I think most theists would admit that they'd still believe in god even if they had no evidence of his existence, which is what makes such a belief faith. In fact, I do not think there are any, at best fantastically few, people who believe in god on the basis of evidence or arguments. The "belief without proof" definition would result in propositions like "I have faith that the bus will hit me if I don't move away," or any statement about the future whatsoever. In fact, belief in any state of affairs which we admit can possibly be different than it appears would be an instance of faith. But nobody uses the word "faith" in this way, and I see no reason why anybody would except to engage in nihilism or religious apologetics. So, yes, I think the manner in which you, personally, are defining "faith" is a result of the special privileges generally granted to religious discourse, and I believe that such concessions are not beneficial.

Well, in order to disprove something only only needs to provide a single example of contradiction. It is not necessary to have an exhaustive definition of god in order to show that some of such an entity's alleged properties make it logically incoherent. For instance, if someone tells me that John is both six feet tall and seven feet tall at the same time, I do not need to know anything else about John to show that John so described does not exist.

Yes, I believe that there is no number "1" if there is nothing to be counted, but I also believe that there is always something to be counted.

The theistic god is the deistic god too, and more. I cannot think of an argument why an unprovable deistic god precludes a provable theistic one. Well, I could, but I think we will simply disagree on the premises, so I will not formulate it. I'm somewhat surprised that you do not seem to find this notion displeasing enough intuitively to reexamine how it arises. Oh well, disagreement is what keeps this fun.

Oh come on, aliens are nothing like a supernatural deity. If aliens exist, it is perfectly possible for me to go and look at them, smell them, touch them, hear them, and taste them. Hmm, I don't think I ever envisioned myself talking about tasting extraterrestrials, but anyway. A deity, or god, by definition is inaccessible to any mode of direct observation, I think we agreed to leave out souls. Even if tomorrow I see a Jesus-looking dude walking on water, that is not the same thing as observing a supernatural entity. Perhaps this is the essence of almost the entirety of our discussion, I feel there are reasons for denying the existence of a supernatural being other than simply a lack of evidence of such. I think these reasons apply from the very definition of such an entity. I believe it is more valid to believe in a Flying Spaghetti Monster, one that obeys the laws of physics, living on some other planet than it is to believe in a supernatural entity. Did you just want to get a rise out of me with this alien stuff?

You say, "I think most theists would admit that they'd still believe in god even if they had no evidence of his existence, which is what makes such a belief faith." I'm not completely sure that's universally true. I can think of a couple of people who say that they believed in God because a creator was the only thing that made sense, but whom later became atheists when their knowledge of science improved. I also think it's possible that you're right in general, but that in many (perhaps most) specific cases theists will not say that they have belief without evidence, even if to you and me they do. For example, some people would call "feeling God's love" evidence.

You are right that one needs only a single contradiction to disprove something, and you are right that one does not need an exhaustive definition of god before contradictions have to be looked for. But one cannot disprove all definitions of "god" by finding contradictions in one definition. I think the problems here are that there are many possible definitions and that a great many theists speak of "God" without even having a real working definition (although they think they have one).

Fortunately, when theists (at least Judeo-Christian theists) start working on a definition they generally run into the kind of problems you speak of pretty quickly. Buddhists and deists, for example, often do better because their deity is more detached from empirical reality.

So, summing up my position, I have no problem arguing against an individual's definition of God, but I hesitate to assume that I can argue against all possible definitions of a deity.

Your thought that there are no numbers without at least one countable is interesting. Off hand, I don't think there is anything wrong with this, but it is a new concept to me. As an aside, would you say that mathematical principles (such as pi) are invented, where I would say they are discovered? Just curious.

I think we got our wires crossed on the subject of deistic vs. theistic (meaning non-deistic) gods. I think I know what you mean when you say that a theistic god is a deistic god and more -- in the same way that (to oversimplify) a scooter might be seen as a skateboard and more, right? I don't know whether I agree with this statement, because if the deistic god does not interfere with reality because of either moral or physical (for want of a better word) restraints, then it is probably significantly different from the theistic god and not just a theistic god that does not interfere.

You are right that there probably isn't a useful argument to prove that an unprovable god precludes a provable one. Sorry if I implied that I thought there was. I would say that disproving a theistic god does not necessarily do anything to disprove a deistic god. And I would say that it might be possible for a theistic god to permanently detach itself from reality at any point and effectively become deistic, possibly rendering its existence impossible to disprove.

There really was a point to my bringing up aliens that had nothing to do with bugging you . I agree that aliens are nothing like a supernatural deity, but the way I argue against statements of their existence is very similar to the way that I argue against statements of the existence of deities.

You say, "If aliens exist, it is perfectly possible for me to go and look at them, smell them, touch them, hear them, and taste them." I think it is this statement that might be at the root of our disagreement, because I wouldn't make it, at least not in so many words. Your statement has an implicit assumption that aliens are accessible, and I am not willing to make that assumption even though I understand that you are speaking in a philosophical sense (because aliens are, in principle, accessible if they exist, even if access to them is not practical).

Let's assume there are aliens (meaning some kind of extraterrestrial life) so I can demonstrate how this has anything to do with anything.

I think that the probability of alien life is very high. I think that the probability that any of it has been observed by humans is very low. So if someone tells me that they tasted an alien (and it tasted like alien chicken), I think they're probably wrong. If they describe the alien in a way that is not logically coherent, then I can prove that they are wrong. If their alien encounter is more easily explained by more normal occurrences (you were sleepwalking and ate some leftover chicken), I consider that more likely. But in my mind, this has nothing at all to do with real alien life out there on some planet somewhere. Disproving every supposed alien encounter I run into would not prove that a) aliens don't exist, b) none of the people imagining that they encountered aliens got some of the details right, c) nobody I haven't run into really did encounter aliens, or d) if aliens wanted to hide from us, we could detect them. And this is assuming that my disproofs are valid.

There are people who say, with complete conviction, that aliens are out there, even if we can't prove it. I can't argue against that, because it's a statement of faith. And I won't agree with it, even though the probability is, for me, high that it is a true statement.

So, applying this thinking to a deity:

Our disagreement over your implied assumption that aliens are accessible is similar to our disagreement over your definition of a supernatural deity as completely detached from the empirical. I would say that aliens are not accessible because, at the moment, we can't access them. I would also not define a deity as necessarily completely detached from the empirical, even though we could never prove its existence empirically.

I think that the probability of a deity is very low. I think that the probability that anyone has proof that a deity exists is low. If someone tells me that they have experienced God, I think they're probably wrong. If they describe God in a way that is not logically coherent, then I can prove that they are wrong. If they offer no proof, I still consider mundane explanations for their experience far more likely. But in my mind the fact that people have developed incorrect religions or that they mistakenly believe that they have interacted with a deity does nothing to do with whether there really is a deity of some kind. I can rule out specific descriptions of a deity, but I can't rule out all possible descriptions or invalidate claims that I can't investigate.

You are right that a big part of our disagreement is whether or not a supernatural entity can be observed. I still do not agree that a supernatural being must by definition remain entirely within the supernatural realm. I don't know what it would mean for God to send part of himself to Earth in the form of Jesus, because I don't know how a supernatural being would work, but my not knowing doesn't make it impossible. Seeing a Jesus-looking guy walking on water wouldn't be proof of the supernatural (because there are non-supernatural explanations that are more likely), but my having a better explanation is not proof that the Jesus guy isn't supernatural.

Looking at this another way, there's a movie in which God is sitting in a courtroom and the judge asks him to show him a miracle. God takes out a deck of cards, spreads, them and asks the judge to "pick a card." If God uses supernatural means to state what card the judge picked, we'd never know it because there are so many mundane ways to do card tricks. For all I know, there is a deity out there that interacts with the world but always does so in a way that appears to follow the laws of physics. There would always be a non-supernatural explanation for the behavior of such a deity.

One last thing, just to keep our conversation traditionally overlong.

Let's look at the Catholic belief of transubstantiation -- if you're not familiar with it, this is the belief and bread and wine become the body and blood of Jesus during a church ceremony. If you run tests on the food products before and after the ceremony, they will appear to be the same thing. If someone asked me whether the bread really became "the body of Christ" during the ceremony, I would not say no. Instead, I would say that I have no idea what transubstantiation really means and therefore can't make a statement. I feel the same way about most definitions of god.

By the way, I'm really enjoying this conversation. I hope it's not driving you nuts!