The principle which states that non-commuting quantum observables cannot be measured together gives rise to interpretative questions in quantum mechanics. In this article we derive this principle, according to the Von Neumann approach, and some of these interpretative questions are discussed. In particular, the sense in which the mentioned principle may be "outflanked" by means of correlations between outcomes of different observables, as in the Einstein, Podolsky and Rosen conceptual experiment, is clarified.