Some additional comments. First, two consistent families \(\FC_a\) and \(\FC_b\) may be such that the (history) projectors in one commute with those in the other, but still the common coarsest refinement does not satisfy the dynamical consistency conditions, in which case they are said to be incommensurate and cannot be combined, at least if one wishes to use the dynamical laws of quantum mechanics to assign them probabilities. Second, measurements play no role in terms of the fundamental mathematical formulation or its physical interpretation. In classical physics there is never any difficulty in imagining events actually occurring inside a closed system, even with no observers or measuring apparatus present. The same is true for quantum physics once one removes “measurement” from its spurious role as an interpretive principle, and instead treats it like any other quantum process, see section 7. Third, the histories approach is time symmetrical in the sense that the rules for assigning probabilities do not single out a particular “direction” or sense of time. (This symmetry is evident in the more complete discussion in Ch. 10 of Griffiths (2002a), which allows more general types of family. That generality has been sacrificed here in the interests of a simpler and more intuitive exposition based on the assumption of a single pure state at the initial time.)