I was just reading this article on the Design Argument contributed to The Blackwell Guide to Philosophy of Religion by Elliot Sober. Here’s a quick two-paragraph quote:
In the continuing conflict (in the United States) between evolutionary biology and creationism, creationists attack evolutionary theory, but never take even the first step toward developing a positive theory of their own. The three-word slogan “God did it” seems to satisfy whatever craving for explanation they may have. Is the sterility of this intellectual tradition a mere accident? Could intelligent design theory be turned into a scientific research program? I am doubtful, but the present point concerns the logic of the design argument, not its future prospects. Creationists sometimes assert that evolutionary theory “cannot explain” this or that finding (e.g., Behe 1996). What they mean is that certain outcomes are very improbable according to the evolutionary hypothesis. Even this more modest claim needs to be scrutinized. However, even if it were true, what would follow about the plausibility of creationism? In a word – nothing.
It isn’t just defenders of the design hypothesis who have fallen into the trap of supposing that there is a probabilistic version of modus tollens. For example, the biologist Richard Dawkins (1986, pp. 144-146) takes up the question of how one should evaluate hypotheses that attempt to explain the origin of life by appeal to strictly mindless natural processes. He says that an acceptable theory of this sort can say that the origin of life on Earth was somewhat improbable, but it cannot go too far. If there are N planets in the universe that are “suitable” locales for life to originate, then an acceptable theory of the origin of life on Earth must say that that event had a probability of at least 1/N. Theories that say that terrestrial life was less probable than this should be rejected. This criterion may look plausible, but I think there is less to it than meets the eye. Suppose only ten lotteries are held in the whole history of the universe and that you have just won one of them. The fact that N=10 does not provide a licence for dismissing any theory about how your lottery worked that says that the probability of your winning was less than 1/10.
For those not conversant in the technical descriptions of logical arguments, modus tollens is an argument that takes this form:
If X then Y
not-Y
not-X
A probabilistic version of modus tollens would take this form:
Pr(Y | X) is high
not-Y
Pr(not-X) is high
where Pr(Y | X) is the conditional probability that Y is true given that X is true. Under modus tollens, if a theory X says that Y is probable, and we learn that in fact Y is not the case, then we should conclude that theory X is probably false.
It is relatively easy to find an example which shows that the probabilistic version of modus tollens is incorrect. Sober gives this example in his paper on Intelligent Design and Probability Reasoning.
It is easy to find counterexamples to this principle. You draw from a deck of cards. You know that if the deck is normal and the draw occurs at random, then the probability is only 1/52 that you’ll obtain the seven of hearts. Suppose you do draw this card. You can’t conclude just from this that it is improbable that the deck is normal and the draw was at random. This example makes it seem obvious that there is no probabilistic analog of modus tollens. However, this feeling of obviousness can fade when we look at other examples in which the relevant probability is far less than 1/52.
I’ve seen good scientists fall into the probabilistic modus tollens trap many times. Pointing out the problems with this kind of reasoning is a great defense against the proponents of ID, but honest scientists have to make sure we don’t fall into the same trap ourselves.
