idea

Classical logic requires each singular term to denote an object in the domain of quantification—which is usually understood as the set of “existing” objects. Free logic does not. Free logic is therefore useful for analyzing discourse containing singular terms that either are or might be empty. A term is empty if it either has no referent or refers to an object outside the domain.
Free logic is formal logic whose quantifiers are interpreted in the usual way—that is, objectually over a specified domain D—but whose singular terms may denote objects outside of D, or not denote at all. Singular terms include proper names (individual constants), definite descriptions, and such functional expressions as ‘2+2’. Since classical (i.e., Fregean) predicate logic requires that singular terms denote members of D, free logic is a “nonclassical” logic. Where D is, as usual, taken to be the class of existing things, free logic may be characterized as logic the referents of whose singular terms need not exist.