On Neutral Relations

Abstract

Is there an explanation of why the state of x's bearing the non‐symmetric binary relation R to y is different from its differential opposite, the state of y's bearing R to x? One traditional view has it that the explanation is that non‐symmetric relations hold of objects in an essentially directional way, ordering the relevant relata. We call this view ‘directionalism’. Kit Fine has suggested that this approach is subject to significant metaphysical difficulties, sufficient to motivate seeking an alternative analysis. He considers two such alternative explanations, which he labels ‘positionalism’ and ‘anti‐positionalism’. Of these he endorses the latter. We argue that anti‐positionalism fails to provide a coherent explanation of the distinction between differential opposites, and that one should simply hold the minimalist position that there is no explanation for this metaphysical difference.

Mereological Nominalism

“…15 But, again, if 14 The worry might instead be the inexplicability of the 'order'/'direction' of relations. But everyone-realist and mereological nominalist alike-has that problem [Donnelly 2016;Fine 2000Fine , 2007Gaskin and Hill 2012;MacBride 2007MacBride , 2014. 15 Gilmore [2013: 199-200] complains that this doesn't help with relations which can have identical relata (e.g.…”

“… The worry might instead be the inexplicability of the ‘order’/‘direction’ of relations. But everyone—realist and mereological nominalist alike—has that problem [Donnelly ; Fine , ; Gaskin and Hill ; MacBride , ]. …”

Coordinate-Free Logic

“…We do not assume that every instance of ENTITY belongs to one of the given subtypes. 7 The antipositionalist view has been criticized (MacBride, 2007;Wieland, 2010;Orilia, 2011;Gaskin and Hill, 2012;MacBride, 2013), but there are good reasons to consider it as the superior view:…”

Positions, Ordering Relations and O-Roles

“…First and foremost there is the phenomenon of relational order. We can preliminarily define it as whatever differentiates a non‐symmetric fact xRy, a fact with a non‐symmetric relating relation, from its differential opposite , yRx (in the terminology of Gaskin and Hill ) . For instance, the fact of Romeo's loving Juliet, rLj, is different from its differential opposite, Juliet's loving Romeo (jLr).…”

“…To the extent that the o‐roles theory (or something in its vicinity ) is successful, one can perhaps defuse the ‘brute fact’ or ‘primitivist’ orientation toward relatedness recently put forward by MacBride () and Gaskin and Hill (), according to which the failure of the extant attempts to analyze relational order suggests that no analysis of it can be given after all. But MacBride grounds his point by casting doubts on the o‐roles theory itself and charges that it also falls prey to the very same problems that he sees in a positionalist view à la Hochberg, as we may call it (although MacBride does not explicitly attribute it to Hochberg).…”