 Sentence  (33)  however has also a second reading, on which it means we did not close the door or did not close the window, but I am not sure which. As Szabolcsi (2002) observed, speakers in many languages including Hungarian, Russian, Italian and French find that their counterpart of  (33)  only has this second reading. On this reading disjunction scopes over negation, and so Szabolcsi proposes to treat disjunction words in these languages as positive polarity items, i.e., roughly, expressions that cannot be interpreted (anti-licensed) in the immediate scope of a negation, unless the negation is itself in a negative or more generally downward entailing (DE) context. Spector introduces a distinction between local and global positive polarity items and argues that single disjunction in French and other languages are local positive polarity items (anti-licensed in the immediate scope of negation, unless certain constraints are met) as Szabolcsi had proposed, but the iterated disjunctive constructions discussed above are global polarity items (anti-licensed under the scope of negation, however distant the negation is, unless certain constraints are met).