  Tarski says that the distinction between logical and extra-logical terms is not entirely arbitrary, because if we were to include signs like the implication sign or the universal quantifier among the extra-logical terms, “our definition of the concept of consequence would lead to results which obviously contradict ordinary usage” (Tarski 1983c, p. 418). This is so because in this case the definition would not declare logical consequences many instances of the relation consecrated by the common usage of logicians. However, Tarski does not seem to worry that the opposite problem may arise. The possibility exists, according to him, of extending the set of logical terms without making the definition of logical consequence useless. Even if all terms of the language are considered logical, the definition results in a characterization of a special concept of consequence, that of material consequence.