•  44
    No Grounds for Fictionalism
    Philosophical Studies 179 (12): 3679-3687. 2022.
    I argue that fictionalism about grounding is unmotivated, focusing on Naomi Thompson’s (2022) recent proposal on which the utility of the grounding fiction lies in its facilitating communication about what metaphysically explains what. I show that, despite its apparent dialectical kinship with other metaphysical debates in which fictionalism has a healthy tradition, the grounding debate is different in two key respects. Firstly, grounding talk is not indispensable, nor even particularly convenie…Read more
  •  455
    Platonic Relations and Mathematical Explanations
    Philosophical Quarterly 71 (3): 623-644. 2021.
    Some scientific explanations appear to turn on pure mathematical claims. The enhanced indispensability argument appeals to these ‘mathematical explanations’ in support of mathematical platonism. I argue that the success of this argument rests on the claim that mathematical explanations locate pure mathematical facts on which their physical explananda depend, and that any account of mathematical explanation that supports this claim fails to provide an adequate understanding of mathematical explan…Read more
  •  39
    Unification and mathematical explanation
    Philosophical Studies 178 (12): 3923-3943. 2021.
    This paper provides a sorely-needed evaluation of the view that mathematical explanations in science explain by unifying. Illustrating with some novel examples, I argue that the view is misguided. For believers in mathematical explanations in science, my discussion rules out one way of spelling out how they work, bringing us one step closer to the right way. For non-believers, it contributes to a divide-and-conquer strategy for showing that there are no such explanations in science. My discussio…Read more
  •  66
    The uncanny accuracy of God's mathematical beliefs
    Religious Studies 57 (2): 333-352. 2021.
    I show how mathematical platonism combined with belief in the God of classical theism can respond to Field's epistemological objection. I defend an account of divine mathematical knowledge by showing that it falls out of an independently motivated general account of divine knowledge. I use this to explain the accuracy of God's mathematical beliefs, which in turn explains the accuracy of our own. My arguments provide good news for theistic platonists, while also shedding new light on Field's infl…Read more
  •  80
    Towards a Fictionalist Philosophy of Mathematics
    Dissertation, University of Manchester. 2015.
    In this thesis, I aim to motivate a particular philosophy of mathematics characterised by the following three claims. First, mathematical sentences are generally speaking false because mathematical objects do not exist. Second, people typically use mathematical sentences to communicate content that does not imply the existence of mathematical objects. Finally, in using mathematical language in this way, speakers are not doing anything out of the ordinary: they are performing straightforward asse…Read more
  •  4
    Semantic Assumptions in the Philosophy of Mathematics
    In Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics, Springer International Publishing. 2016.
    The standard semantic analysis of sentences such as ‘The number of planets in the solar system is eight’ is that they are identity statements that identify certain mathematical objects, namely numbers. The analysis thereby facilitates arguments for a controversial philosophical position, namely realism about mathematical objects. Accordingly, whether or not this analysis is accurate should concern philosophers greatly. Recently, several authors have offered rival analyses of sentences such as th…Read more
  •  1024
    We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, well-motivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp…Read more
  •  170
    Good weasel hunting
    Synthese 192 (10): 3397-3412. 2015.
    The ‘indispensability argument’ for the existence of mathematical objects appeals to the role mathematics plays in science. In a series of publications, Joseph Melia has offered a distinctive reply to the indispensability argument. The purpose of this paper is to clarify Melia’s response to the indispensability argument and to advise Melia and his critics on how best to carry forward the debate. We will begin by presenting Melia’s response and diagnosing some recent misunderstandings of it. Then…Read more