Abstract
States of affairs involving a non-symmetric relation such as loving are said to have a relational order, something that distinguishes, for instance, Romeo’s loving Juliet from Juliet’s loving Romeo. Relational order can be properly understood by appealing to o-roles, i.e., ontological counterparts of what linguists call thematic roles, e.g., agent, patient, instrument, and the like. This move allows us to meet the appropriate desiderata for a theory of relational order. In contrast, the main theories that try to do without o-roles, proposed by philosophers such as Russell, Hochberg, and Fine, are in trouble with one or another of these desiderata. After discussing some alternatives, it is proposed that o-roles are best viewed as very generic properties characterizable as ways in which objects jointly exemplify a relation. This makes for exemplification relations understood as complex entities having o-roles as building blocks.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
More precisely, we should speak of Abelard’s loving Eloise at a certain time and similarly for the other examples that we shall consider. But issues of time and tense may be ignored for present purposes and thus, for simplicity’s sake we shall pretend that times are not involved in the identification of states of affairs. I use “state of affairs” and “fact” as synonymous and “attribute” as meaning either property or relation.
I take for granted in this paper the familiar distinction between propositions (thoughts) and states of affairs (Bealer 1982; Armstrong 1997), both understood as complexes made up of constituents. The former are fine-grained entities in the conceptual realm and the latter —on which I focus here—more coarse-grained entities in the ontological realm par excellence, as we may say, i.e., the natural world, broadly understood (so that, as far as we are concerned here, it may even contain logical or mathematical facts). Not all philosophers accept a similar distinction between propositions and states of affairs and thus, discuss the problem of order from the point of view of propositions, or perhaps from the point of view of a hybrid category of propositions/states of affairs. The Russell of 1903 is a clear-cut example of such a philosopher (he uses the term “proposition” in appealing to this hybrid category). For present purposes, however, I treat these philosophers as if they espoused a distinction between propositions and facts in the way that I do. Accordingly, all theories of relational order to be reviewed below will be understood as concerning states of affairs, even if they were originally conceived of as dealing with propositions or the hybrid category. I leave to the interested reader the task of adapting my proposals to propositions, to propositions/states of affairs, or even to states of affairs conceived of not as complexes but as tropes (Maurin 2002).
Both a fact with n arguments and its attributing attribute will be called, with familiar terminology, n-adic or of degree n, but I shall not take for granted that the attribute can be so classified independently of the fact in question, for, as we shall see, there are theories that take relations to be variably polyadic, capable of taking a different number of arguments in different facts (and indeed it will turn out that I propose one such theory). Relational order can be exhibited by states of affairs of whatever degree higher than 1, e.g., by a fact consisting of an object’s being placed in between two other items. Nevertheless, for simplicity’s sake, I shall concentrate as much as possible on dyadic states of affairs, since whatever results we obtain by discussing them can be easily generalized to “larger” facts.
Following Fine (2000, p. 8), instead of speaking of a relational order exhibited by facts involving a non-symmetric relation, we could say that non-symmetric relations are capable of “differential application,” i.e., of applying to, or being exemplified by, the same relata, in different ways. Fine prefers to use “order” in talking about a specific view of relations, namely directionalism (see below), whereas I use it to describe a general phenomenon that competing theories of relations, including directionalism, strive to account for. Sometimes I say for brevity’s sake “order” rather than “relational order.” In these cases, it should be clear from the context that I mean to speak neither of factual order (to be discussed in section 2), nor for that matter of the order involved in entities that (we shall assume) are not facts, e.g., the series of natural numbers, instants of time, or books in left-to-right alphabetical order in a bookshelf. Of course, that the items in one such series are in a certain order may well be grounded on relational facts that do exhibit relational order of the kind discussed in this paper.
These representations of facts do not commit us to non-existent or non-obtaining states of affairs for they can be regarded as definite descriptions understood à la Russell. For example, (2) below can be understood as “the fact having S as relating relation and b and t as arguments.”
It could perhaps be objected that a fact such as (2) does not really exist, because it is not fundamental enough or because *sibling* is not a primitive relation (it is analyzable on the basis of the parenthood relation). And similar worries could perhaps arise with respect to the other examples used in this paper, e.g., (1), (3), and (4). As I see it, we could view facts such as these as supervening on more fundamental facts, without considering the former as non-existent. In any case, the non-fundamental facts in question can be regarded as mere examples that serve an illustrative purpose (similarly, Armstrong 1997 appeals for illustrative purposes to properties and relations that presumably are not invoked in the ultimate physicalist account of the world, even though in his view only properties and relations invoked in this account really exist). The reader who prefers more fundamental (primitive, unanalyzable) facts should replace my examples with her favorite ones.
A datum underlined in conversation by Greg Landini.
For example, (1), beside having a relational order, has also the factual order given to it by its having as constituent just one attributing attribute, the relating relation *loving*.
Not all linguists would agree with this (see, e.g., Dowty 1989, p. 69), but these details are immaterial for the purposes of this paper.
For those who consider important the formulation of identity conditions, we could add that in a full development of the proto-theory one might want to include identity conditions for o-roles. Tentatively, one could endorse a principle along these lines: r 1 = r′ 1, ..., r n = r′ n if, and only if, for every attribute A and arguments x 1, ..., x n , the facts p and q necessarily co-exist, where p is the fact in which A occurs as attributing attribute, x 1 occurs as argument with role r 1, ..., x n occurs as argument with role r n , and q is like p except that in it the roles r′ 1, ..., r′ n occur instead of r 1, ..., r n , respectively.
As in any approach to states of affairs as complexes, here we must somehow make sense of the idea that one item can have multiple occurrences in a complex. Bigelow and Pargetter (1989) and Wetzel (1993) may be relevant in this respect. For problems, see Lewis (1986) and Armstrong’s (1986) reply to Lewis.
This of course echoes Russell’s (1903) well-known distinction between occurring as a concept and occurring as a term in a proposition.
Before leaving this section, it might be worth dispelling a complaint that has been voiced to me by an anonymous referee. It can be put as follows. Some people are willing to accept conjunctive facts or the like, for example, these two distinct conjunctive facts (a) *a loves b & c loves d* and (b) *a loves d & c loves b*. The proto-theory should grant this distinctness and yet it is unable to do it for in both conjunctive facts the same arguments, a and c, occur with the o-role *agent*, and the same arguments, b and d, occur with the o-role *patient*. But this conclusion is unjustified. The proto-theory may well view a conjunctive fact *p & q* as a fact with *&* as relating relation and such that the facts p and q occur in it as arguments with the same o-role, say *theme*. From this perspective, we can clearly see that the proto-theory count (a) and (b) as distinct, because, as explained above in discussing D1, it counts the four conjuncts in question as distinct. Similarly, an appeal to various distinct facts (whether or not they are taken to give rise to conjunctive facts) may allow the supporter of the proto-theory to counter related worries such as the following one, also brought to my attention by the same referee. Suppose that there are four individuals, a, b, c, d, which, taken in this order, are arranged in a circle. We might then assume that there is a relation such as *circularly arranged*, C, and a fact C(a, b, c, d), wherein the four arguments all occur with the same o-role, say, *theme* (on which basis could we assign them distinct o-roles?). The fact in question is then, according to the proto-theory, devoid of relational order and yet intuitively there seems to be a relational order in it, for in a sense a, b, c, d are not on a par in it. For instance, it is the case that (in the ideal circular line connecting the four individuals) a is next to b, but it is not the case that a is next to c (as b is in between them). However, we can explain this impression of relational order, by bringing to the fore symmetric facts such as *a is next to b*, *b is next to c*, and *c is next to d* (all involving, we might surmise, the o-role *theme*). The idea is to emphasize that, whereas these facts exist, there are no further “nextness facts” involving these individuals, e.g., there is no fact *a is next to c*, which gives us the sense in which b and c are not on a par in the fact C(a, b, c, d). Note that, when we simply say that a, b, c, d are arranged in a circle, nothing about their order in the circle can be inferred. The order can be inferred once we add “in that order”. By adding this phrase, we implicitly invoke further facts such as *a is next to b*, while ruling out other facts, e.g., *a is next to c*. An analogous problem has been raised by Fine (2000, note 10, p. 17) in his discussion of positionalism (an account of order to be considered below). McBride (2007, p. 40) has reacted to it by appealing to considerations of the kind I have resorted to here.
Approaches close in spirit to the anti-positionalism of Fine (2000; see p. 1 therein) are those in Dorr (2004) and Williamson (1985). Other views that I cannot discuss here for reasons of space include those in Bergmann (1992), committed to diads, and Tegtmeier (2004), committed to ordinators. I plan to do full justice to them on another occasion.
In spite, I would say, of the reply in Fine (2007). One of the worries raised by McBride is that Fine’s theory is circular, since its explanatory job is performed by substitution relations, which themselves give rise to relational order. Fine replies that every theory is bound to appeal to relations that involve order, because no theory can avoid a recourse to exemplification relations, which, being non-symmetric, involve order. I agree, but I think that a theory that does not invoke other non-symmetric formal relations, besides those of exemplification is preferable to one that does. As we shall see, my approach is of the former kind. (I use “formal” here to distinguish between relations such as those of substitution and exemplification, appealed to at the theoretical level, and garden variety relations such as *loving*).
Hochberg does not use parentheses, but I have added them for readability and uniformity with other formulas used in this paper. Note that different members of the same unordered complex may have the same position relation to the complex. For instance, since Romeo’s love for Juliet is reciprocated, we must admit that both Romeo and Juliet have the relations F and S to [L, r, j]. This may seem strange, but it can perhaps be accepted.
Presumably, Dowty uses “property,” as is done sometimes, in a generic sense according to which relations are properties of degree higher than 1.
As well as to deal with various other problems in natural language semantics, including the treatment of adverbs, that need not concern us here.
As promised in note 13 above, my proposal does not appeal at the explanatory level to non-symmetric formal relations apart from the exemplification relations, for EC is a symmetric relation. This can be seen intuitively by noting that the order in which we place the representatives of the o-roles in the representation of an exemplification relation is quite irrelevant. For example, “[attribution: ...]-[agent: ...]-[patient: ...]” and “[patient: ...]-[agent: ...]-[attribution: ...]” can be taken to stand for the very same exemplification relation. As far as the recourse to exemplification relations go, it is worth noting that, if one considers appropriate to distinguish between a fact, e.g., (5), and a corresponding “exemplification fact,” *Socrates exemplifies wisdom* (Orilia 2007, Gaskin 2008), the relational order of the latter can still be explained by a recourse to o-roles. That is, *Socrates exemplifies wisdom* should be taken to involve an exemplification relation with the attributive o-role and Socrates and *wisdom* with two distinct argument o-roles. For reasons of space, we cannot go into further details here.
Once we admit that the very same relation can be involved in facts of different degrees, we can view facts such as [attribution: E]-[agent: z]-[patient: w]-[instrument: u] as containing “smaller” facts such as [attribution: E]-[agent: z]-[patient: w]. In other words, if the “larger” fact exists, any “smaller” one “contained” in it must in turn exist. This is as it should be, for we have here an ontological counterpart of what linguists and logicians have called “argument deletion”, which is the inferential rule that allows us to derive, e.g., “Tom is eating the soup” from “Tom is eating the soup with a spoon.”
References
Allen, J., 1988, Natural Language Understanding, Benjamin/Cummins, Menlo Park.
Armstrong, D. M., 1986, “In Defense of Structural Universals”, Australasian Journal of. Philosophy, 64, pp. 85–88.
Armstrong, D. M., 1997, A World of States of Affairs, Cambridge University Press, Cambridge.
Bealer, G., 1982, Quality and Concept, Oxford University Press, Oxford.
Bealer, G., 1989, “Fine-grained Type-free Intensionality”, in Properties, Types and meaning, I, eds. by Chierchia, G., B. Partee and R. Turner, Kluwer, Dordrecht, pp. 177–230.
Bergmann, G., 1992, New Foundations of Ontology, ed. by W. Heald, University of Wisconsin Press, Madison.
Bigelow, J. and R. Pargetter, 1989, “A Theory of Structural Universals”, Australasian Journal of Philosophy, 67, pp. 1–11 (repr. in Laurence and Macdonald 1998, pp. 219–229).
Castañeda, H.N., 1967, “Comments on Davidson’s ‘The logical form of action sentences’”, in N. Rescher, ed., The Logic of Decision and Action, The University of Pittsburgh Press, Pittsburgh, pp. 104–112.
Chierchia, G., 1989, “Structured Meanings, Thematic Roles and Control”, in Properties, Types and meaning, I, eds. by Chierchia, G., B. Partee and R. Turner, Kluwer, Dordrecht, pp. 131–166.
Cross, C. B., 2002, “Armstrong and the Problem of Converse Relations”, Erkenntnis, 56, pp. 215–227.
Dorr, C., 2004, “Non-symmetric Relations,” in D. W. Zimmerman, ed., Oxford Studies in Metaphysics, vol. I, Oxford University Press, Oxford, pp. 155–192.
Dowty, D., 1989, “On the Semantic Content of the Notion of ‘Thematic Role’”, in Properties, Types and meaning, I, eds. by Chierchia, G., B. Partee and R. Turner, Kluwer, Dordrecht, pp. 9–130.
Fine, K., 2000, “Neutral Relations”, Philosophical Review, 14, pp. 1–33.
Fine, K., 2007, “Response to Fraser McBride”, dialectica, 61, pp. 57–62.
Fitch, F. B., 1952, Symbolic Logic. An Introduction, Ronald Press, New York.
Gaskin, R., 2008, The Unity of the Proposition, Oxford University Press, Oxford.
Hochberg, H., 1987, “Russell’s Analysis of Relational Predication and the Asymmetry of the Predication Relation,” Philosophia, 17, pp. 439–459.
Laurence, S. and C. Macdonald (eds.), 1998, Contemporary Readings in the Foundations of Metaphysics, Blackwell, Oxford.
Lewis, D., 1986, “Against Structural Universals”, Australasian Journal of Philosophy, 61, pp. 343–77 (repr. in Laurence and MacDonald 1998, pp. 198–218).
Maurin, A.-S., 2002, If Tropes, Kluwer, Dordrecht.
McBride, F., 2007, “Neutral Relations Revisited”, dialectica, 61, pp. 25–56.
Orilia, F., 2000, “Property Theory and the Revision Theory of Definitions”, Journal of Symbolic Logic, 65, pp. 212–246.
Orilia, F., 2003, “Logical Rules, Principles of Reasoning and Russell’s Paradox”, in The Logica Yearbook 2002, ed. by T. Childers and O. Majer, Filosofia—Institute of Philosophy, Academy of Sciences of the Czech Republic, Praga, pp. 179–192.
Orilia, F., 2007, “Bradley’s Regress: Meinong vs. Bergmann”, in Ontology and Analysis, Essays and Recollections about Gustav Bergmann, ed. by L. Addis, G. Jesson, E. Tegtmeier, Ontos Verlag, Frankfurt, pp. 133–163.
Orilia, F., 2008, “The Problem of Order in Relational States of Affairs: A Leibnizian View”, in Fostering the Ontological Turn. Essays on Gustav Bergmann, ed. by G. Bonino and R. Egidi, Ontos Verlag, Frankfurt, pp. 161–186.
Parsons, T., 1990, Events in the Semantics of English: A Study of Subatomic Semantics, MIT Press, Cambridge.
Russell, B., 1903, The Principles of Mathematics, Cambridge University Press, Cambridge.
Russell, B., 1984, Theory of Knowledge (ed. by E. R. Eames in collaboration with K. Blackwell), Routledge, London.
Tegtmeier, E., 2004, “The Ontological Problem of Order”, in H. Hochberg and K. Mulligan, eds., Relations and Predicates, Ontos Verlag, Frankfurt, pp. 149–160.
Williamson, T., 1985, “Converse Relations”, Philosophical Review, 94, pp. 249–262.
Wetzel, L., 1993, “What are Occurrences of Expressions?”, Journal of Philosophical Logic, 22, pp. 215–219.
Wieland, J. W., 2010, “Anti-Positionalism Regress”, Axiomathes (in press).
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Orilia, F. Relational Order and Onto-Thematic Roles. Int Ontology Metaphysics 12, 1–18 (2011). https://doi.org/10.1007/s12133-010-0072-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12133-010-0072-0