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I'm at a loss for how it is supposed to do this. Complex Specified Information makes sense to me, but he doesn't seem to propose a method to detect any specifications, they must be assumed.
The basic idea is pretty common. Given a fair coin the probability of any sequence of tosses depends only on the length. Obviously it would be daft to say that there must be something odd going on just because you’ve tossed a coins twenty times in a row. But if you get twenty heads in a row - which is a million-to-one shot you would be justified in thinking that maybe there is something making it come up heads.
Dembski does have some ideas on what makes a specification valid and they aren’t too bad, but I don’t think that they are objective enough to call his design inference a mathematical proof. I may quote them later - I do have a copy of the book (remaindered - no way I’d have paid full price)
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Evolutionary mechanisms are ruled out a priori with his method not because of the 'necessary' sieve in his Explanatory Filter, but because natural selection doesn't specify positively any patterns of surviving organisms genome, right?
Evolutionary explanations are supposed to be ruled out based on probability calculations. In reality I’ve never heard of Dembski coming close to doing that - in one case the reason was Behe said so which doesn’t even seem to be true.
(In
Darwin’s Black Box Behe admitted that there were indirect routes of evolution that sidestepped his argument. He assumed that they were too unlikely to count but never made an argument to that effect, and certainly never showed that the probability fell below Dembski’s probability bound. He was almost certainly wrong, too)
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but natural selection is the environmental pressure selecting negatively (akin to Dembski's sieve) the organisms which are unfit, and the rest of the population it is blind to, right? In other words, natural selection is simply death of the unfit, no?
That’s not really accurate. Positive selection for beneficial traits is an important part of evolution. The simplest explanation is that, in aggregate, genes that help individuals successfully reproduce become more common while genes that hinder that become less common.