A lógica como interseção entre Filosofia e Matemática

Abstract

This paper presents a master's thesis in Philosophy from the Federal University of Ceará, whose object of study is logic and its relationship with Mathematics. We investigate the intersection promoted by logic between Philosophy and Mathematics, based on the hypothesis that the teaching of logic in high school Philosophy classes, in addition to fostering critical thinking, also contributes to the development of logical-mathematical reasoning skills. Whether from a historical or operational perspective, we believe that these contents are intrinsically connected. We thus defend logic as an instrument of a "workshop of thought," a concept inspired by Walter Kohan. As one of the main theoretical references for this work, we draw on the ideas of the philosopher and mathematician Gottlob Frege, especially his development of mathematical logic as a pioneering model of symbolic logic and its philosophical implications. We adopted a qualitative-quantitative field research approach, working with a focus group of high school students from a vocational school (EEEP Francisco Paiva Tavares). In this stage, we conducted a mini-course on logic content and then collected data through semi-structured interviews, aiming to assess students' perceptions of the potential contributions of logic teaching in philosophy classes to mathematical reasoning. Both in the analysis of the field research material and in the bibliographic findings, we identified a close relationship between philosophy and mathematics, especially through the intersection of logic content. We also observed that this relationship is not always valued in educational settings, leading to a limited view of the capabilities that philosophy can develop in the teaching-learning relationship. We conclude by advocating for logic as an important content to be taught in philosophy classes in high school.