In the "70s the research on foundations of science recognized two basic options — respectively, on the kind of mathematics and on the kind of logic. By means of these options, the foundations of quantum mechanics are scrutinized anew. It results an intrinsic dualism owing to which the measurement theory takes different choices on these options than the theory of the unperturbed evolution of the system. Moreover, the past two debates on wave-corpuscle dualism and incompleteness are reduced to two definite problems. The last one obtains a definite positive answer when it is analysed in the mathematics which is alternative to the classical one — i.e., constructive mathematics.