•  796
    Losing Confidence in Luminosity
    Noûs (4): 1-30. 2020.
    A mental state is luminous if, whenever an agent is in that state, they are in a position to know that they are. Following Timothy Williamson’s Knowledge and Its Limits, a wave of recent work has explored whether there are any non-trivial luminous mental states. A version of Williamson’s anti-luminosity appeals to a safety- theoretic principle connecting knowledge and confidence: if an agent knows p, then p is true in any nearby scenario where she has a similar level of confidence in p. However,…Read more
  •  293
    A Metasemantic Challenge for Mathematical Determinacy
    Synthese 197 (2): 477-495. 2020.
    This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics. From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate, motivate two important constraints on attempts to meet our challenge, and then use these constraints to develop an argument against det…Read more
  •  188
    Supertasks and Arithmetical Truth
    Philosophical Studies 177 (5): 1275-1282. 2020.
    This paper discusses the relevance of supertask computation for the determinacy of arithmetic. Recent work in the philosophy of physics has made plausible the possibility of supertask computers, capable of running through infinitely many individual computations in a finite time. A natural thought is that, if supertask computers are possible, this implies that arithmetical truth is determinate. In this paper we argue, via a careful analysis of putative arguments from supertask computations to det…Read more
  •  131
    Is Mathematics Unreasonably Effective?
    Australasian Journal of Philosophy 99 (1): 83-99. 2021.
    Many mathematicians, physicists, and philosophers have suggested that the fact that mathematics—an a priori discipline informed substantially by aesthetic considerations—can be applied to natural science is mysterious. This paper sharpens and responds to a challenge to this effect. I argue that the aesthetic considerations used to evaluate and motivate mathematics are much more closely connected with the physical world than one might presume, and (with reference to case-studies within Galois the…Read more
  •  70
    Justification and being in a position to know
    Analysis 82 (2): 289-298. 2022.
    According to an influential recent view, S is propositionally justified in believing p iff S is in no position to know that S is in no position to know p. I argue that this view faces compelling counterexamples.
  •  68
    Many philosophers believe that a deflationist theory of truth must conservatively extend any base theory to which it is added. But when applied to arithmetic, it's argued, the imposition of a conservativeness requirement leads to a serious objection to deflationism: for the Gödel sentence for Peano Arithmetic is not a theorem of PA, but becomes one when PA is extended by adding plausible principles governing truth. This paper argues that no such objection succeeds. The issue turns on how we unde…Read more
  •  65
    Internalism and the Determinacy of Mathematics
    Mind 132 (528): 1028-1052. 2023.
    A major challenge in the philosophy of mathematics is to explain how mathematical language can pick out unique structures and acquire determinate content. In recent work, Button and Walsh have introduced a view they call ‘internalism’, according to which mathematical content is explained by internal categoricity results formulated and proven in second-order logic. In this paper, we critically examine the internalist response to the challenge and discuss the philosophical significance of internal…Read more
  •  56
    Recent work on formal theories of truth has revived an approach, due originally to Tarski, on which syntax and truth theories are sharply distinguished—‘disentangled’—from mathematical base theories. In this paper, we defend a novel philosophical constraint on disentangled theories. We argue that these theories must be epistemically stable: they must possess an intrinsic motivation justifying no strictly stronger theory. In a disentangled setting, even if the base and the syntax theory are indiv…Read more
  •  19
    Justification as ignorance and logical omniscience
    Asian Journal of Philosophy 1 (1): 1-8. 2022.
    I argue that there is a tension between two of the most distinctive theses of Sven Rosenkranz’s Justification as Ignorance: the central thesis concerning justification, according to which an agent has propositional justification to believe p iff they are in no position to know that they are in no position to know p and the desire to avoid logical omniscience by imposing only “realistic” idealizations on epistemic agents.
  •  6
    Losing confidence in luminosity
    Noûs 55 (4): 962-991. 2021.
    A mental state is luminous if, whenever an agent is in that state, they are in a position to know that they are. Following Timothy Williamson's Knowledge and Its Limits, a wave of recent work has explored whether there are any non‐trivial luminous mental states. A version of Williamson's anti‐luminosity appeals to a safety‐theoretic principle connecting knowledge and confidence: if an agent knows p, then p is true in any nearby scenario where she has a similar level of confidence in p. However, …Read more