 The next idea that needs to be introduced is the idea of a converse relation. For any given binary relation \(R\), the converse of \(R\) may be defined as the relation \(R^*\) that \(x\) bears to \(y\) whenever \(y\) bears \(R\) to \(x\) (Fine 2000: 3; van Inwagen 2006: 459). Note that the relationship between a relation and its converse isn’t a matter of happenstance; there’s no possibility of a converse of \(R\) floating free from \(R\) and holding between things independently of how \(R\) arranges them. Rather it’s a more intimate relationship which, if it holds, holds of necessity. For \(x\) to have one to \(y\) is, so to speak, for \(y\) to have the other to \(x\); they neither exist nor can be observed apart from one another but can only be distinguished in thought (Geach 1957: 33). Before and after, above and below are prima facie examples of mutually converse relations. Non-symmetric relations, including asymmetric ones, are distinct from their converses (if they have them). Suppose \(R\) is a non-symmetric relation which \(x\) bears to \(y.\) Then the converse of \(R\) is borne by \(y\) to \(x\). But suppose that \(R\), as it may, fails to be borne by \(y\) to \(x\). Then something is true of the converse of \(R\) that isn’t true of \(R\) itself, viz. that it is borne by \(y\) to \(x\). Hence, the converse of \(R\) must be distinct from \(R\). More generally, whilst a binary non-symmetric relation has only one converse, a ternary one has five mutual, distinct converses, a quadratic relation has 23 converses, etc. The issue of whether relations have converses is another issue to which we will return later.