 The standard account faces the serious objection that it is liable to over-generate relations, specifically converse ones, giving rise to an over-abundance of states that results from the holding of converse relations (Fine 2000: 2–5; cf. Russell 1913: 85–7; Castañeda 1975: 239–40; Armstrong 1978b: 42, 94; for related puzzles arising out of the commitments of Armstrong 1997, see Hochberg 1999: 157–60, Cross 2000 and Newman 2002). Employing the notion of direction that the standard account uses to explain order, we can define the converse of a non-symmetric \(R\) as the relation \(R^*\) that runs from \(b\) to \(a\) whenever \(R\) runs from \(a\) to \(b\). But once given this notion of a (distinct) converse, it is difficult to deny that \(R\) has a converse. This is because it would be arbitrary to admit the existence of \(R\) whilst denying its converse (or vice versa). Hence, the standard view is committed to the general principle,