Time-symmetrized quantum theory and counterfactuals

Recent authors have raised objections to the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz (ABL) rule of time symmetrized quantum theory (TSQT). L. Vaidman has responded to those objections by proposing a new kind of time-symmetrized counterfactual, which he has defined in two different ways. It is argued that both definitions are problematic, and that the ABL rule cannot in general be used counterfactually. In particular, it is shown that Vaidman's counterargument to the Sharp and Shanks inconsistency proof fails. However, it is possible to retain a meaningful counterfactual reading of the ABL rule in a limited special case. This special case, which falls under a class identified by Cohen and Hiley, is discussed from a time-symmetry standpoint.