Explanatory indispensability and the set theoretic multiverse
摘要
Width multiverse approaches to set theory (like Joel David Hamkins’ influential proposal in [Joel Hamkins The multiverse perspective in set theory, 2013]) reject the idea that there’s an intended width hierarchy of sets which contains ‘all possible subsets’ of the sets that it contains. In this paper, I raise an explanatory indispensability worry for the multiverse theorist and distinguish three different possible styles of response to this worry. I will argue that each approach faces some serious prima facie problems. And I’ll suggest that, by clarifying their response to this puzzle about applications, multiverse theorists can helpfully clarify their proposals concerning pure mathematics.