Abstract
What is the nature of symbols? This word is used for traffic signs, for mathematical notations, and motivationally loaded cultural objects, which may inspire war and piece. This chapter explains relationships among symbols, cognition, and language. Symbols are explained as processes in the mind involving cognition and language. Relationships between cognition and language were a mystery until recently. Linguists often considered language as relationships among words and other linguistic entities, separately from its relationships to the world. Mechanisms of language in the mind and brain were considered separate and different from thinking and cognition. Neural mechanisms integrating language and cognition are unknown. Yet, language and cognition are intertwined in evolution, ontogenesis, learning, and in everyday usage, therefore a unified understanding of working of the mind is essential. A mathematical description of such unifying mechanisms is the subject of this paper. We discuss relationships among computational intelligence, known mechanisms of the mind, semiotics, computational linguistics, and describe a process integrating language and cognition. Mathematical mechanisms of concepts, emotions, and instincts are described as a part of information processing in the mind and related to perception and cognition processes in which an event is understood as a concept. Development of such mathematical theories in the past often encountered difficulties of fundamental nature manifested as combinatorial complexity. Here, combinatorial complexity is related to logic underlying algorithms and a new type of logic is introduced, dynamic fuzzy logic, which overcomes past limitations. This new type of logic is related to emotional signals in the brain and combines mechanisms of emotions and concepts. The mathematical mechanism of dynamic logic is applicable to both language and cognition, unifying these two abilities and playing an important role in language acquisition as well as cognitive ontogenesis. The mathematical description of thought processes is related to semiotic notions of signs and symbols.