Published articles
Debunking Multiform Dimensionality: many, Romance tant-PL, & morpho-syntactic opacity (with Luis Miguel Toquero Pérez). Proceedings of SALT 32. 2022.
The interpretation of ‘much/many’ has been argued to be regulated by Uniform Dimensionality (Hackl 2000; Solt 2009): ‘much’ is underspecified but ‘many’ encodes cardinality. However, given some data where ‘many’ denotes ‘volume’, Snyder (2021) proposes the need for Multiform Dimensionality: both ‘much’ and ‘many’ are underspecifed. After reviewing the English data, and in light of novel cross-linguistic data, we argue that neither generalization is fully accurate. Instead, following Wellwood (2015, 2018), we argue for an alternative, Abstract Uniform Dimensionality, which we propose to be universal: MUCH always measures cardinality when it scopes over semantically interpretable plural. We derive the universal by proposing that MUCH can occupy different positions in the NP, only one of which has semantic plural in its scope. Variation is thus not semantic, but morpho-syntactic.
Under review
Blok-Esakia Theorems via Stable Canonical Rules (with Nick Bezhanishvili). Journal of Symbolic Logic. Conditionally accepted.
We present a new uniform method for studying modal companions of superintuitionistic rule systems and related notions, based on the machinery of stable canonical rules. Using this method, we obtain alternative proofs of the Blok-Esakia theorem and of the Dummett-Lemmon conjecture for rule systems. Since stable canonical rules may be developed for any rule system admitting filtration, our method generalizes smoothly to richer signatures. Using essentially the same argument, we obtain a proof of an analogue of the Blok-Esakia theorem for bi-superintuitionistic and tense rule systems, and of the Kuznetsov-Muravitsky isomorphism between rule systems extending the modal intuitionistic logic $\logic{KM}$ and modal rule systems extending the provability logic $\logic{GL}$. In addition, our proof of the Dummett-Lemmon conjecture also generalizes to the bi-superintuitionistic and tense cases.
Work in progress
Quantificationalism. (Email for draft)
Temporalism is the view that some true propositions used to be false or will become false. For example, the proposition that Gavin Newsom is the governor of California is true, but used to be false in the 80s. Analogously, Modalism is the view that some true propositions could have been false. The true proposition that Gavin Newsom is the governor of California could have been false if the 2021 California gubernatorial recall election had gone another way.
I introduce a thesis that is to quantification what Temporalism and Modalism are to time and modality respectively. It is the thesis that some true propositions are false at or relative to some domains of quantifications. I call this view Quantificationalism.
After presenting a programmatic picture of possible applications of Quantificationalism, I present various higher-order logics in which Quantificationalism can be precisely formulated and shown to be consistent. These logics can be given a semantics extending Bacon’s (2019) framework of substitution structures. I apply the resulting framework to formulate and study various notions of philosophical interest.
Metaphysical Predicativity and Intensional Paradoxes. (In preparation)
I defend a novel solution to Prior’s paradox based on the idea that only predicative propositions exist. An impredicative proposition is one that quantifies over a domain that includes that very proposition. The proposition that everything Alice says at t is false is impredicative when said by Alice at t, since it quantifies over the domain of propositions said by Alice at t. The notion of an impredicative proposition is made precise in the setting of Quantificationalism, the view that propositions can be true or false at or relative to domains of quantification.