TOKMAT: Truth, Objectivity, and Knowledge: rethinking the social construction of MAThematics

Description du projet

Explorer la vérité et l’objectivité en mathématiques à travers l’intuitionnisme et la société

En mathématiques, les notions de vérité et d’objectivité font depuis longtemps l’objet d’un débat intense entre les historiens et les philosophes des sciences et des mathématiques. Alors que d’autres activités humaines sont facilement reconnues comme étant socialement construites, les aspects sociaux des mathématiques sont restés controversés. Soutenu par le programme Actions Marie Skłodowska-Curie, le projet TOKMAT recourt à l’intuitionnisme pour développer une perspective socialement orientée sur la vérité mathématique. En considérant les entités mathématiques comme des créations de l’esprit simultanément influencées par des éléments extérieurs, cette approche ouvre la voie à une évaluation complète de la vérité et de l’objectivité. En se plongeant dans l’histoire, la sociologie et la philosophie, TOKMAT vise à comprendre l’interaction complexe entre les mathématiques et la société, et ainsi à contribuer aux débats sur l’épistémologie et l’évolution de la connaissance.

Objectif

Like all human undertakings, mathematics is pursued, promoted, and developed by socially and culturally situated practitioners immersed in the complex collectivities of their communal, practical, and institutional affiliations. However, while few would oppose viewing any other major, artistic, social, political, or religious undertaking as socially constructed, social constructivism in mathematics, specifically regarding the notions of truth and objectivity, remains highly contested among historians and philosophers of science and mathematics. The TOKMAT project uses intuitionism in order to develop a new technique for understanding the concept of truth in mathematics. This technique will be based on a conceptual analysis of the ideas of truth, realism, objectivity, and knowledge in mathematics through the prism of social constructivism. Intuitionism presented an alternate mathematical framework to classical mathematics, that viewed mathematical entities as creations of the mind. As intuitionism acknowledges the social constructivists’ claim that truth is a wholly human construction, it is a springboard towards a wide-reaching rethinking of the main constructivist account of mathematics. As a non-mainstream mathematical school whose ideas are still being discussed, intuitionism is a springboard towards exploring the social organization of scientific knowledge and its impact on our understanding of concepts like truth and objectivity. The project, therefore, brings together the history, sociology and philosophy of mathematics in order to provide new ways of understanding the notions of truth and objectivity in mathematics as shaped by both external and contextual elements. In doing so, this project aspires to contribute to the heady debates on epistemology, philosophy of mathematics, and the social constitution of warranted knowledge.