If the PSR were false, we would expect a profusion of events that would not appear to fit into any kind of nomic causal order. After all, for each way that things could go in accordance with the laws of nature, there is an uncountable infinity of ways - of arbitrary cardinality - that things could, for no reason at all, go contrary to the laws of nature. For instance, if we deny the PSR, then for no reason at all, a cloud of photons, X9314 in number, could suddenly appear ex nihilo just near the moon, heading for San Francisco. (Because the cardinality is so high, some of the photons would have to share the same quantum state; but photons are bosons, so they should be able to do that.) And the number of ways such things could happen seems to have no limit if the PSR fails. Or perhaps, X9314 nonnatural beings could come into existence, each of which could then produce one photon.
Our empirical observations suggest that the probability of such events is very low. On the other hand, if we get our probabilities a priori from some sort of principle of indifference, supposing all arrangements to be equally likely, the messy PSR-violating arrangements would seem much more probable. How to explain the fact that bricks and photon clouds do not show up in the air for no discernible reason? I suggest that the best explanation is that the PSR holds, and that whatever beings there may be (e.g. God) who are capable of causing bricks and photon clouds to show up in the air for no discernible reason are, in fact, disposed not to do so. We need both parts for the explanation: without the PSR, the possibility of this happening for no reason at all would be impossible to rule out, and without the claim that existing beings are unlikely to cause it, the PSR would be insufficient (this suggests that if the cosmological argument can establish the existence of a First Cause, there is reason to think that the First Cause has a predilection for order, a fact relevant to the Gap Problem).
It may seem that I am caught in a vicious circularity here. I have produced a phenomenon - the lack of weird, apparently causeless, events - and have suggested that its explanation needs to involve the PSR. But am I not invoking the PSR in supposing that there is an explanation here? No. I am only invoking inference to best, or only, explanation, an amplia-tive principle that we should all accept. Nor am I applying this principle to some strange fact such as the conjunction of all contingent states of affairs. I am applying the principle to the homely fact that bricks and photon clouds do not show up in the air ex nihilo. And the best explanation of this fact is that they, simply, cannot do that, absent some cause, and that there does not, in fact, exist a cause likely to produce such effects.
One might think that some physical law, say, a conservation law, would do the explanatory work here, a principle other than the PSR. But the logical possibility of miracles shows that it should be possible for a supernatural being to cause photon clouds to show up ex nihilo, and if the PSR is false, such supernatural beings could be coming into existence all the time, causing the weird effects. Our best explanation for why this is not happening is that there is nothing in existence that would be likely to cause such supernatural beings to come into existence, and by the PSR they cannot come into existence uncaused.
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