  A unified conceptual foundation of classical and quantum physics is given,
free of undefined terms.
  Ensembles are defined by extending the `probability via expectation' approach
of Whittle to noncommuting quantities. This approach carries no connotations of
unlimited repeatability; hence it can be applied to unique systems such as the
universe. Precise concepts and traditional results about complementarity,
uncertainty and nonlocality follow with a minimum of technicalities.
Probabilities are introduced in a generality supporting so-called effects
(i.e., fuzzy events).
  States are defined as partial mappings that provide reference values for
certain quantities. An analysis of sharpness properties yields well-known no-go
theorems for hidden variables. By dropping the sharpness requirement, hidden
variable theories such as Bohmian mechanics can be accommodated, but so-called
ensemble states turn out to be a more natural realization of a realistic state
concept. The weak law of large numbers explains the emergence of classical
properties for macroscopic systems.
