I would say the probability of Yellowstone or meteor impact situation are both vastly higher than something like the existance of a specific deity. They're in the realm of possibilities that are worth thinking about.
Careful there. Our intuition of what's in the "realm of possibilities that are worth thinking about" doesn't correspond to any particular probability, rather it is based on whether the thing is possible based on our current model of the world and doesn't take into account how likely that model is to be wrong.
If I understand you correctly, then I agree. However, to me it seems clear that human beings discount probabilities that seem to them to be very small, and it also seems to me that we must do that, because calculating them out and having them weigh our actions by tiny amounts is impossible.
The question of where we should try to set the cut-off point is a more difficult one. It is usually too high, I think. But if, after actual consideration, it seems that something is actually extremely unlikely (as in, somewhere along the lines of 10^{-18} or whatever), ...
Another month has passed and here is a new rationality quotes thread. The usual rules are:
And one new rule: