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
t_{1}, and the possible states of the universe before the advent of living things, call that time
t_{0}. There is then an exact correspondence between the possible states at
t_{1} that exhibit the sort of complexity
C we are trying to explain and the possible states at
t_{0} that would, over the course of
t_{1}−
t_{0} units of time, give rise to
C. Therefore, if the direct probability of
C arising at
t_{1} at random is incredibly low, the probability of getting a state at
t_{0} that would give rise to
C at
t_{1} 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
t_{0} and at
t_{1} 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)=
x^{2}, 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
PoincarÃ© 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
f_{t} from
S to
S, such that by law the universe is in state
s at time
t_{0} if and only if it is in state
f_{t}(
s) at time
t_{0}+
t. Let
C_{1} be the subset of
S containing all states the exhibit the complexity feature
C. Let
C_{0} be the subset of
S containing all states that would result in a state in
C_{1} after the passage of
t_{1}−
t_{0} units of time. In other words,
C_{0}={
s:
f_{t}(
s) is in
C_{1}}, where
t=
t_{1}−
t_{0}. Then the probability of
C_{0} is the same as the probability of
C_{1}. Hence, if our world's present state's being in
C_{1} 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
C_{0} at
t_{0} 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
C_{1} from scratch, Darwinism hasn't done anything to weaken the inference to that theistic hypothesis since
C_{0} is just as unlikely as
C_{1}. Even if the evolutionary theory is correct, we still need an explanation of why the universe's state was in
C_{0} at
t_{0}.
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
- 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
t_{1} but that
- 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:
- 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.