Analysis of quantum probability theory. II (Q1099152)

This paper is a continuation of the author's ''Analysis of quantum probability theory. I'' [ibid. 14, 267-296 (1985; Zbl 0626.03002)], where a new analysis of quantum theory was proposed in order to handle certain technical difficulties, e.g., the difficulty which is associated with the assumption that a physical system does not admit pure states. In this paper, technical details of the analysis are presented. The primitive notions of the technical language in question are, in addition to relevant mathematical notions, ''ensemble'', ''conditional probability'', and ''approximation sample of'', plus a counterfactual conditional. Thus, there exist some readjustments in the technical details; this is due to the fact that in place of first-order properties the author is considering ensembles of actual and potential systems. One of the most interesting new features of the analysis is that it uses counterfactuals to analyze relevant concepts of quantum probability theory, such as ''random event'', ''state'', and ''quantum probability''. This is a way to avoid technical difficulties of the earlier ensemble interpretations of the theory. Why counterfactuals are useful in this analysis is that they offer a way to avoid actual idealizations even though a statistical state is analyzed as a complete determination of projected, ideal sorting probabilities. Another interesting feature of the paper is that it provides a new and simple semantics for counterfactual conditional in terms of a generalized selection function. This approach generalizes the ones proposed by David Lewis and Robert Stalnaker and it is technically well-suited for the author's analysis of quantum probability theory.