This dilemmatic argument starts by distinguishing between nonconceptual awareness in which no concept is applied and no judgment made; and strong awareness, which is conceptual. Strong awareness involves a knowing that or justifiably believing that something is the case. We can adapt this distinction to the two cases of access internalism distinguished earlier, namely weak and strong AJI. To do this we presume that the awareness spoken of in weak AJI is weak, non-conceptual awareness, and that the awareness noted in strong AJI is strong awareness. Then, the dillema for the access internalist, so adapted, is this: If the access internalist requires strong awareness as in strong AJI, then her position will lead to an infinite regress. If, on the other hand, the access internalist settles for non-conceptual awareness, as in weak AJI, then her position will fall prey to the SPO, thus undercutting the best case for access internalism. Thus, access internalism should be rejected.