Several attempts have been made to provide an axiomatic basis for the statistical transformation theory in quantum physics in the form of simple general principles. Thus, in his well-known book on Quantum Mechanics Dirac uses the superposition principle as a fundamental principle. This principle permits indeed to determine many characteristic features of the mathematical formalism. It does not, however, suffice to determine even the algebra of the state calculus, as Dirac has noticed himself. From the present point of view the superposition principle may be looked upon as an ingenious but rather artificial formulation of complementarity.