Classical Logic and Quantum Properties

          @misc{ pirsa_PIRSA:25100170,
            doi = {10.48660/25100170},
            url = {https://pirsa.org/25100170},
            author = {},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Classical Logic and Quantum Properties},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {oct},
            note = {PIRSA:25100170 see, \url{https://pirsa.org}}
          }
          

Abstract

We articulate a collection of desiderata for an account of the dynamical quantities of a physical theory, and we present a theory that meets these desiderata in the case of quantum mechanics. Our theory retains a distinction between the values of dynamical quantities and the truth values of sentences asserting that a system has a particular value of a particular quantity. This allows our theory to incorporate the phenomenon of quantum indeterminacy as a pattern in the properties instantiated by a system in a particular quantum state, while also retaining the semantics of classical logic. We contrast our theory with quantum logic, which flattens the distinction between quantity values and truth values. We discuss the historical origin of the assumptions leading to this feature of quantum logic, and we address a series of objections that have been raised to previous attempts to reconcile quantum indeterminacy with classical logic.