P2: The sky is more likely to be blue in worlds that have had less catastrophic events
C: This world will have had fewer catastrophic events than average
and
P1: The sky is blue
P2: The sky tends to be blue in worlds that have had less catastrophic events
C: Catastrophic events are less likely
Are both valid and don’t actually conflict. They are entitled to both decrease how likely they take the catastrophes to be(due to no catastrophe changing the color of the sky), but they should also think that they are more likely than their historical record indicates.
This is because, if you are in a world where X is true your being in that world should increase how likely you think being in a world where X is true, but it should also make you think you have a data set biased in favor of events correlated with X being true.
I think the anthropic nature of anthropic shadow comes in due to if X is, you exist. Then it doesn’t indicate that it is more likely, only that it is possible because unlike the sky you couldn’t be in a world where you didn’t exist.
I think the Russian roulette can be untangled if we frame it differently, I think you definitely have information that the gun is the 1/1000 because you are more likely to be an observer moment in a universe where it was that gun rather than the other. But you shouldn’t be surprised that you exist, if you learn that it was the 999/1000 gun, you should be suppressed that it was that you are in a universe where your existence is unlikely rather than likely.
“the arguments … Are both valid and don’t actually conflict. They are entitled to both decrease how likely they take the catastrophes to be(due to no catastrophe changing the color of the sky), but they should also think that they are more likely than their historical record indicates. ”
I agree with this. Those are two opposing (but not contradictory) considerations for them to take into account. But what I showed in the post was: once both are taken into account, they are left with the same conclusions as if they had just ignored the colour of the sky completely. That’s what the bayesian calculation shows. The two opposing considerations precisely cancel. The historical record is all they actually need to worry about.
The same will be true in the anthropic case too (so no anthropic shadow) unless you can explain why the first consideration doesn’t apply any more. Pointing out that you can’t observe non-existence is one way to try to do this, but it seems odd. Suppose we take your framing of the Russian roulette example. Doesn’t that lead to the same problems for the anthropic shadow argument? However you explain it, once you allow the conclusion that your gun is more likely to be the safer one, then don’t you have to allow the same conclusion for observers in the anthropic shadow set-up? Observers are allowed to conclude that their existence makes higher catastrophe frequencies less likely. And once they’re allowed to do that, that consideration is going to cancel out the observer-selection bias in their historical record. It becomes exactly analogous to the blue/green-sky case, and then they can actually just ignore anthropic considerations completely, just as observers in the blue/green sky world can ignore the colour of their sky.
The sky tends to be blue in worlds that have had less catastrophic events
C: Catastrophic events are less likely
Is identical in form to,
The historical record lacks catastrophic events
The historical record will tend to lack catastrophic events in worlds that have less catastrophic events
C: Catastrophic events are less likely
However, there is the other argument
The historical record lacks catastrophic events
The historical record will tend to lack catastrophic events in worlds that have less catastrophic events
C: This world will have had fewer catastrophic events than average
These can’t perfectly cancel out or we could never know anything, the net result of these two arguments must still be a decrease in how likely we take catastrophic risks. I do think it’s because we can’t discover we don’t exist that is the relevant distinction.
If I can only exist in a world with a blue sky then the fact that the sky is blue should not make me think it is more likely for worlds to have a blue sky. This is why the argument, that life is likely to exist throughout the universe because it happened here doesn’t work. If I can only exist in a world with life then the fact that life exists in this world shouldn’t influence how likely I think it is to be in another world, other than me knowing it is possible.
I responded to your comment on the other post I am happy to continue chatting in DMs if you like.
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.
EDIT:Added comments on the Russian roulette case
My intuition is that the arguments
P1: The sky is blue
P2: The sky is more likely to be blue in worlds that have had less catastrophic events
C: This world will have had fewer catastrophic events than average
and
P1: The sky is blue
P2: The sky tends to be blue in worlds that have had less catastrophic events
C: Catastrophic events are less likely
Are both valid and don’t actually conflict. They are entitled to both decrease how likely they take the catastrophes to be(due to no catastrophe changing the color of the sky), but they should also think that they are more likely than their historical record indicates.
This is because, if you are in a world where X is true your being in that world should increase how likely you think being in a world where X is true, but it should also make you think you have a data set biased in favor of events correlated with X being true.
I think the anthropic nature of anthropic shadow comes in due to if X is, you exist. Then it doesn’t indicate that it is more likely, only that it is possible because unlike the sky you couldn’t be in a world where you didn’t exist.
I think the Russian roulette can be untangled if we frame it differently, I think you definitely have information that the gun is the 1/1000 because you are more likely to be an observer moment in a universe where it was that gun rather than the other. But you shouldn’t be surprised that you exist, if you learn that it was the 999/1000 gun, you should be suppressed that it was that you are in a universe where your existence is unlikely rather than likely.
“the arguments … Are both valid and don’t actually conflict. They are entitled to both decrease how likely they take the catastrophes to be(due to no catastrophe changing the color of the sky), but they should also think that they are more likely than their historical record indicates. ”
I agree with this. Those are two opposing (but not contradictory) considerations for them to take into account. But what I showed in the post was: once both are taken into account, they are left with the same conclusions as if they had just ignored the colour of the sky completely. That’s what the bayesian calculation shows. The two opposing considerations precisely cancel. The historical record is all they actually need to worry about.
The same will be true in the anthropic case too (so no anthropic shadow) unless you can explain why the first consideration doesn’t apply any more. Pointing out that you can’t observe non-existence is one way to try to do this, but it seems odd. Suppose we take your framing of the Russian roulette example. Doesn’t that lead to the same problems for the anthropic shadow argument? However you explain it, once you allow the conclusion that your gun is more likely to be the safer one, then don’t you have to allow the same conclusion for observers in the anthropic shadow set-up? Observers are allowed to conclude that their existence makes higher catastrophe frequencies less likely. And once they’re allowed to do that, that consideration is going to cancel out the observer-selection bias in their historical record. It becomes exactly analogous to the blue/green-sky case, and then they can actually just ignore anthropic considerations completely, just as observers in the blue/green sky world can ignore the colour of their sky.
These arguments don’t cancel out. The argument
The sky is blue
The sky tends to be blue in worlds that have had less catastrophic events
C: Catastrophic events are less likely
Is identical in form to,
The historical record lacks catastrophic events
The historical record will tend to lack catastrophic events in worlds that have less catastrophic events
C: Catastrophic events are less likely
However, there is the other argument
The historical record lacks catastrophic events
The historical record will tend to lack catastrophic events in worlds that have less catastrophic events
C: This world will have had fewer catastrophic events than average
These can’t perfectly cancel out or we could never know anything, the net result of these two arguments must still be a decrease in how likely we take catastrophic risks. I do think it’s because we can’t discover we don’t exist that is the relevant distinction.
If I can only exist in a world with a blue sky then the fact that the sky is blue should not make me think it is more likely for worlds to have a blue sky. This is why the argument, that life is likely to exist throughout the universe because it happened here doesn’t work. If I can only exist in a world with life then the fact that life exists in this world shouldn’t influence how likely I think it is to be in another world, other than me knowing it is possible.
I responded to your comment on the other post I am happy to continue chatting in DMs if you like.
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.
---
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.