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Tetronian comments on A Problem with Human Intuition about Conventional Statistics: - Less Wrong
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I've tried to explain this when arguing with theists, and it sometimes creates the following unintentional side effect:
The problem, of course, is that the theist forgot (or doesn't understand) the distinction between "(the Judeo-Christian) God exists" and "at least one deity exists." It's really important to stress that the search space of possible gods is huge, otherwise you will create even more confusion.
Overall, though, I definitely agree with the main point of this post. Upvoted.
Quite honestly, I think a bigger problem is theists assuming that P(E|D) = 100%. That given a deity or more exists, they automatically assume the world would turn out like this - I would actually argue the opposite, that the number is very low.
Even assuming an omniscient, omnipotent, omnibenevolent God, he could have still, I argue at least, have made the choice to remove our free will "for our own good". Even if P(E|D) is high, in no way is it close to 100%.
Furthermore, you can never assume a 100% probability!!! (http://yudkowsky.net/rational/technical). You could go to rationalist hell for that!
Conditional probabilities are allowed to be 100%, because they are probability ratios. In particular, P(A|A) is 100% by definition.
But P(E|D) is not 100% by any definition. Conditional probabilities are only 100% if
D-->E. And if that was true, why does this argument exist?
The reason they are assuming P(E|D) = 100% is probably because they are only envisioning what one particular god would do, not the whole search space: they are asking "What would God do?" instead of "What would X percentage of the zillion possible gods in the search space do?" The hard part is getting them to realize that P(E|D) includes Zeus, Loki, and the FSM as well as Jehovah.