Universality and essentiality: elements of a mathematical discourse

Abstract

The present article resulted from data collected during our Master’s Degree investigation, which was concluded in 2017. Most of the time, this investigation assessed the discourse typologies in the sub-project in Mathematics of Programa Institucional de Bolsas de Iniciação à Docência (Institutional Program of Scholarships to Professors). The investigation gathered specific sets of utterances, drawings and comments from five students granted with scholarships, which featured effective references to images of the universe, the world and/or nature. Thus, based on the research corpus, the aim of the present study is to track the discursive functioning of the referred formulations, by taking mathematics itself as the referential object of the discourses. In order to do so, and based on Foucauldian concepts, the idea is to make an enunciation analysis of what was actually said by describing the vertical domains of enunciation productions to expose their formation rules based on their own mathematical dispersion. One can see that the assessed utterances concern an externality ruled by a written historicity in which images of nature, world and universe work among the mathematical dispersion essentiality, totality and universality vectors. Starting from such dispersion, the utterances are featured by an exhausting monism and structuralism whose objects always regard absoluteness and universality, as well as the structural closing of the very discursive game.