 A two-level criterion of identity is thus in the first place an implicit definition of a function “d( )” (e.g., “the direction of”) in terms of which the sortal predicate “is an F” can be defined (“is a direction” can be defined as “is the direction of some line”). Consistently with the two-level criterion of identity stated several distinct functions may be the reference of the functor “d”. Hence, as emphasised by Lowe (1997: section 6), two-level criteria of identity are neither definitions of identity, nor of identity restricted to a certain sort (for identity is universal), nor even of the sortal terms denoting the sorts for which they provide criteria. They merely constrain, but not to uniqueness, the possible referents of the functor “d” they implicitly define and they thus give a merely necessary condition for falling under the sortal predicate “is an F” (where “x is an F” is explained to mean “for some y, x is identical with d(y)”).