Explaining the differential application of non-symmetric relations

Non-symmetric relations like loves or between can apply to the same relata in non-equivalent ways. For example, loves may apply to Abelard and Eloise either by Abelard’s loving Eloise or by Eloise’s loving Abelard. On the standard account of relations (Directionalism), different applications of a relation to fixed relata are distinguished by the direction in which the relation applies to the relata (e.g., from Abelard to Eloise rather than from Eloise to Abelard). But neither Directionalism nor its most popular rival, Positionalism, offer accounts of differential application that generalize to relations of arbitrary symmetry structure. Here, I develop an alternative account, Relative Positionalism, which distinguishes different applications of a relation to fixed relata in terms of the ways in which the relata are characterized relative to one another. In presenting and defending Relative Positionalism, this paper covers some of the same ground as my [2016], but avoids the latter’s algebraic approach and focuses on interpretative issues—in particular, how to make sense of relative property instantiation—that were not addressed in the earlier paper.