This paper discusses a phenomenon known as ‘parasitic licensing’, in which strong Negative Polarity Items (NPIs), such as English in weeks, become acceptable in downward-entailing but non-anti-additive contexts in the presence of a weak NPI, such as English any. We show that in weeks is not special in the sense that it has some particular requirement that restricts it to anti-additive contexts only, rather in weeks is actually a weak NPI whose presuppositional requirementsare such that they are in conflict with the presuppositional requirements of non-anti-additive NPI-licensers. We argue that the conflict between the presuppositional requirements of in weeks-type NPIs and non-anti-additive licensers can be resolved in the presence of a quantificational expression introducing contextual uncertainty, including any. We implement our solution by extending Stalnaker’s diagonalization to presuppositional content (Stalnaker 1978; 2004) and claim that this mechanism is at the heart of the parasitic licensing phenomenon.