In this paper the general definitions of the concepts of consciousness, conscious and subconscious thinking are formulated. In the present article the central problem of the thinking that is how the thinking is governed is considered. It was established that it is governed not directly on the level of the set of thoughts, i. e., mind, but indirectly on the level of the metric space over the mind. This leads, in particular, to the quantum character of our logical thinking (quantum mind). Consequences of it are considered. In particular, this approach allows one to introduce and use the concept of representations like it is done in the quantum mechanics, as well as to define the mathematically based concept of the personality. This concept permits to introduce and to study symmetry properties of the personality and their influence intellectual activity of a person.
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