What does it take for a theological claim to be rational?

I know this is a vague question, and I pose it vaguely on purpose. Consider the following:

1. The universe is either caused or uncaused. (Premise)

This premise is obviously true, since it rests upon the law of excluded middle and a very general consideration of the universe and causation.

Now, suppose someone adopts the first horn of the dilemma: the universe is caused. Is this claim obviously false? I doubt it, but I'm sure there is someone who thinks so. For the rest of us who acknowledge the universe's having a cause as a possibility, however, this leads us to:

2. If the universe is caused, it either has an external cause or it is self-caused. (Premise)

Again, the first horn of the dilemma in (2), "the universe has an external cause," is not obviously false. Now suppose that the conjunction C&E is true (where C = caused, and E = externally caused). On C&E, what can we know? Well, we can know that the external cause of the universe must transcend the universe (universe = the totality of physical space, time, matter and energy), which implies that the universe's cause is timeless, changeless (time is a measurement of change), and immaterial.

A final dilemma may be proposed:

3. If the universe has an external cause, that cause is either personal or non-personal.

If it is rational to believe in a personal external cause of the universe, then such a cause is plausibly God. There may be more reservation about this last one, but from my own intuitive perspective it is not obviously false that the universe's external cause is a personal agent.

Still, rationality usually entails more than the lack of obviously false assertions. Many would presume that we must have sound positive reasons to believe in a proposition, especially a proposition of this magnitude. A discussion of what constitutes rationality is therefore in order. However, there are some highly plausible arguments that suggest there exists a personal external cause of the universe. One of these is the Kalam Cosmological Argument, but the list may be multiplied to include many cosmological and teleological arguments, among others.

Consider, for instance, a sub-argument dealing with the dilemma of (1):

1A. Complex things are most likely caused.
1B. The universe is complex.
1C. Therefore, the universe is most likely caused.

I have found very little resistance to this line of reasoning. It is an inductive argument, and we experience the truth of (1A) all the time. My body is a complex organism, and it is caused by the function of my organs, and so forth (I'm thinking of a sustaining cause here). Of course, (1B) receives even less resistance, given that we clearly perceive that the universe is composed of countless diverse objects that are all interrelated. (1C) is therefore usually granted, even by the theological skeptic.

It is usually in arguing for an external cause of the universe that much more resistance is felt. The most resistance is, of course, reserved for the conclusion that the universe's external cause is personal. This is where the traditional arguments of natural theology come in handy. It is highly plausible, given what we know about the universe's composition, that the universe began to exist at a finite time in the past. Yet, its beginning is either caused or uncaused. I think you know the rest.