 A formula \(\phi\) is stratified if there exists a mapping \(\sigma\) (a stratification) from the variables of \(\phi\) to the natural numbers such that if \(u \in v\) is a subformula of \(\phi\) then \(\sigma(v) = \sigma(u)+1\) and if \(u = v\) is a subformula of \(\phi\) then \(\sigma(v) = \sigma(u)\). Obviously the formula \(x \not\in x\) is not stratified, and thus the NF comprehension principle cannot be used to formulate Russell’s paradox in the theory. Quine’s New Foundations is essentially obtained from type theory by hiding the types from the syntax. Thus, the theory still makes use of a hierarchy approach to avoid the paradoxes, but the hierarchy is made implicit by not representing it in the syntax of formulae. Cantini (2015) has investigated the possibility of mimicking this implicit hierarchy approach in the context of theories of truth (achieving an implicitly represented Tarskian truth hierarchy). 