 In the face of this inconsistency a number of theoretical options are open to us. If we wish to maintain the standard view that non-symmetric relations have direction then something has to give. (1) Either we can give up Identity, Uniqueness, or both, or we can ditch Converses. Indeed it has been argued that Converses should be ditched anyway because it gives rise to a special kind of semantic indeterminacy: we cannot establish by our use of a sign for a binary non-symmetric relation \(R\) that we mean to pick it out rather than its converse \(R^*\). This is because we can shift the referent of a predicate from a given relation to its converse whilst leaving undisturbed the truth conditions of the statement in which the predicate occurs by making compensating adjustments to the manner in which the names flanking the predicate are interpreted (Williamson 1985: 252–55, 1987; van Inwagen 2006: 458–68 but see Liebesman 2013 for a reply to Williamson). But whether Converses is ditched to avoid semantic indeterminacy, or because Converses, Identity and Uniqueness form an inconsistent triad, or for some other reason, the link between Converses and the standard view will have to be broken. (2) Alternatively we can jettison Converses but throw out the standard view with it. But if that’s the option we choose, then we will have to go back to the drawing board to provide a fresh account of differential application that doesn’t appeal to direction.