This argument is based on the ideas of Robert Koons (1997), although I am simplifying it. Starting with the observation that once we admit that some contingent states of affairs have no explanations, a completely new skeptical scenario becomes possible: no demon is deceiving you, but your perceptual states are occurring for no reason at all, with no prior causes.
Moreover, objective probabilities are tied to laws of nature or objective tendencies, and so if an objective probability attaches to some contingent fact, then that situation can be given an explanation in terms of laws of nature or objective tendencies. Hence, if the PSR is false of some contingent fact, no objective probability attaches to the fact.
Thus, we cannot even say that violations of the PSR are improbable if the PSR is false. Consequently, someone who does not affirm the PSR cannot say that Koons' skeptical scenario is objectively improbable. It may be taken to follow from this that if the PSR were false or maybe even not known a priori, we would not know any empirical truths. But we do know empirical truths. Hence, the PSR is true, and maybe even known a priori.
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