Periodic Reporting for period 1 - Philosophy Forcing (Forcing in Contemporary Philosophy of Set Theory)
Reporting period: 2017-05-01 to 2019-04-30
This project is situated in the interdisciplinary field of research of the foundations of mathematics. Here we study the possibility of finding a comprehensive basis for mathematics working with mathematical and philosophical methods. In particular this project studies the impact the so-called forcing technique had on set theory. Since its introduction forcing changed set theory fundamentally and as set theory is one of the most prominent proposals for a foundation of mathematics such a change has mathematical and philosophical consequences for the foundations of mathematics. In this project we are addressing the question of how forcing impacts philosophical considerations and contributes to the current debate in the philosophy of set theory.
"The work in the project can be divided into two parts: the training and the research part. The main aspect of training was to familiarize myself with methods from mathematical philosophy and philosophy in general, as my original area of research is in mathematics. This training took place in the first months of the project and was so successful to allow me to take over teaching duties in this area at the department of philosophy (formal logic and inductive logic). In research I worked both in mathematics and philosophy ; the main outcome lies in a mathematical paper on certain restrictions to forcing approaches and in the philosophical paper on an application of mathematical results in the philosophy of set theory. Furthermore I took part in a workshop in the philosophy of mathematics at Vrije University of Brussels and I presented talks at the University of Bristol, the University of Konstanz and University of Ghent. As an outreach to the general public I took part at the Science Night of the University of Konstanz and an article concering my project was published in the ""Südkurier"" newspaper."
This project is part of a larger scale project about a possible conceptual change in the foundations of mathematics. I was able to acquire third party funding for this larger scale project for a young researcher group for five years, which is also why the Marie Curie project was terminated one year early. The outcome of the Marie Curie project will be continued in the larger scale project and expanded to a more comprehensive investigation that includes seminal question in the philosophy of mathematics such as a possible conceptual change and the question of pluralism in mathematics.