Anthropic Bias Observation Selection Effects in Science and Philosophy Nick Bostrom
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One can model Incubator using  even if we assume that there are two subjectively distinguishable states that the blackbearded observer might be in after learning about his beard color. In order to do that, one has to expand our representation of the problem by considering a more fine-grained partition of the possibilities involved. To be concrete, let us suppose that the blackbearded observer might or might not experience a pain in his little toe during the stage where he knows he has a black beard. If he knew that this pain would occur only if the coin fell Tails (say) then the problem would be trivial; so let’s suppose that he doesn’t have know of any correlation between having the pain and the outcome of the coin toss. We then have four possible worlds to consider (figure 7):
 The possible worlds w1-w4 represent the following possibilities: w1: Heads and the late blackbeard has no little-toe pain. w2: Heads and the late blackbeard has a little-toe pain. w3: Tails and the late blackbeard has a little-toe pain. w4: Tails and the late blackbeard has no little-toe pain. We can assume that the observer-moments share the prior P(wi) = 1/4 (for i = 1,2,3,4). Let h be the hypothesis that the coin fell heads, and e the information available to an observer-moment that knows it has a black beard and pain in the little toe. By , the reference class for such an observer-moment is
Directory: preprints preprints -> Digitally-assisted discovery and proof preprints -> Reorienting the Logic of Abduction preprints -> Supplementary Material Table 1 Download 9.31 Mb. Share with your friends:
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