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I've sketched out the way that a Bayesian might approach design detection, and it frankly makes sense to me. You incorporate the probability that a designer exists a priori, then you evaluate the probability that the designer would produce some data compared to the probability that other causes (natural selection, random weathering, whatever) would produce the same data, along with the probability of those processes occurring. Since the probability that evolution occurs is 1 (even Dembski doesn't disagree), but the probability of a designer existing (absent circular invocations of design) is a purely theological question, it's hard to know what to do. Dembski believes, deep in his heart, that a designer exists. Others assign that a probability of zero, in which case design is irrelevant. If we could pick a prior probability of a designer, we'd still need a coherent model of its capabilities and desires to be able to decide how likely it is that the designer would have made things a particular way.
The existence of life in all its glory is "remarkable" in one sense, because it is so striking. But we know far less about the probability of life emerging than we do about the probability of cookies walking away of their own accord. In fact, I would suggest that calculating the probability of, say, the bacterial flagellum evolving is simply impossible. I have no idea whether it is 10^2, 10^150, 10^500 or 10^1,000,000. And neither does anyone else. The less one knows about the likelihood of something happening, the harder it is to label that event "remarkable" in a probabilistic way. As a result, invoking a design event by an appeal to a spurious notion of probability seems rather shaky - especially when the probability of a designer existing is not estimated at the same time!