Is there a generalization of the law of the excluded middle, where there is a closed set of n MECE propositions and the falsification of 1 proposition, increases the likelihood of the other n-1 in some way? Eg as in Monty Hall problem?
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Law of excluded middle concerns a proposition and it’s negation, so the two possibilities are logically related by negation. But in the generalization, we want to drop need this.
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Basically a generalization and formalization of something like Holmes' principle: when you've eliminated the impossible, whatever remains, however improbable, must be true. True of closed, finite, discrete sets.
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As opposed to the Dirk Gently principle of "don't eliminate the impossible" (which is another way of saying, keep the set open)
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Logicians can probably give more interesting answers, but I think the smartass answer "Bayesian inference" has real merit here.
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