The wonders of irrationality

A few days back The Tin Drummer approached me do engage in a little guest blogging action. He was hoping I'd do a write up on the topic of belief. I'm still working on that, but as I've been thinking on that topic I ran across this piece by Bill Vallicella. He just so happens to set the stage quite nicely for what I'm working on at the moment. Vallicella starts by laying out some objections to Christianity and talks about how Theists typically don't give up their faith in light of these problems. Then he then turns his gaze towards the naturalists:

Let’s start with what philosophers call the phenomenon of intentionality, the peculiar directedness to an object that characterizes (some) mental states. It is very difficult to understand how a purely physical state, a state of the brain for example, could be of, or about, something distinct from it, something that need not exist to be the object of the state in question. How could a physical state have semantic properties, or be true or false? How could a piece of meat be in states that MEAN anything? How do you get meaning out of meat? By squeezing hard? By injecting it with steroids? Does a sufficiently complex hunk of meat suddenly become a semantic engine? How could a brain state, for example, be either true or false? This suggests an argument:

Every belief is either true or false
No brain state is either true or false
So, No belief is a brain state.

Now ask yourself: would any self-respecting naturalist throw up his hands and concede defeat when presented with such an argument? Of course not. He will do exactly the same thing the theist does. Holding fast to his conviction, the naturalist will seek to defuse the anti-naturalist argument. He will deny the minor premise of the above syllogism and try to show how some physical states could be true/false.

Vallicella Goes on to say:

So what is the difference between the theist and the naturalist? In both cases we find a deep and abiding conviction that seeks to transform itself into clear and broad understanding armed at every point against every possible objection. Just like the theist, the naturalist, operating under the aegis of his overarching conviction, never gives up. No matter how often you slap down his theory of intentionality, say, he goes back to the drawing board. Naturalism, he feels, just MUST be true, and the arguments against it just MUST be unsound.

So the question I will leave hanging is this: If by looking at the same information intelligent people cannot agree on these topics, then on what grounds do we form our beliefs? Furthermore, does it even matter?