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.
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.