Symposium on the Foundations of Mathematics

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:

(1) To bring to a wider philosophical audience the different approaches that
one can take to the set-theoretic foundations of mathematics.

(2) To elucidate the pressing issues of meaning and truth that turn on these
different approaches.

(3) 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

Confirmed Speakers:
Sy-David Friedman (Kurt Gödel Research Center for Mathematical Logic)
Hannes Leitgeb (Munich Center for Mathematical Philosophy)

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)