 By 1901, Royce had begun to reframe his metaphysics in terms of the Erlanger Programm, devised by Klein (1893) as a means of classifying different geometries by identifying what is invariant across transformations in each system. Klein demonstrated that the invariants of projective geometry could be captured in a set of postulates that would also hold for Euclidean and other non-Euclidean geometries each of which included the invariants of projective geometry and additional invariants (Bell, 1940, 442–448). Royce argued that Kempe’s system, and Royce’s own System \(\Sigma\), were defined by abstract postulates that would be necessary for any system of order whatever including projective geometry. In unpublished notes from 1901, Royce explicitly attributed the source of his discussion to the Erlanger Programm and argued that invariants of the sort identified by Kempe are illustrated in projective geometry, “just” land transactions, “Kant’s moral world,” musical performance, and selves. For Royce, the invariants of geometry and so findings based upon their analysis could directly inform the analysis of other ordering processes (1901, 96–110).