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Mary Leng [42]Mary Catherine Leng [1]
  1.  57
    Mathematics and Reality.Mary Leng - 2010 - Oxford: Oxford University Press.
    This book offers a defence of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at (...)
  2. Mathematics and reality.Mary Leng - 2010 - Bulletin of Symbolic Logic 17 (2):267-268.
     
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  3. 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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  4. 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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  5.  99
    Mathematical Knowledge.Mary Leng, Alexander Paseau & Michael D. Potter (eds.) - 2007 - Oxford, England: 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.
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  6.  61
    What's there to know? A Fictionalist Approach to Mathematical Knowledge.Mary Leng - 2007 - In Mary Leng, Alexander Paseau & Michael D. Potter (eds.), Mathematical Knowledge. Oxford, England: Oxford University Press.
    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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  7. 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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  8.  43
    Reasoning Under a Presupposition and the Export Problem: The Case of Applied Mathematics.Mary Leng - 2017 - Australasian Philosophical Review 1 (2):133-142.
    ABSTRACT‘expressionist’ accounts of applied mathematics seek to avoid the apparent Platonistic commitments of our scientific theories by holding that we ought only to believe their mathematics-free nominalistic content. The notion of ‘nominalistic content’ is, however, notoriously slippery. Yablo's account of non-catastrophic presupposition failure offers a way of pinning down this notion. However, I argue, its reliance on possible worlds machinery begs key questions against Platonism. I propose instead that abstract expressionists follow Geoffrey Hellman's lead in taking the assertoric content of (...)
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  9. Models, structures, and the explanatory role of mathematics in empirical science.Mary Leng - 2021 - Synthese 199 (3-4):10415-10440.
    Are there genuine mathematical explanations of physical phenomena, and if so, how can mathematical theories, which are typically thought to concern abstract mathematical objects, explain contingent empirical matters? The answer, I argue, is in seeing an important range of mathematical explanations as structural explanations, where structural explanations explain a phenomenon by showing it to have been an inevitable consequence of the structural features instantiated in the physical system under consideration. Such explanations are best cast as deductive arguments which, by virtue (...)
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  10. Debunking, supervenience, and Hume’s Principle.Mary Leng - 2019 - Canadian Journal of Philosophy 49 (8):1083-1103.
    Debunking arguments against both moral and mathematical realism have been pressed, based on the claim that our moral and mathematical beliefs are insensitive to the moral/mathematical facts. In the mathematical case, I argue that the role of Hume’s Principle as a conceptual truth speaks against the debunkers’ claim that it is intelligible to imagine the facts about numbers being otherwise while our evolved responses remain the same. Analogously, I argue, the conceptual supervenience of the moral on the natural speaks presents (...)
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  11.  81
    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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  12. On an Alleged Case of Propaganda: Reply to McKinnon.Sophie R. Allen, Elizabeth Finneron-Burns, Mary Leng, Holly Lawford-Smith, Jane Clare Jones, Rebecca Reilly-Cooper & R. J. Simpson - manuscript
    In her recent paper ‘The Epistemology of Propaganda’ Rachel McKinnon discusses what she refers to as ‘TERF propaganda’. We take issue with three points in her paper. The first is her rejection of the claim that ‘TERF’ is a misogynistic slur. The second is the examples she presents as commitments of so-called ‘TERFs’, in order to establish that radical (and gender critical) feminists rely on a flawed ideology. The third is her claim that standpoint epistemology can be used to establish (...)
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  13. 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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  14. "Algebraic" approaches to mathematics.Mary Leng - unknown
  15.  63
    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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  16. Creation and Discovery in Mathematics.Mary Leng - 2011 - In John Polkinghorne (ed.), Meaning in mathematics. New York: Oxford University Press.
  17.  60
    Amelioration, inclusion, and legal recognition: On sex, gender, and the UK's Gender Recognition Act.Mary Leng - 2023 - Journal of Political Philosophy 31 (2):129-157.
  18. Mathematical explanation doesn't require mathematical truth.Mary Leng - 2017 - In Shamik Dasgupta, Brad Weslake & Ravit Dotan (eds.), Current Controversies in Philosophy of Science. London: Routledge.
     
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  19.  29
    Critical Review of Penelope Maddy, Defending the Axioms.Mary Leng - 2016 - Philosophical Quarterly 66 (265):823-832.
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  20. Structuralism, Fictionalism, and Applied Mathematics.Mary Leng - 2009 - In C. Glymour, D. Westerstahl & W. Wang (eds.), Logic, Methodology and Philosophy of Science. Proceedings of the 13th International Congress. King’s College. pp. 377-389.
  21.  17
    Inseparable Bedfellows: Imagination and Mathematics in Economic Modeling.Fiora Salis & Mary Leng - 2023 - Philosophy of the Social Sciences 53 (4):255-280.
    In this paper we explore the hypothesis that constrained uses of imagination are crucial to economic modeling. We propose a theoretical framework to develop this thesis through a number of specific hypotheses that we test and refine through six new, representative case studies. Our ultimate goal is to develop a philosophical account that is practice oriented and informed by empirical evidence. To do this, we deploy an abductive reasoning strategy. We start from a robust set of hypotheses and leave space (...)
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  22.  38
    Frederick Kroon, Jonathan McKeown-Green, and Stuart Brock. A Critical Introduction to Fictionalism.Mary Leng - 2022 - Philosophia Mathematica 30 (3):382-386.
    Fictionalists about an area of discourse take the view that the value of participating in that discourse does not depend on the truth of the sentences one utter.
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  23. Conventionalism, by Yemima Ben-Menahem.Mary Leng - 2009 - Mind 118 (472):1111-1115.
    (No abstract is available for this citation).
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  24.  92
    An ‘i’ for an i, a Truth for a Truth†.Mary Leng - 2020 - Philosophia Mathematica 28 (3):347-359.
    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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  25. Brendan Larvor, Lakatos: An Introduction Reviewed by.Mary Leng - 1999 - Philosophy in Review 19 (3):198-200.
     
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  26.  38
    Guest editor’s introduction.Mary Leng - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):161-163.
    Guest Editor’s introduction to the Monographic Section.
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  27.  11
    Guest Editor’s Introduction.Mary Leng - 2018 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 33 (2):161-163.
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  28.  53
    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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  29. Imre Lakatos and Paul Feyerabend, For and Against Method Reviewed by.Mary Leng - 2000 - Philosophy in Review 20 (2):115-117.
  30.  36
    Looking the Gift Horse in the Mouth.Mary Leng - 2003 - Metascience 12 (2):227-230.
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  31. Mathematical Practice as a Guide to Ontology: Evaluating Quinean Platonism by its Consequences for Theory Choice.Mary Leng - 2002 - Logique Et Analyse 45.
  32.  25
    Preaxiomatic Mathematical Reasoning : An Algebraic Approach.Mary Leng - unknown
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  33.  30
    Solving the Unsolvable.Mary Leng - 2006 - Metascience 15 (1):155-158.
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  34.  57
    Morality and Mathematics, by Justin Clarke-Doane. [REVIEW]Mary Leng - 2022 - Mind 132 (528):1232-1241.
    From the perspective of a certain kind of physicalist naturalism, both mathematical and moral discourse look problematic. Our knowledge of the world is via caus.
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  35. Hartry Field. Science Without Numbers: A Defense of Nominalism 2nd ed. [REVIEW]Geoffrey Hellman & Mary Leng - 2019 - Philosophia Mathematica 27 (1):139-148.
    FieldHartry. Science Without Numbers: A Defense of Nominalism 2nd ed.Oxford University Press, 2016. ISBN 978-0-19-877792-2. Pp. vi + 56 + vi + 111.
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  36. Brendan Larvor, Lakatos: An Introduction. [REVIEW]Mary Leng - 1999 - Philosophy in Review 19:198-200.
     
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  37. Claire Ortiz Hill and Guillenno E. Rosado Haddock, Husserl or Frege? Meaning, Objectivity, and Mathematics Reviewed by. [REVIEW]Mary Leng - 2002 - Philosophy in Review 22 (5):325-327.
  38. Imre Lakatos and Paul Feyerabend, For and Against Method. [REVIEW]Mary Leng - 2000 - Philosophy in Review 20:115-117.
  39.  26
    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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  40.  21
    Platonism and anti-platonism in mathematics. [REVIEW]Mary Leng - 2002 - Bulletin of Symbolic Logic 8 (4):516-517.
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