Probabilistic Modus Tollens and the Design Argument

Philosopher Elliott Sober thinks that design arguments against naturalism commit a fallacy that he calls 'probabilistic modus tollens', which he takes to be an inference of the following form:

Probably, (if p then q).
Not-q.
Therefore, probably, not-p.

Thus, he construes the argument against naturalism from cosmic fine-tuning as follows:

Probably, (if naturalism were true, then the universe would not be life-permitting).
The universe is life-permitting.
Therefore, probably, naturalism is not true.

He then points out that this pattern of reasoning is problematic:

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.

Clearly the reasoning in this example is bad, but whether that constitutes a serious objection against design arguments depends on whether such arguments do in fact reason in this way. And here I think Sober is mistaken.

In the card example, there is nothing special about the seven of hearts. The antecedent probability of drawing any given card is 1/52. Hence, we'd be in the same position vis-a-vis the issue of the normality of the deck and the randomness of the draw no matter which card was drawn.

Now modify the example slightly. Before you draw the card an enemy puts a gun to your head and says "Draw a seven of hearts or die." Now there is something special about the seven of hearts. It has been singled out independently of the fact that it was drawn as being of special interest. (It is not the case that any draw would be equally noteworthy.) And now, given that you get only one draw, if you do draw the seven of hearts, a design hypothesis fairly suggests itself. That you drew just the card you needed when it was unlikely that you would do so suggests that the draw might have been rigged. (Of course, this inference would be more impressive if the odds against you were a lot higher.)

The fine-tuning argument is more like the second example than the first. We would not expect a random universe to be life-permitting, just like we would not expect a random card to be the seven of hearts. But that's not all. We aren't interested in any random universe. We're interested in a particular kind of universe (a life-permitting one), a kind of universe that can be singled out in advance as one that an intelligent designer would likely have a reason to be interested in. Hence, given the assumption that this is the only universe "drawn", we have reason to suspect design.

Of course, there is one difference. Maybe this is not the only universe that has been "drawn". If there are or have been a great many universes varying in their physical properties, then it may not be so improbable that a life-permitting one has turned up. As to whether this "many universes" theory is better than the "design" theory or not is a tricky issue, one which I'll set aside for now.

My point right now is simply that Sobel has misconstrued the design argument by overlooking the fact that the inference is being driven by several factors: (1) the low probability of a randomly selected universe being life-permitting given naturalism; (2) the fact that such a universe would likely be of independent interest to a putative designer; and (3) assumptions about the available probabilistic resources. So the form of the fine-tuning argument is not that of probabilistic modus tollens, but rather something more like this:

With very high probability, (if naturalism were true, then a randomly selected universe would not be life-permitting).
Probably, (a life-permitting universe would be of special interest to an intelligent designer).
This universe is life-permitting.
There are no other universes.
Therefore, probably, naturalism is false (and there is an intelligent designer).

This strikes me as a reasonable inference. It's certainly not conclusive as it stands - the fourth premise is particularly open to challenge - but neither is it stupid or fallacious as Sobel suggests.