  A philosophically consistent axiomatic approach to classical and quantum
mechanics is given. The approach realizes a strong formal implementation of
Bohr's correspondence principle. In all instances, classical and quantum
concepts are fully parallel: the same general theory has a classical
realization and a quantum realization.
  Extending the `probability via expectation' approach of Whittle to
noncommuting quantities, this paper defines quantities, ensembles, and
experiments as mathematical concepts and shows how to model complementarity,
uncertainty, probability, nonlocality and dynamics in these terms. The approach
carries no connotation of unlimited repeatability; hence it can be applied to
unique systems such as the universe.
  Consistent experiments provide an elegant solution to the reality problem,
confirming the insistence of the orthodox Copenhagen interpretation on that
there is nothing but ensembles, while avoiding its elusive reality picture. The
weak law of large numbers explains the emergence of classical properties for
macroscopic systems.
