  As this passage helps to make clear, the root of the standard medieval objection to polyadic properties is ontological in nature, stemming from a particular conception of subjects and attributes. Following Aristotle, the medievals divide extramental beings into substances and accidents, a division which they take to be both exclusive and exhaustive (since it is given in terms of a contradictory pair of properties, namely, being in a subject vs. not being in a subject) (Cf. Categories 1, 1a20–1b6). Now in the case of substances, it is perhaps clear that they are not polyadic in nature. But medievals typically think the same is also true of their accidents. Thus, as Aquinas says at one point in his Sentences commentary, in response to the question whether it is possible for “numerically one and the same relation” to belong to belong to two subjects at a time: “No, this cannot be, for one accident cannot belong to two subjects” (In Sent. I, d. 27, q. 1, a. 1, ad 2).