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Misha comments on Take heed, for it is a trap - Less Wrong Discussion
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If you know nothing about A and B, then you know something about A&B. You know it is the conjunction of two things you know nothing about.
Since A=B is a possibility the uses of "two things" here is bit specious. You're basically saying you know A&B but that could stand for anything at all.
You know that either A and B are highly correlated (one way or the other) or P(A&B) is close to P(A) P(B).
Yeah, and I know that A is the disjunction of A&B and A&(~B), and that it is the negation of the negation of a proposition I know nothing about, and lots of other things. If we reading a statement and analysing its logical consequences to count as knowledge then we know infinitely many things about everything.