The meaning of elements of reality and quantum counterfactuals: Reply to Kastner

This paper is an answer to the preceding paper by Kastner, in which she con tinued the criticism of the counterfactual usage of the Aharonov-Bergman-Le bowitz rule in the framework of the time-symmetrized quantum theory, in par ticular, by analyzing the three-box "paradox." It is argued that the critic ism is not sound. Paradoxical features of the three-box example are discuss ed. It is explained that the elements of reality in the framework of time-s ymmetrized quantum theory are counterfactual statements, and therefore, eve n conflicting elements of reality can be associated with a single system. I t is shown how such "counterfactual" elements of reality can be useful in t he analysis of a physical experiment (the three-box example). The validity of Kastner's application of the consistent histories approach to the time-s ymmetrized counterfactuals is questioned.