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Cyan comments on Deleting paradoxes with fuzzy logic - Less Wrong
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The rules of probability reduce to the rules of binary logic when the probabilities are all zero or one, so you get binary logic for free just by using probability.
Yes, we all know that ;)
But under this approach the binary logic is NOT operating at a fundamental level -- it is subsumed by a probability theory. In other words, what is true in the binary logic is not really true; it depends on the probability assigned to the statement, which is external to the logic. In like manner, I can assign fuzzy values to a binary logic which are external to the binary logic.