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From my surface understanding of the Design Inference, it is nothing more than a Designer of the Gaps argument backed by bad math. His main thesis seems to be "it is too improbable, therefore magic"
Formally it is more “everything else I can think of is proven too unlikely therefore some unspecified designer did it by unspecified means”.
That’s poor as science (since the conclusion is too damn vague), risks error (it’s too easy to miss something) and pretty much useless where he wants to apply it. (The calculations for evolution would be a ridiculous amount of work even if we had good figures)
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Of course, internally his whole thesis hinges on getting the probabilities right, and from what I have seen he uses the Sharpshooter fallacy where probabilities are calculated after an event has occurred (which is the wrong way to do it).
In my experience it’s more a case of he finds excuses not to do the calculations or does the wrong calculation entirely. He does actually take some steps to avoid the sharpshooter fallacy, but having a more or less valid methodology - in principle - is no good if the application is always seriously lacking.
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In a nutshell, if we look at evolutionary pathways down to the fine grained level of individual mutations then every evolutionary pathway is extremely improbable
Yes, that is a potential flaw of the method but I haven’t seen Dembski do a good enough job of applying his method for that to be a real issue in practice. If Dembski ever gets to calculating the probabilities of evolutionary paths (and he may have, I haven’t looked at his work in the last few years) that might be an issue. But I haven’t seen him even try it, even when he should.
So, I think you are missing the mark somewhat.