The Labyrinth of Quantum Logic. (arXiv:1802.01834v1 [physics.hist-ph])

Quantum mechanics predicts many surprising phenomena, including the two-slit
interference of electrons. It has often been claimed that these phenomena
cannot be understood in classical terms. But the meaning of "classical" is
often not precisely specified. One might, for example, interpret it as
"classical physics" or "classical logic" or "classical probability theory".
Quantum mechanics also suffers from a conceptual difficulty known as the
measurement problem. Early in his career, Hilary Putnam believed that
modifications of classical logic could both solve the measurement problem and
account for the two-slit phenomena. Over 40 years later he had abandoned
quantum logic in favor of the investigation of various theories--using
classical logic and probability theory--that can accomplish these tasks. The
trajectory from Putnam's earlier views to his later views illustrates the
difficulty trying to solve physical problems with alterations of logic or
mathematics.