Forcing: Conceptual Change in the Foundations of Mathematics

The Forcing Project (2018-2023) is concerned with the fundamental question of conceptual change in the formal sciences. The project investigates the claim that such a conceptual change has happened in the unique setting of the so-called forcing technique in modern set theory: Forcing is an exceptionally powerful and versatile set-theoretic technique that allows to build an infinite number of new mathematical universes. Because set theory is not only one of the many fields of mathematics, but is considered the standard for the foundations of mathematics, a conceptual change in set theory could have far-reaching consequences beyond that of set theory alone.

Three disciplines – mathematics, philosophy and history – will be used to show 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 project will address pressing questions in each of these disciplines and coalesce the results into the first comprehensive and interdisciplinary account of forcing in the foundations of mathematics.

Here’s a short visual introduction to the Forcing Project for a broader audience: