I always find anthropic arguments a bit mysterious. I completely agree that if all people live in one of two houses, one with 1 resident and the other with 100, then if we are a randomly chosen person we will most-likely have a lot of people sharing our home.
But when you substitute the word “house” for “universe” something important is different. Only one of the two universes actually exists. The other one is hypothetical. Its in fact more hypothetical than a normal “could have been”, because we don’t even know if chemistry/star formation or whatever could have been different, even in principle. So when we count frequencies to estimate the probability in the “universe” case we are counting people who are by-definition hypothetical.
In the situation where God flicks a coin, and on heads creates a house with 100 people, and on tails creates a house with 1 person. Then I am not sure either way about an anthropic argument that says “I have just found out I exist, which means I am very likely in the crowded house timeline”. But I think that without the guarantee that such a coin toss ever happened, that is without any reason to think the 100 person house was ever a possibility—then my own feeling is that anthropic arguments don’t work. Although I find them enough of a logical minefield that I would not put my certainty super high.
If probability did require some form of objective randomness, then a lot of our probabilistic reasoning would not be justified. Which seems wrong.
For example, assume the universe is deterministic. Assume that our evidence supports the hypothesis that it will rain tomorrow. We conclude that it will probably rain tomorrow. Yet if it won’t rain tomorrow, since the universe is deterministic, it was not possible that it will rain tomorrow. Hence, by your reasoning, it was wrong to think it would probably rain tomorrow. But that’s absurd. Whether rain is likely or not depends on our evidence for rain, not on whether the universe is deterministic.
Or another example: Suppose you have a lot of evidence (from testimony, say) that a particular mathematical conjecture is true. Then it is probably true, relative to your evidence. Now assume, unbeknownst to you, it is false. Then it isn’t possible that it is true, and by your original reasoning, it would be wrong to say that your evidence indicates that it is true. But that’s obviously mistaken: Of course the truth value of mathematical conjectures is predetermined, but that doesn’t affect their probability—the probability depends on the evidence at hand.
Its not about the objective randomness, to me its about the fact that the frequency is by necessity hypothetical. Yes their will only be one tomorrow, and rain might be pre-determined. But we can make arguments about “in a sample of days like tomorrow we know that some % will see rain.” But their can only be one universe, even in principle, so the idea of generalizing to a class of universes and taking our universe as a member of that class I think can cause problems.
While writing this posting, Max and I had several discussions about anthropic bias. It left me pretty uncomfortable with the application of it here as well, although I often took the position of defending it during our debates. I strongly relate to your use of the word “mysterious”.
A prior that “we are not exceptionally special” seems to work pretty good across lots of beliefs that have occurred throughout history. I feel like that prior works really well but is at odds with the anthropic bias argument.
I’m still haven’t resolved whether the anthropic argument is valid here in my own mind. But I share Ben’s discomfort.
I always find anthropic arguments a bit mysterious. I completely agree that if all people live in one of two houses, one with 1 resident and the other with 100, then if we are a randomly chosen person we will most-likely have a lot of people sharing our home.
But when you substitute the word “house” for “universe” something important is different. Only one of the two universes actually exists. The other one is hypothetical. Its in fact more hypothetical than a normal “could have been”, because we don’t even know if chemistry/star formation or whatever could have been different, even in principle. So when we count frequencies to estimate the probability in the “universe” case we are counting people who are by-definition hypothetical.
In the situation where God flicks a coin, and on heads creates a house with 100 people, and on tails creates a house with 1 person. Then I am not sure either way about an anthropic argument that says “I have just found out I exist, which means I am very likely in the crowded house timeline”. But I think that without the guarantee that such a coin toss ever happened, that is without any reason to think the 100 person house was ever a possibility—then my own feeling is that anthropic arguments don’t work. Although I find them enough of a logical minefield that I would not put my certainty super high.
This problem disappears if we assume very large universe with different regions. All regions are real and are like houses. I look more formally in it here: https://www.lesswrong.com/posts/KhwLtJXoAhqfmguzh/sia-becomes-ssa-in-the-multiverse
If probability did require some form of objective randomness, then a lot of our probabilistic reasoning would not be justified. Which seems wrong.
For example, assume the universe is deterministic. Assume that our evidence supports the hypothesis that it will rain tomorrow. We conclude that it will probably rain tomorrow. Yet if it won’t rain tomorrow, since the universe is deterministic, it was not possible that it will rain tomorrow. Hence, by your reasoning, it was wrong to think it would probably rain tomorrow. But that’s absurd. Whether rain is likely or not depends on our evidence for rain, not on whether the universe is deterministic.
Or another example: Suppose you have a lot of evidence (from testimony, say) that a particular mathematical conjecture is true. Then it is probably true, relative to your evidence. Now assume, unbeknownst to you, it is false. Then it isn’t possible that it is true, and by your original reasoning, it would be wrong to say that your evidence indicates that it is true. But that’s obviously mistaken: Of course the truth value of mathematical conjectures is predetermined, but that doesn’t affect their probability—the probability depends on the evidence at hand.
Its not about the objective randomness, to me its about the fact that the frequency is by necessity hypothetical. Yes their will only be one tomorrow, and rain might be pre-determined. But we can make arguments about “in a sample of days like tomorrow we know that some % will see rain.” But their can only be one universe, even in principle, so the idea of generalizing to a class of universes and taking our universe as a member of that class I think can cause problems.
While writing this posting, Max and I had several discussions about anthropic bias. It left me pretty uncomfortable with the application of it here as well, although I often took the position of defending it during our debates. I strongly relate to your use of the word “mysterious”.
A prior that “we are not exceptionally special” seems to work pretty good across lots of beliefs that have occurred throughout history. I feel like that prior works really well but is at odds with the anthropic bias argument.
I’m still haven’t resolved whether the anthropic argument is valid here in my own mind. But I share Ben’s discomfort.