CONCRETE TRUTH IN NONLINEAR SCIENCE
Authors:   Taras Shevchenko National University of Kyiv, Kyiv, Ukraine, Dobronravova Iryna 
Published: September 2024

B a c k g r o u n d . Considering a scientific truth as a process is connected with the understanding a concrete truth as unity of absolute and relative moments of such process. Beginning by Hegel, truth was regarded as linear process with final point of its development. It was absolute truth, as return of absolute idea to itself in absolute spirit by Hegel. It was the third world by Popper as the world of objective truth. Ukrainian philosopher Pavlo Kopnin opened development of truth for future, eliminating from it the final point in his materialistic interpretation of the truth as a process. However, such process was still regarded as linear process. It was natural for the stage of linear science. As I have already wrote (Dobronravova, 2017), modern stage of nonlinear science actualizes the considering of a scientific truth as nonlinear process. In situation of many variants of nonlinear dynamics the understanding of concrete truth needs to be updated. Such updating is the goal of the article. M e t h o d s . Dialectic method in addition to scientific realism is the most natural approach to research the modern nonlinear science. Methodologic conception of genetic constructivism by V. Stepin is foundation to consider the relations between theoretical and empirical levels of nonlinear knowledge. Criticism of correspondent conception of truth in internal realism by H.Putnam is initiative position in looking for right epistemolology of nonlinear science. Concrete truth as nonlinear process means the description of real nonlinear dynamics with knowledge about a choice, made by a self-organizing system between alternatives in bifurcation point. Nonlinear theories reconstruct few options of further development for nonlinear system. To explain a real situation in certain moment of such development means to describe the real choices by system in points of branching the possibilities. It means that nonlinear science becomes historical one that describes irreversible change of events. Methodologically it means the restriction for claim to repeat the results of empirical checking the predictions of theory, because of choice by chance in bifurcation points. This claim can work for nonlinear medium if different options can be realized in it simultaneously (like Benar's cells in layer of heated liquid or different parties in democratic societies). Otherwise things are going in the situations of historical kind, where the irreversible choice between alternatives has place (like historical choice between right-hand and left-hand traffic in different countries). Repetitions in empirical checking the predicted variants are not possible in principle because of random nature of choice in bifurcation points. R e s u l t s . Non-linear physical theories are descriptive, just like biological, geological and geographic theories. So arrogant condemnation of such theories by physicists and philosophers of science who took physics as a sample in many previous years founded on misunderstanding the specificity of different kinds of theories and their objects. Logical structure of explanation and prediction are not the same in non-linear theories. Non-linear theory can predict a set of possibilities but not the realization of certain one in certain moment. Concrete truth can be justified if human intervention provides the realization of special condition to choose selected variant. C o n c l u s i o n s . We have to understand that such task is more complicated, if we take into account the quantitative way to solve the nonlinear equations. The chain of iterations in approximate solution of such equations can rather give computer simulation of non-linear dynamics. Exact prediction with iteration formula of each next step of unfolding non-linear dynamics, does not guarantee the long scale prediction of complex nonlinear system state. It does not mean that knowledge we got about nonlinear phenomena are not useful for human practice. Thus, the change of dimension in fractal structures of "noise" in cardiograms lets to admit the first signs of heart illness and to cure heart in time. Meteorologists can warn pilots about oncoming storm, defining speed of rising flows in atmosphere by fractal dimension of pictures on the screen of radar. Those are the predictions in nonlinear science. Are they the proofs of concrete truth? Perhaps, yes, they are if we recall old formulation about practice as criteria of truth.