If Basic Law V were true, the formal system of Grundgesetze would be consistent, but Frege himself conceded in his appendix to Grundgesetze Vol. II that Russell's paradox destroys the system's foundations.

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Basic Law V(Foundational axiom of Frege's logicist program): Frege's axiom committing to the existence of a set corresponding to every predicate; also called the unrestricted Comprehension Axiom
Formal system(as used in logic and mathematics): A set of rules and symbols (like mathematical axioms) that you use to prove whether statements are true or false, similar to how a chess game has specific rules that determine what moves are legal.
Foundations(as in 'foundations of statistical mechanics'): The basic, underlying principles or assumptions that a field of study is built on—like asking 'what does this really mean at its core?'
Frege, Gottlob(namesake of the distinction being discussed): A German philosopher and mathematician (1848–1925) who developed foundational ideas about how language and meaning work, particularly about the difference between what a word refers to and what it means.

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