Mathematical Discourse in Henri Poincaré and Anna Sfard: A Comparison
Abstract
This paper aims to compare the notion of discours in Henri Poincaré and that of discourse in Anna Sfard’s theory of commognition, with the aim of clarifying the epistemological differences that distinguish them. In particular, we will investigate how, in Poincaré, discours constitutes the condition for the objectivity of science: only what can be transmitted through a shared language can be considered knowledge. Mathematical discours is a rigorous tool that transforms facts in the rough into scientific facts. The theory of commognition reformulates Poincaré’s concept of discours in a communicative key, departing from its cognitive rigour. A synoptic reading of the founding texts of the two authors, separated by a century of history and philosophy of science, allows us to highlight the points of contact and to note the discrepancies.
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