 First, positionalism may be roughly sketched as the view that an \(n\)-ary relation has \(n\) argument positions, where argument positions are conceived as themselves entities, and, crucially, there is no intrinsic order to the argument places of a relation; neither argument position of a binary relation is the first or the second, etc. (Castañeda 1972, 1975; Williamson 1985: 257; Grossman 1992: 57; Armstrong 1997: 90–1; Cross 2002: 219–223, Fine 2000: 10–16; Orilia 2011; Gilmore 2013). In the case of a binary non-symmetric relation \(R\), this amounts to the idea that \(R\) is associated with two further entities, % and #, its argument positions, and \(R\) holds between two given relata \(a\) and \(b\) relative to an assignment of objects to % and #. The difference between \(a\Rel b\) and \(b\Rel a\) (differential application) is then explained in terms of the different relative assignments of \(a\) and \(b\) to % and #: \(a\) to % and \(b\) to # in one case, and \(b\) to % and \(a\) to # in the other. But since the argument positions do not themselves exhibit any significant order or direction, there is no basis here for introducing converses, i.e., relations that differ only with respect to their direction of travel.