Reichenbach and the Logic of Quantum Mechanics

Abstract

It is generally agreed that quantum mechanics (QM) constitutes a revolutionary physical theory, and it has been suggested that the revolutionary character of QM penetrates even to the level of logic. This suggestion stems from at least two sources. First of all, there are the various foundational approaches to QM which propose to formulate quantum theory on the basis of ‘quantum logic’.1 This approach to the postulational foundations of QM originates with the seminal work of Birkhoff and von Neumann (1936), which is based on the Hilbert space formulation of quantum theory expounded by von Neumann in his classic treatise (1932) on the mathematical foundations of QM. A parallel and closely related treatment of QM was proposed by Martin Strauss (1937–38) and developed primarily by Kochen and Specker (see, e.g., 1967). Together these approaches comprise what may be called mainstream (or conventional) quantum logic.2 Secondly, there are a number of nonmainstream quantum logics which have been proposed,3 most notably perhaps by Hans Reichenbach. In his treatise on the philosophical foundations of QM (1944, henceforth PhF), Reichenbach proposed a three-valued truth-functional logic as a means of dealing with certain conceptual tensions arising in the quantum mechanical description of the world.