The goal of set theory, as articulated by Hugh Woodin, is develop a "convincing philosophy of truth." In his recent Rothschild address at the INI, he described the work of set theorists as falling into one of two categories: studying the universe of sets and studying models of set theory. We offer a new perspective on the nature of truth in set theory that may to some extent reconcile these two efforts into one.
Joint work with Shoshana Friedman.