  It is important to differentiate between existence and designation. As things have been set up here, existence is a property of objects, but designation really applies to terms of the formal language, in a context. To use a temporal example from Fitting and Mendelsohn 1998, in the usual sense “George Washington” designates a person who does not exist, though he once did, while “George Washington’s eldest son,” does not designate at all. That an intensional variable \(f\) designates an existent object is expressed by an abstract, \([\lambda x\,E(x)](f)\). We have to be a bit careful about non-existence though. That \(f\) designates a non-existent is not simply the denial of the previous expression, \(\neg [\lambda x\,E(x)](f)\). After all, \([\lambda x\,E(x)](f)\) expresses that \(f\) designates an existent, so its denial says either \(f\) does not designate, or it does, but designates a non-existent. To express that \(f\) designates, but designates a non-existent, we need \([\lambda x\,\neg E(x)](f)\). The formula \(\forall f([\lambda x\,E(x)](f)  \vee \neg [\lambda\)x E\((x)](f))\) is valid, but  \(\forall f([\lambda x\,E(x)](f)  \vee   [\lambda x\,\neg E(x)](f))\) is not—one can easily construct partial FOIL models that invalidate it. What we do have is the following important item.