Semantic incompleteness of quantum physics
The author seeks to provide a formal logical expression of the `incompleteness' of quantum physics, as discussed in the Einstein- Podolsky-Rosen paper. Part of the analysis provided is closely similar to my own work published in 1984. The author outlines a formal language for physics which includes `state' and `effect' predicate symbols. He briefly sketches an interpretation based on the concept of `laboratory', such that states are interpreted as physical objects prepared in a laboratory, and effects are `physical objects which could yield the answer `yes' if tested by means of a device'. While this semantics is quite different from my own work, the further developments in this paper closely follow work of my own, published in ``Modern logic and quantum mechanics'' (1984; Zbl 0586.03003). Specifically a `true domain' and `false domain' are defined and discussed, cf. my own `truth set' and `falsity set' of an interpretation. The incompleteness of quantum physics is expressed in terms of the fact that states cannot determine truth-values of all propositions, or alternatively in the non-exhaustiveness of the truth- and falsity-sets. And most importantly, at the end of the paper, a `compatibility' relation is defined among states, which is exactly comparable to my own `successor' relation, i.e. two states are `compatible' (successors) if they yield non-contradictory information, a relation which was analyzed and discussed in my own work. In my view the semantics sketched here needs far more rigorous development to be convincing. And the analysis of `incompleteness' which is the aim of the semantics, has already been developed in my own work, based on a more general and simpler semantics.
scientific article; zbMATH DE number 95355