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RichardKennaway comments on 0 And 1 Are Not Probabilities - Less Wrong
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Digging up an old thread here, but an interesting point I want to bring up: a friend of mine claims that he internally assigns probability 1 (i.e. an undisprovable belief) only to one statement: that the universe is coherent. Because if not, then mnergarblewtf. Is it reasonable to say that even though no statement can actually have probability 1 if you're a true Bayesian, it's reasonable to internally establish an axiom which, if negated, would just make the universe completely stupid and not worth living in any more?
What is P(A|A)?
What do you mean by "|A"? It's well-defined in mathematics, sure, but in real life, surely the furthest you can go is "|experience/perception of evidence for A".
Also, there's also the probability that the particular version of logic you're using is wrong.
How far you can go depends on what you mean by "go".
It's perfectly possible to calculate, say, P(I see the coin come up heads | the coin is flipped once, it is fair, and I see the outcome), and actually much more difficult to calculate P(I see the coin come up heads | I have experience/perception of evidence for the facts that the coin is flipped once, it is fair, and I see the outcome).
"I see" is what I meant by perception/experience of evidence. Whenever I "see" something, there's always a non-zero chance of my brain deceiving me. The only thing you can really have to base your decisions on is P(I see the coin come up heads | I see/know the coin is flipped once, I know it is fair, and I see the outcome). P(the coin comes up heads|the coin is flipped once, it is fair and I know the outcome) is possible and easy to calculate, but not completely accurate to the world we live in.