The project “Forcing: Conceptual Change in the Foundations of Mathematics” (2018-2023) aims to analyse the development of modern set theory since the introduction of the forcing technique both from a historical and philosophical point of view. It brings together methods and research questions from different research areas in the history and philosophy of mathematics to investigate if and how the extensive use of the forcing method brought about a conceptual change in set theory; and in which ways this may influence the philosophy of set theory and the foundations of mathematics.

The research group organises a series of Networking Conferences with the goal of reaching out to researchers from these different areas. The second instalment will be devoted to the topic of **recent set theory as a bridge between mathematics and philosophy** and focuses on the interaction between mathematical and philosophical arguments and views in set theory. Set theory has long been both a mathematical discipline and a program with foundational motivations. It seems that this dual character makes it a natural crossway between mathematics and philosophy, possibly more so than other mathematical disciplines.

### Topics

We welcome contributions which

a) add to current discussions in the philosophy of set theory (set-theoretic pluralism, height and width potentialism/actualism, the universe/multiverse debate, the forcing technique, justification of new axioms, contrasts with other foundational frameworks) by relating philosophical and mathematical arguments to one another; by working out the philosophical import of set-theoretic results; or by giving set-theoretic explications of philosophical concepts;

b) question or uphold the relevance of philosophical arguments in set theory. For example, according to Penelope Maddy’s naturalism, first philosophical arguments play no justificatory role in set theory. Should (mathematical) naturalism be understood in Maddy’s style? Are there other forms of naturalism that are more tolerant of traditional philosophical questions?

c) analyse the mathematical and philosophical content of the concept “set-theoretic practice” as used in recent set-theoretic programs. For example, do the different foundational programmes offered by the likes of Friedman, Hamkins and Woodin constitute different set-theoretic practices?

d) investigate how the inclusion of alternative set theories (constructive set theory, class theories, set theories based on non-classical logic, categorial theories of sets) impact the philosophy of set theory.

### Submissions

Abstracts of 300-500 words should be submitted in PDF (with LaTeX source) or Word format no later than March 31, 2019, via email to <submissions@forcing-project.com>. Notifications of acceptance will be issued by April 15, 2019.

### Financial support

As we would like to enable early career researchers (including PhD students) to apply, we are in the process of organizing funding for travel and accommodation for the contributed speakers. Please contact the organizers for further information.

### Conference registration

The conference is free (no conference fee) and everyone is welcome to attend. For logistical reasons, please register by sending an email to <registration@forcing-project.com> before July 1, 2019.

### Dates

- March 31, 2019: Deadline for submissions to CfP
- April 15, 2019: Notification of acceptance
- July 1, 2019: Conference registration deadline
- July 29-31, 2019: Conference

### Contact

For inquiries please send an email to the organizers <fpnc2019@forcing-project.com>.