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Cyan comments on Two probabilities - Less Wrong
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I grant that a big world provides an ensemble such that epsilon could make sense. I think that the prosaic explanation fails, though -- a fully specified version of statement two refers either to an instant in time or an interval, and either way, in a small world there will be a fact of the matter.
Hmm, frequentist probability is most usually described in terms of, er, frequency; what fraction of the time we will get a given result when we run the test. But if you take it as referring to an instant of time (and you assume small world and no fuzziness) in that case I agree the epsilon would disappear.
It's a minor point, but wackily enough, the above quote is a subtle equivocation on the word "time". I can flip N exchangeable coins simultaneously and count the number of times I see "heads", and this is perfectly sensible in the frequentist interpretation. Physical clock time is something else again.