  We propose a {\it quantum-like} (QL) model of the functioning of the brain.
It should be sharply distinguished from the reductionist {\it quantum} model.
By the latter cognition is created by {\it physical quantum processes} in the
brain. The crucial point of our modelling is that discovery of the mathematical
formalism of quantum mechanics (QM) was in fact discovery of a very general
formalism describing {\it consistent processing of incomplete information}
about contexts (physical, mental, economic, social). The brain is an advanced
device which developed the ability to create a QL representation of contexts.
Therefore its functioning can also be described by the mathematical formalism
of QM. The possibility of such a description has nothing to do with composing
of the brain of quantum systems (photons, electrons, protons,...). Moreover, we
shall propose a model in that the QL representation is based on conventional
neurophysiological model of the functioning of the brain. The brain uses the QL
rule (given by von Neumann trace formula) for calculation of {\it approximative
averages} for mental functions, but the physical basis of mental functions is
given by neural networks in the brain. The QL representation has a {\it
temporal basis.} Any cognitive process is based on (at least) two time scales:
subcognitive time scale (which is very fine) and cognitive time scale (which is
essentially coarser).
