Descartes, the Metaphysics and the Infinite

Divine infinity in the Cartesian corpus can be diffracted into an infinity of distance, proper to the creation of eternal truths (1630), and an infinity of substance, identifiable in Meditatio III (1641). This distinction reveals the structure of Cartesian metaphysics: the conquest by rationality (accomplished by infinity of substance) of the foundation of rationality (manifested by infinity of distance). Hence the duality of infinity: infinity is a Janus bifrons, both founding and founded. To unfold this paradox, we first need to show that infinity fits into the tradition of metaphysics established by Duns Scotus, according to whom being obeys the primacy of concept, intelligibility and therefore univocity. As a result, the Cartesian idea of infinity paradoxically inherits the Scotian tradition, as further demonstrated by its determination of idea maxime vera, against any suspicion of material falsity. Thus, the metaphysical extraterritoriality of infinity may constitute a paradox at the very heart of the idea of infinity itself.