 Eddington was persuaded that Weyl’s “principle of relativity of length” was “an essential part of the relativistic conception”, a view he retained to the end of his life (e.g., 1939: 28). But he was also convinced that the largely antagonistic reception accorded Weyl’s theory was due to its confusing formulation. The flaw lay in Weyl’s failure to make transparently obvious that the locally scale invariant (“pure infinitesimal”) “world geometry” was not the physical geometry of actual spacetime, but an entirely mathematical construct inherently serving to specify the ideal of an observer-independent external world. To remedy this, Eddington devised a general method of deductive presentation of field physics in which “world geometry” is developed mathematically as conceptually separate from physics. A “world geometry” is a purely mathematical construction the derived objects of which possess only structural properties requisite to the ideal of a completely impersonal world; these are objects, as he wrote in Space, Time and Gravitation (1920), a semi-popular best-seller, represented “from the point of view of no one in particular”. Naturally, this ideal had changed with the progress of physical theory. In the light of relativity theory, such a world is indifferent to specification of reference frame and, after Weyl, of gauge of length (scale). A world geometry is not the physical theory of such a world but a framework or “graphical representation” within whose terms existing physical theory might be displayed, essentially through a purely formal identification of known tensors of the existing physical laws of gravitation and electromagnetism with those derived within the world geometry. Such a geometrical representation of physics cannot really be said to be right or wrong, for it only implements, if it can, current ideas governing the conception of objects and properties of an impersonal objective external world. But when existing physics, in particular, Einstein’s theory of gravitation, is set in the context of Eddington’s world geometry, it yields a surprising consequence: The Einstein law of gravitation appears as a definition! In the form \(R_{\mu\nu} = 0\) it defines what in the “world geometry” appears to the mind as “vacuum” while in the form of the Einstein field equation noted above, it defines what is to be encountered by the mind as “matter”. This result is what is meant by his stated claim of throwing “new light on the origin of the fundamental laws of physics” (see Ryckman 2005: chapters 7 &amp; 8). Eddington’s notoriously difficult and opaque later works (1936, 1946), took their inspiration from this argumentation in attempting to carry out a similar, algebraic not geometric, program of deriving fundamental physical laws, and the constants occurring in them, from a priori epistemological principles.