Correspondence Truth and Quantum Mechanics

TL;DR

This paper explores how the concept of truth in quantum mechanics can be understood through a contextual correspondence framework, contrasting it with classical mechanics and addressing the limitations imposed by quantum no-go theorems.

Contribution

It introduces a novel account of truth in quantum mechanics based on the Bub-Clifton theorem, establishing a consistent notion of truth within a contextual sublattice of propositions.

Findings

Truth in quantum mechanics is context-dependent.

A consistent truth-value assignment is possible within a specific sublattice.

The traditional correspondence theory is a special case of the proposed contextual scheme.

Abstract

The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either 'true' or 'false', describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of 'no go' theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton 'uniqueness theorem' is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The conceptual implications of the resulting account are traced down and analyzed at length. In this light, the traditional conception of correspondence truth may be viewed as a species or as a limit case of the more generic proposed scheme of contextual correspondence when the non-explicit specification of a context of discourse poses no further consequences.