Forcing in Contemporary Philosophy of Set Theory

Projektinformationen

Philosophy Forcing

ID Finanzhilfevereinbarung: 752211

DOI

10.3030/752211

Das Projekt endete am 30 April 2018

EK-Unterschriftsdatum 14 März 2017

Startdatum 1 Mai 2017

Enddatum 30 April 2019

Finanziert unter

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Gesamtkosten

€ 171 460,80

EU-Beitrag

€ 171 460,80

Koordiniert durch

UNIVERSITAT KONSTANZ
Germany

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

Berichtszeitraum: 2017-05-01 bis 2019-04-30

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

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.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

"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."

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

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