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.
1
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.
3
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.
Replying to
As opposed to the Dirk Gently principle of "don't eliminate the impossible" (which is another way of saying, keep the set open)
1
1

