Slides here.

This will be a talk at Nanyang Technological University at a philosophy of physics workshop on 14 October 2026. I’ll focus on the philosophy of physics side of things as compared to the talk a few days prior!

Abstract: At some level, every mathematician is a pluralist (i.e. they hold that there are multiple legitimate ways to go about doing mathematics). This said, mathematics is often seen to be a paradigm case of certainty, and mathematicians are able to share and use each other’s results. Two responses to this problem have emerged. The dominant view is that such apparent difference is (mostly) illusory, and just a matter of the way our minds work. Mathematical reality is uniform, and all that changes is how we refer to that reality. A different (and more radical) answer is that it is the uniformity that is illusory; really mathematical reality is fractured, and it is only by dint of similarity of proofs that we can transfer results from one area to another. In this paper I try to find a middle ground. Drawing on work in the literature on perspectivism in the philosophy of science, combined with a particular moderate perspective on metasemantics, I argue that we can view mathematics as perspectival in nature.

Slides here.

This will be a talk at Nankai University at the conference Math and Truth on 10 October 2026.

Abstract: At some level, every mathematician is a pluralist (i.e. they hold that there are multiple legitimate ways to go about doing mathematics). This said, mathematics is often seen to be a paradigm case of certainty, and mathematicians are able to share and use each other’s results. Two responses to this problem have emerged. The dominant view is that such apparent difference is (mostly) illusory, and just a matter of the way our minds work. Mathematical reality is uniform, and all that changes is how we refer to that reality. A different (and more radical) answer is that it is the uniformity that is illusory; really mathematical reality is fractured, and it is only by dint of similarity of proofs that we can transfer results from one area to another. In this paper I try to find a middle ground. Drawing on work in the literature on perspectivism in the philosophy of science, combined with a particular moderate perspective on metasemantics, I argue that we can view mathematics as perspectival in nature.

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.