Tarski did not think that the construction of section 3 completely solved the problem of offering “a materially adequate definition of the concept of consequence” (Tarski 1983c, p. 418).  According to Tarski, perhaps the most important difficulty that remained toward solving that problem is created by the fact that “underlying our whole construction is the division of all terms of the language discussed into logical and extra-logical” (Tarski 1983c, p.  418). This situation is tolerable because, as Tarski says in a letter of 1944, “it is clear that for all languages which are familiar to us such definitions [of ‘logical term’ and ‘logical truth’] can be given (or rather: have been given); moreover, they prove fruitful, and this is really the most important. We can define ‘logical terms’, e.g., by enumeration” (Tarski 1987, p. 29). But since the division is not based on a previous characterization of logical terms generally applicable to arbitrary languages, to that extent the definition of logical consequence is not fully general, and hence unsatisfactory. In the final paragraph of the consequence paper Tarski says that a positive solution to the problem would “enable us to justify the traditional boundary between logical and extra-logical expressions” (Tarski 1983c, p. 420). In fact, this is the boundary which for Tarski is “underlying our whole discussion”.