 Kreisel called attention to the fact that (6) together with (4) implies that model-theoretic validity is sound with respect to logical truth, i.e., that the first implication of (5) holds. (Strictly speaking, this is a strong generalization of Kreisel's remark, which in place of “\(\text{LT}(F)\)” had something like “\(F\) is true in all class structures” (structures with a class, possibly proper, as domain of the individual variables).) This means that when (6) holds the notion of model-theoretic validity offers an extensionally correct characterization of logical truth. (See Etchemendy 1990, ch. 11, Hanson 1997, Gómez-Torrente 1998/9, and Field 2008, ch. 2, for versions of this observation, and Smith 2011 and Griffiths 2014 for objections.) Also, (6), together with (4), implies that the notion of derivability is complete with respect to logical truth (the second implication in (5)) and hence offers an extensionally correct characterization of this notion. Note that this reasoning is very general and independent of what our particular pretheoretic conception of logical truth is.