Vacuous quantification

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

Links

 * Utrecht Lexicon of Linguistics