It occurred to me that for the diehard skeptic, the uniformity of nature/principle of induction may not be readily accepted. Of course, I've always known this, and Hume makes it abundantly clear that he doesn't believe that the uniformity of nature is something demonstrable. Nevertheless, I've been thinking about possible arguments that would demonstrate the irrationality of denying the uniformity of nature. Here's one:
1. In order for a belief B to be rationally compelling, there must be a probability of B > .5. (Premise)
2. Necessarily, if nature is not uniform (represented by ~B), then ~B > .5. (Implied by 1)
3. Necessarily, if ~B, then the probability of ~B is inscrutable. (Premise)
4. Necessarily, if ~B is inscrutable, then it is not the case that ~B > .5. (Definition)
5. Hence, it is not the case that ~B > .5. (From 3 and 4)
6. Therefore, ~B is not rationally compelling. (From 1 and 5)
Based on this argument, it's easy to see how ~B is not rationally acceptable, either. Assuming that rational acceptability requires some level of probability, then ~B does not even meet this criterion. After all, inscrutability is the inability to ascertain a belief's probability, whereas rational acceptability necessitates that there be such an ability.