  It is shown that the independence of the continuum hypothesis points to the
unique definite status of the set of intermediate cardinality: the intermediate
set exists only as a subset of continuum. This latent status is a consequence
of duality of the members of the set. Due to the structural inhomogeneity of
the intermediate set, its complete description falls into several "sections"
(theories) with their special main laws, dimensions, and directions, i.e., the
complete description of the one-dimensional intermediate set is
multidimensional. Quantum mechanics is one of these theories.
