•  9
    Inseparable Bedfellows: Imagination and Mathematics in Economic Modeling
    Philosophy of the Social Sciences 53 (4): 255-280. 2023.
    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 lea…Read more
  •  237
    Mathematical Knowledge (edited book)
    with Alexander Paseau and Michael D. Potter
    Oxford University Press. 2007.
    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.
  •  33
  •  40
    Critical studies/book reviews
    Philosophia Mathematica 9 (2): 244-246. 2001.
  • Book reviews (review)
    International Studies in the Philosophy of Science 12 (2): 197-203. 1998.
    What is Mathematics, Really?. Reuben Hersh, 1997 New York, Oxford University Press xxiv+343, $CAN 51.95, $US 35.00, ISBN 0–19–511368–3 Philosophy of Mathematics: Structure and Ontology. Stewart Shapiro, 1997. Oxford, Oxford University Press x + 277, $CAN 73.95, ISBN 0–19–509452–2
  •  29
    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.
  •  43
    Morality and Mathematics, by Justin Clarke-Doane (review)
    Mind 132 (528): 1232-1241. 2022.
    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.
  •  89
    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 …Read more
  •  7
    Guest Editor’s Introduction
    Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 33 (2): 161-163. 2018.
  •  91
    Hartry Field. Science Without Numbers: A Defense of Nominalism 2nd ed (review)
    Philosophia Mathematica 27 (1): 139-148. 2019.
    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.
  •  89
    Debunking, supervenience, and Hume’s Principle
    Canadian Journal of Philosophy 49 (8): 1083-1103. 2019.
    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…Read more
  •  10875
    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 that suc…Read more
  •  31
    Reasoning Under a Presupposition and the Export Problem: The Case of Applied Mathematics
    Australasian Philosophical Review 1 (2): 133-142. 2017.
    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…Read more
  •  33
    Guest editor’s introduction
    Theoria : An International Journal for Theory, History and Fundations of Science 33 (2): 161-163. 2018.
    Guest Editor’s introduction to the Monographic Section.
  •  75
    An ‘i’ for an i, a Truth for a Truth†
    Philosophia Mathematica 28 (3): 347-359. 2020.
    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 releva…Read more
  •  23
    Critical Review of Penelope Maddy, Defending the Axioms
    Philosophical Quarterly 66 (265): 823-832. 2016.
  •  50
    XI- Naturalism and Placement, or, What Should a Good Quinean Say about Mathematical and Moral Truth?
    Proceedings of the Aristotelian Society 116 (3): 237-260. 2016.
    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 scie…Read more
  •  4
    Mathematics and reality
    Bulletin of Symbolic Logic 17 (2): 267-268. 2010.
  • Proof, Practice, and Progress
    Dissertation, University of Toronto (Canada). 2002.
    This thesis presents an anti-realist account of mathematics as 'recreational', and argues that such a view can answer the central dilemma for the philosophy of mathematics as presented in Benacerraf's 'Mathematical Truth'. I argue that we should only be satisfied with a naturalistic solution to this dilemma, where I understand 'naturalism' minimally as requiring natural scientific explanations of our mathematical knowledge. In Chapter 2 I thus discuss several broadly naturalist attempts to under…Read more
  •  175
    Revolutionary Fictionalism: A Call to Arms
    Philosophia Mathematica 13 (3): 277-293. 2005.
    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 meaning…Read more
  •  26
    Looking the Gift Horse in the Mouth
    Metascience 12 (2): 227-230. 2003.
  •  1
    Brendan Larvor, Lakatos: An Introduction Reviewed by
    Philosophy in Review 19 (3): 198-200. 1999.
  •  54
    What's there to know? A Fictionalist Approach to Mathematical Knowledge
    In Mary Leng, Alexander Paseau & Michael Potter (eds.), Mathematical Knowledge, Oxford University Press. 2007.
    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.
  •  12
    Platonism and anti-platonism in mathematics (review)
    Bulletin of Symbolic Logic 8 (4): 516-517. 2002.
  •  14