Abstract
The authors consider as the main hypothesis about the possibility of constructing the mathematics of the brain, the statement that the supposed basis of any context of thinking is primarily formed by a system of axioms, which is the foundation of abstract thinking, realized or materialized through some language. The authors investigate the problem of the applicability of language as the main instrument of cultural continuity and form a research program that includes: the development of a unified ontology that describes objects, actions, qualities and relationships; studying the nature of the context and presenting it with unambiguous concepts of a unified ontology; determining the applicability of actions to objects as partially-defined functions to mathematical categories; model of subjective choice of semantic categories according to relevance in a certain context.
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