This piece, by exapologist, is one that I have been meaning to answer for some time, as one of the primary defenders of an anti-naturalistic apologetic argument. I should point out, first, that C. S. Lewis never took his argument as an immediate inference from an argument against what he calls naturalism (which might be identified as some conservative form of naturalism) to the conclusion that God exists. Lewis bought the argument in the course of discussion with the anthroposophist Owen Barfield, and it was the springboard for his conversion, not to theism, but to absolute idealism. So, in my most recent treatments of the Argument from Reason, I start by asking a fundamental question: are the basic causes of the universe mentalistic or non-mentalistic. There are surely other possible mentalistic world-views that are mentalistic but not traditionally theistic, but we are going to have to see what thsoe are.
Next, I identify four features of the mental: intentionality, purpose, subjectivity and normativity. Admission of any of these into the basic building blocks of the universe (as opposed to system by-products at the level of, say, brains), has to be excluded on any view that can be reasonably called naturalistic.
In fact there are three doctrines of what I would call a minimal naturalism: mechanism at the basic level, which means exclusion of the four features of the mental, the causal closure of the basic level, and the supervenience of at least anything in causal connection upon what is on the basic level.
What this does with abstract objects is interesting. It doesn't rule them out by definition. However, since the physical has to be causally closed, they can't have anything to do with anything that goes on in the world or, in particular, what goes on in the mind or brain. Otherwise, either the basic level isn't mechanistic, or the basic level isn't causally closed. If this minimal naturalism is true, then it seems like, even if there are abstract objects, I couldn't know that they exist.
Now, why should naturalistic accept this kind of picture? Well, think about it. The world began, if it did, with a big bang. Nothing mental was going on. Matter moved around and obeyed the laws of matter. Then "the mental" emerged. Now, a traditional naturalist will just say that the mental is a system by-product of the physical. I maintain that, if that were so, there would be some logical entailment from the non-mental to the mental. But, as I have argued at some length, there isn't. All the non-mental information, in however much detail it is given, has to leave the mental, at best, indeterminate. And yet there have to be determinate truths about what we mean when we say things.
If we now put the "mental" into the basic building-blocks, what happens? If Mind really is behind everything, you can avoid the notion of the personal God of theism, but you have knocked out some pretty significant options, and theism, among other doctrines, at the very least, gets to pick up some of the probabilistic slack.
ex-apologist: On a Common Apologetic Strategy