This paper aims to answer the question of whether or not Frege’s solution limited to value-ranges and truth-values proposed to resolve the “problem of indeterminacy of reference” in Section 10 of Grundgesetze is a violation of his principle of complete determination, which states that a predicate must be defined to apply for all objects in general. Closely related to this doubt is the common allegation that Frege was unable to solve a persistent version of the Caesar problem for value-ranges. It is argued that, in Frege’s standards of reducing arithmetic to logic, his solution to the indeterminacy does not give rise to any sort of Caesar problem in the book.
Bruno Bentzen. "Frege on Referentiality and Julius Caesar in Grundgesetze Section 10." Notre Dame J. Formal Logic 60 (4) 617 - 637, November 2019. https://doi.org/10.1215/00294527-2019-0022