•  21
    In this paper we propose and defend the Synonymy account, a novel account of metaphysical equivalence which draws on the idea (Rayo in The Construction of Logical Space, Oxford University Press, Oxford, 2013) that part of what it is to formulate a theory is to lay down a theoretical hypothesis concerning logical space. Roughly, two theories are synonymous—and so, in our view, equivalent—just in case (i) they take the same propositions to stand in the same entailment relations, and (ii) they are …Read more
  •  8
    A Theory of Marginal and Large Difference
    with Bruno Dinis
    Erkenntnis 1-28. forthcoming.
    We propose a new theory based on the notions of marginal and large difference which has natural models in the context of nonstandard mathematics. We introduce the notion of finite marginality and show a representation result which ensures, for finitely marginal countable models, the existence of a homomorphism of the structure of marginal and large difference into a nonstandard model of the natural numbers, and show the extent to which any such homomorphism is unique. Finally, we show that our t…Read more
  •  69
    Models for Hylomorphism
    with Aaron Cotnoir
    Journal of Philosophical Logic 48 (5): 909-955. 2019.
    In a series of papers, 137–158; 1994, Midwest Studies in Philosophy, 23, 61–74, 1999) Fine develops his hylomorphic theory of embodiments. In this article, we supply a formal semantics for this theory that is adequate to the principles laid down for it in. In Section 1, we lay out the theory of embodiments as Fine presents it. In Section 2, we argue on Cantorian grounds that the theory needs to be stabilized, and sketch some ways forward, discussing various choice points in modeling the view. In…Read more
  •  120
    Serious Actualism and Higher-Order Predication
    Journal of Philosophical Logic 48 (3): 471-499. 2019.
    Serious actualism is the prima facie plausible thesis that things couldn’t have been related while being nothing. The thesis plays an important role in a number of arguments in metaphysics, e.g., in Plantinga’s argument for the claim that propositions do not ontologically depend on the things that they are about and in Williamson’s argument for the claim that he, Williamson, is necessarily something. Salmon has put forward that which is, arguably, the most pressing challenge to serious actualist…Read more
  •  286
    Bridge Principles and Epistemic Norms
    with Claire Https://Orcidorg Field
    Erkenntnis 1-53. 2022.
    Is logic normative for belief? A standard approach to answering this question has been to investigate bridge principles relating claims of logical consequence to norms for belief. Although the question is naturally an epistemic one, bridge principles have typically been investigated in isolation from epistemic debates over the correct norms for belief. In this paper we tackle the question of whether logic is normative for belief by proposing a Kripkean model theory accounting for the interaction…Read more
  •  90
    Strongly Millian Second-Order Modal Logics
    Review of Symbolic Logic 10 (3): 397-454. 2017.
    The most common first- and second-order modal logics either have as theorems every instance of the Barcan and Converse Barcan formulae and of their second-order analogues, or else fail to capture the actual truth of every theorem of classical first- and second-order logic. In this paper we characterise and motivate sound and complete first- and second-order modal logics that successfully capture the actual truth of every theorem of classical first- and second-order logic and yet do not possess c…Read more
  •  69
    Knowing Who: How Perspectives and Contexts Interact
    In Franck Lihoreau & Manuel Rebuschi (eds.), Epistemology, Context, and Formalism, Springer Verlag. 2014.
  •  315
    General-Elimination Stability
    Studia Logica 105 (2): 361-405. 2017.
    General-elimination harmony articulates Gentzen’s idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given of generatin…Read more
  •  96
    Necessitism, Contingentism, and Theory Equivalence
    Bulletin of Symbolic Logic 27 (2): 217-218. 2021.
    Necessitism, Contingentism, and Theory Equivalence is a dissertation on issues in higher-order modal metaphysics. Consider a modal higher-order language with identity in which the universal quantifier is interpreted as expressing universal quantification and the necessity operator is interpreted as expressing metaphysical necessity. The main question addressed in the dissertation concerns the correct theory formulated in this language. A different question that also takes centre stage in the dis…Read more