There are at least as many responses to the hole argument as authors who have written on it. One line of thought simply agrees that the hole argument makes acceptance of Leibniz equivalence compelling. It seeks to make more transparent what that acceptance involves by trying to find a single mathematical structure that represents a physical spacetime system rather than the equivalence class of intertransformable structures licensed by Leibniz equivalence. One such attempt involves the notion of a “Leibniz algebra.” (See Earman, 1989, Ch. 9, Sect. 9) It has become unclear that such attempts can succeed.  Just as intertransformable fields represent the same physical system, there are distinct but intertransformable Leibniz algebras with the same physical import. If the formalisms of manifolds and of Leibniz algebras are intertranslatable, one would expect the hole argument to reappear in the latter formalism as well under this translation. (See Rynasiewicz, 1992.)