All right, I think I concede your point. (Not to say I will stop thinking about this issue, of course -- have to be in a constant state of "crisis of belief" &c.) I also think we agree fundamentally about a great many of these points you made in this comment to begin with and perhaps I did not verbalize them coherently -- such as "behaving for all practical purposes as if a given T were true" and so on. The majority of your last paragraph is new to me, however. Thanks.

I both agree and disagree with you.

I would say they are equivalent "for all practical purposes," but that qualifier is necessary. A low prior on a complicated hypothesis is not as relevant as one might think due to the washing out of priors (which is how we can have subjective priors such as "deciding" that the existence of Thor has low prior probability).

And as I said in another comment, you cannot call a probability of 0.9998 and a probability of 1 equivalent. If they were equivalent, your probability would = 1. If it is not, you cannot be rationally justified in making such an absolute statement.

I think we share the same perspective on this issue. My main point regarding the existence/non-existence of a god was that one cannot say with a P of 1 that there is certainly no god. In fact, such an assertion seems to me to be absurd. However, given other evidence, we can have very low confidence in the existence of a god and very high confidence in the non-existence of a god.

However, as a scientist and philosopher of science, I cannot accept that missing evidence infers any one alternative hypothesis. This was one of the many criticisms of Karl Popper's falsification theory: finding evidence that says research program T is not true may imply that not-T is true, may imply there is an auxiliary hypothesis in T that needs to be adjusted but that the other assumptions surrounding that theory are still acceptable, etc. If T is false and not-T is true, there is no immediately obvious standard by which to choose which of the theoretically infinite alternative theories is true.

This is getting more theoretical, though, and does not really apply to a binary problem like existence/nonexistence of god, so I'm afraid I've gone off on a bit of a tangent here. At base, I agree with you that the non-existence of god seems to have a probability very close to 1. However, it is not 1, and I would be loathe to say it is close enough to 1 for the difference to be "negligible." If your probability is 1 (or 0), then it is 1 (or 0). If it is close to but not quite 1 (or 0), you are not justified in making an absolute statement.

As Lakatos wrote, it is not irrational to continue working within a degenerating research program, for such programs have been seen historically to have comebacks when new evidence is discovered. Personally, however, I'd place my money on the non-existence of god (which seems, to me, to be the progressive research program).

Just a few points:

1) I would not call atheism "rationality." Atheism requires a certain degree of blind faith and accepting lack of evidence for religion as evidence of not-religion which is not in concordance with the principles of rationality. Perhaps "agnostic atheism" would be a more reasonable perspective. "There is a god" and "there is no god" are both non-falsifiable assertions, and I can think of few things that I would accept as corroborating evidence thereof. You cannot deduce atheism from the fact that religion does not seem to be correct. You can, however, reasonably state that while there might be a god, there probably is not.

2) Occam's razor is not necessarily applicable sui generis. I would direct you to Elliott Sober's excellent paper on the subject, "Let's Razor Occam's Razor." It is a useful argument against the existence of a god, but certainly not definitive.

I took the survey! I also assumed the probabilities were meant to be first-glance intuitive. I wish I'd known people were actually doing research, for I would have done the calculations!