The problem is that the terms "rabbit" and "aliens" do not refer to a specific entity. Therefore, showing one rabbit or one group of aliens to be nonexistent does not show that all rabbits or aliens do not exist. The term "god" refers, in monotheism, to a specific entity, regardless of how one might describe that entity. Your original god~aliens analogy works like this: "well look, we cannot generalize from the nonexistence of a specific group of aliens to all the different possible aliens, and therefore we cannot generalize from the nonexistence of a specific god to the nonexistence of all the different possible gods." But, if we are focusing on monotheism, there are no different possible gods, so what you are really comparing are possible existence of different entities to possible existence of different properties of an entity, which is not a valid comparison, because I can then say "well, just because you didn't find the thirty-clawed rabbit in your pants doesn't mean that the thirty-one-clawed rabbit isn't in there." You would probably respond "who cares how many claws the rabbit might have, there is no rabbit in my pants," but then, if you still want to maintain that the absence of god defined in one way does not preclude the absence of god defined in another, you would then have to admit that it is not just the definitions of the term "rabbit" or "aliens" and "god" differ, but the manner in which you define them. And if you define "god" in some unique manner, all analogies go out the window anyway.

By the way, how can you tell someone that do not believe in god unless you define the term? In many of your exchanges you tell believers that you do not believe in god, whose god is it that you do not believe in, theirs or yours? How can you venture to make the statement "I do not believe in god" if you think that the people interpreting that statement have either a totally different conception of the term "god" than you do or they don't have one at all?

If it's impossible to prove that god does not exist, than it's impossible to prove that he does exist. If the proposition "God exists" is neither verifiable nor falsifiable, then it isn't meaningful.

Actually, my view on the whole thing could be better described as "strong" agnosticism than atheism. I think that humans cannot conceive of anything other than the empirical realm, and so the proposition "a supernatural god exists" is nonsensical. There is no such thing as "existence" outside of space and time, or space-time, if you prefer, because humans are simply incapable of defining existence outside of space and time. Theism and deism is thus an oft unfortunate byproduct of our capacity to make inferences, generalizations, or abstractions.

I think we may have come to the roots of our disagreement.

You are right that, in monotheism, "god" refers to a specific, individual entity. Where we differ is that, to me, all definitions of a monotheistic god are not equal. This is different than counting the claws on a rabbit, because in some cases different proofs are used to show that different definitions of god are problematic. For example, a discussion of whether God is "good" can go very differently when speaking with a Catholic than with a Lutheran. For the "claws on a rabbit" analogy to be true, there would have to be a proof that no possible deities exist, and I am not yet convinced that one does exist.

I would say that the definitions of "aliens" and "god" actually do have some similarities that are important to understanding my way of thinking about this problem. In our current context, "aliens" refers to two different things: A) aliens as described by people on Earth who say that they have experience with such things, and B) whatever extraterrestrial life is really out there. We have no idea what B is, but if it showed up, we'd call it an alien. I think of the concept of god in the same way. Protestants don't believe in the deistic god, but if there were some way to prove deism true, I'm guessing Protestants would still call this being "god" even though it was nothing like what they had been worshipping.

I think one of the reasons we keep going back and forth on some subjects is that I won't say "there is no god" just because some class of deity has been ruled out. Even if we were to completely agree that the monotheistic, non-deistic god didn't exist, I still wouldn't make that statement because polytheistic, Buddhist, deistic, and other concepts of god have not been ruled out. I think that these concepts are distinct enough from the god of Christianity to be considered different gods.

I am also extremely wary of an ontological argument against the existence of a deity. If we agree that humans know nothing definitive about the supernatural, then I am very uncomfortable making definite statements about supernatural aspects of supernatural things.

You ask how I can tell someone that I don't believe in god without defining the term -- whose god don't I believe in, mine or theirs? That's a good question. From my perspective, since I say that I don't believe in god since I have seen no compelling proof for the existence of a deity, I feel that I'm covering all possible definitions of god. It is a true statement that I have not seen any compelling proof for anything that I could meaningfully label "god."

"If it's impossible to prove that god does not exist, than it's impossible to prove that he does exist." Well, that's not true in and of itself, but it is true in the context of our conversation (ignoring personal revelation, which I think we've agreed to disagree on). You continue, "If the proposition 'God exists' is neither verifiable nor falsifiable, then it isn't meaningful." That depends on what you mean by "meaningful." Certainly the statement has important emotional meaning for many. From a scientific perspective, there are many things in science which can't be verified or falsified, only speculated on based on existing evidence (for example, other universes and some historical truths).

At most, I would say that deities do not appear to be necessary.

I think your final paragraph may sum up our disagreement perfectly. You say that there is nothing outside of space and time because humans cannot define anything outside of space and time. I say that the inability to define something does not prove that something does not exist, particularly when we're talking about my personal ability (which is all I have to work with). I also feel uncomfortable assuming that there will never be an idea or concept or means of proof that I haven't thought of but that would change my mind.

For me, this is a comfortable place. I am never put in the position of having to prove a negative. And from a pragmatic perspective (as we've discussed before) this allows me to bypass trying to convince people to give up something based on feelings alone and concentrate my efforts on aspects of religion that are more significant from a social perspective.