 By abandoning the assumption that differential application is to be explained locally, anti-positionalism in effect tells us that we’re misconceiving the logical form of our ordinary relational judgements. Contrary to their surface form, relational judgements always have a suppressed argument position for other states, by which means the state we are making a judgement about is implicitly compared to another. The following two objections arise (MacBride 2007: 47–53). First of all, anti-positionalism presupposes a non-symmetric relation of substitution to explain differential application. But this suggests that the explanation anti-positonalism provides involves a circularity because it uses a non-symmetric relation, substitution, whose differential application is take for granted. Take the state \(a\Rel b\). The result of substituting \(a\) for \(b\) is the state \(a\Rel a\); where the result of substituting \(b\) for \(a\) is the state \(b\Rel b\). The outcomes are different so the substitution relation must be order sensitive. Secondly, anti-positionalism entails that there cannot be lonely binary relations, i.e., relations which only hold of exactly two things. But prima facie we should be able to distinguish \(a\Rel b\) from \(b\Rel a\) even if \(R\) holds between nothing except \(a\) and \(b\), Antony’s loving Cleopatra from Cleopatra’s loving Antony even if the world is otherwise loveless (see, for replies to these objections, Fine 2007: 59–62, Wieland 2010: 487–93, Leo 2014: 279–81).