Set theory is taken to serve as a foundation for mathematics. But it is well-known that there are set-theoretic statements that cannot be settled by the standard axioms of set theory. The Zermelo-Fraenkel axioms, with the Axiom of Choice (ZFC), are incomplete. The primary goal of this symposium is to explore the different approaches that one can take to the phenomenon of incompleteness.
One option is to maintain the traditional “universe” view and hold that there is a single, objective, determinate domain of sets. Accordingly, there is a single correct conception of set, and mathematical statements have a determinate meaning and truth-value according to this conception. We should therefore seek new axioms of set theory to extend the ZFC axioms and minimize incompleteness. It is then crucial to determine what justifies some new axioms over others.
Alternatively, one can argue that there are multiple conceptions of set, depending on how one settles particular undecided statements. These different conceptions give rise to parallel set-theoretic universes, collectively known as the “multiverse”. What mathematical statements are true can then shift from one universe to the next. From within the multiverse view, however, one could argue that some universes are more preferable than others.
These different approaches to incompleteness have wider consequences for the concepts of meaning and truth in mathematics and beyond. The conference will address these foundational issues at the intersection of philosophy and mathematics. The primary goal of the conference is to showcase contemporary philosophical research on different approaches to the incompleteness phenomenon.
To accomplish this, the conference has the following general aims and objectives:
To bring to a wider philosophical audience the different approaches that one can take to the set-theoretic foundations of mathematics.
To elucidate the pressing issues of meaning and truth that turn on these different approaches.
To address philosophical questions concerning the need for a foundation of mathematics, and whether or not set theory can provide the necessary foundation
Date and Venue: 7-8 July 2014 – Kurt Gödel Research Center, Vienna
Sy-David Friedman (Kurt Gödel Research Center for Mathematical Logic),
Hannes Leitgeb (Munich Center for Mathematical Philosophy)
Call for Papers: We welcome submissions from scholars (in particular, young scholars, i.e. early career researchers or post-graduate students) on any area of the foundations of mathematics (broadly construed). Particularly desired are submissions that address the role of set theory in the foundations of mathematics, or the foundations of set theory (universe/multiverse dichotomy, new axioms, etc.) and related ontological and epistemological issues. Applicants should prepare an extended abstract (maximum 1’500 words) for blind review, and send it to sotfom [at] gmail [dot] com. The successful applicants will be invited to give a talk at the conference and will be refunded the cost of accommodation in Vienna for two days (7-8 July).
Submission Deadline: 31 March 2014
Notification of Acceptance: 30 April 2014
Scientific Committee: Philip Welch (University of Bristol), Sy-David Friedman (Kurt Gödel Research Center), Ian Rumfitt (University of Birmigham), John Wigglesworth (London School of Economics), Claudio Ternullo (Kurt Gödel Research Center), Neil Barton (Birkbeck College), Chris Scambler (Birkbeck College), Jonathan Payne (Institute of Philosophy), Andrea Sereni (Università Vita-Salute S. Raffaele), Giorgio Venturi (Université de Paris VII, “Denis Diderot” – Scuola Normale Superiore)
Organisers: Sy-David Friedman (Kurt Gödel Research Center), John Wigglesworth (London School of Economics), Claudio Ternullo (Kurt Gödel Research Center), Neil Barton (Birkbeck College), Carolin Antos (Kurt Gödel Research Center)
Conference Website: sotfom [dot] wordpress [dot] com
Further Inquiries: please contact
Claudio Ternullo (ternulc7 [at] univie [dot] ac [dot] at)
Neil Barton (bartonna [at] gmail [dot] com)
John Wigglesworth (jmwigglesworth [at] gmail [dot] com)