosophia Mathematica 18 (2):144-165.
    This paper explores how to explain the applicability of classical mathematics to the physical world in a radically naturalistic and nominalistic philosophy of mathematics. The applicability claim is first formulated as an ordinary scientific assertion about natural regularity in a class of natural phenomena and then turned into a logical problem by some scientific simplification and abstraction. I argue that there are some genuine logical puzzles regarding applicability and no current philosophy of mathematics has resolved these puzzles. Then I introduce (...)
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  • Are There Genuine Mathematical Explanations of Physical Phenomena?Alan Baker - 2005 - Mind 114 (454):223-238.
    Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title question impacts on broader (...)
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  • Mathematical Existence.Penelope Maddy - 2005 - Bulletin of Symbolic Logic 11 (3):351-376.
    Despite some discomfort with this grandly philosophical topic, I do in fact hope to address a venerable pair of philosophical chestnuts: mathematical truth and existence. My plan is to set out three possible stands on these issues, for an exercise in compare and contrast.' A word of warning, though, to philosophical purists (and perhaps of comfort to more mathematical readers): I will explore these philosophical positions with an eye to their interconnections with some concrete issues of set theoretic method.
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  • Abstract Objects: A Case Study.Stephen Yablo - 2002 - Noûs 36 (s1):220 - 240.
  • Which Undecidable Mathematical Sentences Have Determinate Truth Values.Hartry Field - 1998 - In H. G. Dales & Gianluigi Oliveri (eds.), Truth in Mathematics. Oxford University Press, Usa. pp. 291--310.
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  • Dialogues on Mathematics.Alfréd Rényi - 1967 - San Francisco, Holden-Day.