ABSTRACT
Einstein's lecture ostensibly revisits the dispute over the foundations of geometry between geometric empiricism and geometric conventionalism, set now in the new context provided by the general theory of relativity. Einstein's sharp distinction between empirical "practical" physical geometry and purely formal axiomatic geometry went in tandem with the logical empiricist account of pure mathematics as grounded ultimately in logic. At the time of Poincare's essay, around the turn of the century, geometric empiricism was primarily associated with another of 19th-century Germany's most notable scientists, physicist and physiologist Hermann von Helmholtz. Weyl's geometrical theory of gravitation and electromagnetism essentially rests upon a generalization of the Riemannian geometry of the theory of general relativity. In the spring of 1918, mathematician Hermann Weyl raised an objection of principle to the pragmatic assumptions of Einstein's practical geometry. Responding to Weyl's presentation at Bad Nauheim, Einstein reiterated that general relativity is empirically based on measuring-rod geometry.
