19 found
Sort by:
  1. Mary Leng (2012). Taking It Easy: A Response to Colyvan. 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.
    No categories
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  2. Christopher Pincock, Alan Baker, Alexander Paseau & Mary Leng (2012). Science and Mathematics: The Scope and Limits of Mathematical Fictionalism. [REVIEW] 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.
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  3. Mary Leng (2011). Creation and Discovery in Mathematics. In John Polkinghorne (ed.), Meaning in Mathematics. Oup Oxford.
    No categories
     
    My bibliography  
     
    Export citation  
  4. Mary Leng (2010). Mathematics and Reality. OUP Oxford.
    Mary Leng offers a defense 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 (...)
     
    My bibliography  
     
    Export citation  
  5. Mary Leng, Preaxiomatic Mathematical Reasoning : An Algebraic Approach.
    No categories
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  6. Mary Leng, "Algebraic" Approaches to Mathematics.
    No categories
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  7. Mary Leng, Conventionalism.
    No categories
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  8. Mary Leng, Structuralism, Fictionalism, and Applied Mathematics.
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  9. Mary Leng, Alexander Paseau & Michael D. Potter (eds.) (2007). Mathematical Knowledge. 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. (...)
    Direct download  
     
    My bibliography  
     
    Export citation  
  10. Mary Leng (2006). Solving the Unsolvable. Metascience 15 (1):155-158.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  11. Mary Leng (2005). Platonism and Anti-Platonism: Why Worry? 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 (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  12. Mary Leng (2005). Revolutionary Fictionalism: A Call to Arms. 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 (...)
    Direct download (11 more)  
     
    My bibliography  
     
    Export citation  
  13. Mary Leng (2003). Looking the Gift Horse in the Mouth. Metascience 12 (2):227-230.
    No categories
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  14. Mary Leng (2002). Claire Ortiz Hill and Guillenno E. Rosado Haddock, Husserl or Frege? Meaning, Objectivity, and Mathematics Reviewed By. Philosophy in Review 22 (5):325-327.
  15. Mary Leng (2002). Phenomenology and Mathematical Practice. 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, (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  16. Mary Leng (2002). What's Wrong with Indispensability? 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 (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  17. Mary Leng (2002). Review: Mark Balaguer, Platonism and Anti-Platonism in Mathematics. [REVIEW] Bulletin of Symbolic Logic 8 (4):516-518.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  18. Mary Leng (2000). Imre Lakatos and Paul Feyerabend, For and Against Method Reviewed By. Philosophy in Review 20 (2):115-117.
  19. Mary Leng (1999). Brendan Larvor, Lakatos: An Introduction Reviewed By. Philosophy in Review 19 (3):198-200.
    Direct download  
     
    My bibliography  
     
    Export citation