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.