Narrowness

A few days ago, I was puzzled by a reference Dale Ahlquist made about the 'narrowness' of certain philosophies. Today I read chapter 2 of 'Orthodoxy' and I understand Chesterton's argument about narrowness a little bit better.
Chesterton starts of with a question: if a man is not to believe in himself, in what is he to believe? Then he does something surprising: instead of starting at the obvious beginning of Christian apologetics, namely sin, the starts at the madhouse. The reason he gives is that some modern philosophers apparently deny sins (even then).
The point of mentioning the madhouse is that a maniac is often highly rational: he uses reason to account for the whole world (e.g. everything evolves around there being one big conspiracy). One cannot fruitfully argue with such a person, at best one can point out that his world is a very narrow one. It is consistent and complete, like a circle, but it is a very small circle.
According to Chesterton, the same goes for the materialist (and some other philosophies): they offer a rational explanation, but this materialistic universe is so small. There is no free will, there is not freedom to believe in anything more, there is no room for imagination, poetry, mysticism.
Chesterton argues that there is much more freedom in a Christian worldview, which accepts miracles, then in a materialistic worldview, which categorically rejects any possibility of miracles.
In the end, we should not be so narrowly bound by reason, if we do not want to become insane. We should mitigate reason with a measure of common sense, just as the common man always has, and accept that there may be mysteries that we cannot explain fully at the moment.
The concluding images of a circle and a cross remind me of the novel Chesterton wrote a year later: 'The ball and the cross', which illustrates similar viewpoints.