Helix, you are asking important questions now, and questions that have been asked and debated for thousands of years. I know you want to approach this entirely logically, so I'll try a bit -- keeping in mind that our elections were yesterday and we stayed up quite late watching results and I am going to bed just as soon as we get Chris (our retarded 20 year old son) in bed! So from a sleepy brain, here's a bit to at least think about.
1. Matter itself is either eternal or not. That is an a/non-a fact. If matter is eternal, then how did it organize itself into the universe and life itself? We know of no self-organizing properties of matter per se. In fact the general tendency of the universe towards net entropy seems to indicate that it started in some kind of highly ordered stated and has been going downhill since. How did this highly ordered matter start? Is it possible for matter to reverse properties as we know them and go from instrinsically ordered to non-ordered and somehow back again?
2. If matter is not eternal and cannot order itself, then something invented/created it as well as ordered it. The Intelligent Design group, to my mind, is looking at the cosmos from this point of view and doing well with this approach. Their claim is that, taking what we know of design and structure, of purpose and plan, in our own experience, if we extrapolate that to the larger realm of the cosmos, we see every evidence of plan and purpose -- of intentional, intelligent design. Thus there is possible evidence from this point of view that there is a Designer of some kind who is partially or fully responsible for all we are aware of.
3. Cause and effect. In physics, in thermodynamics, we see that every effect has a somewhat larger cause, for there is always a loss of energy or order somewhre between cause and effect. If you keep going back and back, you end up with an Ultimate Cause at some point -- where all energy and all order originate.
4. Ethics and morality. We have covered this before, but the presence of the CONCEPT of these things in human beings is unique and does not appear to have a physical basis (as oppsed to a physical translator or transmission). Just as it is impossible for mankind to 'invent' a new primary color, it is impossible for us to invent anything totally new.
We tend to put together things and ideas from pre-existing things and ideas. We are great at re-ordering structures and ideas, but we cannot invent totally new ones. We are not creative in that sense. Following this idea, where did the concept of morality and ethics come from? Neither is helpful in the Darwinian sense of evolution, and yet they are universal withiin men. This indicates very strongly that they may have sources outside of men and imposed upon men.
Thus, Helix, I can indicate God as a logical necessity, but I cannot prove Him, for He is not small enough to manipulate. If He was small enough to be provable, then He would not be God. God is not subject to man, but rather man to God.
It was once said, as the ultimate reduction "I think, therefore I am."
I would offer a corollary: "I think, therefore God is." Not because my thinking invented Him, but rather because He invented my ability to think, to reason, to write to you in abstract symbols using abstract thoughts...
OK, the clock is at 8 p.m. here and I can get Chris to bed and then sleep myself. God bless --