Hi. I'm Will, a philosophy PhD candidate at NYU. I work in metaphysics, logic, language, and epistemology. I also have a side interest in classical Indian philosophy.
My dissertation defends a view of metaphysical structure which I call Horizontal Fregeanism. My advisors are Hartry Field (main), Cian Dorr, Marko Malink, and Graham Priest.
Here's my CV and here's my PhilPeople page. You can email me at william.nava@nyu.edu.
My dissertation comprises three chapters. The first chapter uses considerations from natural language semantics—particularly, the phenomenon of anaphoric self-application—to argue against the use of higher-order languages in metaphysics. Instead, I argue, a language adequate to theorizing metaphysics must allow self-application. The second chapter introduces a formal language of this kind, in a novel syntax that is neither first-order nor higher-order. I use this language to axiomatize—using only logical vocabulary—a non-hierarchical conception of reality, in which properties and propositions are understood along Fregean lines (i.e. not as objects). The third chapter addresses paradoxes—versions of Russell's and the Liar—that arise in the purely logical fragment of this language. I argue that, contrary to orthodoxy, Russell's paradox and the Liar are best theorized as purely logical paradoxes and not as paradoxes governing specific subject matter. This has important upshots for the general project of addressing these paradoxes in their various guises.
Adopting an Inference Rule: A How-to Guide (Mind, forthcoming)
Abstract: This paper argues that inference rule adoption is a diachronic process during which agents are inferentially guided by a statement of the rule they are adopting, but during which they do not use that rule. Rather, the ability to use the rule is the outcome at the end of the process. This account avoids a regress objection to inferentially guided adoption recently posed by Boghossian and Wright. Adoption, on this model, involves the use of six privileged inference rules, including universal instantiation, modus ponens, and the naive truth rules. However, though these rules play a special role in adoption, they are not indispensable to the process in their full generality: so long as one has reasonably robust restrictions of them, the adoption process is unimpeded. Furthermore, there are no general forms that constitute the minimal restrictions of these rules required for adoption. It follows that these rules, in their fully generality, are themselves adoptable, so long as one begins with reasonable restrictions of them. It is argued that this is enough to overcome the ‘adoption problem’ as a challenge to anti-exceptionalism about logic and to the normative significance of proposals for alternative logics.
Dissolving the Paradoxicality Paradox (Australasian Journal of Logic, 2022)
[journal (open access)]
Abstract: Non-classical solutions to semantic paradox can be associated with conceptions of paradoxicality understood in terms of entailment facts. In a K3-based theory of truth, for example, it is prima facie natural to say that a sentence φ is paradoxical iff φ∨¬φ entails an absurdity. In a recent paper, Julien Murzi and Lorenzo Rossi exploit this idea to introduce revenge paradoxes for a number of non-classical approaches, including K3. In this paper, I show that on no understanding of ‘is paradoxical’ (for K3) should both rules needed for their paradox be expected to hold unrestrictedly. Just which rule fails, however, depends on various factors, including whether the derivability relation of a target system of reasoning is arithmetically definable.
(Email me if interested in a draft)
An argument, based on anaphoric self-application in English, against the use of higher-order languages in metaphysics (under review)
A defense of a non-hierarchical theory of metaphysical structure, axiomatized in a novel syntax that allows for self-application (in progress)
A paper on the generality of inference rules (in progress)
A definition of logical consequence as preservation of truth-in-a-model, given within a non-classical model theory (early stages)
Logic (Fall 2024, Spring 2025)
Metaphysics (Summer 2024)
Philosophy of Religion: Hinduism, Buddhism, Daoism (Summer 2023)
Philosophy of Language: Paradoxes (Summer 2022)
Early Modern European Philosophy (Spring 2023)
Main instructor: Tim Maudlin
Modal Logic (Spring 2022)
Main instructor: Matthew Mandelkern
Ancient Greek and Roman Philosophy (Fall 2021)
Main instructor: Tim Maudlin