In recent years, set theory has been uniquely interesting for philosophers due to the presence of non-proof-based forms of reasoning not often found in other areas of mathematics. While many areas of ‘core’ mathematics take their axioms as given, and focus on proving theorems from these axioms, in set theory the matter of which axioms should be accepted remains a live research question. Historically, much of this effort focused on identifying and justifying the now-standard theory ZFC, or its widely accepted extension \(ZFC+LCs\) ; today, the aim of axiom selection has shifted to finding new, defensible axioms capable of settling independent questions like the Continuum Hypothesis. Given that traditional proof methods cannot be any help in defending new axioms candidates—since axioms must be accepted prior to any proving—an important epistemological question is what methods are used to justify axiom choices in set theory, and whether those methods are rationally defensible.