A relation is obtained between weak values of quantum observables and the
consistency criterion for histories of quantum events. It is shown that
``strange'' weak values for projection operators (such as values less than
zero) always correspond to inconsistent families of histories. It is argued
that using the ABL rule to obtain probabilities for counterfactual measurements
corresponding to those strange weak values gives inconsistent results. This
problem is shown to be remedied by using the conditional weight, or
pseudo-probability, obtained from the multiple-time application of Luders'
Rule. It is argued that an assumption of reverse causality (a form of time
symmetry) implies that weak values obtain, in a restricted sense, at the time
of the weak measurement as well as at the time of post-selection. Finally, it
is argued that weak values are more appropriately characterised as
multiple-time amplitudes than expectation values, and as such can have little
to say about counterfactual questions.Comment: Final version, to appear in Studies in History and Philosophy of
Modern Physic
