Clarke-Doane and Ash (2024) argues that mathematics and philosophy are on a par as a priori disciplines. In particular, each fails to be objective. Should this be so, it is unclear that philosophy can do anything for set theory or that new axioms can ever be rationally justified. Blue (2024) explicates a methodology for rationally justifying new axioms. I will argue against (Clarke-Doane and Ash 2024) by buttressing (Blue 2024), describing how it accounts for the case for Definable Determinacy and how it might extend to a potential case for Baire category principles. Along the way, I will describe a not-yet-refuted scenario for positively answering Todorčević’s question “In order to have the true structure theory of \(\wp (\omega _1)\) do we really need to retreat to an inner model of the universe of sets?” (Todorcevic 2024, Question 4.7).
