This, however, is not yet an argument for foundationalism as much as an argument against what we might call “inferentialism”—the view that all justification is inferential—for it leaves open the skeptical position that we are not, and could not be, justified in believing anything at all, whether by inference or otherwise. This most radical of all skepticisms seems absurd (it entails that one couldn’t even be justified in believing it). But, strictly speaking, none of this shows that we have non-inferential justification for any of our beliefs, or even that non-inferential justification is possible. At best, it shows only that, if justification is possible, or if we are or could be justified in believing anything at all, then that justification must take a foundationalist structure. The epistemic regress argument for foundationalism thus needs an additional premise, though one that all but the most radical skeptics would accept: that epistemic justification is in principle possible for beings like us.
If we accept the more controversial second clause of PIJ, the looming regresses proliferate. Not only must S above be justified in believing E1, S must also be justified in believing that E1 makes likely P, a proposition he would have to infer (if there are no foundations) from some other proposition F1, which he would have to infer from F2, which he would have to infer from F3, and so on ad infinitum. But S would also need to be justified in believing that F1 does in fact make likely that E1 makes likely P, a proposition he would need to infer from some other proposition G1, which he would need to infer from some other proposition G2, and so on. And he would need to infer that G1 does indeed make likely that F1 makes likely that E1 makes likely P, and so on. Without noninferentially justified beliefs, it would seem that we would need to complete an infinite number of infinitely long chains of reasoning in order to be justified in believing anything!
PIJ is controversial, especially its second clause. It is important to note that either clause of the principle can be used by itself to generate the allegedly vicious regress for the philosopher who rejects foundations. It is the two clauses combined that are supposed to present the anti-foundationalist with an infinite number of vicious regresses. A number of philosophers (among them foundationalists) would argue that the second clause of PIJ confuses levels of epistemic questions. It is far too strong to require someone to have a justified belief in a probabilistic connection between available evidence and the conclusion reached on the basis of that evidence. Such a requirement is at best plausible for having second-level justification, justification for the epistemic belief that one has an inferentially justified belief. In responding to a challenge presented to one’s having an inferentially justified belief in P on the basis of E, one might find oneself searching for justification to support the claim that E makes probable P, but that is only because in the context of the challenge one is trying to support or justify the claim that one has a justified belief. A similar claim might be made with respect to clause (1) of the principle, although it is more difficult to generate the supporting intuition.