Abstract
I examine and discuss in this paper Orilia’s theory of external, non-symmetrical relations, that is based on ontological roles (O-Roles). I explore several attempts to interpret O-Roles from an ontological viewpoint and I reject them because of two problems concerning the status of asymmetrical relations (to be distinguished from non-symmetrical relations simpliciter) and of exemplification as an external, non-symmetrical relation. Finally, following Heil’s and Lowe’s characterization of modes as particular properties that ontologically depend on their “bearers”, I introduce relational modes in order to define a new solution to the problems of the ontological status of both external, non-symmetrical relations and O-Roles. I also deal with five objections raised by Fraser MacBride against relational modes and O-Roles and I elaborate an analysis of the relations of being to the left of and being to the right of.
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Notes
I shall use italic fonts in order to individuate properties and relations in the text.
Here, I take whole ontological dependence as a relation between entities or sorts of entities, which can be reduced to other relations (e.g., supervenience, realization, etc.), even if we could also take it as a primitive, irreducible relation. See more on whole ontological dependence in Section 4. Moreover, I assume that there is a distinction between intrinsic and extrinsic properties, i.e., between the properties that something has regardless of other things and the properties that it has (also or only) in virtue of its being related with other things.
Such a metaphysical necessity is grounded on the nature of the relation involved. Anyway, if one aims at claiming that being symmetrical, non-symmetrical, and asymmetrical are contingent, non-necessary features of relations, s/he can use weaker modal operators.
I adopt the convention of isolating the names of O-Roles within two “*”.
In this framework, an unordered complex is constituted by a relation R and its relata, taken regardless of the way in which R connects them.
This might not be a problem for Orilia, since he accepts fact infinitism, i.e., the idea that there are infinite chains of foundational dependence between facts (see Orilia 2006, 2007, and 2009). However, if you want to reach a fundamental level of the universe which is not grounded on anything else, then you can accept neither fact infinitism nor this view of the ontological status of O-Roles. Of course, the infinite foundational regress problem with respect to exemplification is nothing but a version of Bradley’s famous regress (see, for example, Maurin 2012).
Orilia (2008: 185) deals with this objection by claiming that there is no problem of foundational infinite regress for exemplification, since exemplification is a necessarily asymmetrical relation and necessarily asymmetrical relations do not have relational order. Yet, see the discussion on asymmetrical relations in the next section.
Such an asymmetrical relation is even stronger than the being under relation that I have briefly discussed in Section 1. In fact, it is not simply the case that, as a matter of metaphysical necessity, if one of the relata stands in the asymmetrical relation to the other relatum, then the latter does not stand in that relation to the former. O-Roles relations are such that one category of relata, i.e., entities such as loving-a, cannot occupy one of the places of the relation (the place occupied by Romeo). This introduces a sub-category of asymmetrical relations, i.e., strongly asymmetrical relations. A dyadic relation such as *agent* between relata a and b (so that a is *agent* to b) is a strongly asymmetrical relation iff it cannot be the case that b is *agent* to a. Afterwards, if exemplification is a relation, then it is a strongly asymmetrical relation, at least with respect to objects and their properties.
Incidentally, it can be argued that even symmetrical relations, if they have O-Roles, do not directly connect their relata. Thus, there remains an infinite foundational regress problem for the co-occurrence relation too.
This also demonstrates that exemplification is a strongly asymmetrical relation, at least with respect to objects and their properties. Perhaps there are cases of non-strongly asymmetrical exemplifications or of non-asymmetrical exemplifications between properties. Yet, I cannot provide here examples.
Moreover, modes differ from tropes, as long as some trope theorists take tropes as particular properties which do not ontologically depend on their bearers.
See Paolini Paoletti (2015).
Of course, e1 could wholly ontologically depend on only one entity. Yet, I have used the plural “entities” in this characterization of whole ontological dependence for the sake of clarity.
I use “loving-c” here in order to distinguish this sort of relational mode from the relations of loving, loving-a and loving-b.
Orilia (2014: 298f) introduces the O-Roles *theme* for participants in a location or undergoing a change of location.
I use being near-a here in order to distinguish this sort of relational mode from the relation of being near, which should seemingly connect Romeo and Juliet—at least if you admit that there is such a relation.
In contrast, if relations and/or O-Roles are universals, one must deal with the problematic status of exemplification and with further problems depending on the sort of solution she prefers. I have examined some possible solutions based on the tacit assumption that relations and O-Roles are universals in Sections 2 and 3.
This solution resembles, at least in part, Anna-Sofia Maurin (2010)’s solution to Bradley’s regress within trope theory. According to Maurin, the compresence relation between certain tropes asymmetrically depends on those tropes, whereas those tropes do not depend on it. This means that there is a possible world in which those tropes exist and are not compresent, whereas there is no possible world in which compresence relation exists without relating those tropes. However, what I wish to claim here is that there is no exemplification problem for modes, since modes ontologically depend on their “bearers” and such a dependence is asymmetrical. Contrariwise, in many theories of tropes, tropes are more fundamental than substances and they cannot ontologically depend on them. Thus, there is no possibility of having Bradley’s regress within mode theory (i.e., the view according to which there are both substances and modes and modes ontologically depend on substances). Yet, you have that possibility within those trope theories that introduce compresence relations (or other sorts of relations) in order to allow for the dependence of substances on tropes. As I shall explain in the next section, in mode theory, the ontological dependence between Romeo’s being a man and Romeo himself is not an external, asymmetrical relation, but an internal, asymmetrical relation, since its “instantiation” by Romeo’s being a man and Romeo himself wholly depends on the essence (and on the existence) of the mode Romeo’s being a man. Moreover, if you claim that modes ontologically depend on particular entities different from them, you can justify the thesis that (at least some) relations between modes (i.e., some relational modes) ontologically depend on the related modes. I shall discuss in the next section Simons (2010)’s solution, according to which relational tropes are necessarily bound to their relata: it is not possible for a trope to exist and not to relate the relata it actually relates.
The O-Role *instrument* is mentioned in Orilia (2014). Moreover, it is worth noticing that, in my example, statements such as (8) do not simply describe the same situation described by (7) by specifying something more (the instrument). In fact, in the truhmaker of (7), there is no instrument that is used by Romeo.
Lowe (2006)’s four-category ontology could help here: Lowe admits that, besides substances and modes, there are also kinds and (universal) properties. Modes are modes of (universal) properties. Yet, substances and modes do not literally exemplify (universal) properties: substances are characterized by modes that are modes of certain (universal) properties.
A similar result can be perhaps achieved by claiming that different relations of eating with different numbers of “places to fill” have the same second-order property (a property of properties of substances), i.e., the property of being eating relations.
Yet, modes are not complex entities, such as facts and states of affairs. They are simple entities that ontologically depend on other entities.
It is worth adding that, even if the relations of ontological dependence between the relational modes in question and their relata are internal, the relational modes do not turn out to be internal relational modes for this reason: they also but not wholly ontologically depend on their relata.
This implies that, being internal and asymmetrical (and non-symmetrical) relations, relations of ontological dependence are such that you could also apply O-Roles within them (at least if you think that internal relations have O-Roles), without having infinite foundational regresses. Yet, as I shall clarify in a few pages, I do not think that internal relations have O-Roles.
I assume here that MacBride’s argument roughly works as follows: if relations (or relational entities) exist, then you have Bradley’s regress and you cannot avoid that regress by claiming that it is part of the nature of relations (or of relational entities) to have a primitive and unexplained capacity to relate—since that capacity is somehow left unexplained. Thus, it is an argument against a viable response to Bradley’s regress. A different and more general concern would be the following: why do we have to accept that there are relations (or essentially relational entities)—or that such entities are ontologically fundamental? This article is not concerned with giving an answer to this worry. I do not wish to claim that we have to accept primitively and essentially relational entities only because they are the best solution to Bradley’s regress. On the contrary, one should have independent reasons for believing that there are relations or essentially relational entities (or that they are fundamental). In sum, my response to MacBride’s argument is not a proof of the existence of relational entities, but it is only a defense of a viable way to reply to one proof of their (alleged) non-existence (i.e., Bradley’s regress).
Orilia (2014: 300–301) could seemingly agree with my solution: according to him, there are no comparison facts between magnitudes.
However, my solution would also work in a non-substantivalist framework. In this case, space points and spatial entities would be derivative entities wholly dependent on other entities, and they would take part in the relations depicted below.
Yet, p1, i.e., viewpoint-1’s source, is to the right of p3 with respect to viewpoint-1.
Moreover, left-a relational modes are not asymmetrical comparisons between certain entities—such as p3—and certain standards of comparison—such as viewpoint-1. I think that the only legitimate comparisons are the ones that wholly ontologically depend on the intrinsic qualities of the entities to be compared, such as being taller than in (3). There are no spatial qualities of modes to be compared here: modes occupy no space. In my substantivalist view of space, if modes occupied a space, they would stand in some relation with some space point (or with some spatial region), and that relation—being a mode—would stand in some other relation with some space point (or with some spatial region), and so on, ad infinitum, thus having a proliferation of modes.
This implies that, in my view, *theme* is not necessarily correlated with *location*.
Of course, if we had two substances both at the left with respect to a certain viewpoint, in order to determine which substance is to the left of the other, we should choose a new viewpoint between their positions.
Yet, you might also have relations between viewpoints different from oppositeness, i.e., if the right with respect to a certain viewpoint is 45 degrees to the right with respect to another viewpoint.
One could use the *agent* O-Role even when the action is not explicit. I think that, in this case, the implicit action consists in establishing an equivalence or, more presumably, that there are two possible actions of rotating with respect to one another involving viewpoint-1 and viewpoint-2. Alternatively, since the oppositeness in question still is a spatial relation, one could invoke the O-Role *theme* for them.
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Paolini Paoletti, M. Non-Symmetrical Relations, O-Roles, and Modes. Acta Anal 31, 373–395 (2016). https://doi.org/10.1007/s12136-016-0286-z
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DOI: https://doi.org/10.1007/s12136-016-0286-z