Set Theory: Bridging Mathematics and Philosophy


The second Forcing Project Networking Conference (FPNC 2019) is devoted to 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 mathe- matical 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.

Organizing unit

The project “Forcing: Conceptual Change in the Foundations of Mathematics” (2018–2023) aims to analyze, from a historical and philosophical point of view, the development of modern set theory since the introduction of the forcing technique. 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, finally, the foundations of mathematics.

More information is available at

Video Recordings:

Monday, July 29th

"Boolean-valued sets as arbitrary objects"
(Leon Horsten, University of Bristol)

"Can all things be counted"
(Chris Scambler, New York University)

Tuesday, July 30th

"Is set theory pure or applied mathematics? On the ontological power of set theory and its limits"
(Mirna Dzamonja, University of East Anglia)

"Cantor's Paradise on Skolem's Earth"
(Mangesh Patwardhan, National Insurance Academy Pune)

"Categories of amenable embeddings and what canonicity in set theory cannot be"
(Monroe Eskew, university of Vienna)

"How does a qualitative interview study inform the philosophy of set theory?"
(Deborah Kant, University of Constance)

"An inconsistent multiverse?"
(Caroline Antos & Daniel Kuby, University of Constance)

"Set-theoretic Truth"
(Godehard Link, MCMP, Munich)

Wednesday, July 31st

"The V-logic multiverse"
Matteo de Ceglie  (University of Salzburg) &
Claudio Ternullo  (KGRC, Vienna)

"A Semantic Approach to Independence"
Giorgio Venturi  (Universidade Estadual de Campinas)

"Philosophical Implications of Some Recent Breakthroughs in Set Theory"
Joan Bagaria  (University of Barcelona)