About the incommensurate entities in the philosophy of Pythagoreans. To the philosophical grounds of irrational proportions in science and culture
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Philosophical Thought
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About the incommensurate entities in the philosophy of Pythagoreans. To the philosophical grounds of irrational proportions in science and culture
Lipov Anatolii Nikolaevich

PhD in Philosophy

research assistant at Institute of Philosophy of the Russian Academy of Sciences

119 330, Russia, g. Moscow, ul. Mosfil'movskaya, 41, of. 54

antolip@yandex.ru

 

 

DOI:

10.25136/2409-8728.2018.11.26855

Review date:

13-07-2018


Publish date:

20-11-2018


Abstract.

The subject of this research is the philosophical grounds that predetermined the discovery of proof of the existence of incommensurate or irrational magnitudes in the philosophy of Pythagoreans at the time when the very notion of irrationality was an anathema for those suggesting that the numbers were the rational entities underlying the Universe. Therefore, it became possible to express both, physical and cultural-aesthetic consistencies, by the similar to each other mathematical rows and geometrical proportions that predetermines the calculation methods for harmonic structures, uninterrupted proportions and limiting values – the first premise to the structure of ancient teaching on formation. Based on the interdisciplinary analysis and comparative method of research, the article analyzes the history of discovery of the phenomenon of incommensurability and irrationality. A conclusion is made that back in Pythagoras’ times, this discovery led to the need for substantial transformation of the entire fabric of elementary geometry in anticipation of structuring the general theory of proportions, causing the first in history crisis of ancient philosophy and mathematics. The author also substantiates and traces the discovered by Pythagoreans correlation between the irrational proportions and irrational mathematical constant of “golden ratio” that underlies the architectural proportions in the history of culture, as well as reflected in various regularities and spheres of human existence – science, culture, architecture, and art. Among the main conclusion is also the author’s hypothesis that universality of the irrationality of magnitudes of “golden ration” and their prevalence in the diverse natural and cultural regularities up to the present encourages the pursuance of meanings, which would unite them into a certain common theory that generalizes and expresses the structure of global constants.

Keywords: golden section, pentagram, pentagonal symmetry, irrational proportions, irrational numerical relationships, irrational numbers, incommensurable entities, proportional harmonic relations, Pythagorean philosophy, ideal form principle
This article written in Russian. You can find full text of article in Russian here .

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