Immanent Activity and Equivocity of intensio in Leibniz’s a priori Argument

Leibniz’s readers know that his a posteriori argument, which seeks to establish that force, measured by mv^2 rather than mv, is conserved in the universe, has direct bearing on his metaphysics of substance. Leibniz is not simply introducing a new physical quantity and an argument for its conservation. He takes this argument to play a corroborative role in his metaphysical project of resuscitating substantial forms. Leibniz also gave an a priori argument for the conservation of actio. The place of this argument in his metaphysical project is somewhat more complex. I argue that one way to understand the function of this argument is in terms of a metaphysical reduction – in the argument, Leibniz brackets the realm of sensible matter and empirical hypotheses, such as the law of uniform acceleration, and isolates a metaphysical element of activity constitutive of a singularity of a corporeal substance. Key to Leibniz’s strategy is his redeployment of the medieval notion of intensio as a degree of ontological perfection. Leibniz scholars have traced this notion to the medieval language of latitudo formarum. I contend that it denotes a degree of primitive activity constitutive of a singularity of substance, understood in a Scotist sense of the term.