The objective of the paper is to present a comprehensive picture of Bell-type theorems, by giving both the theorems and the proofs of them.Special care is given to specifying the assumptions of the arguments and their physical or metaphysical significance. Taking the EPR argument as a point of departure, the paper discusses four probabilitic Bell-type theorems,which are then followed by two versions on non-probailitic (GHZ) arguments.The final section provides the reader with a classification of the assumptions, which specifies which assumption is used in which proof.
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 twoslit 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.