I am really only completely comfortable with EST (easy set theory, hehe), but I know enough to know that BW is correct in his statement that some infinite sets are uncountable because their cardinal numbers are larger than the cardinal number of the set of natural numbers. I think one example of an uncountable infinite set is the set of real numbers (look up Cantor's diagonal argument to see that this is true...not that I even really understand most of the elements of the argument that he presents ).
So basically, a set whose cardinality is not finite, and is not equal to the cardinality of the set of natural numbers, is uncountable.
Or if I say it in reverse, an infinite set is countable only if it has cardinality equal to that of the set of natural numbers (i.e., aleph-null). And this is only possible when the set in question has one-to-one correspondence with some subset of the set of natural numbers.
What any of this has to do with the existence of the Christian God is beyond the scope of my response.
Edit: Actually no, I think that Cantor himself had some weird idea that the absolute infinite is God. I know nothing further.
Anyone feel free to correct me if I'm wrong on any point, as I am no practicing mathematician (just see my help with mathematical induction thread for proof positive).
Edit Again: And actually, I was just going over BW's post again and noticed that he had several things wrong. One is the part quoted by dissonance about finite sets being defined as having a one-one relationship with the set of natural numbers. This is not true. A finite set is simply one whose cardinal number is a natural number (including zero). This is intuitively understandable because the cardinal number of a finite set is simply the number of members included in the set.