Tuesday, November 30, 2010

Darwinian evolution and determinism

Once I was looking at an old issue of a journal, probably the Review of Metaphysics from the 1950s or 60s, and I came across an intriguing paper arguing that evolution does not help explain the complex structures we find in organisms. The paper tacitly presupposed determinism and in effect noted that there was an exact correspondence between the possible states of the universe now, call it t1, and the possible states of the universe before the advent of living things, call that time t0. There is then an exact correspondence between the possible states at t1 that exhibit the sort of complexity C we are trying to explain and the possible states at t0 that would, over the course of t1t0 units of time, give rise to C. Therefore, if the direct probability of C arising at t1 at random is incredibly low, the probability of getting a state at t0 that would give rise to C at t1 is exactly the same, and hence also incredibly low, and evolution has made no progress. Consequently, evolution does nothing to undercut design arguments for the existence of God.
Now, the argument as it stands has two obvious holes. First, it assumes not only determinism, but two-way determinism. Determinism says that from any earlier state and the laws, the later states logically follow. Two-way determinism adds that from any later state and the laws, the earlier states logically follow. Fortunately for the argument, actual deterministic theories have been two-way deterministic. Second, the argument assumes that the exact correspondence between states at t0 and at t1 preserves probabilities. This need not be true. If we consider the set [0,1] (all numbers between 0 and 1, both inclusive), and the function f(x)=x2, then f provides an exact correspondence between [0,1] and [0,1], but if X is uniformly distributed on [0,1], then the probability that X is in [0,1/4] is 1/4, while the probability that f(X) is in [0,1/4] is 1/2 (since for f(X) to be in [0,1/4], X need only be in [0,1/2]). But, again, in the kind of classical physics setting that underlies classical thermodynamic results like the Poincaré recurrence theorem, the transformations between states preserve phase-space volume, and it is very plausible that if you preserve phase-space volume, you preserve probabilities.
Once we add two-way determinism and phase-space volume preservation, which are reasonable assumptions in a classical setting, the argument is in much better shape. (Actually, if you can still have something relevantly like phase-space volume preservation, you could drop the determinism. I don't know enough physics to know how helpful this is.) The argument is now this. Let S be the set of all possible physical states of the universe. For any real number t, the two-way deterministic physics defines a one-to-one and onto function ft from S to S, such that by law the universe is in state s at time t0 if and only if it is in state ft(s) at time t0+t. Let C1 be the subset of S containing all states the exhibit the complexity feature C. Let C0 be the subset of S containing all states that would result in a state in C1 after the passage of t1t0 units of time. In other words, C0={s:ft(s) is in C1}, where t=t1t0. Then the probability of C0 is the same as the probability of C1. Hence, if our world's present state's being in C1 was too unlikely for chance to be a reasonable expectation, then the Darwinian explanation in terms of the world having been in a state from C0 at t0 is no better. In particular, if a theistic design hypothesis would do better than randomness if it were a matter of generating a state in C1 from scratch, Darwinism hasn't done anything to weaken the inference to that theistic hypothesis since C0 is just as unlikely as C1. Even if the evolutionary theory is correct, we still need an explanation of why the universe's state was in C0 at t0.
This argument is on its face pretty neat. One weakness is the physics it relies on. But bracket that. The kind of measure-preservation that classical dynamics had is likely to be at least a decent approximation to our actual dynamics. But there is a more serious hole in the argument.
The hole is this. If what evolution was supposed to explain is why it is that the universe is now in a state exhibiting C, the argument would work. But that isn't what evolution is supposed to explain. Suppose C is the existence of minded beings like us. Then it seems that we are puzzled why C is exhibited at some time or other, not why
  1. C is exhibited now.
Sure, evolution can't do a very good job explaining why C is exhibited now, as opposed to, say, 10 million years ago.
So perhaps the explanandum is not that C is exhibited at t1 but that
  1. C is exhibited at some time or other.
But we can predict (1) with unit probability without any posit of evolution simply by assuming that the dynamical system is ergodic: an ergodic system will exhibit C infinitely often from almost every starting point, given reasonable assumptions on C. Thus, if (2) is the explanandum, and we have the classical setting, we don't need evolution. We just need enough time. And, by the same token, (2) is no basis for a design argument.
Maybe the puzzle is not about (1) or (2), but about:
  1. C is exhibited within 14 billion of the beginning of our universe.
Ergodicity makes (2) all but inevitable, but it is puzzling that C should be exhibited so soon. After all, 14 billion years is not that much. It's only about three times the age of the sun. This account of what it is that evolution accomplishes in respect of C seems to turn on its head Darwin's emphasis on the "countless ages" that evolution required—in fact, evolution accomplished its task very quickly, and that speed is what the theory explains. Ergodicity without the selective mechanisms would very likely take much longer.
One problem with this as the account of what evolution does to explain C is that currently we do not have very good mathematical estimates of how long we can expect evolutionary processes to take to produce something like C, where C has any significant amount of complexity. So perhaps we do not really know if evolution explains (3).
Another move that one can make is to say that evolution does explain (1), and it does so by giving a plausible genealogical story about C, but the evolutionary explanation does not confer a non-tiny probability on (1). If so, then the evolutionary explanation may be a fine candidate for a statistical explanation of (1), but it will not be much of a competitor to the design hypothesis if the design hypothesis confers a moderate probability to (1).
In fact, we can use the above observations to run a nice little design argument. Suppose that C is the existence of intelligent contingent beings. Then for an arbitrary time t, the hypothesis of theistic design gives at least a moderate probability of the existence of intelligent contingent beings at t, since God is at least moderately likely to fill most of time with intelligent creatures. (And Christian tradition suggests that he in fact did, creating angels first and then later human beings.) Therefore, evolutionary theory assigns incredibly tiny probability to (1)—equal to the probability of getting C from scratch at random—but the design hypothesis assigns a much higher probability to (1). We thus have very strong confirmation of theism.[note 1]
But that assumes an outdated dynamics. Whether the argument can be made to work in a more realistic physics is an open question.


Alexander R Pruss said...

I posted a different version of the same basic point here.

Crude said...

I've had similar thoughts, and an issue related to this is covered in this blog entry, in a limited way. In that entry, Michael Ruse is quoted arguing that the arrival of 'intelligent, moral' beings is supposed to be ridiculously low on Darwinism - in fact, he argues (though I don't think he understands the consequences of what he's saying) that to make the arrival of "intelligent, moral" beings likely on Darwinism, you'd have to embrace some variant of the multiverse theory. Ruse is trying to urge Christians to reject an omniscient, omnipotent God and accept multiverses in order to be true to Darwinism while remaining "Christian", but going by his words alone he seems to be giving an intelligent design argument unintentionally.

Of course, the other side of the problem is that if the odds of arriving at T1 'at random' is high, that would imply directionality in the processes and mechanisms of evolution, wouldn't it? Which, again, Ruse himself regards as also being friendly to theism, even though he doesn't want to go down that road (in part because he thinks it goes against the commitments of Darwinism.)

That seems to be a Catch-22 for naturalism, doesn't it? If the universe is such that the arrival of humans is taken to be likely, then evolution starts to look like a teleological process - which of course naturalists don't want. But if the arrival of humans is taken to be unlikely, then the fact that we're here becomes puzzling and design of a different variety is inferred.

My main problem with Darwinian evolution on this front is that the only way it seems to help out the naturalist is through assuming the one thing that no lab experiment could ever hope to demonstrate - that there was no design or intention in the way evolution unfolded. (After all, evolutionary principles are used by some programmers - we can imagine that to God, evolution could or would just be another means to an end.) Without that assumption smuggled in, Darwinism seems to be of almost no use to the naturalist re: design. (Putting aside Problem of Evil complaints.)

Dustin Crummett said...

I'm not entirely sure I understand everything that's going on in the argument, but why couldn't a response go something like this: we see C, and we judge it to be really unlikely. However, Darwinian evolution shows us that C follows from a lot of states that really aren't all that unlikely. Therefore, what Darwinian evolution shows is that C isn't nearly as unlikely as we thought it was.

Alexander R Pruss said...

That is a neat answer, and it's come up in the prosblogion discussion of the argument, too. I think the fragility of C militates against C being likely--pretty small modifications make C not be there, so for any state that has C, there are many nearby ones that don't.

Dustin Crummett said...

Doesn't Darwinian evolution give us an explanation of why C is more likely than those other states, though?

Hassan Abdillah said...

Professor Pruss, can you share the link to your paper "Western Monotheism and Evolution"? I cannot find it anywhere. Thanks!