¿Qué es un teorema (en la práctica)? El papel de la metamatemática en la construcción de las matemáticas
Resumen
Aprovechando la literatura de la sociología de la ciencia, este artículo aboga por los beneficios de una perspectiva sociológica en la filosofía de la práctica matemática. Para ello, propone un enfoque de la práctica matemática que se fundamenta en la noción de comunidad matemática, al tiempo que evalúa el papel de la noción de metamatemática en el cambio matemático y en las prácticas matemáticas estabilizadas. Su punto de partida es un estudio de caso: la aparición de la teoría del control geométrico a principios de los años 70 y las prácticas de citación asociadas a la comunidad de la teoría del control desde mediados de los 90. En él se expone que la introducción de las herramientas geométricas en la teoría del control a finales de los años 60 condujo a un cambio en las opiniones metamatemáticas que los teóricos del control tenían de sus objetos. A continuación, se muestra cómo la pertenencia a la comunidad de la teoría del control da forma a la producción y recepción de los teoremas de Štefan, Sussmann y Nagano. Por último, la interpretación del desarrollo histórico y de las prácticas de citación de esta comunidad, a través de la perspectiva de la metamatemática, concluye con una discusión del papel del teorema de la órbita en la teoría del control, tanto como etiqueta que designa un determinado contenido cognitivo, como marcador social de pertenencia a esa comunidad.
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