Lady Welby, Charles Peirce e a relação entre linguagem e matemática

Abstract

When relating Mathematics and Language, we had as main challenge to understand whether Mathematics is a Language or not. This debate is millenary and, throughout history, it has found great thinkers with consistent theories, some defending that it does, others defending that it does not. However, in the 21st century, after so many discoveries and advances, both in Mathematics and in Language, which side should we, teachers of Mathematics, conduct learning? For such reflection, we base the theoretical foundation of the evolution of Language and Mathematics on the Significant and Semiotic theories of the philosophers Welby and Peirce, respectively, today considered the parents of Modern Semiotics. The research methodology for the development of this thesis was Peirce's Semiotics and the Complementarity Principle in Otte's Mathematics Education. The objective of this study was to investigate, from an epistemological and semiotic point of view, what mathematical objects are, what reality they belong to and how language and mathematics have been related over time. In an eagerness to always seek to contextualize the facts, we present our protagonists, their personalities, their works, their desires and how much they still contribute significantly to science; we show that the meanings of objects, including mathematical objects, oscillated according to the beliefs of each era; we point out the factors that promoted the changes in the meanings of things; we highlight the similarities and differences between the semiotic theories of Peirce and Welby, proving that Language and Mathematics are two (important and different) references of Mathematical Education; we demonstrate that interpretation is the same as representation and it is the relationships that define objects and transform them into signs. We argue that the teacher, when understanding the relationship and the difference between Language and Mathematics, will realize that knowledge depends on concepts and intuitions, as Kant defended, and, interpreting this in terms of complementarity, as taught by Peirce and Otte, we conclude that Mathematics is not a language but an activity that involves thoughts, concepts, abstractions, representations, which are always in tune, or would need to be, because the object of Mathematics ceases to be the sign itself to assume semiotic behavior, that is, it would not be possible to work with signs without having access to them, as signs can serve both to think about objects and mathematical representations and to represent the result of an analysis. Through Modern Semiotics, we had the opportunity to understand, for example, that both Pure Mathematics and Applied Mathematics are essential, although distinct, and the complementarity makes them even greater, as well as Mathematics and Language. In this way, the human being only knows the world because, in some way, he represents it and only interprets that representation in another representation. For this reason, a sign is something whose knowledge depends on what is represented by it and, then, it will make sense for the study of Mathematics if we finally consider that science develops linked to the culture, customs, economics and needs of each society.