The Problem of Order in Relational States of Affairs: A Leibnizian View

Positions, Ordering Relations and O-Roles

“…Gaskin and Hill also criticize an approach based on o‐roles, namely the “Leibnizian” view of Orilia , which is however different in important respects from the o‐roles view defended here. I shall thus avoid discussing their criticisms in this paper.…”

“…Hochberg, who, as we shall see, also appeals to formal relations to explain relational order, follows Russell's lead in this (Hochberg , 441) . Although I have myself taken a road of this sort in the past (Orilia ), I have then argued that it is wrong and that a different answer can and should be offered to this objection (Orilia ). There is no room to dwell further on this issue here and thus I shall set it aside.…”

“…As is well‐known, Russell previously defended, in The Principles of Mathematics ( PoM , ), a different ‘directionalist’ approach, which I shall neglect here (see Orilia for a criticism of it).…”

On Neutral Relations

“…Before we begin our detailed consideration of anti‐positionalism, we should like to consider a variant of the positionalist view that has recently been defended by Francesco Orilia (Orilia 2008, sections 8–11; cf. also Orilia 2000), following a hint from Leibniz, who at one point suggested analysing “Paris loves Helen” as “Paris is a lover and by virtue of that very fact [ eo ipso ] Helen is loved” (Leibniz 1903, 287; translated Leibniz 1966, 14).…”

Relational Order and Onto-Thematic Roles

“…One can be found in the "Leibnizian view" proposed in Orilia 2008, where oroles are taken to be something like determinables that can be determined by relations so as to generate more determinate properties. For example, *loving* (L) determines *agent* so as to generate L[agent], i.e., *lover*, and *hate* (H), determines *agent* so as to generate H[agent], *hater*.…”