•  1579
    A logic for epistemic two-dimensional semantics
    Synthese 190 (10): 1753-1770. 2013.
    Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional sema…Read more
  •  1496
    What is the correct logic of necessity, actuality and apriority?
    Review of Symbolic Logic 7 (3): 385-414. 2014.
    This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid…Read more
  •  1392
    Higher-Order Metaphysics: An Introduction
    In Peter Fritz & Nicholas K. Jones (eds.), Higher-order Metaphysics, Oxford University Press. forthcoming.
    This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in …Read more
  •  1107
    Modal Ontology and Generalized Quantifiers
    Journal of Philosophical Logic 42 (4): 643-678. 2013.
    Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relat…Read more
  •  1075
    Operator arguments revisited
    Philosophical Studies 176 (11): 2933-2959. 2019.
    Certain passages in Kaplan’s ‘Demonstratives’ are often taken to show that non-vacuous sentential operators associated with a certain parameter of sentential truth require a corresponding relativism concerning assertoric contents: namely, their truth values also must vary with that parameter. Thus, for example, the non-vacuity of a temporal sentential operator ‘always’ would require some of its operands to have contents that have different truth values at different times. While making no claims …Read more
  •  902
    Higher-Order Contingentism, Part 1: Closure and Generation
    Journal of Philosophical Logic 45 (6): 645-695. 2016.
    This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that,…Read more
  •  778
    Counting Incompossibles
    Mind 126 (504). 2017.
    We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such p…Read more
  •  768
    Closed Structure
    Journal of Philosophical Logic 50 (6): 1249-1291. 2021.
    According to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, w…Read more
  •  767
    First-order modal logic in the necessary framework of objects
    Canadian Journal of Philosophy 46 (4-5): 584-609. 2016.
    I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that o…Read more
  •  757
    Propositional Contingentism
    Review of Symbolic Logic 9 (1): 123-142. 2016.
    According to propositional contingentism, it is contingent what propositions there are. This paper presents two ways of modeling contingency in what propositions there are using two classes of possible worlds models. The two classes of models are shown to be equivalent as models of contingency in what propositions there are, although they differ as to which other aspects of reality they represent. These constructions are based on recent work by Robert Stalnaker; the aim of this paper is to expla…Read more
  •  613
    Can modalities save naive set theory?
    with Harvey Lederman, Tiankai Liu, and Dana Scott
    Review of Symbolic Logic 11 (1): 21-47. 2018.
  •  542
    A Purely Recombinatorial Puzzle
    Noûs 51 (3): 547-564. 2017.
    A new puzzle of modal recombination is presented which relies purely on resources of first-order modal logic. It shows that naive recombinatorial reasoning, which has previously been shown to be inconsistent with various assumptions concerning propositions, sets and classes, leads to inconsistency by itself. The context sensitivity of modal expressions is suggested as the source of the puzzle, and it is argued that it gives us reason to reconsider the assumption that the notion of metaphysical n…Read more
  •  490
    Standard State Space Models of Unawareness
    with Harvey Lederman
    Theoretical Aspects of Rationality and Knowledge 15. 2015.
    The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate that standard state-space models cannot be used to represent unawareness. We first show that Dekel, Lipman and Rustichini do not establish this claim. We then distinguish three notions of awareness, and argue that although one of them may not be adequately modeled using standard state spaces, there is no reason to think that standard state spaces cannot provide models of the other two notions. In fact, stan…Read more
  •  422
    In his book The Boundary Stones of Thought, Ian Rumfitt considers five arguments in favour of intuitionistic logic over classical logic. Two of these arguments are based on reflections concerning the meaning of statements in general, due to Michael Dummett and John McDowell. The remaining three are more specific, concerning statements about the infinite and the infinitesimal, statements involving vague terms, and statements about sets.Rumfitt is sympathetic to the premisses of many of these argu…Read more
  •  386
    Higher-Order Contingentism, Part 3: Expressive Limitations
    Journal of Philosophical Logic 47 (4): 649-671. 2018.
    Two expressive limitations of an infinitary higher-order modal language interpreted on models for higher-order contingentism – the thesis that it is contingent what propositions, properties and relations there are – are established: First, the inexpressibility of certain relations, which leads to the fact that certain model-theoretic existence conditions for relations cannot equivalently be reformulated in terms of being expressible in such a language. Second, the inexpressibility of certain mod…Read more
  •  386
    Higher-Order Contingentism, Part 2: Patterns of Indistinguishability
    Journal of Philosophical Logic 47 (3): 407-418. 2017.
    The models of contingency in what propositions, properties and relations there are developed in Part 1 are related to models of contingency in what propositions there are due to Robert Stalnaker. It is shown that some but not all of the classes of models of Part 1 agree with Stalnaker’s models concerning the patterns of contingency in what propositions there are they admit. Further structural connections between the two kinds of models are explored.
  •  365
    Post Completeness in Congruential Modal Logics
    In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11, College Publications. pp. 288-301. 2016.
    Well-known results due to David Makinson show that there are exactly two Post complete normal modal logics, that in both of them, the modal operator is truth-functional, and that every consistent normal modal logic can be extended to at least one of them. Lloyd Humberstone has recently shown that a natural analog of this result in congruential modal logics fails, by showing that not every congruential modal logic can be extended to one in which the modal operator is truth-functional. As Humberst…Read more
  •  359
    Ground and Grain
    Philosophy and Phenomenological Research 105 (2): 299-330. 2021.
    Current views of metaphysical ground suggest that a true conjunction is immediately grounded in its conjuncts, and only its conjuncts. Similar principles are suggested for disjunction and universal quantification. Here, it is shown that these principles are jointly inconsistent: They require that there is a distinct truth for any plurality of truths. By a variant of Cantor’s Theorem, such a fine-grained individuation of truths is inconsistent. This shows that the notion of grounding is either no…Read more
  •  313
    Appendix to Juhani Yli-Vakkuri’s ‘Epistemicism and Modality’
    Canadian Journal of Philosophy 46 (4-5): 836-838. 2016.
    A formal result is proved which is used in Juhani Yli-Vakkuri’s ‘Epistemicism and Modality’ to argue that certain two-dimensional possible world models are inadequate for a language with operators for ‘necessarily’, ‘actually’, and ‘definitely’.
  •  205
    I want to look at recent developments of representing AGM-style belief revision in dynamic epistemic logics and the options for doing something similar for ranking theory. Formally, my aim will be modest: I will define a version of basic dynamic doxastic logic using ranking functions as the semantics. I will show why formalizing ranking theory this way is useful for the ranking theorist first by showing how it enables one to compare ranking theory more easily with other approaches to belief revi…Read more
  •  191
    Two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. Usually, this theory is presented in an informal manner. In this thesis, I take first steps in formalizing it, and use the formalization to present some considerations in favor of two-dimensional semantics. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actual…Read more
  •  176
    On Stalnaker’s Simple Theory of Propositions
    Journal of Philosophical Logic 50 (1): 1-31. 2020.
    Robert Stalnaker recently proposed a simple theory of propositions using the notion of a set of propositions being consistent, and conjectured that this theory is equivalent to the claim that propositions form a complete atomic Boolean algebra. This paper clarifies and confirms this conjecture. Stalnaker also noted that some of the principles of his theory may be given up, depending on the intended notion of proposition. This paper therefore also investigates weakened constraints on consistency …Read more
  •  155
    Intensional type theory for higher-order contingentism
    Dissertation, University of Oxford. 2015.
    Things could have been different, but could it also have been different what things there are? It is natural to think so, since I could have failed to be born, and it is natural to think that I would then not have been anything. But what about entities like propositions, properties and relations? Had I not been anything, would there have been the property of being me? In this thesis, I formally develop and assess views according to which it is both contingent what individuals there are and conti…Read more
  •  146
    Structure by proxy, with an application to grounding
    Synthese 198 (7): 6045-6063. 2019.
    An argument going back to Russell shows that the view that propositions are structured is inconsistent in standard type theories. Here, it is shown that such type theories may nevertheless provide entities which can serve as proxies for structured propositions. As an illustration, such proxies are applied to the case of grounding, as standard views of grounding require a degree of propositional structure which suffices for a version of Russell’s argument. While this application solves some of th…Read more
  •  135
    Operands and Instances
    Review of Symbolic Logic 16 (1): 188-209. 2023.
    Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions…Read more
  •  114
    On higher-order logical grounds
    Analysis 80 (4): 656-666. 2020.
    Existential claims are widely held to be grounded in their true instances. However, this principle is shown to be problematic by arguments due to Kit Fine. Stephan Krämer has given an especially simple form of such an argument using propositional quantifiers. This note shows that even if a schematic principle of existential grounds for propositional quantifiers has to be restricted, this does not immediately apply to a corresponding non-schematic principle in higher-order logic.
  •  110
    Propositional Quantification in Bimodal S5
    Erkenntnis 85 (2): 455-465. 2020.
    Propositional quantifiers are added to a propositional modal language with two modal operators. The resulting language is interpreted over so-called products of Kripke frames whose accessibility relations are equivalence relations, letting propositional quantifiers range over the powerset of the set of worlds of the frame. It is first shown that full second-order logic can be recursively embedded in the resulting logic, which entails that the two logics are recursively isomorphic. The embedding …Read more
  •  104
    Being Somehow Without (Possibly) Being Something
    Mind 132 (526): 348-371. 2023.
    Contingentists—who hold that it is contingent what there is—are divided on the claim that having a property or standing in a relation requires being something. This claim can be formulated as a natural schematic principle of higher-order modal logic. On this formulation, I argue that contingentists who are also higher-order contingentists—and so hold that it is contingent what propositions, properties and relations there are—should reject the claim. Moreover, I argue that given higher-order cont…Read more
  •  103
    Everything, More or Less: A Defence of Generality Relativism (review)
    Philosophical Review 130 (4): 623-627. 2021.