Newton's Principia presupposes a particular philosophy of mathematics and, especially, an ontology of mathematical objects. For this to be relevant, however, it must somehow have consequences for comprehending Newton's warnings about the forces, referred to in the first theorems of Principia, as being considered in a mathematical way. In this article, I attempt to show that these warnings, contrary to what they may suggest, do not empty the mathematics - and the forces considered mathematically - of all ontological commitment. They are structured by a kind of non-Aristotelian ontology in which relations have primacy over essences. This ontology has clear antecedents in what Marion (1975) called Descartes' gray ontology.
Newtonianism; Universal gravitation; Mathematical objects; Ontology of nature; Cartesianism