The whole notion of probability in quantum mechanics requires to be reviewed constantly in the light of newer advances. I. J. Good, summing up some recent versions of 'subjective probability', said that some modification of the familiar postulate that the sum of two stochastic variables (measurable functions) yields a stochastic variable (measurable function) may be needed. Suppose f2 is a 'state space', 'monotonic' and 'bounded' may not suffice for positive convergence. Ian Hacking, in the British Journal for the Philosophy of Science for February, 1966 wrote: "One had thought of statistical independence as a physical property of some part of the world. De Finetti has proved it de trop."
Suppes [32] has recently unfolded the possible non,classical bases of the probability logic of quantum mechanics. An essential feature of some newer approaches to the logic of quantum probabilities is that the familiar identity of much standard information theory:
P (A + B) = P (A) + P (B) -P (AB),
is said to provide no deep insight into the impossibility of the simultaneous measurement of two 'observables'. Davidon and Ekstein [4] have claimed that von Neumann's selfadjoint operators [33] do not always conform to feasible measurements. If, for instance, p and q are two non-commuting observables, no unambiguous method is prescribed for measuring p +q. Kahan [18] has summed up the argument of Suppes in a categorical fashion: "La logique fonctionnelle ou effective de la m6canique quantiqu6 n'est pas classique." I propose to raise some epistemological issues involved in the attempts to generalize classical probability theory.
Several recent writers on quantum logic, Varadarajan [34,35], Jauch [16], Jauch and Piron [17], Piron [25], and Ludwig [20], have dwelt on the situation that, if a probability function is defined in the ordinary fashion, as a normalized, additive, real-valued function in a a-algebra, the properties of the microsystem in quantum mechanics do not, in general, conform to a Boolean lattice.