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.