An analysis of the kantian influence on the acceptance of non-eucliden geometries

Abstract

This article, of a bibliographic nature, seeks to analyze the influences of Kantian philosophy on the acceptance of non-Euclidean Geometries. Historical records indicate that until the mid-19th century, Euclidean Geometry was considered the only possible geometry. It was then that non-Euclidean Geometries appeared. Such geometries were not easily accepted by the mathematical community and remained in the obscure field of mathematics for some time. At this same time, the dominant philosophy, both for the church and for the academic community, was Kantian philosophy. The main objective of this work is to discuss the influence of Kantian philosophy on the acceptance of non-Euclidean Geometries. The conclusions indicate that there was an influence of Kantian philosophy on the acceptance of non-Euclidean Geometries, however, it was the ideal of Euclidean Geometry that caused the mathematical community not to accept the existence of new geometries. Non-Euclidean Geometries were considered aberrations of human knowledge and remained in the shadow of mathematics until the moment they met the new discourses produced by capitalist society and were used to refute Kantian apriorism.