•  452
    The (Metaphysical) Foundations of Arithmetic?
    Noûs 51 (4): 775-801. 2017.
    Gideon Rosen and Robert Schwartzkopff have independently suggested (variants of) the following claim, which is a varian of Hume's Principle: When the number of Fs is identical to the number of Gs, this fact is grounded by the fact that there is a one-to-one correspondence between the Fs and Gs. My paper is a detailed critique of the proposal. I don't find any decisive refutation of the proposal. At the same time, it has some consequences which many will find objectionable.
  •  343
    Platitudes in mathematics
    Synthese 192 (6): 1799-1820. 2015.
    The term ‘continuous’ in real analysis wasn’t given an adequate formal definition until 1817. However, important theorems about continuity were proven long before that. How was this possible? In this paper, I introduce and refine a proposed answer to this question, derived from the work of Frank Jackson, David Lewis and other proponents of the ‘Canberra plan’. In brief, the proposal is that before 1817 the meaning of the term ‘continuous’ was determined by a number of ‘platitudes’ which had some…Read more
  •  315
    Reading the Book of the World
    Philosophical Studies 172 (4): 1051-1077. 2015.
    In Writing the Book of the World, Ted Sider argues that David Lewis’s distinction between those predicates which are ‘perfectly natural’ and those which are not can be extended so that it applies to words of all semantic types. Just as there are perfectly natural predicates, there may be perfectly natural connectives, operators, singular terms and so on. According to Sider, one of our goals as metaphysicians should be to identify the perfectly natural words. Sider claims that there is a perfectl…Read more
  •  230
    If There Were No Numbers, What Would You Think?
    Thought: A Journal of Philosophy 3 (4): 283-287. 2014.
    Hartry Field has argued that mathematical realism is epistemologically problematic, because the realist is unable to explain the supposed reliability of our mathematical beliefs. In some of his discussions of this point, Field backs up his argument by saying that our purely mathematical beliefs do not ‘counterfactually depend on the facts’. I argue that counterfactual dependence is irrelevant in this context; it does nothing to bolster Field's argument
  •  165
    A Trivialist's Travails
    Philosophia Mathematica 22 (3): 380-401. 2014.
    This paper is an exposition and evaluation of the Agustín Rayo's views about the epistemology and metaphysics of mathematics, as they are presented in his book The Construction of Logical Space.
  •  164
    Review of Øystein Linnebo, Thin Objects (review)
    Philosophia Mathematica 6. forthcoming.
    A brief review of Øystein Linnebo's Thin Objects. The review ends with a brief discussion of cardinal number and metaphysical ground.
  •  120
    We discuss abstraction principles in the context of modal and temporal logic. It is argued that abstractionism conflicts with both serious presentism and serious actualism.
  •  107
    David Armstrong on the Metaphysics of Mathematics
    Dialectica 74 (4): 113-136. 2020.
    This paper has two components. The first, longer component (sec. 1-6) is a critical exposition of Armstrong’s views about the metaphysics of mathematics, as they are presented in Truth and Truthmakers and Sketch for a Systematic Metaphysics. In particular, I discuss Armstrong’s views about the nature of the cardinal numbers, and his account of how modal truths are made true. In the second component of the paper (sec. 7), which is shorter and more tentative, I sketch an alternative account of the…Read more
  •  98
    The American Pragmatists (review)
    Philosophical Review 123 (3): 355-359. 2014.
  •  76
    In Michael J. Raven (ed.), The Routledge Handbook of Metaphysical Grounding, . pp. 288-299. 2020.
    I consider the claim that analytic statements are "true in virtue meaning", giving the claim a ground-theoretic interpretation.
  •  72
    Modal Normativism and De Re Modality
    Argumenta 7 (2): 293-307. 2022.
    In the middle of the last century, it was common to explain the notion of necessity in linguistic terms. A necessary truth, it was said, is a sentence whose truth is guaranteed by linguistic rules. Quine famously argued that, on this view, de re modal claims do not make sense. “Porcupettes are porcupines” is necessarily true, but it would be a mistake to say of a particular porcupette that it is necessarily a porcupine, or that it is possibly purple. Linguistic theories of necessity fell out of …Read more
  •  54
    What was James's Theory of Truth?
    In Oxford Handbook of William James, Oxford University Press. forthcoming.
    In Pragmatism, James promised his readers a theory of truth. However, many of his readers (even those sympathetic with other parts of James’s work) have concluded that James’s “theory” was little more than a tangle of mistakes. In this chapter, I offer an interpretation and defence of James’s theory of truth. I emphasize James’s truth pluralism.