Methodological approaches in the study of recent mathematics – Forcing Project: First Networking Conference
17 – 21 September 2018, University of Konstanz
Young Researcher Workshop: Forcing and Philosophy
18 – 19 January 2018, University of Konstanz
Sixty years ago the development of forcing dramatically changed set theory, leading to an explosion of mathematical results. It also brought about a re-orientation and re-structuring of the whole field as forcing provided a very general method to build set-theoretic models that satisfy a variety of mathematical statements independent from the standard axiomatization ZFC. Today it is normal for a set theorist to work with the most diverse models and to build and explore new ones, each suited to the mathematical task at hand. Because set theory plays an important role in philosophical questions connected to the foundations of mathematics, it is crucial to investigate this development from a philosophical point of view.
A prominent instance of how the mathematical work with forcing can impact philosophical positions is the claim that we can no longer hope to find a unique extension of the standard axiomatic system, but have to take into account all possible extensions given by the various models created through forcing (the multiverse view).
This is one example of how larger research programs in the philosophy of set theory are working with the philosophical implication of the results forcing provides us with. In this workshop, we want to focus on the forcing method itself and explore what possible influence the technical details of forcing can have on work done in the philosophy of set theory. These details range from the different ways in which forcing can be defined mathematically to the question of which types of forcing can and should be considered, such as class forcing or forcing in different axiomatic systems.
Ultimately, the workshop’s goal is to work towards answering the question whether forcing can be considered to be a philosophically neutral method or not.
Neil Barton (KGRC, Vienna)
Merlin Carl (Konstanz)
Victoria Gitman (CUNY)
Deborah Kant (Berlin)
Regula Krapf (Koblenz-Landau), confirmed
Sam Roberts (Oslo), confirmed