Workshop: Forcing and Philosophy

Donnerstag, 18. Januar 2018
– Freitag, 19. Januar 2018

University of Konstanz, Y132

Carolin Antos (Zukunftskolleg Fellow/Dept. of Philosophy), Daniel Kuby (Dept. of Philosophy).

Neil Barton (KGRC), Merlin Carl (Konstanz), Victoria Gitman (CUNY), Deborah Kant (Berlin), Regula Krapf (Koblenz-Landau), Sam Roberts (Oslo)

The Philosophy Department and the Zukunftskolleg at the University of Konstanz are pleased to announce a two-day Young Researchers' Workshop on Forcing and Philosophy.

Sixty years ago the development of the forcing technique 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 set theorists 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.

In this workshop we want to bring upcoming scholars together to focus on the forcing method 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 whether the choice of forcing is already philosophically loaded.

Workshop Programme
18 January 2018

10:00-10:20 Welcome reception
10:30-12:00 Neil Barton (KGRC): "Large Cardinals and the Iterative Conception of Set: Is every set countable?"
12:00-14:30 Lunch
14:30-16:00 Merlin Carl (Konstanz): "Generic Objects and Algorithmic Randomness"
16:00-17:00 Discussion coffee break
17:00-18:30 Victoria Gitman (CUNY): "The Emerging Zoo of Second-Order Set Theories" (Logik Kolloquium, Building G Room 307)

19 January 2018

10:00-10:30 Coffee
10:30-12:00 Deborah Kant (Berlin): "A Practice-Based Approach on the Independence Problem in Set Theory"
12:00-14:00 Lunch
14:00-15:30 Regula Krapf (Koblenz-Landau): "Characterizations of Pretameness"
15:30-16:30 Discussion coffee break
16:30-18:00 Sam Roberts (Oslo): "Classes in the Multiverse"

Attendance is free and open to all, but registration is welcome (just send an email to the organizers). For information please contact Daniel Kuby.