SOME TOPICAL ISSUES OF OF FORMALIZATION OF COGNITIVE SCIENCE
DOI:
https://doi.org/10.34185/1991-7848.itmm.2025.01.067Keywords:
Biomathematics, Mathematics of Autonomy, Intelligent Mathematics, Possibility Spaces, Living Smart/Cog-Structure, Paradigm of Limiting GeneralizationsAbstract
The known laws of nature in the physical sciences are well expressed in the language of mathematics. Recently, the discussion on the limits of application of mathematics for modeling biological systems has been considerably revived. Biological systems principally resist mathematical formalization. The authors of the work "The Reasonable Ineffectiveness of Mathematics in the Biological Sciences" (Seymour Garte, Perry Marshall, Stuart Kauffman) believe that the creativity of nature goes beyond the framework of mathematical formalism and that a search for new non-reductive formalisms is necessary. Scientists even talk about the need for a “third great paradigmatic transition” after Newton and quantum mechanics. To solve the problem, the authors propose the concept of biomathematics. The problem of formalization is significantly more complicated for high-level biological cognitive systems. The author of the study, using his own models, demonstrates the limits of agentive behavior modeling. Some basic elements of intelligent mathematics are discussed.
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