I think that this is actually possible, i.e. it is possible to state "Yahweh doesn't exist" with certainty: if Yahweh is internally mathematically inconsistent, i.e. Yahweh's existence would be a proof that 1 = 0.
However, there are probabilities involved in any assertion that Yahweh is inconsistent; unless you have a complete definition of Yahweh (e.g. highlighted phrases in a specific Bible) that involves something as clear as "Yahweh is green" and "Yahweh is not green", but there are the standard problems due to language being imperfect telepathy (etc) that make this unlikely to be possible.
Well, Eliezer Yudkowsky doesn't assign probability exactly 1 to 2 + 2 = 4 either, and whereas at first I thought that was nuts, this made me realize he does have a point (as I think any difference between “2 + 2 = 4” and “51 is prime” is only quantitative).
A friend recently asked how strongly I believe that my deconversion from Christianity was not a mistake. Here's my response, and for those of you who are not Christians, I'm just wondering what numbers you would give:
"There is a part of me that wants to say the chance is far less than 1 percent. But when I consider what 1% must mean about my ability to follow complex arguments and base my judgement on the right premises, it seems absurd to say that.
Trying to honestly estimate the chance that I'm wrong about the Bible being generally reliable is a fascinating exercise... I know the number is low, but I'm not sure how low.
Today I would give myself a 1 in 20 chance of being wrong. If I were to consider the arguments of 20 other groups similar to Christian theologians, I would probably misunderstand them at least 1 time in 20. After talking with 20 groups that have a very different worldview, I might think they are all are mistaken, but once in a while, maybe 5% of the time, it would actually be me.
Wow, 5%!?! If I convert that into "There is a 5% probability that the God of the Bible exists and will send me to hell", I feel scared. But I know how to cheer myself up: I just say, "No way, the chance I'll end up in hell MUST be less than 5%. After all, the God of the Bible is CLEARLY just a big, mean alpha-monkey and... [rehearse all the atheistic arguments here]".
This back-and-forth from certainty to uncertainty makes me feel like I'm doing something seriously wrong.
So what about you? What chance do you place on some variant of Christianity turning up to be true, and what chance do you think a god of some sort exists?"
Numbers please.