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Critical Analysis of the Foundations of Pure Mathematics

Author:

Kalanov, Temur Z.

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

June 12, 2016

File:

/Research Papers-Mathematics and Applied Mathematics/Download/6544

Downloads:

718

Keywords:

mathematics, geometry, mathematical physics, physics, engineering, formal logic, dialectics, philosophy of science

Abstract:

The critical analysis of the foundations of pure mathematics is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. The main result is as follows: the concept of “mathematical quantity” – starting and central concept in mathematics – is meaningless, erroneous, and inadmissible one because it represents the following formal-logical and dialectical-materialistic errors: negation of existence of the essential sign (feature) of concept (i.e., negation of existence of the essence (content, intension) of the concept) and negation of existence of measure of material object. The correct metrical-geometrical and physical interpretations of mathematical relationships show that the set of standard mathematical functions represents error, mistake, and blunder. Therefore, pure mathematics does not satisfy the general-scientific criterion of truth: practice is criterion of truth. The obtained results lead to the conclusion that the generally accepted foundations of pure mathematics are a false one, and they should be reconsidered.

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