DESCRIPTION: Teresa Grabińska holds a PhD in theoretical physics and a postdoctoral degree in philosophy, and is a professor at the Land Forces Academy in Wrocław. She has published approximately 400 scientific papers in Poland and abroad on quantum physics, physical cosmology, philosophy of nature, philosophy of science, personalism, transhumanism, and securitology. In the article in question, the author discusses the fractal conceptualization of natural phenomena and its relationship to iterative solutions of nonlinear differential equations. In her opinion, the traditional relationship between determinism and reductionism should be revisited, taking into account fractal models: a holistic combination of parts and the whole is preferred. Considerations regarding regular solutions to nonlinear differential equations and their chaotic counterparts imply Metallmann's theorem on strict and statistical determinism. However, the indeterminism of chaos cannot be questioned. "Accepting Metallmann's thesis of determinism frees us from the troublesome (also from the point of view of fractal description) relationship between determinism (strict) and reductionism: the relationship between successive states of an object can also be holistic or structuralist. In the first case, it is guaranteed by the construction (fragmentation) procedure, in the second – by the simulation or iteration procedure. However, we cannot accept Metallmann's position regarding the rejection of indeterminism. The course of nonlinear phenomena can become chaotic in a strong sense. Then statistical determinism does not occur for fundamental reasons: the basic distinguishing feature of the determinism of a phenomenon, as given by Metallmann, does not apply in this case. An object in a state of strong chaos behaves non-deterministically: it is impossible to determine the relationship between successive states. It is true that a state of strong chaos (strange attractor) is mathematically related to weak chaos (in which statistical description is possible), that chaos is fractal in nature, and that its structure can be studied as the structure of a mathematical object. However, this does not change the fact that when a strange attractor occurs in a natural process, that process becomes indeterministic" (p. 29).
Table of contents: 1. The regularity of solutions to differential equations and the determinism of physical phenomena. 2. The relationship between determinism and reductionism. 3. The holistic concept of object structure in the light of fractal geometry. 4. Deterministic processes in the light of attractor theory. 5. The new role of mathematics in relation to fractal and attractor models of phenomena. 6. The determinism of fractal description and the indeterminism of chaos.
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