A solution to the second measurement problem, determining what prior microscopic properties can be inferred from measurement outcomes (pointer positions), is worked out for projective and generalized (POVM) measurements, using consistent histories. The result supports the idea that equipment properly designed and calibrated reveals the properties it was designed to measure. Applications include Einsteins hemisphere and Wheelers delayed choice paradoxes, and a method for analyzing weak measurements without recourse to weak values. Quantum measurements are noncontextual in the original sense employed by Bell and Mermin: if $[A,B]=[A,C]=0,, [B,C] eq 0$, the outcome of an $A$ measurement does not depend on whether it is measured with $B$ or with $C$. An application to Bohms model of the Einstein-Podolsky-Rosen situation suggests that a faulty understanding of quantum measurements is at the root of this paradox.
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