Will_Sawin comments on Taking Ideas Seriously - Less Wrong

51 Post author: Will_Newsome 13 August 2010 04:50PM

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Comment author: Will_Sawin 11 September 2010 08:16:32PM 0 points [-]

1: By using the counterfactuals in the Tegmark Level IV multiverse.

2: By giving it a probability of 0. If T is falsified, that means P(D|T)=0 - we obtained data that T claims is impossible. In this case, Bayes' theorem sets P(T|D)=0. Bayesianism includes all correct thinking tools, including Popperian epistemology.

But is P(D|T) really 0? We could have made a mistake and not recorded the correct data. Certainly scientists in the past have done so, and thought that they falsified theories that they didn't falsify. In this case, P(D|T) is very small but nonzero, and so is P(T|D) (unless p(D|~T) is also very small.)

3: You cannot avoid giving a probability. Because of Cox's theorem, which says we must use probability theory to reason about uncertainty (although I must confess that the assumption that we must use a single real number to reason is rather strong.)