Slides here. This will be a talk on 28th August 2026 at the 25th Annual Meet of Calcutta Logic Circle.

Abstract: : The question of how its axioms are justified has always been a contentious issue for the study of infinite sets. From Cantor’s initial justificatory worries in the face of the paradoxes, to Gödel’s discussion of intrinsic and extrinsic justification, to Maddy’s isolation of specific justificatory axes, scholars have worried about the sources of our belief in the axioms of set theory, whether and how they are warranted, and indeed whether we should be aiming for “justification” at all. This paper takes a step back and asks “What is the project of justification aiming at?”. It might seem like the answer is obvious: We aim at truth with our set-theoretic justifications. In this paper, I argue that this solely epistemic conception of justification is liable to lead to confusion and a narrowing of its correct scope. I think that if we instead view justification as a more diverse normative phenomenon, we can make better sense of different justificatory projects, without reducing the phenomenon to the question of truth and access.

Slides here. This will be a plenary talk at the ASL sessions of the Central APA in Chicago on 21. February 2026.

Abstract: The Continuum Hypothesis featured top of Hilbert’s list of 23 problems in 1900. Today, we still consider the question, with various programmes pulling in different directions. This conceptual diversity raises a puzzle: In what sense do we disagree when we talk about it? A standard assumption takes it that the content of our thought about classes and the Continuum Hypothesis is uniform between agents. Assuming a moderate view of how content is determined, I reject this assumption. However, I also argue that whilst the Continuum Hypothesis can have different content for different agents, it can also be determinate for them. In particular, I suggest that there is a fault line between those who think there are uncountable sets and recent countabilist views.

Handout here. This will be a short response for a symposium on Bu’s paper at the 2026 meeting of the American Philosophical Association in Chicago.

Slides here. Paused slides here. This will be a talk at HoMeWork 8 at New York University on 16 November 2025.

Abstract:

In light of the development of forcing, philosophers and mathematicians have wondered whether the truths of mathematics might be contingent. This talk investigates that idea in the framework of higher-order logic. Our main result is that forcing-related contingency (e.g., contingency of the continuum hypothesis) is consistent in the higher-order logic Bacon and Dorr call Classicism + Rigid Comprehension, which permits quantification over both properties and modally rigid classes.

This will be a talk at NUSC Philosophy.

Slides here.