Descripción del proyecto
Resolver un problema controvertido sobre el infinito en los fundamentos de las matemáticas
El infinito es un misterio que ha intrigado a los matemáticos durante miles de años. Es uno de los problemas más controvertidos de las matemáticas y no es de extrañar que existan innumerables visiones del infinito. El proyecto INFINITY, financiado con fondos europeos, realizará un análisis sistemático filosófico y matemático de la crítica al concepto de infinito. Partirá de la aparición de la crítica al infinito a principios del siglo XX y se adentrará en los debates actuales que vuelven a surgir debido a las aplicaciones informáticas. El proyecto arrojará nueva luz sobre lo que se objeta en relación con el infinito y por qué mediante el análisis interdisciplinar del infinito matemático a través de los ojos de las comunidades matemáticas y filosóficas de Europa.
Objetivo
This project’s research goal is a systematic philosophical and mathematical analysis of critical views of infinity: views which have questioned one or more aspects of standard approaches to infinity in mathematics. Criticism of infinity originates in fundamental debates at the turn of the 20th century and re-emerges in contemporary mathematics under the stimulus of computer applications. The project’s first aim is to develop a novel rigorous examination of what is objected to infinity and why. The next goal is a philosophical and mathematical analysis of this criticism and of strategies proposed to overcome the perceived problematic nature of the infinite.
To achieve these goals, the ER will integrate precise philosophical inquiry with state of the art knowledge of contemporary mathematics. She will analyse the early 20th century texts and compare that criticism of infinity with the one which emerges in contemporary mathematics; she will use a range of logical tools to sharpen and analyse the fundamental concepts of this debate.
The ER has the ideal profile to initiate, with the support of the host institution, an interdisciplinary analysis of the mathematical infinite, as she is simultaneously a mathematician and a philosopher, with years-long experience in logic. The Department of Philosophy at the University of Oslo is the perfect research environment for carrying out this project: the supervisor, Professor Øystein Linnebo, is leading figure in EU’s philosophy of mathematics and this project is very well aligned with his group’s research interests. Through a programme of training through research, the ER will strengthen her philosophical readership, broaden her range of competences, forge new connections to the philosophical community and gain skills in dissemination and communication. This project will be an important point of departure for her future academic career, proposing her as unique bridge between the EU’s philosophical and mathematical communities.
Ámbito científico
Programa(s)
Régimen de financiación
MSCA-IF-EF-ST - Standard EFCoordinador
0313 Oslo
Noruega