Classical Logic in Quantum Context

TL;DR

This paper argues that classical logic can be restored in quantum contexts through Bohmian mechanics, challenging the idea that quantum logic is universally necessary for all quantum theories.

Contribution

It demonstrates that Bohmian mechanics provides the conceptual tools to reintroduce classical logic in quantum theory, emphasizing its primitive ontology and measurement theory.

Findings

Classical logic can be rehabilitated in quantum contexts using Bohmian mechanics.

Bohmian mechanics offers a clear metaphysical framework supporting classical propositional calculus.

The primitive ontology of Bohmian mechanics is key to this logical restoration.

Abstract

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 in virtue of its clear metaphysical picture and its theory of measurement. More precisely, it will be showed that the rehabilitation of a classical propositional calculus is a consequence of the primitive ontology of the theory, a fact which is not yet sufficiently recognized in the literature concerning Bohmian mechanics. This work aims to fill this gap.