Аннотация:System-informational culture (SIC) is full of science big data anthropogenic environment of artificial intelligence (IA) applications. Mankind has to live in networks of virtual worlds. Cultural evolution extends scientific thinking to everyone in the boundaries of synthetic presentations of systems. Traditional education has become over weighted problem. Because of that it is necessary to learn a person to learn oneself. Achieving level of cognogenesis educa-tional process in SIC is to be directed on consciousness – thinking objectiza-tion. Personal self – building leans on axiomatic method and mathematical universalities. For the objective of auto-poiesis, a person come untwisted as universal rational one possessing trans – semantic consciousness. Gender phenomenology in SIC presents thinking – knowledge by IA tools needing consonant partnership with man. The latter is based on epistemology to ex-tend hermeneutic circle of SIC. Like that up-to-date noosphere poses objecti-zation problem to attain Lamarck’s human evolution on the ground of Leib-nitz’s mathesis universalis in the form of categories language. It can be solved only by means of deep – learned and natural intelligences adaptive partnership.Keywords: System-Informational Culture ∙ Deep-Learned Artificial Intelli-gence ∙ System Axiomatic Method ∙ Consciousness - Thinking ∙ Objectization ∙ Language of Categories ∙ Cogno -Ontological Knowledge Base.Keywords: System-Informational Culture ∙ Deep-Learned Artificial Intelli-gence ∙ System Axiomatic Method ∙ Consciousness - Thinking ∙ Objectization ∙ Language of Categories ∙ Cogno -Ontological Knowledge Base.