The article presents the possible role of consciousness in quantum-mechanical description of physical reality. The widely spread interpretations of quantum phenomena are considered as indicating the apparent connection between conscious processes (such as observation) and the properties of the microcosm. The reasons for discrepancies between the results of observations of the microcosm and macrocosm and the potential association of consciousness with these reasons are closely investigated. The mentioned connection is meant to be interpreted in the sense that the probable requirement for a complete understanding of quantum theory is the adequate description of consciousness within it and that the correct theory of consciousness should include quantum-mechanical theoretical apparatus. In this context, the question about the methods of scientific cognition is discussed, in particular, the problem of the place and the importance of intellectual intuition in science and philosophy of science. The author draws the conclusiions about the current state of the “measuring” problem in its relationship with consciousness.