>>12946142It literally does not work in quantum mechanics. This is the entire basis of Birkhoff-von Neumann approach to Quantum Logics.
>inb4 I don't know QMStrictly speaking this is correct, but I know functional analysis, and some basics of representation theory of Lie Algebra, so I basically know quantum mechanics, minus all the stuff about particles and the like. But particles are really irrelevant anyway. That's just slang for talk about matrices and actions of lie groups on a vector space.
Also this
>>12946080Also, incompleteness is a good reason to reject LEM. So is common sense reasoning, for example in epistemic logic, and other systems of knowledge representation (an area of AI), it is often that case that agents poses imperfect knowledge, in which case it makes perfect sense to have neither K(x) nor ~K(x). This point is even stronger, when we consider representing things like preference orders, which are generally going to have even less constraints than the set of formula that an agent believes/knows.
