
41Hartry Field. Science Without Numbers: A Defense of Nominalism 2nd ed (review)Philosophia Mathematica 27 (1): 139148. 2019.FieldHartry. Science Without Numbers: A Defense of Nominalism 2nd ed.Oxford University Press, 2016. ISBN 9780198777922. Pp. vi + 56 + vi + 111.

15Mark Balaguer. Platonism and antiplatonism in mathematics. Oxford University Press, Oxford and New York 1998, x + 217 pp (review)Bulletin of Symbolic Logic 8 (4): 516518. 2002.

47Debunking, supervenience, and Hume’s PrincipleCanadian Journal of Philosophy 49 (8): 10831103. 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

6231In 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 socalled ‘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

13Reasoning Under a Presupposition and the Export Problem: The Case of Applied MathematicsAustralasian Philosophical Review 1 (2): 133142. 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 mathematicsfree nominalistic content. The notion of ‘nominalistic content’ is, however, notoriously slippery. Yablo's account of noncatastrophic 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

22Guest editor’s introductionTheoria : An International Journal for Theory, History and Fundations of Science 33 (2): 161163. 2018.Guest Editor’s introduction to the Monographic Section.

33An ‘i’ for an i, a Truth for a TruthPhilosophia Mathematica. forthcoming.Stewart Shapiro’s ante rem structuralism recognizes the structural or ‘algebraic’ aspects of mathematical practice while still offering a facevalue 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 facevalue 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

22God Over All: Divine Aseity and the Challenge of Platonism, by William Lane CraigFaith and Philosophy 34 (4): 497504. 2017.

9Critical Review of Penelope Maddy, Defending the AxiomsPhilosophical Quarterly 66 (265): 823832. 2016.

22XI—Naturalism and Placement, or, What Should a Good Quinean Say about Mathematical and Moral Truth?Proceedings of the Aristotelian Society 116 (3): 237260. 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 worldview. 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

Proof, Practice, and ProgressDissertation, University of Toronto (Canada). 2002.This thesis presents an antirealist 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

Imre Lakatos and Paul Feyerabend, For and Against Method (review)Philosophy in Review 20 115117. 2000.

84Taking it Easy: A Response to ColyvanMind 121 (484): 983995. 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.

136Platonism 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 antiPlatonism 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

190Conventionalism, by Yemima BenMenahemMind 118 (472): 11111115. 2009.(No abstract is available for this citation)

122Revolutionary Fictionalism: A Call to ArmsPhilosophia Mathematica 13 (3): 277293. 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

25What's there to know? A Fictionalist Approach to Mathematical KnowledgeIn 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.

7Platonism and antiplatonism in mathematics (review)Bulletin of Symbolic Logic 8 (4): 516517. 2002.

14Creation and Discovery in MathematicsIn John Polkinghorne (ed.), Meaning in Mathematics, Oxford University Press. 2011.

7Mathematics 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.

139What'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

35Phenomenology and mathematical practicePhilosophia Mathematica 10 (1): 314. 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 antirealist account of mathematics could be develope…Read more

5Imre Lakatos and Paul Feyerabend, For and Against Method Reviewed byPhilosophy in Review 20 (2): 115117. 2000.