On the Epistemological Limits of Language: Mathematical Knowledge and Social Practice during the Renaissance

An important characteristic of contemporary reflections in mathematics education is the attention given to language and discourse. No longer viewed as only a more or less useful tool to express thought, language today appears to be invested with unprecedented cognitive and epistemological possibilities. One would say that the wall between language and thought has crumbled to the point that now we no longer know where one ends and the other begins. At any rate, the thesis that there is independence between the elaboration of a thought and its codification is no longer acceptable. The attention given to language cannot ignore, nevertheless, the question of its epistemological limits. More precisely, can we ascribe to language and to the discursive activity the force of creating the theoretical objects of the world of individuals? In this article, I suggest that all efforts to understand the conceptual reality and the production of knowledge cannot restrict themselves to language and the discursive activity, but that they equally need to include the social practices that underlie them. This point is illustrated through the analysis of the relationship between mathematical knowledge and the social practice of the Renaissance.