Short history of cognitive science is described. One problem of cognitive science is considered in a more detailed way, the problem of computer intelligence. What kind of intelligence, if at all, has a computer? Various pros and cons are reviewed: the Church-Turing theorem, Turing test, Gödel theorem, and Searle's Chinese Room argument. An outline of author's own considerations toward the solution of the problem are described with a reference to the recently published author's monograph ("Semognostics. Intellectual phenomena and Information", Vilnius University Press), where the problem of human and computer intelligence is considered in a separate chapter. Both positions toward the existence of computer intelligence have a common shortcoming: the very notion of intelligence, in fact, is not satisfactorily explained by now. The problem is proposed to be considered in a deeper, the philosophical level. Intelligence is proposed to be viewed as "a world in the world", the latter (the outer one) being the physical one, and the first (the inner one), being both a physical and a mental world. Both worlds are proposed to be explained using the idea of categories, that describe main aspects of the world. As an example, the ten Aristotelian categories (substance, time, place, etc.) are viewed. The inner world should consist of models of the categories. The models must be materialized to form an "inner world". It is postulated, that intelligence emerges when the materialized models of the categories, forming an inner world, interact with similar aspects of the outer world.

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