Abstract: Thomas Kuhn's The Structure of Scientific Revolutions (1962) has been taken to challenge the long-held belief that the natural and mathematical sciences embody a special kind of objectivity and rationality. In particular, deep conceptual revolutions — like the transition from Newton to Einstein — were characterized by what Kuhn called "incommensurability" between earlier and later scientific paradigms, and this suggested to many that the transition from one to another is not strictly speaking rational or objective. I will explain how paying close attention to the parallel developments in scientific philosophy that guided and accompanied the transition from Newton to Einstein — developments involving Kant, Helmholtz, Mach, and Poincaré — allows us to view this transition as fully objective and rational despite the phenomenon of Kuhnian incommensurability.