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?
Conversation
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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If there are an apple and an orange in a bag, and I take out the apple, the orange remains, but ‘apple’ is not the negation of ‘orange’.
In general, n elements that are related only by virtue of constituting a MECE set.
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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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not a law but a corollary of the fact that probabilities sum to 1: if previously P(X)>0 but now P(X)=0, then P(~X) must increase commensurately, distributed across the options
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