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On The Problem Of Axiomatization Of Geometry

Author:

Kalanov, Temur Z.

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

November 9, 2021

Downloads:

38

Keywords:

geometry, engineering, applied mathematics, general mathematics, methodology of mathematics, philosophy of mathematics, history of mathematics, higher education, formal logic, dialectics, epistemology

Abstract:

An analysis of the foundations of geometry within the framework of the correct methodological basis – the unity of formal logic and rational dialectics – is proposed. The analysis leads to the following result: (1) geometry is an engineering science, but not a field of mathematics; (2) the essence of geometry is the construction of material figures (systems) and study of their properties; (3) the starting point of geometry is the following system principle: the properties of material figures (systems) determine the properties of the elements of figures; the properties of elements characterize the properties of figures (systems); (4) the axiomatization of geometry is a way of construction of the science as a set (system) of practical principles. Sets (systems) of practice principles can be complete or incomplete; (5) the book, “The Foundations of Geometry” by David Hilbert, represents a methodologically incorrect work. .../...

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