  (i) and the parenthetical comment that comes after it embody fairly accurately the basic idea behind the (relativized) definition of a logical notion offered in Tarski (1986a), and (ii) offers the (absolute) definition of the concept of logical constant. There is no apparent obstacle to applying (ii) to wider classes of languages than the class considered for special purposes of their investigation by Tarski and Givant. It seems safe to assume that the definition can be applied to a large class of languages in the classical hierarchy of quantificational languages. Tarski and Givant themselves say that the usual logical constants of languages not in the class considered by them, like the symbols for the truth-functional connectives and quantifiers, “can also be subsumed under logical constants in the sense of (ii)” (Tarski and Givant 1987, p. 57), presumably through some artifice in the style of the one discussed above. (As we will soon see, at the very least Tarski clearly would want his definition to be applicable to some languages whose set of sentences is that of some formulations of the simple theory of types.)