The logic of thought and mathematical logic: an epistemological analysis based on the study of the historical-logical movement of the concept of measure

Abstract

This article aims to discuss the problem of the consistency of mathematics in the context of formal logic and its relationship with the logic of thought, relating it to the Logical-Historical development of the concept of measure as a way of materializing the thesis according to which the logic of mathematics, as the logic of thought, not only encompasses formal logic, but surpasses it, as it considers the cultural and social content of mathematical concepts and their original conditions, which brought them to the concrete world, which is indispensable for an investigation based on the Logical-Historical movement. The methodology consisted of a bibliographical review, from which it was possible to carry out a historical-epistemological analysis, relating mathematical logic and formal logic in the context of the logic of thought in order to draw up a historical synthesis that encompasses the origin, mathematical foundations and social content underlying the concept of measurement, seeking epistemological elements that make it possible to elucidate the process of constructing measurements. In general, the results support the main thesis defended in this article.  It also corroborates Kopnin's (1978) thesis that the fundamental logic of thought moves upwards from the simple to the concrete, from the inferior to the superior, reflecting the laws that determine the development of the concept in the objective world.