•  178
    The Logic of Hyperlogic. Part A: Foundations
    Review of Symbolic Logic 1-27. forthcoming.
    Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., "Intuitionistic logic is correct" or "The law of excluded middle holds") into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical co…Read more
  •  72
    A supplemental document for "The Logic of Hyperlogic. Part A: Foundations".
  •  108
    What Can You Say? Measuring the Expressive Power of Languages
    Dissertation, University of California, Berkeley. 2018.
    There are many different ways to talk about the world. Some ways of talking are more expressive than others—that is, they enable us to say more things about the world. But what exactly does this mean? When is one language able to express more about the world than another? In my dissertation, I systematically investigate different ways of answering this question and develop a formal theory of expressive power, translation, and notational variance. In doing so, I show how these investigations help…Read more
  •  178
    Logic talk
    Synthese 199 (5-6): 13661-13688. 2021.
    Sentences about logic are often used to show that certain embedding expressions are hyperintensional. Yet it is not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. In this paper, I develop a formal system called hyperlogic that is designed to do just that. I provide a hyperintensional semantics for hyperlogic that doesn’t appeal to logically impossible worlds, as traditionally understood, but instead uses a shiftable pa…Read more
  •  299
    Does Chance Undermine Would?
    Mind. forthcoming.
    Counterfactual skepticism holds that most ordinary counterfactuals are false. The main argument for this view appeals to a ‘chance undermines would’ principle: if ψ would have some chance of not obtaining had φ obtained, then φ []–> ψ is false. This principle seems to follow from two fairly weak principles, viz., that ‘chance ensures could’ and that φ []–> ψ and φ <>–> ψ clash. Despite their initial plausibility, I show that these principles are independently problematic: given some modest closu…Read more
  •  281
    The Dynamics of Argumentative Discourse
    Journal of Philosophical Logic 51 (2): 413-456. 2021.
    Arguments have always played a central role within logic and philosophy. But little attention has been paid to arguments as a distinctive kind of discourse, with its own semantics and pragmatics. The goal of this essay is to study the mechanisms by means of which we make arguments in discourse, starting from the semantics of argument connectives such as `therefore'. While some proposals have been made in the literature, they fail to account for the distinctive anaphoric behavior of `therefore', …Read more
  •  155
    Comparing conventions
    Semantics and Linguistic Theory 30 294-313. 2020.
    We offer a novel account of metalinguistic comparatives, such as 'Al is more wise than clever'. On our view, metalinguistic comparatives express comparative commitments to conventions. Thus, 'Al is more wise than clever' expresses that the speaker has a stronger commitment to a convention on which Al is wise than to a convention on which she is clever. This view avoids problems facing previous approaches to metalinguistic comparatives. It also fits within a broader framework—independently motiva…Read more
  •  637
    Counterlogicals as Counterconventionals
    with Ethan J. Jerzak
    Journal of Philosophical Logic 50 (4): 673-704. 2021.
    We develop and defend a new approach to counterlogicals. Non-vacuous counterlogicals, we argue, fall within a broader class of counterfactuals known as counterconventionals. Existing semantics for counterconventionals, 459–482 ) and, 1–27 ) allow counterfactuals to shift the interpretation of predicates and relations. We extend these theories to counterlogicals by allowing counterfactuals to shift the interpretation of logical vocabulary. This yields an elegant semantics for counterlogicals that…Read more
  •  23
    A Two-Dimensional Logic for Two Paradoxes of Deontic Modality
    Review of Symbolic Logic 1-32. forthcoming.
    In this paper, we axiomatize the deontic logic in Fusco, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general t…Read more
  •  809
    In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more gene…Read more
  •  268
    The Problem of Cross-world Predication
    Journal of Philosophical Logic 45 (6): 697-742. 2016.
    While standard first-order modal logic is quite powerful, it cannot express even very simple sentences like “I could have been taller than I actually am” or “Everyone could have been smarter than they actually are”. These are examples of cross-world predication, whereby objects in one world are related to objects in another world. Extending first-order modal logic to allow for cross-world predication in a motivated way has proven to be notoriously difficult. In this paper, I argue that the stand…Read more
  •  289
    Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these…Read more
  •  287
    On the Concept of a Notational Variant
    In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan), . pp. 284-298. 2017.
    In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally i…Read more
  •  708
    Against Conventional Wisdom
    Philosophers' Imprint 20 (22): 1-27. 2020.
    Conventional wisdom has it that truth is always evaluated using our actual linguistic conventions, even when considering counterfactual scenarios in which different conventions are adopted. This principle has been invoked in a number of philosophical arguments, including Kripke’s defense of the necessity of identity and Lewy’s objection to modal conventionalism. But it is false. It fails in the presence of what Einheuser (2006) calls c-monsters, or convention-shifting expressions (on analogy wit…Read more
  •  158
    Hyperlogic: A System for Talking about Logics
    Proceedings for the 22nd Amsterdam Colloquium. 2019.
    Sentences about logic are often used to show that certain embedding expressions, including attitude verbs, conditionals, and epistemic modals, are hyperintensional. Yet it not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. This paper does two things. First, it argues against a standard account of logic talk, viz., the impossible worlds semantics. It is shown that this semantics does not easily extend to a language with…Read more
  •  1144
    It is widely held that counterfactuals, unlike attitude ascriptions, preserve the referential transparency of their constituents, i.e., that counterfactuals validate the substitution of identicals when their constituents do. The only putative counterexamples in the literature come from counterpossibles, i.e., counterfactuals with impossible antecedents. Advocates of counterpossibilism, i.e., the view that counterpossibles are not all vacuous, argue that counterpossibles can generate referential …Read more
  •  634
    Counteridenticals
    The Philosophical Review 127 (3): 323-369. 2018.
    A counteridentical is a counterfactual with an identity statement in the antecedent. While counteridenticals generally seem non-trivial, most semantic theories for counterfactuals, when combined with the necessity of identity and distinctness, attribute vacuous truth conditions to such counterfactuals. In light of this, one could try to save the orthodox theories either by appealing to pragmatics or by denying that the antecedents of alleged counteridenticals really contain identity claims. Or o…Read more