 The problem with a live-and-let-live attitude toward differences between logics differing over the logical powers of a connective when the weaker set of powers already suffice for unique characterization (¬i vs. ¬c in Section  3)  was already pointed out in Popper (1948), and often re-surfaces in subsequent literature e.g., Harris (1982), Hand (1993), Fariñas del Cerro and Herzig (1996); see also the opening paragraph of the present section. Uniquely characterized connectives are sometimes spoken of as implicitly defined, but there are definite risks involved in the latter usage—see Došen and Schroeder-Heister (1985). The “implicit” in the title of Caicedo (2004) does not carry quite the same risks, and refers to a special case of unique characterization, essentially amounting to unique characterization by zero-premiss rules in Fmla—i.e., by axioms. Similarly, the “functionally dependent” connectives of Smiley (1962) are those uniquely characterized by zero-premiss rules, taken in concert with the standard structural rules, in Set-Fmla—though Smiley’s definition is put in terms of consequence relations. This class of connectives may well coincide with the class of projection-conjunction connectives. It does not include disjunction or implication, as treated in intuitionistic or classical logic, which are uniquely characterized by rules essentially containing a non-zero-premiss rule—though these would be uniquely characterized by zero-premiss rules (together with the structural rules) in Set-Set. Makinson (2014) also addresses questions of existence and uniqueness in connection with connectives, but his existence questions concern, not the existence of a connective satisfying certain rules (or more generally, certain conditions), but the existence of rules (or this or that kind) satisfied by a given connective, where connectives are individuated semantically (more specifically, by association with bivalent truth-functions). The various notions of uniqueness considered by Makinson do apply to connectives rather than rules, and are defined in terms of the rules satisfied but the connectives themselves are again individuated truth-functionally and so none ends up amouting to unique characterization as understood here. See note 1, p. 365, in Makinson (2014) for a discussion contrasting his concerns with those found “in some proof-theoretic studies”, and citing Došen and Schroeder-Heister (1988). (In fact in the footnote, though not in the bibliography, the date is given as 1998.) 