A couple weeks back I attended a lecture by Dr. Ned Keller, a physicist who teaches college in Grand Rapids Michigan. The lecture was entitled "The Nature of Knowledge" and was the first in a series he did discussing "Theories of Origins" at an area church. In it Dr. Keller provided a basic outline of how we know what we know in order to provide a foundation for what he was to talk about the rest of the weekend. Although I didn't get to attend any but the first lecture, I found it interesting that among his preliminary topics for the weekend was:
The preliminary question is whether the universe is best described with a natural or a supernatural worldview. What are miracles? Can they occur and have the occurred?
To answer this question Keller went to chapter 3 of C.S. Lewis’ 1947 book Miracles titled “The Cardinal Difficulty of Naturalism”. In that chapter Lewis makes an argument for God and against Naturalism (that nature is the “whole show”) based on the existence of human reason. Interestingly, after Miracles was first published a debate on Lewis’ argument was held at the Oxford Socratic Club between Lewis and philosopher Elizabeth Anscombe. By all accounts Lewis lost the debate and subsequently rewrote the chapter for subsequent editions of the book.
In his lecture Keller talks both about chapter 3 and about miracles in general.
Lewis’ argument for the existence of the supernatural is known as the “Argument From Reason” or the "Argument From Mind". In short Lewis puts the argument in syllogistic terms like so:
- If supernaturalism is not true, then Nature is all there is and so "every finite thing or event must be (in principal) explicable in terms of the Total System [i.e. Nature]." This is called physicalism by Moreland.
- Therefore if any one thing can be shown to be not explicable in terms of the Total System, then naturalism is not true
- Human reasoning can be shown to be something not explicable in purely physical terms and so naturalism is therefore not true. Man’s "rationality is the little tell-tale rift in Nature which shows that there is something beyond or behind her." 
Lewis then defends his conclusion by starting with the premise that all knowledge depends on the validity of our reasoning. If reasoning does not lead us to true conclusions about the world around us, but is rather a product of feelings in our own mind, then all science and all knowledge is worthless. This, says Lewis, points out that strict materialism or physicalism is self-defeating. In other words physicalism may be true, but one cannot argue that it should be believed based on evidence or reasoning.
Lewis then goes on to argue why it is that human reasoning cannot be explained in terms of the “whole show”. He illustrates this through the two different senses of the word "because". In the first sense because can be used to mean a cause and effect relationship ("Grandfather is ill today because he ate lobster yesterday"). In the second sense because is used in a Ground and Consequent relation, for example, "Grandfather must be ill today because he hasn’t got up yet (and we know he is an invariably early riser when he is well"). The first sense indicates a connection between a state of affairs while the second is a logical relation between beliefs that involves an act of knowing or seeing or rational insight. Another example of the second sense of because is the mathematical reasoning if A=B and B=C then A=C.
Lewis then explains that every event in nature, including our very thoughts, must be of the first type if naturalism is true. If this is the case, then when we ask "Why do you think this?", the actual answer must always begin with a Cause-Effect style because. As a result, all of the thoughts that go into answering the question lie in a cause-effect relationship to one another including the final answer. But we know that to be caused is not to proved and so the physicalist, if he is consistent, must admit he has no way to know whether what he thinks is true. He has no way to bridge the gap between the two distinct senses of because. In fact, as Lewis notes, in argumentation people often act as if the two were unrelated so that if a person can find some bit of background about you that might indicate why you believe something (Cause-Effect) they can more easily discount your position. However, in our experience we know that not all of our thoughts are based on wholly on Cause-Effects relationships (we don’t draw all of the inferences possible from each thought). Some of our thoughts can cause other thoughts by being seen to be a ground for them (Ground-Consequent). Therefore, since some of our thoughts can be shown to be true acts of knowing or seeing that cannot be accounted for by naturalism, then naturalism is false. This then explains why all human reasoning and therefore science and knowledge must be thrown out for the physicalist since it depends on Ground-Consequent style thinking including the physicalist’s own conclusion that nature is the whole show. This is why that position is self-refuting. As Lewis conludes:
"But this, as it seems to me, is what Natualism is bound to do. It offers what professes to be a full account of our mental behaviour; but this account, on inspection, leaves no room for the acts of knowing or insight on which the whole value of our thinking, as a means to truth, depends."
He also goes on to address the naturalists claim that our reasoning is the product of natural selection and/or cultural evolution. Against natural selection as the origin he argues that natural selection can only improve man’s physical responses to the world around him and could never in principle develop a relationship between knowledge and truth since there is no connection between the two, no way to bridge the gap. Against cultural evolution or the belief that over time, men were conditioned to make inferences based on experience (where there is smoke there is fire), Lewis argues that inferences are the basis of animal, not human reasoning. The real difference between animal and human reasoning is that human reason need not appeal to experience at all. For example, our belief that A=C as above is not derived from our experience that we’ve never not know A to equal C. Rather, it is based on a real insight that "it must be so". These are the insights that a physicalist cannot explain.
 There are several other arguments for God’s existence that can be used including the Ontological Argument, the Cosmological Argument (which has three different forms), and the Argument from Design. The books Scaling the Secular City by J.P. Moreland and Reasonable Faith by William Lane Craig have very readable introductions to these arguments.
 Moreland also gives other reasons for thinking that there are entities that cannot be explained naturalistically including moral values, numbers, and universals (concepts such as color)