The quantified sentences are not read as quantifying over names: they rather quantify over objects that could be named by a name placed in the position of a variable. Similarly when we bind predicate variables, we "treat predicate positions suddenly as name positions, and hence …treat ...
The article investigates important semantic properties of fuzzy quantifiers, namely restriction and living on a (fuzzy) set. These properties are introduced in the novel frame of fuzzy quantifiers over fuzzy universes.