>> If Christianity was a conclusion reached after a set of rational arguments, you would be right. But belief in Christianity is sort of logically prior to rational argumentation. Of course, we have Christian apologetics, which make arguments for certain aspects of Christianity, but this isn't really the reason to believe so much as it is just motivation for people who think in more intellectual terms to take it seriously. Faith is beyond the domain of human reason - the Christian's belief is founded in a kind of immediate, self-evident spiritual experience that comes logically prior to arguments. We might still discover internal inconsistencies that might motivate us to rethink this worldview, of course.
I respectfully disagree with every sentence (except the last).
Firstly, I think God's existence can be proved rationally, using arguments that take very basic empirical observations as premises (for example: "things change", "things behave predictably", "there are multiple instances of the same thing"). I don't think these are arguments that fit into a combox, which is frustrating but that's the reality -- although I think most of the common arguments against God's existence can be dealt without many words.
Secondly, once God's existence is established, I think the empirical basis of Christianity specifically (evidence for the resurrection) is sound. I think the common objections fail. Many of the objections are variants on Hume's, which amounts to "the resurrection is so unlikely given my philosophical assumptions that literally any explanation for the observed facts is more likely". Once Hume's assumptions are undermined (in stage 1), the facts take on a very different light.
Thirdly, I think Catholicism is internally consistent and has further evidence in its favour -- including miracles, continuity of institutions and continuity of teaching -- whereas I think Protestantism and Eastern Orthodoxy lack these qualities. While intra-Christian disputes may seen beyond the scope of this discussion, I think they have some bearing. For example:
>> Faith is beyond the domain of human reason - the Christian's belief is founded in a kind of immediate, self-evident spiritual experience that comes logically prior to arguments.
This is a specifically Protestant view (although many Catholics mistakenly hold to it since it chimes so easily with the post-Enlightenment concept of religion). I would say faith is a rational assent to revelation. But more importantly for the present discussion, I would say God's existence that can be established by pure reason, independently of faith.
> "I" exist. Presumably the universe I experience also exists. Why? There's a First Cause that brought them into existence. We can call it God. This is the closest religion and science can get, because this definition of God is without any pre-defined qualities. For instance, God can be non-dualistic (God _is_ the universe, or in other words, the universe is its own cause), and even mathematical (Physics' Theory of Everything, Mathematical Universe Hypothesis). We only have a set of possibilities here.
There are solid arguments against all these and in favour of monotheism. Again, no way of summarising in a combox, but I can give a few thoughts, which should not be taken as even an adequate description, let alone a complete defence that is intended to convince you :-).
Pantheism is false because it can't explain change. A thing can only be changed by something else; therefore the first principle (First Cause) of reality can't change, because otherwise it would not be first. But the universe is changing; hence the universe can't be the first principle of reality. Each of these points is obviously controversial, but I think defensible.
Alternatively one could argue that change is an illusion, like many eastern religions do. But speaking very generally, one object is distinguished from another by how it changes (that is, how it acts or is acted upon). We distinguish the presence of hydrogen from that of helium by how they act, or how other things act on them. We also distinguish a human being from a dog by how they act -- not least, how they act on our sight, sound, etc. And so on. If change (that is, action and being acted on) is an illusion, it means that individual objects (like stones, trees, dogs, human beings) are not actually individual at all; their individuality is only an illusion. But if this is so, predication is impossible, because we are predicating only of our illusions. Since this is not so (because if it were, why are we even bothering with this discussion?), pantheism must be false. Such is the vague outline of another argument that a monotheist would make.
Alternatively one could argue that a thing need not be changed by something else -- that it can change itself. The trouble with this is it fails to explain why things act in one way rather than another. If things could change themselves, they would act completely randomly, because there would be no cause of their change, and therefore no reason. This is not so.
Pythagoras was the first to propose that mathematics was the basis of everything. But there are things that are not numeric or can be reduced to number. For example, non-mathematical logic, which is a fundamental aspect of reality, and can't be reduced to number. Again, a counter-argument would proceed on these lines.
I'm not going to attempt any other answers in a combox because these are profound questions that require, and have received, book-length expositions. I am only attempting to give you the vaguest idea of the thought processes I go through in arriving at my beliefs. But I have not yet found an argument that makes me doubt my Catholicism, and I think it's profoundly false to say that Christianity is independent of logic or observation.
