 In 1956 Carnap introduced a new criterion of significance specifically for theoretical terms (1956b). This criterion was explicitly theory-relative. Roughly, Carnap first defined the concept of the “relative significance” of a theoretical term. A term is relatively significant if and only if there exists a statement in the theoretical language that contains it as the only non-logical term and from which, in conjunction with another theoretical statement and the sets of theoretical postulates and correspondence rules, an observational statement is derivable that is not derivable from that other theoretical statement and the sets of theoretical postulates and correspondence rules alone. Then Carnap defined the “significance” of a theoretical term in terms of it belonging to a sequence of such terms such that each is relatively significant to the class of those terms that precede it in the sequence. Now those theoretical statements were legitimate and cognitively significant that were well-formed and whose descriptive constants were significant the sense just specified. It is clear that by the stepwise introduction of theoretical terms as specified, Carnap sought to avoid the deleterious situations that rendered Ayer’s criterion false (and his own of 1928). Nevertheless, this proposal too was subjected to criticism (e.g., Rozeboom 1960, Kaplan 1975a). A common impression amongst philosophers appears to be that this criterion failed as well, but this judgement is by no means universally shared (for the majority view see Glymour 1980, for a contrary assessment see Sarkar 2001). Thus it has been argued that subject to some further refinements, Carnap’s proposal can be made to work (see for discussion Creath 1976, Justus 2014, Lutz 2017)—as long as the sharp distinction between observational and theoretical terms can be sustained. (In light of the objections to the latter distinction one wants to add: or by a dichotomy of terms functionally equivalent to it.)