  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 Einstein's hemisphere and Wheeler's 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 $[A,B]=[A,C]=0,\, [B,C]\neq 0$, the outcome of
an $A$ measurement does not depend on whether it is measured with $B$ or with
$C$. An application to Bohm's model of the Einstein-Podolsky-Rosen situation
suggests that a faulty understanding of quantum measurements is at the root of
this paradox.
