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hairyfigment comments on Practicing what you preach - Less Wrong
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To focus on one point that seems straightforward:
My first response was, no they can't. I'll change that to, "how, exactly?"
I suppose the verbal utterance of "P=1" can be revised. Just not any belief system with a P=1 in it without external hacking (or bad updating).
By being wrong when you made said statement. Or by a fundamental shift in reality.
I don't think you understand what P(X)=1 means. It doesn't just mean X is going to happen if the laws of the universe remain the same, it doesn't just mean X going to happen if 3^^^3 coins are flipped and at least one lands on heads.
It means that X happens in every possible version of our universe from this point onward. Including ones where the universe is a simulation that explicitly disallows X.
(The only time P(X) = 1 makes sense is in mathematics, e.g. P(two random lines in 2D space are not parallel) = 1)
Ergo, for P(X)=1 to be revised requires the person making that assertion be wrong, or for there to be a fundamental shift in reality.
Yeah, the person making the assertion can be wrong.
Huh? Did you read what I wrote:
Every. Possible. Universe. This accounts for "fundamental shift[s] in reality".
Yup, I most assuredly did.
Saving for those in which the principle you related is altered. Don't try to wrap your head around it. It's a paradox.
Which principle?
"[P(X)=1] doesn't just mean X is going to happen if the laws of the universe remain the same, it doesn't just mean X going to happen if 3^^^3 coins are flipped and at least one lands on heads.
It means that X happens in every possible version of our universe from this point onward. Including ones where the universe is a simulation that explicitly disallows X."
There is no paradox. Mathematics is independent of the physics of the universe in which it is being discussed, e.g. "The integers" satisfy the same properties as they do for us, even if there are 20 spatial dimensions and 20 temporal ones.
Sure, you can change the axioms you start with, but then you are talking about different objects.
The principles by which mathematics operates, certainly. Two things here:
1) I did not say a fundamental shift in the physics of reality.
2) The mathematics of probability describe real-world scenarios. Descriptions are subject to change.
In this, you have my total agreement.