Some theories (e.g., Beaver, 1994, 2001) assume that sentences with presupposition triggers in the scope of a quantifier carry an existential presupposition, as in (2), others (e.g., Heim, 1983 or Schlenker, 2008a,b) assume that they carry a universal presupposition, as in (3). (1) No student knows that he is lucky. (2) Existential presupposition: At least one student is lucky. (3) Universal pr...