It was shown that mental representations of objects created in human minds during the learning process, which take the form of hierarchically connected neurons called semblions, have properties explaining the hierarchical structure of metaphors and other mind tools embodied in Lakoff’s cognitive linguistics concept. It was proven that, at the neurological level, semblions of objects, concepts, ideas and models can be associated with neuronal representations of phonemes heard in coincidence with other objects, creating new semblions which correspond to words. It was shown how activation of semblions can result in recalling, associating, thinking and other higher mental functions which are necessary to use natural language. It was considered why semblions representing mathematical notions enable an adequate description of numerous phenomena of the physical world but, at the same time, their polymodal counterparts can be used to describe qualia. The complementarity between Horzyk’s associative intelligence model and Galus’ model of architecture of self-aware systems was pointed out, which can be used to create artificial self-aware systems able to use both natural language and formal languages with understanding.