(December 29, 2022 at 2:48 pm)Angrboda Wrote:(December 29, 2022 at 12:32 pm)Jehanne Wrote: Wikipedia -- Hartle–Hawking state
I think Mister Agenda's point is that there is a valid instance of the excluded middle here, and Hawking-Hartle doesn't rebut that conclusion.
It's the same as saying that an atheist lacks a belief in a god, yet in some way, unspecified, an ignostic doesn't fall into that category.
Quote:The present paper demonstrates the failure of the principle of excluded middle (PEM) in the lattice of all closed linear subspaces of a Hilbert space (usually defined as quantum logic). Namely, it is shown that for a qubit, a proposition and its negation can be both false. Since PEM is the assumed theorem of quantum logic, this raises the question: If PEM holds in the orthocomplemented lattice of all propositions of the quantum system, then how the failure of PEM in quantum logic can be explained? Alternatively, if the propositions relating to the quantum system do not obey PEM, then what is the semantics of those propositions? Possible answers to these questions are analyzed in the present paper.
arXiv -- Do quantum propositions obey the principle of excluded middle?
It's one (preprint) paper by one author, which doesn't prove anything, but, maybe there is more here than meets the eye, or Aristotelian dialectic logic.
