Anthropic Bias Observation Selection Effects in Science and Philosophy Nick Bostrom
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This looks like an auspicious beginning. It seems to fit the other example considered near the beginning of this section: one person winning three lotteries with a thousand tickets could make us suspect foul play, whereas one person winning a billion-ticket lottery would not in general have any tendency do so. Or ponder the case of a monkey typing out the sequence “Give me a banana!”. This is surprising and it makes us change our belief that the monkey types out a random sequence. We would think that maybe the monkey had been trained to type that specific sequence, or maybe that the typewriter was rigged; but the chance hypothesis is disconfirmed. By contrast, if the monkey types out “r78o479024io; jl;”, this is unsurprising and does not challenge our assumptions about the setup. So far so good. What Ramsey’s suggestion does not tell us is what it is about events such as the monkey’s typing a meaningful sentence or the run of 1000 heads that makes us change our minds about the system of chances. And we need to know that if the suggestion is to throw light on the fine-tuning case. For the problem there is precisely that it is not immediately clear – lest the question be begged – whether we ought to change our system and find some alternative explanation or be satisfied with letting chance pay the bill by regarding fine-tuning as a coincidence. Ramsey’s suggestion is thus insufficient for the present purpose. Paul Horwich takes the analysis a little further. He proposes the following as a necessary condition for the truth of a statement E being surprising: [T]he truth of E is surprising only if the supposed circumstances C, which made E seem improbable, are themselves substantially diminished in probability by the truth of E…and if there is some initially implausible (but not widely implausible) alternative view K about the circumstances, relative to which E would be highly probable. ((Horwich 1982), p. 101) If we combine this with the condition that “our beliefs C are such as to give rise to  ”, we get what Horwich thinks is a necessary and sufficient condition for the truth of a statement being surprising. We can sum this up by saying that the truth of E is surprising iff the following holds:
(i)
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