Can quantum mechanics be shown to be incomplete in principle?

Given four plausible principles, quantum mechanics (QM) can be shown to contradict the standard expression of completeness, the eigenstate-eigenvalue link (EE). Consider: (P0) If, for a proposition A (describing a possible event), a theory T yields another proposition p(A)>0, then it is not the case that T, A perpendicular to. (P1) A QM probability, being of the form p([A]=ai)=Tr(W(t)P(ai)), is to be interpreted as p([A]=ai(t)) (''the probability that S has ai of A at t''). (P2) There is a parameter t within QM such that the expression [A]=ai is read as [A]=ai(t)(''S has ai of A at t''). (P3) Function P:S(H)→[0,1] (collecting the QM probabilities for some suitable Hilbert space H) can be defined as a generalised probability function. It is easy to show, for a non-eigenstate of some observable A and QM probabilities interpreted as prescribed by (P1), that (EE) transforms QM into a theory contradicting (P0). But (P0) is eminently plausible, so the defender of (EE) will naturally reject (P1). It can now be shown that retaining (P0) entails the rejection of all of (P1)-(P3). (orig.)