  We introduce the concept of a "classical observable" as an operator with
vanishingly small quantum fluctuations on a set of density matrices. It is
shown how to construct them for a time evolved pure state. The study of
classical observables provides a natural starting point to analyse the quantum
measurement problem. In particular, it allows to identify Schr\"odinger cats
and the associated projection operators intrinsically, without the need to
invoke an environment. We discuss how our new approach relates to the open
system analysis of the quantum measurement problem.
