Einstein located the foundations of general relativity in simple and vivid physical principles: the principle of equivalence, an extended principle of relativity and Mach's principle. While these ideas played an important heuristic role in Einstein's thinking, they provide a dubious logical foundation for his final theory. Einstein was also guided to his final theory, I argue, by a second tier of more prosaic heuristics. I trace one strand among them. The principle of equivalence guided Einstein well until it led him (...) to a theory that contradicted the conservation of momentum. Einstein converted the requirement of conservation of energy and momentum into a procedure that he used repeatedly for finding gravitational field equations. That procedure survives in present day developments of general relativity. (shrink)

This paper attempts to explain the emergence of the logical empiricist philosophy of space and time as a collision of mathematical traditions. The historical development of the ``Riemannian'' and ``Helmholtzian'' traditions in 19th century mathematics is investigated. Whereas Helmholtz's insistence on rigid bodies in geometry was developed group theoretically by Lie and philosophically by Poincaré, Riemann's Habilitationsvotrag triggered Christoffel's and Lipschitz's work on quadratic differential forms, paving the way to Ricci's absolute differential calculus. The transition from special to general relativity (...) is briefly sketched as a process of escaping from the Helmholtzian tradition and entering the Riemannian one. Early logical empiricist conventionalism, it is argued, emerges as the failed attempt to interpret Einstein's reflections on rods and clocks in general relativity through the conceptual resources of the Helmholtzian tradition. Einstein's epistemology of geometry should, in spite of his rhetorical appeal to Helmholtz and Poincaré, be understood in the wake the Riemannian tradition and of its aftermath in the work of Levi-Civita, Weyl, Eddington, and others. (shrink)