 Both the standard view and the different versions of positionalism assume that the differential application of a non-symmetric relation \(R\) with respect to \(a\) and \(b\) is to be explained “locally” in terms of \(R\), whether its direction or argument positions, and the things it relates, \(a\) and \(b\). Anti-positionalism is the doctrine, due to Kit Fine, which eschews direction and argument positions and explains differential application by abandoning the assumption that differential application is to be explained locally (Fine 2000: 20–32). According to anti-positionalism, the difference between \(a\Rel b\) and \(b\Rel a\) arises from how these states are inter-connected with other states that arise from \(R\) holding of other relata. So order is not a feature of given state capable of being isolated, but only emerges over a totality of states to which \(R\) gives rise. What distinguishes \(a\Rel b\) from \(b\Rel a\) is that inter-connectedness with other states such as \(c\Rel d\). Pay special attention to the relative arrangement of the schematic names in the following sentence. Whereas the state \(a\Rel b\) is a completion of \(R\) by \(a, b\) in the same manner as \(c\Rel d\) is a completion of \(R\) by \(c, d\), the state \(b\Rel a\) isn’t. The state \(b\Rel a\) is a completion of \(R\) by \(b\), \(a\) in the same manner as \(c\Rel d\) is a completion of \(R\) by \(c, d\) (Fine 2000: 21). However, Fine doesn’t take the notion of two states being put together “in the same manner” as primitive, but explains this in terms of a substitution relation. To say that a state \(s\) is a completion of relation \(R\) by \(a_1, a_2 \ldots, a_n\) in the same manner as a state \(t\) is completion of \(R\) by \(b_1, b_2 \ldots, b_n\) is to say that \(s\) is completion of \(R\) by \(a_1, a_2 \ldots, a_n\) that results from simultaneously substituting \(a_1, a_2 \ldots, a_n\) for \(b_1\), b\(_2 \ldots, b_n\) in \(t\) (and vice versa) (Fine 2000: 25–6). Fine goes on to suggest that the notion of simultaneous substitution of many objects may be defined, under certain conditions, in terms of the single substitution of one object (Fine 2000: 26 n. 15). Converses is avoided because the notion of direction, in terms of which the distinction between converse relations is drawn, is eschewed. This is because substitution is doing all the work.