Forcing in Contemporary Philosophy of Set Theory

Project Information

Philosophy Forcing

Grant agreement ID: 752211

DOI

10.3030/752211

Project terminated on 30 April 2018

EC signature date 14 March 2017

Start date 1 May 2017

End date 30 April 2019

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 171 460,80

EU contribution

€ 171 460,80

Coordinated by

UNIVERSITAT KONSTANZ
Germany

Periodic Reporting for period 1 - Philosophy Forcing (Forcing in Contemporary Philosophy of Set Theory)

Reporting period: 2017-05-01 to 2019-04-30

Summary of the context and overall objectives of the project

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.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

"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."

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

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.

Independence-interpretetaions in set theory