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Infinity in Mathematics: A Philosophical analysis of Critical Views of Infinity

Project description

Solving a controversial problem on infinity in the foundations of mathematics

Infinity is a mystery that has intrigued mathematicians for thousands of years. It’s one of the most controversial problems in mathematics. Not surprisingly, there are countless views of infinity. The EU-funded INFINITY project will conduct a systematic philosophical and mathematical analysis of the criticism. It will start from the emergence of criticism of infinity at the turn of the 20th century and delve into today’s re-emerging debates triggered by computer applications. As an interdisciplinary analysis of the mathematical infinite through the eyes of Europe’s mathematical and philosophical communities, the project will shed new light on what is objected to infinity and why.

Objective

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.

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Coordinator

UNIVERSITETET I OSLO
Net EU contribution
€ 214 158,72
Address
Problemveien 5-7
0313 Oslo
Norway

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Region
Norge Oslo og Viken Oslo
Activity type
Higher or Secondary Education Establishments
Links
Other funding
€ 0,00