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Patrick comments on Take heed, for it is a trap - Less Wrong
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"Bayesian Bob: ... I meant that in a vacuum we should believe it with 50% certainty..."
No we shouldn't: http://lesswrong.com/lw/jp/occams_razor/
As for proving a negative, I've got two words: Modus Tollens.
Bob does need to go back to math class! ;)
You're right, I should have said "proving non-existence".
As for the Occam razor (and any formalizations thereof) it's still 50% for an arbitrary proposition P. You need evidence (for instance in terms of the complexity of the proposition itself) in order to lower the probability of the proposition.
Otherwise I can just present you with two propositions P and Q, where Q happens to be non-P and you'll assign the same sub-50% probabilities to P and Q, even though exactly one of them is guaranteed to be true. I think that would make you exploitable.
Modus Tollens is: If P, then Q. Not Q. Therefore, not P
But you can't prove not Q in the first place.
Three more words then, reductio ad absurdum.
Ok, fair.