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Ati comments on Raising the Sanity Waterline - Less Wrong
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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.
You're right, but that doesn't mean what you're saying is useful.
At some point, I have to make decisions, including what to say I believe. It is far less confusing to say 'I believe that god does not exist' than to say 'I hold a vanishingly low belief in the class of things you refer to when you say 'God.''
Saying that you believe a thing is true, or don't believe a thing is true, is not the same thing as saying that your probability estimates are 1 and 0, respectively. That would mean that no evidence would be adequate to change your beliefs, because you have infinite confidence, and that would obviously be stupid. The implication you're inferring from the term 'atheist' doesn't even really logically follow from the definition. I think the class of atheists that actually do mean that they slavishly and unquestioningly disbelieve in God is small enough to be safely disregarded. Most of the people who call themselves atheists simply hold very very low beliefs in God.