On the epistemological limits of language: Mathematical knowledge and social practice during the renaissance

An important characteristic ofcontemporary reflections in mathematicseducation is the attention given tolanguage and discourse. No longer viewed asonly a more or less useful tool to expressthought, language today appears to beinvested with unprecedented cognitive andepistemological possibilities. One wouldsay that the wall between language andthought has crumbled to the point that nowwe no longer know where one ends and theother begins. At any rate, the thesis thatthere is independence between theelaboration of a thought and itscodification is no longer acceptable. Theattention given to language cannot ignore,nevertheless, the question of itsepistemological limits. More precisely,can we ascribe to language and to thediscursive activity the force of creatingthe theoretical objects of the world ofindividuals? In this article, I suggestthat all efforts to understand theconceptual reality and the production ofknowledge cannot restrict themselves tolanguage and the discursive activity, butthat they equally need to include thesocial practices that underlie them. Thispoint is illustrated through the analysisof the relationship between mathematicalknowledge and the social practice of theRenaissance.