How to Know God Exists is in part of summary of the book so far. Ray reprises his arguments that the universe is extraordinarily fine-tuned, that the universe can not have come from nothing, that abiogenesis is impossible without miracles, and that evolution is impossible.
Fine-tuning, of course, means that the universe has properties that permit stars and planets to form naturally and persist for billions of years: conditions permitting evolution. It always strikes me as odd when a young-earth creationist, or a "no one knows how old the universe is" creationist, brings up fine-tuning. Young-earth creationists are fond of arguing that this or that feature of the universe could not persist for millions, much less billions, of years, that (though they don't quite put it that way) God has slapped together some Yugo universe that will fall apart after a few thousand years of normal use. A young-earther wouldn't expect and cannot explain fine-tuning (an evolutionist might be reduced to uncertain speculation about the cause of fine-tuning, but he'd certainly expect it).
Assuming that the universe could not have come from literally nothing, this does not, of course, rule out the possibilities that it came from not very much at all, or has existed for all time (all time perhaps being a finite amount of time, or the universe having existed in other forms before this). "The universe must have come from something" is very short of a demonstration that the universe must have been manufactured by an uncreated omnipotent Creator.
Noting that we have as yet no very detailed and well-tested theory of abiogenesis does not prove that no such theory is possible or that abiogenesis would require supernatural intervention, any more than ignorance of Plasmodium parasites before the modern age meant that malaria was, in the past, caused by bad smells or demons.
And Ray simply asserts, about evolution, things that are demonstrably not true: that there is no concrete evidence for it (thus ignoring transitional fossils, comparative anatomy, comparative genomics, ERVs, pseudogenes, biogeography, etc.), that the Law of Biogenesis, which permits Brussels sprouts and cauliflower to be bred from the same species, somehow prevents changes from accumulating enough to transgress the nebulous boundaries around "created kinds."
On the subject of evolution, Ray does not so much quote-mine as simply miss the point of a statement by Stephen Gould that Homo sapiens is a "glorious accident," the result of an estimated sixty trillion contingent events. Ray wonders how anyone could accept evolution in view of those odds and the fact that we are, after all, here: how could one believe that all those events just happened to occur in exactly the right way at exactly the right time? But one could raise the same question about Ray himself, or any of his readers: starting with the first humans, how many hundreds of generations of ancestors had to marry just the right people, how many times did just the right sperm have to encounter just the right egg, to produce all our ancestors and any of us? If things had gone differently, different people would be here, just as blithely unconcerned with the unlikelihood of their ancestors as we are. And if evolution had taken a different route at any of those sixty trillion turning points (and Gould's point, of course, was that it very well could have), vastly different species and vastly different individuals would be here, but perhaps some of them would be intelligent and just as complacently certain as Ray that any plausible theory of origins had to explain why they were inevitable.
The bulk of the chapter consists of pointing out that historically, a lot of really smart people have believed in God. Ray asserts that science cannot contradict Christianity, since science arose in a Christian culture, and that faith itself cannot be a problem, since since we all have faith in something, whether God or human reason. Against the first point, I note that Christian culture, even more than Christianity itself, is a complex thing with many intellectual and ideological elements and no guarantee that they are all self-consistent and consistent with each other. It doesn't follow that because Christianity contains some elements that are science-friendly that Christianity as a whole is consistent with science, much less supported by it.
Against the second, I note that everyone must have some faith in human observation and reason just to get out of bed in the morning (or, indeed, to conclude in the morning that he is in bed). "Faith" in the working of your computer or your car or your logic is not the same thing as "faith" that some collection of ancient writings simply must be self-consistent and inerrant, and that any evidence to the contrary must be fake or misunderstood. Ray tries to ask us to give up faith in mere humans for faith in humans' infallible Creator, but he must end up asking us to keep that faith in mere humans, and add to it faith in a set of ideas compiled and interpreted by more mere humans.
Indeed, in some ways, it seems, Ray has more faith in human reason than I do: given that historically, quite a few very smart human beings have believed that, e.g. the sun orbits the Earth, I wouldn't assume that Isaac Newton's conviction that the universe exhibited the marks of an intelligent Designer automatically carried the same weight as his laws of motion and gravity. Whether we're talking about Albert Einstein or Antony Flew, they achieved fame and a reputation for genius because their ideas stood up to examination and turned out to be brilliant; their ideas were not considered brilliant or right merely because they were geniuses. And this applies to their views on God as much as to their views on gravity: Steno, for example, was not only a geological genius (and expert anatomist); he was a convert to Roman Catholicism who ended his life as a bishop. Would Ray have us embrace his Catholicism along with his theism, or will Ray have us suppose that Steno could, like the rest of us, be wrong sometimes, even in his theological opinions?