Set theory: universe or multiverse? Vienna, 2011

This talk was held as part of the Logic Cafe series at the Institute of Philosophy at the University of Vienna, October 31, 2011.Discussing set theory in Vienna

A traditional Platonist view in set theory, what 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. On the multiverse view, in constrast, there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe, and a corresponding pluralism of set-theoretic truths. In this talk, after framing the debate, I shall argue that the multiverse position explains our experience with the enormous diversity of set-theoretic possibilities, a phenomenon that 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.

Slides | Article | Logic Cafe, Uni. Wien

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