 Frege was assuming a ‘logically perfect’ language, in which every well-formed term—including any class-abstractive term of the form {x | Φx}—denotes. If, by contrast, one countenances the possibility that certain well-formed singular terms in one’s language might not denote objects, then one has to employ a different kind of logic—a so-called free logic. (It is ‘free’ of the background assumption that all singular terms denote.) Such a logic qualifies the quantifier rules with ‘existential presuppositions’ concerning the terms involved. For example, instead of being able to infer directly from “for all x, F(x)” to “F(t)”, as one may, when using the unfree logic of a logically perfect language: 