Vazirov, H., & Yaqubzadе, T. [2025]. Ontology of Numbers in the Light of the Laws of Dialectics. History of Science journal, 6(1), pp.112-125. https://doi.org/10.33864/2790-0037.2025.v6.i1.112-125
Abstract
For the first time it was established, that geometric line constructed from dots is not solid, but a dashed line. And there can’t be solid lines without voids. The same words can be said about surfaces and planes. It is shown, that rational and irrational numbers are qualitatively different from a philosophical point of view and therefore not comparable. For this reason, they can`t be placed on the same numerical axis. New mathematical-philosophical paradoxes had been considered. Today it is commonly supposed, that physical continuum is solid, continuous, without voids. It is shown, that continuum is having holes in truth. And the interaction of the holes of the continuum with its dots is the source of the philosophical movement. For the first time a new concept of philosophical freedom (archefolia) has been proposed in the article. To explain the essence of this new concept, the authors chose the methodology of mathematics. For the first time, attention called to the fact that there is no number whose square is equal to the transcendental "number" π (or other transcendental number). Therefore, when graphing the functions imperceptible microscopic discontinuities are formed on the curve. On this basis we come to the conclusion that there are no curves without discontinuities. For the first time in the article it is shown that flat geometrical figures or their parts, in principle, cannot touch each other and be solid. It is shown that the number axis is uniformly leaky. If there is no material between physical bodies or philosophical things, then there is no distance between them. Distance is possible only if the gap between these things is filled with something material or Being.
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