I am very confident that the arguments do perfectly cancel out in the sky-colour case. There is nothing philosophically confusing about the sky-colour case, it’s just an application of conditional probability.
That doesn’t mean we can never learn anything. It just means that if X and Y are independent after controlling for a third variable Z, then learning X can give you no additional information about Y if you already know Z. That’s true in general. Here X is the colour of the sky, Y is the probability of a catastrophic event occurring, and Z is the number of times the catastrophic event has occurred in the past.
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In the Russian roulette example, you can only exist if the gun doesn’t fire, but you can still use your existence to conclude that it is more likely that the gun won’t fire (i.e. that you picked up the safer gun). The same should be true in anthropic shadow, at least in the one world case.
Fine tuning is helpful to think about here too. Fine tuning can be explained anthropically, but only if a large number of worlds actually exist. If there was only one solar system, with only one planet, then the fine tuning of conditions on that planet for life would be surprising. Saying that we couldn’t have existed otherwise does not explain it away (at least in my opinion, for reasons I tried to justify in the ‘possible solution #1’ section).
In analogy with the anthropic explanation of fine-tuning, anthropic shadow might come back if there are many observer-containing worlds. You learn less from your existence in that case, so there’s not necessarily a neat cancellation of the two arguments. But I explored that potential justification for anthropic shadow in the second section, and couldn’t make that work either.
I am very confident that the arguments do perfectly cancel out in the sky-colour case. There is nothing philosophically confusing about the sky-colour case, it’s just an application of conditional probability.
That doesn’t mean we can never learn anything. It just means that if X and Y are independent after controlling for a third variable Z, then learning X can give you no additional information about Y if you already know Z. That’s true in general. Here X is the colour of the sky, Y is the probability of a catastrophic event occurring, and Z is the number of times the catastrophic event has occurred in the past.
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In the Russian roulette example, you can only exist if the gun doesn’t fire, but you can still use your existence to conclude that it is more likely that the gun won’t fire (i.e. that you picked up the safer gun). The same should be true in anthropic shadow, at least in the one world case.
Fine tuning is helpful to think about here too. Fine tuning can be explained anthropically, but only if a large number of worlds actually exist. If there was only one solar system, with only one planet, then the fine tuning of conditions on that planet for life would be surprising. Saying that we couldn’t have existed otherwise does not explain it away (at least in my opinion, for reasons I tried to justify in the ‘possible solution #1’ section).
In analogy with the anthropic explanation of fine-tuning, anthropic shadow might come back if there are many observer-containing worlds. You learn less from your existence in that case, so there’s not necessarily a neat cancellation of the two arguments. But I explored that potential justification for anthropic shadow in the second section, and couldn’t make that work either.