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Mary Leng [32]Mary Catherine Leng [1]
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Mary Leng
University of York
  1. Mathematics and Reality.Mary Leng - 2010 - Oxford University Press.
    Mary Leng defends a philosophical account of the nature of mathematics which views it as a kind of fiction. On this view, the claims of our ordinary mathematical theories are more closely analogous to utterances made in the context of storytelling than to utterances whose aim is to assert literal truths.
     
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  2. Mathematics and Reality.Mary Leng - 2011 - Bulletin of Symbolic Logic 17 (2):267-268.
     
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  3.  94
    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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  4.  15
    An ‘I’ for an I, a Truth for a Truth.Mary Leng - forthcoming - Philosophia Mathematica:nky005.
    Stewart Shapiro’s ante rem structuralism recognizes the structural or ‘algebraic’ aspects of mathematical practice while still offering a face-value semantics. Fictionalism, as a purely ‘algebraic’ approach, is held to be at a disadvantage, as compared with Shapiro’s structuralism, in not interpreting mathematics at face value. However, the face-value reading of mathematical singular terms has difficulty explaining how we can use such terms to pick out a unique referent in cases where the relevant mathematical structures admit non-trivial automorphisms. Shapiro offers a (...)
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  5. Mathematical Knowledge.Mary Leng, Alexander Paseau & Michael Potter (eds.) - 2007 - Oxford University Press.
    What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions. Written by some of the world's leading philosophers of mathematics, psychologists, and mathematicians, Mathematical Knowledge gives a lively sense of the current state of debate in this fascinating field. Contents 1. (...)
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  6. 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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  7. Platonism and Anti-Platonism: Why Worry?Mary Leng - 2005 - International Studies in the Philosophy of Science 19 (1):65 – 84.
    This paper argues that it is scientific realists who should be most concerned about the issue of Platonism and anti-Platonism in mathematics. If one is merely interested in accounting for the practice of pure mathematics, it is unlikely that a story about the ontology of mathematical theories will be essential to such an account. The question of mathematical ontology comes to the fore, however, once one considers our scientific theories. Given that those theories include amongst their laws assertions that imply (...)
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  8. Science and Mathematics: The Scope and Limits of Mathematical Fictionalism. [REVIEW]Christopher Pincock, Alan Baker, Alexander Paseau & Mary Leng - 2012 - Metascience 21 (2):269-294.
    Science and mathematics: the scope and limits of mathematical fictionalism Content Type Journal Article Category Book Symposium Pages 1-26 DOI 10.1007/s11016-011-9640-3 Authors Christopher Pincock, University of Missouri, 438 Strickland Hall, Columbia, MO 65211-4160, USA Alan Baker, Department of Philosophy, Swarthmore College, Swarthmore, PA 19081, USA Alexander Paseau, Wadham College, Oxford, OX1 3PN UK Mary Leng, Department of Philosophy, University of York, Heslington, York, YO10 5DD UK Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
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  9.  57
    Taking It Easy: A Response to Colyvan.Mary Leng - 2012 - Mind 121 (484):983-995.
    This discussion note responds to Mark Colyvan’s claim that there is no easy road to nominalism. While Colyvan is right to note that the existence of mathematical explanations presents a more serious challenge to nominalists than is often thought, it is argued that nominalist accounts do have the resources to account for the existence of mathematical explanations whose explanatory role resides elsewhere than in their nominalistic content.
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  10. Conventionalism, by Yemima Ben-Menahem.Mary Leng - 2009 - Mind 118 (472):1111-1115.
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  11.  7
    God Over All: Divine Aseity and the Challenge of Platonism, by William Lane Craig.Mary Leng - 2017 - Faith and Philosophy 34 (4):497-504.
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  12.  9
    XI- Naturalism and Placement, or, What Should a Good Quinean Say About Mathematical and Moral Truth?Mary Leng - 2016 - Proceedings of the Aristotelian Society 116 (3):237-260.
    What should a Quinean naturalist say about moral and mathematical truth? If Quine’s naturalism is understood as the view that we should look to natural science as the ultimate ‘arbiter of truth’, this leads rather quickly to what Huw Price has called ‘placement problems’ of placing moral and mathematical truth in an empirical scientific world-view. Against this understanding of the demands of naturalism, I argue that a proper understanding of the reasons Quine gives for privileging ‘natural science’ as authoritative when (...)
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  13.  8
    What's There to Know?Mary Leng - unknown
    Defends an account of mathematical knowledge in which mathematical knowledge is a kind of modal knowledge. Leng argues that nominalists should take mathematical knowledge to consist in knowledge of the consistency of mathematical axiomatic systems, and knowledge of what necessarily follows from those axioms. She defends this view against objections that modal knowledge requires knowledge of abstract objects, and argues that we should understand possibility and necessity in a primative way.
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  14.  23
    Phenomenology and Mathematical Practice.Mary Leng - 2002 - Philosophia Mathematica 10 (1):3-14.
    A phenomenological approach to mathematical practice is sketched out, and some problems with this sort of approach are considered. The approach outlined takes mathematical practices as its data, and seeks to provide an empirically adequate philosophy of mathematics based on observation of these practices. Some observations are presented, based on two case studies of some research into the classification of C*-algebras. It is suggested that an anti-realist account of mathematics could be developed on the basis of these and other studies, (...)
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  15. Mathematical Practice as a Guide to Ontology: Evaluating Quinean Platonism by its Consequences for Theory Choice.Mary Leng - 2002 - Logique Et Analyse 45.
  16.  40
    Review: Mark Balaguer, Platonism and Anti-Platonism in Mathematics. [REVIEW]Mary Leng - 2002 - Bulletin of Symbolic Logic 8 (4):516-518.
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  17. Creation and Discovery in Mathematics.Mary Leng - 2011 - In John Polkinghorne (ed.), Meaning in Mathematics. Oxford University Press.
     
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  18. Claire Ortiz Hill and Guillenno E. Rosado Haddock, Husserl or Frege? Meaning, Objectivity, and Mathematics Reviewed By.Mary Leng - 2002 - Philosophy in Review 22 (5):325-327.
  19. Structuralism, Fictionalism, and Applied Mathematics.Mary Leng - unknown
  20.  1
    Critical Review of Penelope Maddy, Defending the Axioms.Mary Leng - 2016 - Philosophical Quarterly 66 (265):823-832.
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  21.  4
    Platonism and Anti-Platonism in Mathematics. Mark Balaguer. Platonism and Anti-Platonism in Mathematics. Oxford University Press, Oxford and New York 1998, X + 217 Pp. [REVIEW]Mary Leng - 2002 - Bulletin of Symbolic Logic 8 (4):516-518.
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  22. Imre Lakatos and Paul Feyerabend, For and Against Method Reviewed By.Mary Leng - 2000 - Philosophy in Review 20 (2):115-117.
     
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  23. Brendan Larvor, Lakatos: An Introduction Reviewed By.Mary Leng - 1999 - Philosophy in Review 19 (3):198-200.
     
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  24.  8
    Looking the Gift Horse in the Mouth.Mary Leng - 2003 - Metascience 12 (2):227-230.
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  25.  4
    Preaxiomatic Mathematical Reasoning : An Algebraic Approach.Mary Leng - unknown
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  26.  4
    Solving the Unsolvable.Mary Leng - 2006 - Metascience 15 (1):155-158.
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  27.  2
    Platonism and Anti-Platonism in Mathematics. [REVIEW]Mary Leng - 2002 - Bulletin of Symbolic Logic 8 (4):516-517.
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  28. "Algebraic" Approaches to Mathematics.Mary Leng - unknown
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  29. Brendan Larvor, Lakatos: An Introduction. [REVIEW]Mary Leng - 1999 - Philosophy in Review 19:198-200.
     
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  30. Imre Lakatos and Paul Feyerabend, For and Against Method. [REVIEW]Mary Leng - 2000 - Philosophy in Review 20:115-117.
     
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