The Probability of the Law of Excluded Middle

The Law of Excluded Middle says that for any statement P, “P or not P” is true.

Is this law true? In classical logic it is. But in intuitionistic logic it’s not.

So, in intuitionistic logic we can ask what’s the probability that a randomly chosen statement obeys the Law of Excluded Middle. And the answer is “at most 2/3—or else your logic is classical”.

This is a very nice new result by Benjamin Bumpus and Zoltan Kocsis:

• Benjamin Bumpus, Degree of classicality, Merlin’s Notebook, 27 Februa...