Firstly, let's look at what Sober seems to consider to be the heart of his challenge to design theory. Sober writes:

The first premiss in the likelihood formulation of the design argument – that Pr(O | Chance) is very low – is correct, then the only question that remains is whether Pr (O | Design) is higher. This, I believe, is the Achilles' heel of the design argument ... The problem is that the design hypothesis confers a probability on the observation only when it is supplemented with further assumptions about what the designer's goals and abilities would be if he existed. (p.10)I take issue with Sober in a couple of areas at the heart of this analysis, and it is gratifying that the discussions on this blog have already highlighted the weakness of his thesis.

The first issue is that of probabilities. In effect, Sober says that, since we don't know the prior likelihood of there being a designer, we can't estimate the likelihood of the design hypothesis.

A “quick and dirty” response to this is to estimate the likelihood of there being a designer who is appropriately qualified to do the work that is claimed of him. This sounds absurd (“What is the likelihood of there being a god?”) but the nature of this argument against design makes it into a serious question. It isn't reasonable to say that we don't know the likelihood of there being a God and then disallow attempts to establish bounds on this figure.

In a sense, it could be objected that the answer to this is arbitrary. But, given the wide spread of religious beliefs, is it reasonable to charge that the likelihood that there is a designer is much lower than (say) one in a million? We can't meaningfully estimate the likelihood that there is a designer; but I think it is reasonable to place bounds on the likelihood. Once the bounds are in place, it is then reasonable to draw inferences based on those bounds, whilst acknowledging as always the fact that such inferences are provisional.

The second, more formal, response is that, whilst Sober's analysis is all very well for “high” probabilities, and in principle it can be argued that it works for all probabilities, in practice when probabilities reach sufficiently small levels, they pass the point where chance is a reasonable explanation.

To demonstrate this, let's attach some numbers, for the sake of argument. Let's suppose that the probability of (say) the transition from prokaryotic life to eukaryotic life turns out to be 10

^{-200}. Dembski argues for a Universal Probability Boundary (UPB) – a concept that, incidentally, Sober makes no reference to. Dembski says that once a specified event becomes so improbable that it exhausts the probabilistic resources available in the universe, the chance explanation is no longer reasonable. The boundary he suggests is 10

^{-150}.

Sober argues that the key question is the relationship between the chance hypothesis and the design hypothesis. “My claim,” he says, “is not that design theorists must have independent evidence that singles out the exact goals and abilities of the putative intelligent designer.” (p.11) However, he adds, they do have to show that the design hypothesis is more likely than the chance hypothesis. The chance hypothesis may be improbable, but since we can't establish the likelihood of the design hypothesis, a design inference would not be safe.

But Dembski, on behalf of design theory, argues that once the probability of the chance hypothesis is below the level of the UPB, the chance hypothesis is no longer viable either. If the probability of the prokaryote/eukaryote transition is 10

^{-200}, then the relative likelihood of the design hypothesis is irrelevant, because the chance hypothesis is so small that chance isn't a reasonable explanation. We would need 10

^{50}universes, all directed to nothing other than achieving this transition, before we would expect to see the transition occurring even once. Of course, in that many universes, you would hardly be likely to “see” any single event at all!

Now, the example I have given is imaginary. But the point made by design theorists is that, if something is sufficiently improbable, then the chance explanation simply isn't reasonable. It isn't the case that the chance explanation is somehow acceptable at any arbitrarily small probability – if the probability is too small, then the chance explanation has to be excluded as well.

So what are we then left with? ID is particularly interested in specified events of small probability. Barring any alternatives, we have left a design hypothesis of indeterminate probability, or a chance hypothesis which the universe (or the relevant system) does not have sufficient probabilistic resources to justify. In this situation, it becomes apparent that the inference that somebody will draw depends almost entirely on their presuppositions. If somebody can accept the idea of a designer, then they will be happy with the design hypothesis. If they can't, then regardless of the fact that it is impossible – potentially far less possible than Dawkins would accept as a limiting case (see The Blind Watchmaker) - they have to accept the chance hypothesis.

Of course, there is a danger that a design hypothesis is “unscientific” - because at its barest (as Sober says on p.7) it consists of the statement “God did it”. Any event can be ascribed to design, and as opponents of design theory argue, this simply closes down science. The probability of the event simply becomes the same as the likelihood of there being a God.

However, the Intelligent Design movement has never been interested in this approach. In Darwin's Black Box, Behe never pushes for an early conclusion of a design inference, and neither does he argue that a design inference ought to be the last word. This is important, of course; both Kepler and Newton made non-naturalistic assumptions, according to Sober (p.1); this didn't stop science from considering what shaped the surface of the moon, or how the solar system was formed. A provisional inference of design shouldn't shut down science. It may, however, discourage an unfruitful line of scientific enquiry in favour of more profitable ones.

Next time: The Designer's Goals and Abilities