As noted above, Hempel's model requires that an explanation make use of at least one law-like generalization. This presents another sort of problem for the DN model. Hempel was careful to distinguish law-like generalizations from accidental generalizations. The latter are generalizations that may be true, but not in virtue of any law of nature. (for example, "All of my shirts are stained with coffee" may be true, but it is- I hope- just an accidental fact, not a law of nature.) Although the idea that explanation consists in subsuming events under natural laws has wide appeal in the philosophy of science, it is doubtful whether this requirement can be made consistent with Hempel's epistemic view of explanation. The reason is simply that no one has ever articulated an epistemically sound criterion for distinguishing between law-like generalizations and accidental generalizations. This is essentially just Hume's problem of induction, namely, that no finite number of observations can justify the claim that a regularity in nature is due to an natural necessity. In the absence of such a criterion, Hempel's model seems to violate the spirit of the epistemic view of explanation, as well as the idea that explanation can be understood in purely logical terms.
Now, granted that we cannot possibly entertain an infinite number of justifying propositions, one possible way out of the regress would be simply to reject an assumption used to generate it, namely, that only propositions a person believes can count as his evidence. If we reject this assumption, perhaps we can hold, on the one hand, that the regress does terminate in what S is justified in believing, but on the other, the evidence for these beliefs does not consist in other propositions he believes. And aren't we perfectly familiar with such cases? Consider beliefs we have about our own perceptual experiences. I believe that I have a pain in my lower back. What justifies this belief is surely not some other belief I have, but simply my experience of pain in my lower back . Here, the belief is grounded directly in the perceptual experience itself, and not in any other proposition I believe. Or consider my belief that there is something yellow in my visual field. Again, what justifies this belief is not any other proposition I believe, but simply my experience of something yellow in my visual field. Moreover, the point arguably need not be limited to beliefs about our perceptual experiences (Audi, 2003; see also Pryor 2000). For example, suppose I hear thunder and a patter at my window, and come to believe that it is raining outside. That it is raining outside is not a belief about my perceptual experiences, yet seems to be grounded in them.