ABSTRACT
Helmholtz’s philosophical analysis of the relation between geometry and experience played a central part in the early development of logical empiricism. The chapter analyzes how, in reaction to non-Euclidean geometries, Helmholtz developed his conception of “physical geometry” in relation to Riemann’s conception of the mathematical manifold and the basic facts of measurement. It also shows how his empiricist view stands in contrast to Poincaré’s conventionalist view of geometry, and then traces how Helmholtz’s view shaped the early conceptions of Schlick, Reichenbach, and Carnap in their attempt to overcome the Kantian conception of spatial intuition and to draw the philosophical consequences of Einstein’s application of non-Euclidean geometry to physics.
