 Weyl speaks here in the language of axiomatic systems and their structurally identical—isomorphic—models, a language largely articulated at the beginning of the twentieth century by David Hilbert. But Hilbert had only made more precise the notions of structuralism that went further back and had animated a great deal of nineteenth-century mathematics (see Schiemer 2013), culminating in the group-theoretic (algebraic) understanding of the new non-Euclidean geometries and Felix Klein’s celebrated “Erlanger Programm” for the unification of geometry by this means, which also inspired the early Bertrand Russell. Russell himself, and before him Gottlob Frege and Richard Dedekind, had given “top-down” definitions of structural concepts by means of higher-order logical quantifiers (as in Frege’s 1879 famous definition of the ancestral of a relation in his Begriffsschrift, or in Dedekind’s 1888 definition of simply infinite system in his Was sind und was sollen die Zahlen?, or in Whitehead and Russell’s 1910–1913 Principia Mathematica), all of which influenced Carnap significantly. An equally important influence, at about the same time as Klein, was the epistemological structuralism of Hermann von Helmholtz. Carnap was clearly inspired by these ideas, not only in his earliest work, but all through his career, even into his work on probability and induction, as we will see below  (section 8).  