Restricting the PSR to things with a finite past

A correspondent asked me why not to simply believe in a restricted Principle of Sufficient Reason (PSR) that says that everything contingent that has a beginning in time has an explanation. (Graham Oppy has once proposed such an idea.)

One of the reasons for accepting the PSR is that without it we fall into skepticism. If violations of the PSR are possible, they have no meaningful probabilities, and in particular cannot be said to be unlikely. E.g., without the PSR, we have to say it is not unlikely that we just popped into existence five minutes ago for no reason at all, and so we cannot say that skeptical hypotheses about the past are improbable.

There are two types of skepticism. On weak skepticism about X, we conclude we can’t know about X. On strong skepticism about X, we conclude that we can’t have a reasonable belief about X. Weak skepticism is not a big deal. Strong skepticism is. This is strong skepticism about the past.

The specific case of the five minute past doesn’t survive if we have the PSR restricted to things with a beginning. But another argument does. Suppose the full PSR is false but the restricted PSR is true. Now consider the scenario where reality consists of a large number of persons who for an infinite amount of time have been caught in an endless five minute loop of experiences just like mine. Violations of the PSR have no meaningful probabilities, so we cannot say that this hypothesis is unlikely. So, we get skepticism. Of the strong kind.