Although C. S. Lewis criticized naturalism by arguing that it is inconsistent with the possibility of rational inference, he didn't give the kind of full description of rational inference that he gives in an essay entitled "Why I am Not a Pacifist," which contains no argument against naturalism at all. It is found in The Weight of Glory, p. 34.
"Now any concrete train of reasoning involves three elements: Firstly, there is the reception of facts to reason about. These facts are received either from our own senses, or from the report of other minds; that is, either experience or authority supplies us with our material. But each man’s experience is so limited that the second source is the more usual; of every hundred facts upon which to reason, ninety-nine depend on authority. Secondly, there is the direct, simple act of the mind perceiving self-evident truth, as when we see that if A and B both equal C, then they equal each other. This act I call intuition. Thirdly, there is an art or skill of arranging the facts so as to yield a series of such intuitions, which linked together produce, a proof of the truth of the propositions we are considering. This in a geometrical proof each step is seen by intuition, and to fail to see it is to be not a bad geometrician but an idiot. The skill comes in arranging the material into a series of intuitable “steps”. Failure to do this does not mean idiocy, but only lack of ingenuity or invention. Failure to follow it need not mean idiocy, but either inattention or a defect of memory which forbids us to hold all the intuitions together.”
The power of intuition, the second step, seems to be the most difficult to account for in naturalistic terms.
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