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Infinity, Language, and non-Euclidean Geometries

Author:

Leon, Antonio

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

August 09, 2023

File:

/Research Papers-Mathematics and Applied Mathematics/Download/9552

Downloads:

Keywords:

actual infinity, potential infinity, infinite regress, straight lines, parallelism, equidistance, non-Euclidean geometries, Euclidean geometries.

Abstract:

This article includes a very simple and short proof of the inconsistency of the Hypothesis of the Actual Infinity subsumed in the Axiom of Infinity. And it reminds us that contemporary mathematics, geometry and mathematical physics are infinitist disciplines that assume that axiom. The second part of the article recalls the infinite (in this case potential) regress of arguments, definitions and causes that, among other things, makes inevitable the use of primitive concepts in all sciences. As we will see here, from this necessity derive certain abuses of language that, in the case of non-Euclidean geometries, have ended up giving a very distorted and unreal image of their relationship with Euclidean geometry. It is also recalled that since 2021 there is a new foundational basis of this Euclidean geometry in which the Parallel Postulate can be proved.