The theory of concepts: Bolzanian and set-theoretical traditions

The traditional (essentially Aristotelian) theories of concepts mostly identify concepts with universal (general) concepts, moreover, they are construed as set-theoretical objects. Even the great modern logician G. Frege defines concepts (Begriffe) as (characteristic functions of) sets. Then, of course, what is called 'content' or "comprehension" (Inhalt) Of a concept cannot be distinguished from the concept itself. Also, when concepts are identified with intensions, then they are again viewed as set-theoretical entities, at least within the framework of possible-world semantics, where intensions are functions (mappings) from possible worlds. The first logician who broke this tradition was Bolzano in his Wissenschfaftslehre, where he defined concepts as (objective) complexes, namely as unity of the comprehension (non-traditionally viewed as the set of simple concepts makings up the building-stones of the given concept) and the way the elements of this comprehension are held together. Tichy's notions of constructions makes it possible to realize this Bolzanian idea in terms of exact notions of the contemporary logic.