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Vacuous quantification

SEMANTICS: vacuous quantification obtains when a quantifier fails to bind a variable, either because the variable is not in the scope of that quantifier (cf. All(x) in (i)a), or because there is another quantifier already binding the variable (cf. All(x) in (i)b).

(i) a  All(x) [ P(j) ] & Q(x)

    b  All(x) [ P(j) & ThereIs(x) [ Q(x) ]]

LIT. Partee, B.H., A. ter Meulen, and R. Wall (1990)