Histories in quantum mechanics: distinguishing between formalism and interpretation

In spite of being a well articulated proposal, the theory of quantum histories (TQH), in its different versions, suffers from certain difficulties that have been pointed out in the literature. Nevertheless, two facets of the proposal have not been sufficiently stressed. On the one hand, it is a non-collapse formalism that should be technically appropriate to supply descriptions based on quantum properties at different times. On the other hand, it intends to provide an interpretation of quantum mechanics that solves the traditional puzzles of the theory. In this article we spell out the main criticisms to TQH and classify them into two groups: theoretical and interpretive. Whereas the latter might be ignored if the TQH were considered as a quantum formalism with its minimum interpretation, the former seems to point toward technical difficulties that must be faced in a theoretically adequate proposal. Precisely with the purpose of solving these difficulties, we introduce a different perspective, called Formalism of Generalized Contexts or Formalism of Contextual Histories (FCH), which supplies a precise condition for consistently talking of quantum properties at different times without the theoretical shortcomings of the TQH.