Infinity in Mathematics
The project aims to develop a systematic philosophical and mathematical analysis of critical views of infinity in mathematics.
About the project
This project’s objective is an analysis of critical views of infinity: views which have questioned one or more aspects of standard "Cantorian" approaches to infinity in mathematics. Criticism of infinity originated in fundamental debates at the turn of the 20th century and re-emerges in contemporary constructive mathematics under the stimulus of computer applications. The purpose is to bring new light to that decisive chapter in the foundations of mathematics and to draw new revealing correlations between the old debate and the new one.
The project’s first aim is to develop a rigorous examination of what is objected to infinity and of why criticism is levelled against standard approaches to it. The next aim is to develop an analysis of this criticism, and of strategies proposed to overcome the perceived problematic nature of the infinite, focusing especially on Poincaré and Weyl’s approaches to predicativity and the form of predicativity that characterises Martin-Löf type theory.
The outcomes will help us explicate ideas underlying today’s constructive approaches to mathematics and also allow for a clearer understanding of the commitments implicit in more standard approaches to infinity.
July 2019 – June 2021.
Workshop with Crispin Wright, 2–3 June 2020, University of Oslo.
Workshop on Critical views of infinity: Historical and mathematical perspectives, 23-4 June 2020, University of Oslo.