Philosophical Justifications for the Axiom of Choice

This paper investigates two kinds of philosophical justifications—intrinsic and extrinsic justifications—for the Axiom of Choice. A standard intrinsic justification for the Axiom of Choice is based on the iterative conception of set. However, this form of justification implicitly adopts the maximality principle of sets, which is incoherent. The extrinsic justification turns out to be more effective due to the theoretical merits of the Axiom of Choice, despite the paradoxes caused by AC.