A Supplement to Putnam's Quantum Logic

To examine Putnam's views on the application of quantum logic is the aim of this paper. Hilary Putnam defends quantum logic in his works. According to him, classical logic cannot answer the problems arising in quantum mechanics. Therefore, we need to present a non-classical logic, namely quantum logic. Putnam argues three main reasons for the transition from classical logic to quantum: I. to be false some of the necessary truths of logic, II. have to change of logic, III. the pattern of three-valued logic. Putnam's views about this transition to quantum logic can be considered from several points: First, despite Putnam's criticism of classical logic, he defends quantum logic through the rules of classical logic. Second, it is a bulky claim to know of quantum logic as “true” logic. Third, the conclusions of the Cartesian product have changed in Putnam's analysis. Fourth, in his logic system, Putnam pays attention to “intuition” instead of relying on “axioms.” Fifth, the middle value of truth is ineffective and erroneous in quantum logic. Despite these criticisms, many of them can be answered analytically.