25/Mar/2013: Simon Thomas and Joel Hamkins

Rutgers Logic Seminars
Spring 2013
Rooms 423 & 705, Hill Center

Descriptive Set Theory Seminar
Hill 423
Monday Mar 25th, 3:20-4:40 pm
Simon Thomas, Rutgers
Invariant random subgroups VI

Rutgers Logic Seminar
Hill 705
Monday Mar 25th, 5:00-6:20 pm
Joel Hamkins, CUNY
Pluralism in mathematics: the multiverse view in set theory
and the question of whether every mathematical statement has
a definite truth value

Abstract: I shall describe the debate on pluralism in the philosophy of set
theory, specifically on the question of whether every mathematical and
set-theoretic assertion has a definite truth value. A traditional Platonist
view in set theory, which I call the universe view, holds that there is an
absolute background concept of set and a corresponding absolute background
set-theoretic universe in which every set-theoretic assertion has a final,
definitive truth value. I shall try to tease apart two often-blurred aspects
of this perspective, namely, to separate the claim that the set-theoretic
universe has a real mathematical existence from the claim that it is unique.
A competing view, the multiverse view, accepts the former claim and rejects
the latter, by holding that there are many distinct concepts of set, each
instantiated in a corresponding set-theoretic universe, and a corresponding
pluralism of set-theoretic truths. After framing the dispute, I shall argue
that the multiverse position explains our experience with the enormous
diversity of set-theoretic possibility, a phenomenon that is one of the
central set-theoretic discoveries of the past fifty years and one which
challenges the universe view. In particular, I shall argue that the
continuum hypothesis is settled on the multiverse view by our extensive
knowledge about how it behaves in the multiverse, and as a result it can no
longer be settled in the manner formerly hoped for.

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