Quantum Logic and Meaning

Abstract

This paper gives a formulation of quantum logic in the abstract algebraic setting laid out by Dunn and Hardegree (2001). On this basis, it provides a comparative analysis of viable quantum logical bivalent semantics and their classical counterparts, thereby showing that the truth-functional status of classical and quantum connectives is not as different as usually thought. Then it points out that bivalent semantics for quantum logic -- compatible with realism about quantum mechanics -- can be maintained, albeit at the price of truth-functionality. Finally, the paper critically addresses Geoffrey Hellman's argument (1980) that this lack of truth-functionality entails a change of meaning between classical and quantum connectives.