Forcing in Contemporary Philosophy of Set Theory

Informazioni relative al progetto

Philosophy Forcing

ID dell’accordo di sovvenzione: 752211

DOI

10.3030/752211

Progetto concluso il 30 Aprile 2018

Data della firma CE 14 Marzo 2017

Data di avvio 1 Maggio 2017

Data di completamento 30 Aprile 2019

Finanziato da

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Costo totale

€ 171 460,80

Contributo UE

€ 171 460,80

Coordinato da

UNIVERSITAT KONSTANZ
Germany

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

Periodo di rendicontazione: 2017-05-01 al 2019-04-30

Sintesi del contesto e degli obiettivi generali del progetto

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.

Lavoro eseguito dall’inizio del progetto fino alla fine del periodo coperto dalla relazione e principali risultati finora ottenuti

"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."

Progressi oltre lo stato dell’arte e potenziale impatto previsto (incluso l’impatto socioeconomico e le implicazioni sociali più ampie del progetto fino ad ora)

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