Against the widely accepted view defended in Kai von Fintel's 'NPI-Licensing, Strawson-Entailment, and Context-Dependency', the paper establishes for the first time that presuppositions can disrupt NPI licensing in English. It offers empirical grounds for rejecting the notion of Strawson-entailment introduced in the aforementioned article to account for the licensing of weak NPIs by presupposition triggers such as only and surprise: the novel data concerns the disruptive effect of the additive particle too, as well as the non-licensing of NPIs in the restrictor of the universal quantifier each and of plural the. It thus offers the first diagnosis of the triggering of existence presuppositions by quantifiers. Lastly, it shows that von Fintel's theory, whose original formulation is too weak to predict non-licensing in the restrictor of singular the and therefore overgenerates, cannot be strengthened without also undergenerating with respect to other presupposition triggers, namely it-clefts.