 But the point perhaps can be made even more clearly if we consider Newton’s theory of universal gravitation. For Newton’s Principia had already shown clearly how we can empirically discover the law of universal gravitation—on the presupposition, that is, of the Newtonian laws of motion and Euclidean geometry. Without these presuppositions, however, we certainly would not have been able to discover the law of gravitation. And the same example also shows clearly how each level in the hierarchy of sciences presupposes all of the preceding levels: we would have no laws of motion if we did not presuppose spatial geometry, no geometry if we did not presuppose the theory of mathematical magnitude, and of course no mathematics at all if we did not presuppose arithmetic (Friedman 1999, 76).