The Multiverse View and Set-Theoretic Practice

Abstract

Hamkins’ multiverse view is a prominent position on the nature of set theory. It is posited against the universe view and proposed as a philosophical theory explaining current set-theoretic practice. This paper confronts the multiverse view with the results of an interview study investigating current set-theoretic practice. The study reveals a heterogeneity of set-theoretic research practices. The multiverse view is found to align well with pluralist research practices but not with absolutist practices. The generalisation claim of the multiverse view fails because of this heterogeneity; only a reduced interpretation of the multiverse view might hold generally. Furthermore, Hamkins’ prediction that the community as a whole will not adopt axioms deciding the continuum hypothesis is found probably true, but for different reasons: although part of the community has already accepted axioms beyond ZFC, another part of the community will withdraw from doing so. In conclusion, I argue that Hamkins’ multiverse view is best interpreted as a valuable perspective on pluralist set-theoretic practices.