Formal Approaches to Semantic Microvariation: Adverbial ...

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This class of quantifiers is defined by a key semantic property: all of the negative
quantifiers that license de are anti-additive quantifiers.
(4) A function f is anti-additive iff f (X ∨Y ) ⇔ f (X) ∧ f (Y ) (Zwarts (1986))
We can see that the quantifiers in (2) are anti-additive because the following inferences
hold.
(5) a. Jean a pas chanté ou dansé ⇔ Jean a pas chanté et Jean a pas dansé
b. Personne a chanté ou dansé ⇔ Personne a chanté et personne a dansé
c. Jean a jamais chanté ou dansé ⇔ Jean a jamais chanté et Jean a jamais
dansé
d. Jean est parti sans chanter ou danser ⇔ Jean est parti sans chanter et Jean
est parti sans danser
etc.
Having identified the formal semantic class that licenses de phrases, we might ask
what it is about anti-additivity that licenses these phrases. I propose that what licenses
de phrases under anti-additive quantifiers is exactly what licenses them under
degree quantifiers: polyadic quantification. In other words, I propose that anti-additive
quantifiers in French can be polyadic quantifiers, and, as such, they can combine with
complex predicates containing de phrases to yield a truth value.
The proposal that the class of French N-words are polyadic operators in not original
to this thesis. In fact, this has been independently proposed by Haegeman & Zanuttini
(1996), Déprez (2000), and de Swart & Sag (2002). These authors analyze N-words
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