In Ajdukiewicz’s framework [1974: 24], the logical conception of language assumed that“for its characteristics each language requires 1) defining the resource of expressions and2) unambiguous assigning defined meanings to these expressions.”Language, in the logical conception, is an idealizing reconstruction of real languages. In the paper, the foundations of the general theory of language are outlined. Then, language L that is described according to logical conception is characterized categorially. The language L is defined when the set S of all its well-formed expressions (briefly wfes) is determined, satisfying the requirements of categorial syntax and categorial semantics. The language L, syntactically characterized as a categorial language, is a language, wfes of S of which are generated by a categorial grammar whose idea originated from Ajdukiewicz (1935, 1960). Each constituent of a wfe of S hasa determined syntactic category and semantic categories (extensional and intensional), can havea meaning assigned to it and also denotation. The syntactic categories of wfes of L, and also the indicated categories corresponding to them, are determined by attributing to them categorial indices which were introduced by Ajdukiewicz (1935) in logical semiotics for examining their syntactic connection. The categorial indices are useful not only while examining syntactic connection of wfes of L. They appear simultaneously in the role of a tool coordinating meaningful expressions and extralinguistic objects (see: Suszko, 1958, 1960; Ajdukiewicz, 1960; Stanosz & Nowaczyk, 1976). They also serve to describe categorial adequacy – a main aspect of language adequacy (see Wybraniec-Skardowska, 2022).