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

Descripción del proyecto

Estudio de los conceptos de verdad y objetividad en las matemáticas a través del intuicionismo y la sociedad

En matemáticas, los conceptos de verdad y objetividad han sido durante mucho tiempo objeto de un acalorado debate entre historiadores y filósofos de la ciencia y las matemáticas. Mientras que otras actividades humanas se reconocen fácilmente como «constructos sociales», los aspectos sociales de las matemáticas han seguido siendo polémicos. En el proyecto TOKMAT, que cuenta con el apoyo de las acciones Marie Skłodowska-Curie, emplea el intuicionismo para desarrollar una perspectiva social de la verdad matemática. Al tratar las entidades matemáticas como creaciones de la mente influidas simultáneamente por elementos externos, este enfoque abre las puertas a una evaluación exhaustiva de la verdad y la objetividad. Al ahondar en la historia, la sociología y la filosofía, en TOKMAT se pretende desvelar la intrincada interacción entre matemáticas y sociedad, contribuyendo a los debates sobre epistemología y evolución del conocimiento.

Objetivo

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.