Howell Pacific Philosophical Quarterly, 89, 348–358 and Mizrahi and Morrow Ratio, 28, 1–13 offer a group of reductio arguments to rebut the CP thesis, i.e., the hypothesis that ideal conceivability entails possibility. Each of them has a conceivability premise: it is ideally conceivable that CP is false. According to the same CP, one can infer that CP’s being false is possible, from which it follows that CP is false. In other words, CP is shown to be self-defeating and therefore false (...) if any of these reductio arguments is proved sound. In this paper, I aim to disprove these arguments. I first show that neither Howell nor Mizrahi & Morrow provide adequate justification for their conceivability premises. I go on to argue that these reductio arguments face a dilemma: either their conceivability premises cannot be adequately justified, or they are redundant. Finally, I argue that, although this dilemma resists the reductio arguments against CP, on the other hand, it also reveals that CP lacks epistemic fruitfulness: it is of no practical use in the realm of apriority as well as necessity. (shrink)