John_Maxwell_IV comments on A taxonomy of Oracle AIs - Less Wrong
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I found this sentence confusing.
By the total probability rule, we can say that the probability of the data being seen in the future is the sum of these two numbers:
If we assume for the sake of argument that the probability of model M being true is 1, then the second number becomes zero. By the definition of conditional probability, the first number is the product of the probability of the data being seen given that model M is true and the probability that model M is true. Since we are assuming that the probability of model M being true is one, this reduces to the probability of the data being seen given that model M is true.
So could we rewrite that sentence as
Or
In any case, it seems to me that the formalism does not add much here, and you could communicate the same idea by saying something like
It isn't clear that this applies to prediction systems like Solomonoff induction or Levin search - which superficially do not appear to be goal-directed.
I found an example:
It is also discussed here.