Suppose we have a phenomenon and several plausible explanations. We then reasonably assume that the best of these explanations is probably the right one, at least if it is significantly better than the runner-up. How we measure the goodness of an explanation is, of course, controverted: prior probability, simplicity, explanatory power, and so on are all candidates. Or, if we have ruled out all explanations but one, we take the remaining one to be true (White 1979) - this is what the maxim that "when you have eliminated the impossible, whatever remains, however improbable, must be the truth" comes down to in Sherlock Holmes's actual practice (Doyle 1890, p. 93; italics in the original).
But suppose we admit, contrary to the PSR, the possibility that the phenomenon has no explanation at all. What reason do we have to suppose that the best or the only explanation is likely to be true? To argue for that explanation, we compared it with its competitors. But the hypothesis that the phenomenon has no explanation at all was not one of these competitors. Indeed, we do not know how to compare this hypothesis with its competitors. The hypothesis that there is no explanation is, in one sense, simpler than any explanatory explanation. On the other hand, it altogether lacks explanatory power. Still, it is unfair to rule it out just because it lacks explanatory power unless one believes in the PSR.
Perhaps the no-explanation hypothesis can be ruled out, not because it is impossible, as the defender of the PSR will say, but because it is simply less probable than its competitors. But does it make any sense to assign a probability to the hypothesis that a brick comes to exist ex nihilo in midair in front of us for no reason at all, assuming this is possible? We certainly cannot assign a probability grounded in the laws of nature to a brick's coming into existence ex nihilo, in the way in which we can to the electron's moving upwards in the Stern-Gerlach experiment, since the brick's entry into existence would arguably not be governed by the laws if it happens "for no reason at all."
But maybe we can argue that such an arising ex nihilo is impossible, since it is contrary to the laws. However, the laws of nature only specify what happens in the absence of external influence. They do not, thus, exclude the possibility of a brick coming into existence by the power of a nonphysical being, say, God. But if the PSR does not hold, intuitively any laws that do not preclude the possibility of a brick coming into existence by the power of a nonphysical being should not exclude the possibility of the brick coming into existence ex nihilo. The possibility of a nonphysical being's producing such a brick shows that there is no innate contradiction between the brick's coming into existence and there being such-and-such laws of nature. And it would be odd indeed if the laws of nature entailed that any bricks that come into existence should have causes of some sort or other, whether natural or not. Furthermore, if my argument is taken seriously, then we may not have good reason to believe in the laws of nature in the first place (without the PSR, that is) - for the phenomena that we tried to explain in terms of them might just be lacking in explanation.
Suppose, however, that we grant that the laws of nature exist and entail that physical events have causes, natural or not, but continue to balk at the full PSR because we are not sure whether nonphysical facts have to have explanations. Then, at least on probabilistic grounds, we cannot exclude the following explanatory hypothesis, available for any phenomenon F: there came into existence, ex nihilo and for no reason at all, a nonphysical being whose only basic nonformal property was the disposition to cause F as soon as the being is in existence, a property that the being has essentially, and this being came into existence for precisely the amount of time needed for the activation of this disposition. Why did Jones fall asleep? Because a nonphysical being came into existence for no reason at all, a being characterized by an essential dispositio dormitiva and by nothing else. No nomic probabilities can be assigned to the hypothesis of such a nonphysical being's coming into existence. (It might be that there is some argument available that only God can create ex nihilo, and so such a being cannot create a brick ex nihilo. Fine, but at least it should be able to create it out of air.)
One might try to assign nonnomic probabilities to the no-explanation hypothesis and the hypothesis of ex nihilo creation by a nonnatural being. But then, the no-explanation hypothesis would be on par with each explanatory explanation. And there would be an infinitude of explanatory hypotheses in terms of nonnatural beings that came into existence ex nihilo, for we could suppose that, in addition to the disposition to cause F, they do have some other essential property (say, being happy or being beautiful), and they differ in respect of it. Why would we take a "normal" scientific explanation over one of these, then?
It is tempting here to say: "Well, we don't know anything either way about the likelihoods of these weird hypotheses that contradict the PSR. So we should just dismiss them all." As practical advice for doing our best in finding predictions, this may be fine. But if we are to hope for scientific knowledge, that surely will not do. A complete inability to estimate the likelihood of an alternate hypothesis is surely a serious problem.
It is easy not to take these odd hypotheses seriously. And that may well be because we do, in fact, have a deep commitment to the PSR and maybe even to a defeasible principle that causes have a resemblance to their effects. If I am right, the PSR is essential to the practice of science, even outside of evolutionary biology.
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