I. Book I Chapter 3- The Reality of the Law
A. The Law of Human nature is an odd sort of fact; it is not a truth about the way things are, but a truth about the way things ought to be.
1. Is this law of nature a fact about what is helpful for human beings? No, someone sitting in the seat I would like to sit in is not breaking any rules, but is inconveniencing me. Someone who tries to trip me but fails is doing something wrong, but does no harm to me.
2. Is decent behavior the behavior that pays? No, it may pay people as a whole, but does not pay people individually. It may require me to do things which are not in our own self-interest.
II. Conculsion: The Law of human nature is real, and its claims cannot be reduced to claims about what serves my interests, or what is helpful to me.
II. Book I Chapter 4-What Lies behind the law
A. Two types of world view
1. The materialist world view-everything happened by chance or fluke. This is sometimes misinterpreted; what he means is that the characteristics of the universe arose without intelligent design. The ultimate causes at work in the world possess no intelligence. This is what scientist Richard Dawkins has in mind when he talks about the Blind Watchmaker. That blind watchmaker is the evolutionary process, which has no purposes, but simulates purpose through trial and error.
2. The Religious View: the ultimate causes of the universe are "more like a mind than anything else we know. That is to say, it is conscious, it has purposes, and prefers one thing to another."
3. Science cannot decide which of these views is true. Science analyzes what is observable; whether or not there is something "beyond" or "behind" the observable world is not something that science can decide.
I (VR) think that this greatly oversimplifies the situation with respect to science. It does seem to me that scientific evidence can provide inductive support, or may inductively undermine, religious claims.
4. If God were to make himself aware of his existence, it would have to be through an inner law, not through some observable facts. We know, from the inside, that we are under a law, and that law was not created by ourselves. Looking at this moral law, we can see that it makes sense on the religious view, but does not make sense on the materialist view. Therefore we have good reason to believe that the religious view is true.
In other writings, Lewis appeals to other considerations than just a moral law to determine whether or not there is a power behind the universe; so I have some objection to this way of framing the argument.
However, perhaps we can frame the argument in terms of Bayesian confirmation. Well, I don't think I can very well go into Bayesian theory in this post (though you might look at this from Fides Quaerens Intellecutm http://blog.johndepoe.com/2005/10/how-to-build-bayess-theorem.html). But here's the idea. Suppose you are thinking about the question of God, and you haven't thought carefully about the idea of moral phenomena as it relates to theism. Suppose, just for the sake of argument, you are a pure agnostic about God, thinking that God's existence is about as unlikely as it is likely. Suppose we now start considering Lewis's three phenomena, that virtually eveyone in actual practice presupposes that there is a moral law, that there is an underlying agreement on moral prinicple even in the face of differing normative conclusions, and that there we are inclined to think a society's moral standards can get better, or get worse.
How likely are these moral phenomena to occur in a theistic universe? Are they what you should expect? I think so? Are they possible in a naturalistic universe? Well, maye, at least the naturalist is certainly going to bring out the tools offered by evolutionary psychology to explain all of this. But I'm still reasonably sure that the probability of our having a sense of moral law given theism is greater than the probability of having a sense of moral law on the assumption that God does not exist. So I think that Lewis's moral argument shows a way to confirm theism, even though he did not fully develop the argument himself.
For another treatment of Bayes' theorem as it applies to miracles, see this paper I did on Internet Infidels.