I really wanted to like this book, and there are parts of it with which I agree at least in principle. But in the end I can't give it more than three stars.
There are two main reasons for this, both having to do with what William Dembski believes himself to be arguing.
First: The news in this book is supposed to be Dembski's notion of "specified complexity." This is made to sound much more innovative than it is, and few mathematicians are likely to be impressed by Dembski's alleged originality here. The idea is just that when we see patterns rather than apparent chaos, and we find that we can describe the pattern independently, we don't attribute the phenomenon in question to chance; we know there must be something more to it.
But as an argument for "intelligent design," this is an _ignoratio elenchi_. There's no evolutionist in the world who thinks complex biological structures developed by sheer chance, just as there's no cosmologist in the world who would propose _randomness_ as the sole alternative to divine intervention as the origin of the cosmos. Every one of Dembski's ideological opponents would argue that "specified complexity" -- in pretty much any non-question-begging way Dembski wants to define it -- is _exactly_ what evolution-by-natural-selection produces, and Dembski hasn't even begun to show this to be false.
So if there were anything new in Dembski's argument, it would have to be, not his notion of "specified complexity," but his claim that order and information can't arise from chaos. But you'll look in vain for any argument to this effect.
You'll also look in vain for any admission that scientists _always_ look for order and almost _never_ attribute it to "design." Dembski's examples are chosen to suggest the opposite: we know that watches were made by watchmakers; we know (or would know) that patterned signals from outer space come from alien intelligences rather than from random bursts of cosmic rays. But we also know that, say, the circumference of a circle is _always_ precisely pi times its diameter, and no scientist in the world would take this as conclusive evidence of "design" -- just of "intelligibility," which even Dembski himself is (properly) careful to _distinguish_ from "design."
So when all is said and done, we still haven't got a way to distinguish the "specified complexity" that results from intelligent design from the "specified complexity" that results from simple intelligibility. (There _is_ a cosmological argument that intelligibility itself implies an underlying intelligence, but Dembski doesn't give it. See Hugo Meynell's _The Intelligible Universe_, which I favorably reviewed a long time ago.) Maybe _The Design Inference_ covers this stuff better than this book does; at any rate Dembski keeps referring us to that book for all the arguments he isn't going to bother offering in this one, making sure to let us know that it's all very technical. But I find this sort of thing tiresome and full of handwaving.
Which brings us to the second problem, where Dembski's handwaving gets a whole lot worse. It's pretty disingenuous to claim that "intelligent design" isn't specifically Christian, and then write an entire book on the presumption that atheism and Christianity are the only two alternatives. Hasn't Dembski heard of any other theistic religions? (Hint: One of them starts with J, and Jesus himself was raised in it. And it believes the universe to be the product of intelligent design just as surely as Dembski's religion does.)
But somehow, when Dembski wants to indulge in tub-thumping Christian triumphalism, all those other versions of theism never bother making an appearance. This probably won't bother any Christian triumphalists among his readership, but it should bother anybody who takes seriously his claim that belief in "intelligent design" doesn't commit anyone to Christianity.
And boy, do the hands start waving when we learn that "Christ is the completion of science"! First we receive a fairly good exposition of the way the set of real numbers completes the set of rational numbers. (But even for this, the lay reader is referred in a footnote, not to a helpful introductory book, but to Walter Rudin's excellent but hardly elementary _Principles of Mathematical Analysis_. Really. How many lay readers are going to go look this one up? If Dembski had wanted to be helpful and enlightening rather than impressive and technically forbidding, wasn't there some other more elementary source to which he could have referred?)
And this is offered as an analogy for the way Christ completes science. The analogy is never explained, so Dembski's target audience will presumably just nod their heads. Readers with mathematical backgrounds, however, may have a different reaction. So may philosophers, who will probably recognize that one can perfectly well believe in the _logos_ without identifying it with "Christ."
In general, Dembski's philosophical sophistication is not great (yes, yes, I know he has a Ph.D. in the field). Here again, I think we're supposed to be impressed rather than enlightened, as when he makes a brief and general remark about naturalistic philosophers "like" John Searle and David Malet Armstrong, and then refers us in a footnote (in the _same_ footnote) to _The Construction of Social Reality_ and _Universals: An Opinionated Introduction_ without bothering to explain what _either_ philosopher argues in _either_ of these books. Good thing I'd already read them; I'd never have learned anything about them from Dembski.
His scientific sophistication isn't exactly on display either. For a book that's supposed to provide a "bridge between science and theology," there sure isn't much science in it. And if Dembski wants to show us how to distinguish design from simple order, he really, _really_ needs to get down to cases.
He's also very dismissive of what he likes to call "enlightenment rationalism," as distinguished, one presumes, from his own Christian rationalism. This sometimes lead to odd results, as when he remarks in a footnote (regarding those silly rationalists and their desire for "neat, self-contained explanations") that "Christ always destroys our neat categories." Really? Like "Christian" vs. "non-Christian"? Or like "design" vs. "accident"?
Yawn. I'm at least a quasi-theist (of the "panentheist" variety) myself, I'm generally very favorable to critiques of Darwinism (which, you understand, is not to say that I think they _succeed_, but that I think well-founded criticism is helpful to the scientific enterprise), and I do think the cosmos is best understood philosophically as the activity of a single absolute mind that I have no objection to calling divine. But based on the quality of argumentation and exposition I found here, I don't think I'll be reading _The Design Inference_ any time soon.