Invariance under permutations as a semantic motivation for Stratification

Abstract: This article examines the notion of invariance under different kinds of permutations in a milieu of a theory of classes and sets, as a semantic motivation for Quine's new foundations "NF". The approach largely depends on interpreting a finite axiomatization of NF beginning from the least restrictions on permutations and then gradually upgrading those restrictions as to enable interpreting NF. Comparisons with earlier works are drawn.