Quantum theory as a theory in a classical propositional calculus

Harald Atmanspacher A, F.R. Krueger, H. Scheingraber

Franz W. Kamber

Andréa Oldofredi

It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in order to model the propositions of every quantum theory is challenged. In the present essay, we critically discuss this claim by showing that classical logic can be rehabilitated in a quantum context by taking into account Bohmian mechanics. It will be argued, indeed, that such a theoretical framework provides the necessary conceptual tools to reintroduce a classical logic of experimental propositions by virtue of its clear metaphysical picture and its theory of measurement. More precisely, it will be shown that the rehabilitation of a classical propositional calculus is a consequence of the primitive ontology of the theory, a fact that is not yet sufficiently recognized in the literature concerning Bohmian mechanics. This work aims to fill this gap.

Bernard d’Espagnat

Knowledge of the classical and nonclassical theories of logical propositions is not required for an understanding of the analysis of the nonseparability of systems. Some very elementary notions about that matter may help to place the general problem in appropriate perspective. Classically, physical propositions bear upon physical systems. A proposition a bearing on a system S is a qualitative statement about S. The quantum calculus of propositions has been successfully used as an alternative and more general basis for the foundations of quantum mechanics. It is a truism that the advent of the modern physical theories—relativity, quantum mechanics, quantum electrodynamics, S matrix theory, and so on—has induced us to abandon many familiar intuitive concepts. All the successful theories mentioned above are built on elaborate sets of axioms that are justified only a posteriori, that is, by agreement between some of their consequences and observed facts.

Christian DE RONDE, Graciela Domenech, Héctor Freytes