One doesn't need to examine all possible avenues to come to non-belief in something. If I were to tell you that a teapot is in orbit around the Sun, would you have to examine every inch of the sky to prove me wrong to be justified in your disbelief? No, you only need ask, "show me." If I cannot show you, then you have every right to drop the issue there and rightly doubt my claim.
(This is a concept called Russell's Teapot.)
Branwen,
Oh, I'm really bored tonight and for some reason I remembered this post, so I think I'll destroy Russell's Teapot real quick. My initial response was to give the moral argument as a reason for belief in God while there is no reason to believe in the teapot thing. It didn't get much of a look, so I'll go ahead and finish the teapot story off so I'll never have to see it in here again.
First, your argument has a fallacy of equivication. You equate God to a teapot. This is a terrible comparrison. A teapot is of course a manmade object and cannot be orbiting the sun, moon, or whatever without a human putting it there. God is transcendent and nothing like a manmade object, much less a teapot. So the teapot is a bad example and is very "ad hoc". So 2 major fallacies with Russell's Teapot (1) equivicatoin (2) ad hoc. But you could always think of something else to get the point across so I'll head off those bad examples too.
What you're really driving at and what your real point is, is that "absense of evidence is evidence of absense". Well, unfortunately for you, this is also fallacious. Absense of evidence does not necessarily mean evidence of absense. For example, if I said there is an elephant in your house, then definately, the absense of the elephant means there is no elephant in your house. However, if I said that there is a flea in your house, then absense of evidence does not equal evidence of absense. There could very well be a flea in your house and you would have no evidence whatsoever.
In the case with God, you must show 2 things. (1) That God would leave more evidence for His existence than He did and (2) That we have adequately surveyed all the evidence for God's existence. This is of course a huge burden of proof that I need to see before I can concede that absense of evidence for God's existence is evidence of His absense. Not an easy task.
Since I've seen you reference Bertrand Russell several times before, I assume you have read him. So you must also know of a problem Russell runs into called the inductive principle or principle of the uniformity of nature. It's a principle that says that the future will be relatively similiar to the past or that nature and everything behaves in a somewhat predictible fashion. Without this pinciple, we could not make sense out of anything.
For exmple, the earth will be orbiting the sun tomorrow because of the laws of nature. My bed will not turn into a T-Rex and chomp me up tonight because matter does not reorganize itself like that. The laws of logic and the laws of nature will be the same tomorrow as they were today and yesterday. I can do science because nature behaves in a predictible fashion (inductive principle).
We use this principle every day. It is unavoidable. Now the problem is, where does this principle come from? Why is it there? If you say it's a product of the human mind you would be incorrect. This principle exists weather we do or not. Logic and natural laws exist independent of us and they were in existence before we were. If you say it's a product of evolution you would be incorrect. If this principle is subject to evolving and changing, the laws of logic and natural laws would cease to exist and we would have nothing.
You, like Russell, and like the rest of us, live and use this principle every day. The problem is that as an athiest you just assume it for some arbitrary reason. It's something that exists and is absolute and transcendent and I want to know where you think it comes from. If you assume it without reason or call it a brute fact then you commit the fallacy of begging the question....where does it come from and why is it there? Also, watch out for circular reasoning when thinking of the answer.
Maybe after this we can both agree to never call on Betrand Russell again.