•  41
    Hartry Field. Science Without Numbers: A Defense of Nominalism 2nd ed (review)
    with Geoffrey Hellman
    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.
  •  47
    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
  •  6231
    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
  •  13
    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
  •  22
    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.
  •  33
    An ‘i’ for an i, a Truth for a Truth
    Philosophia Mathematica. forthcoming.
    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
  •  9
    Critical Review of Penelope Maddy, Defending the Axioms
    Philosophical Quarterly 66 (265): 823-832. 2016.
  •  22
    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
  •  2
    Mathematics and reality
    Bulletin of Symbolic Logic 17 (2): 267-268. 2011.
  • 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
  •  84
    Taking it Easy: A Response to Colyvan
    Mind 121 (484): 983-995. 2012.
    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.
  •  136
    Platonism and anti‐Platonism: Why worry?
    International Studies in the Philosophy of Science 19 (1). 2005.
    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 asser…Read more
  •  190
    Conventionalism, by Yemima Ben-Menahem
    Mind 118 (472): 1111-1115. 2009.
    (No abstract is available for this citation)
  •  122
    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
  •  23
    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.
  •  25
    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.
  •  7
    Platonism and anti-platonism in mathematics (review)
    Bulletin of Symbolic Logic 8 (4): 516-517. 2002.
  •  14
  •  7
    Mathematics and Reality (edited book)
    Oxford University Press. 2010.
    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.
  • Brendan Larvor, Lakatos: An Introduction (review)
    Philosophy in Review 19 198-200. 1999.
  •  139
    What's wrong with indispensability?
    Synthese 131 (3). 2002.
    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…Read more
  •  35
    Phenomenology and mathematical practice
    Philosophia Mathematica 10 (1): 3-14. 2002.
    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 develope…Read more