Why Did Frege take his Wertverlauf as logical?

Why Did Frege take his Wertverlauf as logical?

Professor Christian Thiel says*1:

Frege concluded that with theorem χ*2 “the extension of the concept in the trasitional sense has been abolished” (GGA II, 260), and that “the usual understanding of the words ‘extension of a concept’ stands in need of correction” (GGA II, 256a: “dass die bisherige Auffassung der Worte ‘Umfang eines Begriffes’ einer Berichtigung bedarf”). This directs our attention to the fact (a fact important for the historian of logic and of the foundations of mathematics), that in Frege's time classes were clearly identified with the extensions of concepts (Begriffsumfänge), whereas today we identify them with sets and keep logic and set theory apart as disciplines, close as their cooperation may be. But for traditional logic, and obviously for Frege also, the doctrine of the extension of concepts is a genuine part of the logic of the concept (Begriffslogik or Begriffslehre), and it is in this sense that Frege can call his Wertverlaufe logical objects, and basic law V a fundamental law of logic.

Also, see the following entries of this diary, ‘Regeneration of the Concept The Extensions of the Concepts’ (September 13, 2008), and ‘Traditional Logic, Concepts, and Sets’ (September 21, 2008).

*1:Christian Thiel, “On the Structure of Frege's System of Logic,” in: Matthias Schirn, ed., Frege: importance and legacy, Walter de Gruyter, Perspektiven der analytischen Philosophie = Perspectives in analytical philosophy, Bd. 13, 1996, p. 269.

*2:‘That is, for every second-level function of one argument of type 2 there are concepts which if taken as arguments of this function determine the same value, although not all objects falling under one of these concepts also fall under the other.’ Gottlob Frege, The Basic Laws of Arithmetic: Exposition of the System, tr. and ed. with an intro. by Montgomery Furth, University of California Press, 1964 (Second printing in 1967), p. 136.