A sentence containing free variables, i.e. an expression that is not itself interpretable as true or false, but that requires the addition of one or more quantifiers to become a closed sentence. ‘ x loves y ’ is an open sentence; ‘(∃x )(∀y ) x loves y ’ is a closed sentence, saying that someone loves everyone. An open sentence with n free variables may be thought of as an n-place predicate.
Philosophy dictionary. Academic. 2011.