Overview
My research centers on topics in metaphysics and philosophical logic approached within the framework of higher-order logic. My main project is a systematic study of Quantificationalism, the view that propositions can be true or false at or relative to domains of quantification, in much the same sense they can be true at times or possible worlds.
Quantificationalism is a powerful framework with a wide range of applications. My current work on Quantificationalism touches on topics as diverse as the notion of predicativity, intensional paradoxes, grounding, the metaphysics of modality, the metaphysics of identity, and the interpretation of higher-order quantification. In the future, I hope to explore applications of Quantificationalism in the philosophy of mathematics and the philosophy of language.
In mathematical logic, I’m interested in topics at the intersection of logic, algebra and topology. My published work applies stable canonical rules to the theory of modal companions.
Publications
Pre-Filtration, Pre-Stable Canonical Rules, and the Kuznetsov-Muravitsky Isomorphism (with Nick Bezhanishvili)
For The Legacy of A.V. Kuznetsov in Logic, Algebra and Foundations of Mathematics, forthcoming. Penultimate draft.
We introduce pre-filtrations and pre-stable canonical rules for the Kuznetsov–Muravitsky system of intuitionistic modal logic and provide a new proof of the Kuznetsov–Muravitsky isomorphism, along with several preservation results. The proofs employ these rules and a duality between modal (Heyting) algebras and their corresponding order-topological spaces.
Blok-Esakia Theorems via Stable Canonical Rules (with Nick Bezhanishvili)
The Journal of Symbolic Logic, 2026. Published version.
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. Our methods yields an alternative proof of the Blok Esakia Theorem that smoothly generalizes to richer signatures.
Debunking Multiform Dimensionality: many, Romance tant-PL, & morpho-syntactic opacity (with Luis Miguel Toquero Perez)
Proceedings of SALT 32, 2022. Published version.
Using English data and novel cross-linguistic data from Italian and Spanish, we argue for the universal Abstract Uniform Dimensionality: 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.
Work in progress
Quantificationalism
In preparation. Email for draft.
Quantificationalism is the view that some true propositions are false at or relative to some domains of quantification, in much the same sense in which propositions can be true or false at times or possible worlds. This paper elucidates the content of Quantificationalism and argues for its philosophical fruitfulness, by outlining applications in metaphysics and the philosophy of logic.
The Logic of Quantificationalism: Foundations.
Under review. Draft.
I formulate and explore a higher-order logic, Q, in which Quantificationalism can be precisely formulated and shown to be consistent. This logic can be given a sound and complete semantics over quantificational substitution structures (QSS).
An Algebraic Approach to Necessities
In preparation. Draft.
@Bacon2023APItHOL defines a necessity by internalizing the proof theory of normal modal logics. I introduce a concept of necessity that instead internalizes the algebraic semantics of normal modal logics. I show that the two concepts are equivalent. Then, I apply the algebraic perspective to show that, in Classicism, necessities form a Heyting algebra with respect to entailment, solving an open problem from @BaconZeng2022AToN. Pseudocomplements of necessities are intimately connected with the idea of an infinitely closed necessity
A Harris Result for Quantificationalist Free Quantifiers
In preparation. Email for draft.
Classical quantifiers are uniquely pins down their meaning up to logical equivalence. Orthodoxy has it that free quantifiers are not. I show that Quantificationalists have independent reasons to regard the correct inferential role of free quantifiers as richer than it is normally taken to be. This richer inferential role turns out to be strong enough to single out the meaning of free quantifiers uniquely.
Metaphysical Predicativity
In preparation.
Predicativity is widely taken to be a property of linguistic entities, namely definitions: a definition is impredicative when it quantifies over a domain that includes the definiens. I show that Quantificationalists can introduce a metaphysical notion of predicativity, that applies directly to propositions, properties and relations without any detour through language. I apply the resulting notion to sketch novel predicativist solutions to a number of paradoxes.
Quantificationalist Modal Realism
In preparation.
I sketch a Quantificationalist version of Modal Realism and argue it offers a superior solution to the problem of advanced modalizing than extant approaches in the literature. In addition, Quantificationalist Modal Realism offers an that can be formulated as a higher-order generalization, as opposed to a schematic biconditional. This means the syntactic structure of a sentence is irrelevant for determining the semantic effect of a modal operator applied to it. All that matters is what the sentence means.