Thirteenth-century interpreters of Aristotle’s Topics put forward metaphysical accounts aiming to underpin Aristotle’s account of dialectical argumentation. The reason for this, I surmise, is that they took Aristotelian logic to be a scientific method, a crucial part of which is the dialectical method provided in the Topics. Dialectical arguments proceed distinctively from acceptable premises which are not necessarily true. So, if dialectical argumentation is to be a tool to produce scientific knowledge, dialectical arguments must meet the world at least at some joints. In other words, the warrants of dialectical arguments, the topoi, must somehow bring about some adequation between the dialectical conclusion and the ontological structure of the world. The solution of some Parisian masters of Arts is to propose a basic ontology that grounds the topical strategies (topoi) described by Aristotle in Topics II to VII. The aim of this chapter is to use the topoi of the accident as a case-study to reveal this ontology and illustrate how it is subsidiary to their understanding of the functional role of topical warrants in dialectical arguments.