Contemporary physics from its beginning in the 17* century has been
progressing in two parallel directions, i.e. empirical and mathematical.
One unresolved problem of epistemology is that these two branches are
not really well combined in the scientific theories. Each of them has its
role. The empirical methods are used for governing the facts concerning
a phenomenon and testing the inferences of a hypothetical theory. Mathematical
methods are used for description of the hypothetical physical
ideas and making mathematical inferences from these hypotheses. The
assumption is made that the mathematical inferences can be tested
empirically and that such tests may perhaps not prove but at least validate
the theory. Nevertheless empirical validation is insufficient for combining
the methods. There is no proof for theories that remain in essence
hypothetical. The successful alignment of essentially different methods
can be achieved by employing logical structure as a mediating method.