Chapter 8 - Nonmonotonic nonlinear dynamical modeling

Abstract

The allure of presuming linearity in phenomena and analyses is their intuitive tractability even in the face of high complexity. Any alternative must confront the prospects of intuitive intractability. The latter makes if very difficult to appreciate the nonlinearities in the actual experiences in the observations. Thus there is little alternative to model the dynamics with the hope that the model provides metaphors to facilitate an expanded intuitive ability. However, this has always been the case except in the most trivial of situations or circumstances. The question then becomes how to assess the validity and productivity of proposed models. The notion of logical Consistency and logical Completeness can be used to evaluate models. Approaches can be descriptive based solely on the observations or narrative based on fundamental principles. Any model confronts the problem of the Paradox of Reductionism and the relation between “parts and wholes” that is Mereology.