2011/08/22 by Joel David Hamkins · 1 voice · 3 citations
Arts and Humanities · Mathematics · Psychology · #Advanced Topology and Set Theory #Philosophy and History of Science #Philosophy and Theoretical Science #math.LO #msc:03Axx #msc:03Exx
paper · pdf · doi:10.1017/s1755020311000359
published as Review of Symbolic Logic 5:416-449 (2012) · 35 pages
arxiv created 2011/08/22 · arxiv published 2011/08/22 · arxiv updated 2011/08/22 · openalex publication_date 2012/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous diversity of set-theoretic possibilities, a phenomenon that challenges the universe view. In particular, I 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.