It is shown that the complementarity principle does not really eliminate the conceptual difficulties of the coexistence of wave-like and particle-like features in quantum phenomena. In order to overcome them a purely formal consideration of quantum sentences must first be applied, which provides a consistent implicit contextual definition of the concepts involved. This is enough for providing exact meanings of these concepts and for eliminating contradictions. At the same time it opens the possibility of constructing models of the microworld that may be endowed with physical meaning though not being intuitive.