Correspondence Truth and Quantum Mechanics

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.Comment: 19 page

Contextual semantics in quantum mechanics from a categorical point of view

“…Propositional content seems to be linked to a context. This connection between referential context and propositional content means that a descriptive elementary proposition in the domain of quantum mechanics is, in a sense, incomplete unless it is accompanied by the specified conditions of an experimental context under which the proposition becomes effectively truth-valued (see, in addition, Karakostas 2014). In view of our approach, the latter observation underlines the fact that the conceptual significance of a logic of propositions referring to the description of a quantum system lies at the level of contextual propositions holding in distinct Boolean frames.…”

Hilbert Space Quantum Mechanics is Contextual (Reply to R. B. Griffiths)

“…[Op. cit., p. 180] (emphasis added) [4], in Bub's bohmian version of the modal interpretation [5] or the contextual approaches by Karakostas [15] and Svozil [19]. 8 Given a vector in Hilbert space, Ψ, the Born rule allows us to predict the average value of (any) observable O, Ψ|O|Ψ = O .…”

On the Structure and Function of Scientific Perspectivism in Categorical Quantum Mechanics

“…Especially, in relation to empirical testing of theories in contemporary physics, theoretical and methodological considerations specify the perspective from which we articulate the elementary yes-no experimental propositions or questions associated with properties of physical systems, in the sense that, on the one hand, they supply with a well-defined meaning the question that is put to nature, and, on the other hand, they specify the kind of the operations to be performed in order to ascertain particular answers to them (Karakostas [2014]). In this sense, it is legitimate to say that the perspectival nature of experimental/empirical knowledge is an essential characteristic of acquiring scientific knowledge.…”