Classic Paley-style design arguments go like this: There is some complex biological feature C which is such that
- God would have good reason to produce C, and
- C is extremely unlikely to occur through a random combination of elements.
It is concluded that probably God produced C, and hence probably God exists. The standard story is that Darwin undercut Paley-style arguments by providing a plausible explanation that does not involve God.
I shall suggest that the story is not so simple, and that, in fact, a very powerful Paley-style design argument may continue to go through.
The reason I say “suggest” reather than “argue” is that my argument is based on a crucial simplifying assumption. I shall assume a physics with a classical Hamiltonian dynamics satisfying Liouville’s Theorem. (To some readers this may already give a lot of my game away.) The justification is two-fold. First, for aught that we know, the correct dynamics of the world, whether deterministic or not, is such as to support some analogue of Liouville’s Theorem. Second, Darwin’s work appears to be consistent with classical mechanics, and was developed when classical mechanics was king. Thus, if Darwin’s work refutes classic Paley-style design arguments, this refutation should be consistent with classical mechanics.
Now, begin by posing this question: The standard story claims that Darwin naturalistically explained the explanandum of a Paley-style argument in a way that undercut that arguments–what is that explanandum?
Here are three options for the explanandum of a Paley-style argument, where t1 is the present:
- C occurs at t1
- C occurs at some time or other
- C occurs as soon as it does.
The most obvious option seems to be (3). Here is the watch upon the heath, and we wonder why there is here and now a watch upon the heath. But if (3) is the explanandum, then we have a serious problem for the Darwinian alternative to the design hypothesis. The Darwinian alternative is supposed to go something like this. We grant that it is “astronomically unlikely” (I’ll use that loose phrase for something like 10−30 or lower) that a random combination of elements should immediately produce C. In other words, we grant that it is astronomically unlikely that a random state of the universe should be such as to exemplify C. But we claim that the state of the world at t1 wasn’t produced randomly from scratch—it evolved, by means of variation and natural selection, from an earlier simpler state at t0. And this evolutionary story makes C more likely.
Except it doesn’t. Let S be the set of all possible physical states of the universe. Let C1 be the subset of S at which C is exhibited. Let C0 be the subset of S consisting of all the states s which have the property that according to the laws, if s occurs, then t1−t0 units of time later C will be exhibited. Then because in classical mechanics we have two-way deterministic laws (so that not only do earlier states determine later ones, but later ones determine earlier ones) only, there is a one-to-one correspondence between C0 and C1. Intuitively, then, if it was astronomically unlikely that the state of the world at t1 should be in C1, it will be astronomically unlikely that the state of the world at t0 should be in C0. But if it is just as astronomically unlikely that the universe should be in C0 as that it should be in C1, then the Darwinian explanation hasn’t accomplished anything to undercut the design argument. So far this isn’t my own argument—I once came across a paper, which I did not note down the author of, in some journal from the 1950s or 1960s, perhaps the Review of Metaphysics, that made this argument. I wrongly dismissed the argument as uninteresting until I got to thinking about it again recently.
My initial reason for rejecting the argument was two-fold. First, the argument assumed determinism. Second, the argument, if my memory of it is accurate, had a serious hole. The mere existence of a one-to-one correspondence between possible states of the universe at t0 and at t1 only shows that the cardinalities of C0 and C1 are equal, not that their probabilities are equal (any non-zero-length interval of real numbers has the same cardinality, but in general given a probability measure they will not all have the same probability).
But in regard to the assumption of determinism, see my opening remarks. And in regard to the hole, Liouville’s Theorem exactly plugs that. Liouville’s theorem says that the evolution of a system governed by Hamiltonian mechanics—and classical systems will be like that—preserves volume in phase space (i.e., in the phase of all states of the system). And volume in phase space seems exactly the right measure of probability—at least, that’s what the classical statistical dynamics assumes. (There are some technical worries about infinite volumes, but perhaps one can do some limiting procedure in my argments.) Consequently, we learn from Liouville’s Theorem that the one-to-one correspondence between C0 and C1 preserves probability, and hence we can correctly conclude that the probability of C0 is astronomically low given that the probability of C1 is astronomically low. In other words, probabilistically, C0 is just as remarkable as C1.
Trent Dougherty gave me this vivid illustration of the point. Imagine Laplace’s demon, who knowing the state of the universe at one time immediately sees what state the universe must have at all other times. We look at the universe at t1 and exclaim: “By golly, we have C. How unlikely!” And when we look at the universe at t0—at which time we may have only the simplest life forms or even no life forms on earth—we find nothing remarkable. But Laplace’s demon could look at the universe at t0 and exclaim: “By golly, this universe is such that it will exhibit C in t1−t0 units of time. How unlikely!”
I am not disputing that Darwinian evolution may provide a correct explanation of (3). But it does not provide a probability-raising explanation of (3), and to challenge a design argument based on (3) it would need to provide a probability-raising explanation of (3).
What about (4)? Maybe the reason why Darwinism couldn’t provide a probability-raising probability of (3) was because of (3)’s reference to a particular time. But if the explanandum is (4), maybe we can indeed get probability-raising.
However, without accounting for Darwinism, in our classical setting we can say that the physical probability of (4) is one. For classical mechanics turns out to be ergodic. From “almost all” (this is a precise term in measure theory: a property holds of almost all points in a space provided that the set of points of which it doesn’t hold has measure zero; for instance, almost all real numbers are irrational, if we are working with Lebesgue measure) starting points, we will visit arbitrary small neighborhoods of all points infinitely often. Now the kinds of features C that Paley-style arguments are run on have non-zero tolerances—in other words, if s is the present state of the universe, not only is C exhibited in s, but there will be a small neighborhood of s at all points of which C is exhibited. (If C is the existence of human-type brains, then any world whose particles are sufficiently close in position and momentum to those of our world will also have human-type brains, albeit just slightly differently shaped.) It follows from ergodicity that from almost all starting points the system will eventually produce C, and will even do so infinitely often, and hence the physical probability of (4) is one, without taking any account of evolutionary theory.
Thus, a design argument based on (4) is indeed undercut. However it is not undercut by evolutionary theory, but simply by the underlying classical mechanics.
This leaves (5). This may be the best bet for what evolutionary theorists should say in respect of the explanation of C. It is a puzzling fact that complex features like C should occur so soon after the beginning of the universe. We are less than 14 billion years from the Big Bang. This isn’t really all that long. Darwin famously talked of countless ages for evolution to work in. But if (5) is the explanandum that the evolutionary theory explains, then the talk of countless ages should be de-emphasized. (If an age is 1000 years, then 14 billion years is not at all a countless number of ages—if I counted the ages, counting out one age each second, 12 hours a day, I would be done in less than 11 months.) Ergodicity all but guaranteed, in an appropriate classical setting, that C would occur. But the wonder of evolutionary theory is that C occurred so quickly. Now, there is a fly in the ointment here: I doubt that the mathematics of evolutionary theory is yet sufficiently advanced to be able to pre
dict that the processes of variation and selection are fast enough to be at all likely to produce C in the amount of time available. But where one cannot prove, one may sometimes reasonably speculate, and I am happy to grant that evolutionary theory may well give a good probability-raising explanation of (5). But (5) need not be the design theorist’s explanandum. And if it’s not, then evolutionary theory’s success in respect of (5)—impressive as it is scientifically—is not relevant to the design argument.
So far I’ve looked at how the three explananda (3)-(5) do given evolutionary theory, on my assumption of classical mechanics. We have seen that in cases (4) and (5), we may well be able to give good probability-raising naturalistic explanations—though, interestingly, in case (4) we can do this without any mention of evolutionary theory. So these are not promising candidates for a design argument. But (3) is. So let me now give such an argument.
Suppose C is the existence of contingent intelligent beings. Let t1 be the present time. Given the discussion of (3), we see that evolution does not raise the probability of C occurring at t1 beyond the presumably astronomically small probability that it would occur at t1 by a completely chance coming-together of elements. I shall also assume that we have only one universe, and it is not so incredibly large that as to make C better than astronomically unlikely. (On multiverse theories, or theories with a very large universe, we get (3) with high probability, but again without evolutionary theory playing much of a role.) Give our assumptions, the conditional probability that C occurs at t1 astronomically small on naturalism. But God is responsive to reasons, and hence at any given time, if God exists, it is not very unlikely that he has created intelligent beings that exist at that time. Thus, the conditional probability that C occurs at t1 given theism is not very low. If theism and naturalism are our only hypotheses, this gives very strong confirmation to theism.
Let’s assign some numbers. Suppose the probability of C occurring completely at random at t1 given naturalism is 10−30. The probability of a state at t0 that evolves into a state that exhibits C at t1 is also 10−30. So, P(C at t0|naturalism)=10−30. Now the probability that God would have created intelligent beings that exist at t1 is surely at least 10−9. Granted, we may worry that God might take a long time to prepare the universe for intelligent beings. But God also has good reason to ensure that there always are intelligent creatures, or that they be there as soon as possible. I don’t know how to evaluate these probabilities but one in a billion is very conservative. So P(C at t0|theism)=10−9, say. Suppose that theism and naturalism are our only options, so P(naturalism)=1−P(theism), and suppose that the prior probability of theism is one a trillion: P(theism)=10−12 (this is crazy, of course, given the explanatory power of theism). We can now plug the numbers into Bayes’ theorem and get, to a very good approximation, P(theism|C at t0)=0.999999999. And how much more could one want from an inductive argument?
Of course, this argument neglects three important factors: (a) multiverse hypothesis; (b) giant universe hypothesis; and (c) non-classical mechanics. Note that (a) and (b) are not Darwinian in nature. And while (c) might make Darwinian explanations of (3) be probability-raising, that this is so would need to be argued for. One might, for instance, think that the kinds of statistical results that Liouville’s Theorem yields are likely to hold at least approximately for the time-evolution of macroscopic objects.
Let me add that the argument is partly inspired by reflection on an unpublished multiverse-based argument by Mike Rota.