 Even though propositional provability logic is a modal logic with a kind of “necessity” operator, it withstands Quine’s (1976) controversial critique of modal notions as unintelligible, already because of its clear and unambiguous arithmetic interpretation. For example, unlike for many other modal logics, formulas with nested modalities like \(\Box\Diamond p \rightarrow \Box\bot\) are not problematic, nor are there any disputes about which ones should be tautologies. In fact, provability logic embodies all the desiderata that Quine (1953) set out for syntactic treatments of modality.