The scope of the PSR

For simplicity, I shall stipulatively use the term "fact" for a true proposition. The PSR states that every fact, or every contingent fact, has an explanation, and this is the standard tool in Leibnizian arguments for handling the Glendower and Regress problems.

Some authors restrict the PSR to contingent facts. The advantage of a restriction to contingent facts is that we do not know very much about how the explanation of necessary truths works and, hence, may not be in a position to justify the PSR for necessary truths. To explain the Pythagorean Theorem, presumably, I should prove it from the axioms. But which proof counts as explanatory? Which axioms are the right ones to start from? Is there a fact of the matter here?

On the other hand, maybe the case of necessary facts is not a real worry, for it might be that any necessary truth p can be explained by citing its necessity: p holds because p necessarily holds. This leads into a regress since that p necessarily holds will also be a necessary truth by Axiom S4 of modal logic; but perhaps this regress is somehow to be distinguished from vicious ones.

Alternatively, the defender of an unrestricted PSR can say that while we do not yet know how the explanation of necessary truths works, we do know some cases of it. For instance, it might be that the proposition that 1 = 1 is self-explanatory, namely explained by the very same proposition 1 = 1, while the proposition that, necessarily, 1 = 1 is explained by the proposition that 1 = 1 together with the fact that mathematical truths are necessary truths. The necessary truth that all dogs are mammals, assuming this is indeed metaphysically necessary, is explained by the genetic similarity between dogs and the first mammals, together with some necessary truths about how biological classification works. The necessary truth that making false promises is wrong might be explained by the fact that falsely promising treats the promisee as a mere means. In other words, while we have no general account of the explanation of necessary truths, we do have many examples. And, anyway, the requirement that we have a general account of explanation would also be a problem for a PSR restricted to contingent propositions, since it is not clear that we yet have a general account of explanation of contingent propositions, although we have many clear examples.

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