Anthropic Bias Observation Selection Effects in Science and Philosophy Nick Bostrom
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In a nutshell: although hM makes it more probable that  should exist, hM also makes it more probable that there are other observer-containing universes. And the greater the number of observer-containing universes, the smaller the probability that we should observe any particular one of them. These two effects balance each other. The result is that the messenger’s tidings are evidence in favor of theories on which it is probable that at least one observer-containing universe would exist; but this evidence does not favor theories on which it is probable that there are many observer-containing universes over theories on which it is probable that there are merely a few observer-containing universes.
We can get an intuitive grasp of this if we consider a two-step procedure. Suppose the messenger first tells you that some observer-containing universe x exists. This rules out all hypotheses on which there would be no such universes; it counts against hypotheses on which it would be very unlikely that there are any observer-containing universes; and it favors hypotheses on which it would be very likely or certain that there is one or more observer-containing universes. In the second step, the messenger tells you that x = . This should not change your beliefs as to how many observer-containing universes there are (assuming you don’t think there is anything special about ). One might say that if God were equally likely to create any universe, then the probability that should exist is proportional to the number of universes God created. True. But the full evidence you have is not only that exists but also that the messenger told you about . If the messenger selected the universe he reports randomly from the class of all actual observer-containing universes, then the probability that he would select , given that is an actual observer-containing universe, is inversely proportional to the number of actual observer-containing universes. The messenger’s report therefore does not allow you to discriminate between general hypotheses8 that imply that at least one observer-containing universe exists.
In our actual situation our knowledge is not mediated by a messenger; but the idea is that the data we get about the world are subjected to observation selection effects that mimic the reporting biases present in Case 3. (Not quite, though. A better analogy yet would be one in which (Case 4) the messenger selects a random observer from among the observers that God has created, thus biasing the universe-selection in favor of those universes that have relatively large populations. But more on this in a later chapter. To keep things simple here, we can imagine all the observer-containing universes as having the same number of observers.) 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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