Newton pointed natural philosophy in a new direction. He offered mathematical analysis anchored in inescapable empirical fact as the new foundation for a rigorous account of the cosmos. From this perspective, the great error of both Aristotelian and the new mechanical natural philosophy was its failure to adhere strictly enough to empirical facts. Vortical mechanics, for example, claimed that matter was moved by the action of an invisible agent, yet this, the Newtonians began to argue, was not to explain what is really happening but to imagine a fiction that gives us a speciously satisfactory rational explanation of it. Natural philosophy needs to resist the allure of such rational imaginings and to instead deal only with the empirically provable. Moreover, the Newtonians argued, if a set of irrefutable facts cannot be explained other then by accepting the brute facticity of their truth, this is not a failure of philosophical explanation so much as a devotion to appropriate rigor. Such epistemological battles became especially intense around Newton’s theory of universal gravitation. Few questioned that Newton had demonstrated an irrefutable mathematical law whereby bodies appear to attract one another in relation to their masses and in inverse relation to the square of the distance between them. But was this rigorous mathematical and empirical description a philosophical account of bodies in motion? Critics such as Leibniz said no, since mathematical description was not the same thing as philosophical explanation, and Newton refused to offer an explanation of how and why gravity operated the way that it did. The Newtonians countered that phenomenal descriptions were scientifically adequate so long as they were grounded in empirical facts, and since no facts had yet been discerned that explained what gravity is or how it works, no scientific account of it was yet possible. They further insisted that it was enough that gravity did operate the way that Newton said it did, and that this was its own justification for accepting his theory. They further mocked those who insisted on dreaming up chimeras like the celestial vortices as explanations for phenomena when no empirical evidence existed to support of such theories.