  His solution to the vis viva dispute is especially interesting, because it presages his later approach to philosophical controversy. Rather than offering a conclusive argument in favor of one position, Kant seeks to mediate between the two parties, Leibnizian and Cartesian. He argues that each measure of force is correct, but in different contexts. Kant distinguishes two ways of studying bodies, “mathematical” and “metaphysical,” and claims that they presuppose distinct conceptions of body. According to mathematical mechanics, a body cannot accelerate unless an external cause acts on it; for that reason, Kant declares, the Cartesians' quantity mv is the only one appropriate measure of force in this context. “Natural bodies,” in contrast, have features that mathematics brackets. One such feature is a capacity for “vivification,” whereby a body increases by itself the force of motion that an external cause merely “awakens.” In light of that, Kant concludes, the Leibnizian quantity mv2 is the correct measure of force in metaphysical considerations of “natural bodies” (1:140f).  