But at what price? The histories approach introduces a variety of concepts that go beyond textbook quantum theory, and these can be summarized under two headings. First, quantum dynamics is treated as stochastic or probabilistic. Not just when measurements are carried out, but always. Born’s rule, together with its extensions, is a fundamental axiom of quantum theory. The task of Schrödinger’s time-dependent equation is to assist in assigning probabilities. Second, following Sec. III.5 of J. von Neumann (1932), quantum properties, which are what the probabilities refer to, are associated with subspaces of the quantum Hilbert space. But then new logical principles are required to consistently deal with the difference between the quantum Hilbert space and a classical phase space. These principles are related to, but not identical with, those of the quantum logic initiated by Birkhoff &amp; Neumann (1936).