Can mathematics change in a fundamental way? This long-standing question has to be reconsidered when studying the mathematical technique of forcing. With forcing one can build an infinite plurality of mathematical worlds and study the differing mathematical truths in them. As such, forcing is both a mathematical technique and a philosophical concept through its use in the foundations of mathematics.
In this project we want to study forcing from a historical, philosophical and mathematical perspective. We claim that forcing developed from an independence-proving and, more generally, theorem-producing technique to a paradigmatic concept, i.e. a way to understand set theory differently. We will investigate how forcing was created, accepted and developed in the set-theoretic community; how it influences philosophical questions and research programs; and finally how it restructured the field of set theory and the foundations of mathematics.
The research project is hosted at the University of Konstanz and consists of myself as the project leader; philosopher and historian Daniel Kuby; as well as a second PostDoc position (TBA). Nick de Hoog is an associated member. If you are interested in coming to Konstanz and doing project-related work, please contact us for funding possibilities.
A short video explains the project for a general audience: