  In quantum logic, i.e., within the structure of the Hilbert lattice imposed
on all closed linear subspaces of a Hilbert space, the assignment of truth
values to quantum propositions (i.e., experimentally verifiable propositions
relating to a quantum system) is unambiguously determined by the state of the
system. So, if only pure states of the system are considered, can a probability
measure mapping the probability space for truth values to the unit interval be
assigned to quantum propositions? In other words, is a probability concept
contingent or emergent in the logic of quantum propositions? Until this
question is answered, the cause of probabilities in quantum theory cannot be
completely understood. In the present paper it is shown that the interaction of
the quantum system with its environment causes the irreducible randomness in
the relation between quantum propositions and truth values.
