  This paper is the answer to the paper by Kastner [Found. Phys., to be
published, quant-ph/9807037] in which she continued the criticism of the
counterfactual usage of the Aharonov-Bergman-Lebowitz rule in the framework of
the time-symmetrized quantum theory, in particular, by analyzing the three-box
``paradox''. It is argued that the criticism is not sound. Paradoxical features
of the three-box example has been explained. It is explained that the elements
of reality in the framework of time-symmetrized quantum theory are
counterfactual statements and, therefore, even conflicting elements of reality
can be associated with a single particle. It is shown how such
``counterfactual'' elements of reality can be useful in the analysis of a
physical experiment (the three-box example). The validity of Kastner's
application of the consistent histories approach to the time-symmetrized
counterfactuals is questioned.
