Paul_Gowder comments on Absolute Authority - Less Wrong
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Poke, that's a really unhelpful way of thinking about the problem of induction. The problem of induction is a problem of logic in the first instance -- a description of the fact that we *do* have absolute knowledge of the truth of deductive arguments (conditional on the premises being true) but we don't have absolute knowledge of the truth of inductive arguments. And that's just because the conclusion of a deductive argument is (in some sense) contained in the premises, whereas the conclusion of a generalization isn't contained in the individual observations. What's contained in the individual observations (putting on social scientist hat here) is a probability, given one's underlying distribution, of finding data like what you found if the world is a certain way.
That's a real distinction -- it doesn't come from somehow giving weight to imaginary possibilities, it reflects the difference between logical truth (which IS absolute) and empirical truth (which is not).