One of my graduate students suggested in discussion that if one rejects the PSR, our knowledge of evolution may be undercut. We can use this insight to generate an ad hominem argument for the PSR. Most atheists and agnostics (and many theists as well, but it is to atheists and agnostics that the argument is addressed) believe that there is a complete naturalistic evolutionary explanation of the development of the human species from a single-celled organism. I claim that they are not justified in believing this if they do not accept the PSR.
For consider what could be the argument for thinking that there is such an explanation. We might first try an inductive argument. Some features of some organisms can be given naturalistic evolutionary explanations. Therefore, all features of all organisms can be given naturalistic evolutionary explanations. But this argument is as bad as inductive arguments can come. The error in the argument is that we are reasoning from a biased sample, namely those features for which we already have found an explanation. Such features are only a small portion of the features of organisms in nature - as is always the case in science, what we do not know far exceeds what we know.
Once we admit the selection bias, the argument becomes this: "all the features of organisms for which we know the explanation can be explained through naturalistic evolutionary means, and so all the features of organisms can be explained through naturalistic evolutionary means." There are at least two things wrong with this argument. The first is that it might just be that naturalistic explanations are easier to find than nonnaturalistic ones; hence, it is no surprise that we first found those explanations that are naturalistic. But even if one could get around this objection, it would not obviate the need for the PSR. For the argument, at most, gives us reason to accept the claim that those features that have explanations have naturalistic evolutionary explanations. The inductive data is that all the explanations of biological features that we have found are naturalistic and evolutionary. The only conclusion that can be drawn without the PSR is that all the explanations of biological features that there are are naturalistic and evolutionary, not that all biological features have naturalistic evolutionary explanations.
A different approach would be to suppose that natural occurrences have naturalistic explanations, and evolution is the only naturalistic form of explanation of biological features that we know of; therefore, it is likely that the development of the human race has a naturalistic evolutionary explanation. But what plausibility is there in the claim that natural occurrences have naturalistic explanations if one does not accept the PSR for contingent propositions? After all, if it is possible for contingent propositions to simply fail to have an explanation, what reason do we have for confidence that, at least, those contingent propositions that report natural occurrences have explanations? If "natural occurrence" is taken as entailing the existence of a naturalistic explanation, the argument for an evolutionary explanation of the development of the human race begs the question in its assumption that the development was a natural occurrence. But if "natural occurrence" is taken more weakly as a physical event or process, whether or not it has a natural explanation, then the naturalness of the occurrence does not give us reason to think that the occurrence has an explanation, much less a naturalistic one, absent the PSR. If we had the PSR in play, we could at least try to use a principle, perhaps defeasible, that the cause is ontologically like the effect, so that if the effect is natural, the cause is likely such as well. (It is interesting that this principle itself could be useful to theists with respect to the Gap Problem - see the perfection axiom in Section 5.4.)
Consider a final way to justify the evolutionary claim. We have good inductive reason to think that everything physical obeys the laws of physics. But everything that is governed by the laws of physics has a naturalistic explanation. Hence, the development of the human race has a naturalistic explanation, and an evolutionary one is the best candidate we have.
The claim that everything that obeys the laws of physics has a naturalistic explanation, however, has not been justified. The claim was more plausible back when we thought that everything could be explained in a Newtonian manner, but even then the claim could be falsified. Consider John Norton's (2003) ball-on-dome example. We have a rigid dome, on the exact top of which there sits a perfectly round ball, and the dome is in a constant downward gravitational field of acceleration g. The dome is rotationally symmetric, and its height as a function of the distance r from its central axis is h = (2/3g)r"2. It turns out to be consistent with Newtonian physics that the ball should either remain still at the top of the dome or start to roll down in any direction whatsoever, in the absence of any external forces. One might wonder how this squares with Newton's second law - how there could be an acceleration without an external force. It turns out, however, that because of the shape of the dome, in the first instant of the ball's movement, its acceleration would be zero, and after that it would have an acceleration given by the gravitational force. The physics would fail to explain the ball's standing still at the top of the dome or the ball's moving in one direction or another; it would fail to explain this either deterministically or stochastically. Thus, even Newtonian physics is not sufficient to yield the claim that everything that obeys the laws of physics can be explained in terms of the laws of physics.
And I doubt we do any better with non-Newtonian physics. After all, we do not actually right now know what the correct physics is going to be, and in particular we do not know whether the correct physics will make true the claim that everything that obeys the laws of physics can be explained in terms of the laws of physics. Besides, surely it would be an implausible claim that justification for the claim that the human race developed through evolutionary means depends on speculation about what the final physics will be like.
I do not have an argument that there is no other way of arguing for the evolutionary claim absent the PSR. But, intuitively, if one were not confident of something very much like the PSR, it would be hard to be justifiably confident that no biological features of the human species arose for no reason at all - say, that an ape walked into a swamp, and out walked a human, with no explanation of why.
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