Secondly: Bertrand Russell's famous china teapot thought experiment. Thirdly: Quine and Two Dogmas of Empiricism.
Tea! In Space!Russell's china teapot was one which is a matter for belief. Is it right for me to believe that there is a china teapot orbiting around earth at this moment? The point is that I can't know, nor do I have any way of checking, whether there is or is not a china teapot. I only know that it would be very strange if there were one, as I have not heard of anyone launching a china teapot into orbit, and anyways it probably would not last long (Mythbusters should test that last one, if they haven't yet). But still, there might be a china teapot orbiting the earth. Maybe someone had one specially put into orbit just a moment ago, and I just didn't hear about it.
Russell claimed that one should not, and that it would be silly. This is part the "extraordinary claims require extraordinary evidence" argument against theism. I have seen people argue that theism is not such an extraordinary claim, and I have seen arguments to the contrary.
Removing AssumptionsW.V.O. Quine wrote Two Dogmas of Empiricism, which you can read of you click the link above. In that article, he effected the end of Logical Positivism, a line of thinking which involved a theory of truth where a statement had empirical content, which thus must be verifiable through sense experience, in order to be true, and is also thus interchangeable with other statements with the same empirical content. Logical Positivist philosophy is also famous for arguing that the term "God" has no meaning (since it seems to have no empirical content).
The article includes one line where Quine says, "Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system," that is, our system of beliefs.
Back to Russell's for TeaMy point in all this is that "x is true come what may" may be translated as "x is 100% likely to be true." Thus, since what Russell is saying when he says that theistic belief is an "extraordinary claim in need of extraordinary evidence" is that theistic belief is not 100% likely to be true, Quine has also removed that argument from the game as it stands.
This is not to say that an argument might be able to be worked out that said "x is unlikely, and we have no proof for it, so let's not believe it." It is, rather, to say that such an argument rests on the assumption that x is unlikely. Russell's argument from unlikelihood really is a nothing argument. To make it a real argument against the existence of God, he would have to show that God's existence is actually unlikely. This is what the problem of evil tries to do, and why it is so successful (when met in person, rather than in a classroom, at least).
To those who debate atheists: congratulations, you both take God's existence or non-existence as true come what may. A Christian sees no problem of evil because he has the belief that God exists, and God is good, so the problem of evil poses no real problem for his belief. On the other hand, the atheist sees the problem of evil quite clearly, and is not satisfied with the Christians faith in a good God without some kind of answer to the problem of evil. Now, I'm not saying that there is no use to trying to figure out how it can be that God exists and there is apparent evil in the world, just that a lack of explication is not grounds for dropping one belief over the other, only grounds for holding an unresolved tension with the expectation that it can be resolved, or for dropping one of the two beliefs. What I am saying is that when a Christian and an atheist debate such things as faith, they are coming at it with largely different views on the matter, such that the problems one has with the other person's view may not even make sense to the other person. So, yeah, good luck (I'll save my thoughts on how to do apologetics well for later).
Also: I do not see why God's existence is so much more unlikely than, say, living in a world where there is matter and energy (and they can be converted into one another--that is weird) and your senses can actually, rather reliably, tell you what that matter and energy is doing. (I'm sure there are numerous other things of the same sort)