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Relationism and the Problem of Order

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Abstract

Relationism holds that objects entirely depend on relations or that they must be eliminated in favour of the latter. In this article, I raise a problem for relationism. I argue that relationism cannot account for the order in which non-symmetrical relations apply to their relata. In Section 1, I introduce some concepts in the ontology of relations and define relationism. In Section 2, I present the Problem of Order for non-symmetrical relations, after distinguishing it from the Problem of Differential Application. I also examine four main existing strategies to solve it. In Section 3, I develop my argument. The first step consists in arguing that—among those strategies—relationism can only accept directionalism. The second step consists in arguing that directionalism is affected by a serious problem: the Problem of Converses. I also show that relationists who embrace directionalism cannot solve this problem. In Section 4, I introduce and rebut several strategies on behalf of relationists to cope with my argument. In Section 5, I briefly draw some conclusions.

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Notes

  1. I call “symmetrical” here those relations that Donnelly (2021) calls “completely symmetric”.

  2. On the ontology of relations, see MacBride (2020), Heil (2021) and Paolini Paoletti (2016). Another distinction that is often drawn is that between internal and external relations. I shall not delve into such a distinction here, as it will not be relevant for this article.

  3. See for example Tahko and Lowe (2020).

  4. In what follows, I shall also examine the possibility that objects depend on relations in some respect(s) and that relations depend on objects in some further respect(s). In this case, depending in some respect(s) need not be an asymmetrical relation.

  5. Here “entirely” points to the number of dependees. However, in this context, there is another sense in which objects entirely depend on relations. As we have seen, the former depend on the latter for every aspect.

  6. However, if, in addition to this claim, one held that relational properties do not depend on relations, one could then construct two corresponding versions of relationism based on relational properties.

  7. Or insofar as everything is taken to entirely depend on the micro-physical level, where (DR) and/or (ER) holds. On ontic structuralism, see Ladyman (1998, 2007, 2014), Ladyman and Ross (2007), French (2006, 2010, 2014) and French and Ladyman (2003a).

  8. See for example Saunders (2003, 2006), Muller and Saunders (2008), Muller and Seevinck (2009) and Muller (2011a, 2015).

  9. See for example Dipert (1997), Leitgeb and Ladyman (2008), Shackel (2011) and Leitgeb (2020, 2021).

  10. See for example Shapiro (1997, 2000), Resnik (1997) and Parsons (2008).

  11. Additionally, Mertz (2016) defends the view that the only fundamental entities are relational instances.

  12. See Esfeld (2004), Esfeld and Lam (2008) and Esfeld (2020).

  13. See Morganti (2019).

  14. I wish to thank one anonymous reviewer for this objection.

  15. See Linnebo (2008), Wolff (2011) and O’Conaill (2014).

  16. See McKenzie (2020).

  17. See McKenzie (2014a) and Bianchi and Giannotti (2021).

  18. See for example Psillos (1995, 2001, 2006, 2012), Keränen (2001), Cao (2003), McArthur (2003), Morganti (2004), Ketland (2006), MacBride (2006), Chakravartty (2007), Jantzen (2011), Wolff (2011) and Briceño and Mumford (2016). For a critical discussion of some varieties of structuralism, see Sider (2020). For some replies on behalf of ontic structuralists, see for example French and Ladyman (2003b) and French (2014).

  19. I am well aware that relational order is primarily taken to be a feature of relational facts, such as Othello’s hating Cassius, and not of relations (see for example Orilia 2008). However, as we shall see, relationism must explain the order of relational facts in terms of relations. Therefore, within this perspective, it is legitimate to claim that relational order is also (or only) a feature of relations or a feature of relational facts imposed by relations on the objects that take part in such facts. It goes without saying that I do not assume that order is only a feature of relations either. Therefore, the Problem of Order does not only affect directionalism (see below).

  20. For an overview, see MacBride (2007, 2020).

  21. See for example Williamson (1985), Grossman (1992: 57), Orilia (2011, 2014), Gilmore (2013), Paolini Paoletti (2016), Donnelly (2016) and Dixon (2018).

  22. Therefore, on positionalism, R does not ‘apply’ to A and B with a certain order. But it imposes a certain order on the resulting relational fact with A and B in virtue of its being filled in a certain way.

  23. See Fine (2000). Manners are not reified. They are reduced to relations of simultaneous substitutions.

  24. See MacBride (2014).

  25. See for example Russell (1903) and Grossman (1983: 164).

  26. It does not help here (and in the rest of our discussion) to distinguish between specific and generic dependence. Namely, between R’s being ordered depending on certain specific objects or on some object or another. In both cases, (NO) gets violated. Indeed, even when R’s being ordered depends on some object or another, R turns out to depend on objects.

  27. Moreover, being objects included in the essence of relations, objects and relations would turn out to be equifundamental. And this would be at odds with (DR) as well.

  28. This argument also holds with a very thin conception of objects, according to which objects are nothing but nodes in relational structures. The relations within such structures would either depend on nodes/objects for their being ordered (thus violating (NO)), or they would include nodes/objects in their essence, or everything would depend on some underlying and mysterious reality, or such relations would be endowed with directions.

  29. See for example Dorr (2004) and MacBride (2014, 2015, 2020). To make sense of opposition of directions, MacBride (2015) appeals to series of relata. But this move is not available to relationists. For series of relata should primarily be series of objects, insofar as the relata at stake are objects. And objects would then contribute to making sense of opposition of directions.

  30. The necessity here is conceptual. Indeed, at the moment, we are not dealing with distinct converse relations, but with distinct linguistic items whose use is regulated by conceptual norms.

  31. A version of this argument has been developed by Williamson (1985). Liebesman (2013) offers a solution that is based on nominalizing the corresponding converse predicates in different ways. For example, “the hating” successfully refers to hating, whereas “the being hated” successfully refers to being hated. However, it seems to me that, if only hating exists, it is still legitimate to successfully refer to it by both “the hating” and “the being hated”—insofar as the latter nominalizations come together as a matter of conceptual necessity. For example, when Othello stands in the hating relation to Cassius, it is legitimate to successfully refer to hating by both “the hating of Othello with respect to Cassius” and “the being hated of Cassius by Othello”.

  32. See Tahko (2018).

  33. See Dasgupta (2009). For a criticism, see Glick (2020).

  34. See for example Orilia and Paolini Paoletti (2020).

  35. This regress is discussed by Morganti (2020).

  36. Similar arguments against a world of abstract, Platonic structures are presented by Briceño and Mumford (2016). A milder option consists in holding that basic Platonic relations do not start to be instantiated. They are always there, so to say. What starts to obtain are certain facts: that the basic Platonic relations are related by further relations. Yet, in order to account for such a change in fully relational terms, one would need to invoke further Platonic relations and their starting to get instantiated. And a regress would begin.

  37. See for example Psillos (2001, 2006), Busch (2003), Kantorovich (2009) and Chakravartty (2012, 2017).

  38. Aristotelian bundle theorists may reply that objects are nothing but bundles of relations, so that they entirely depend on the latter (see for example Mertz 1996). If relations depended in turn for their existence on their constituting such bundles, they would depend on themselves, so to say. More precisely, in order for a relation to exist, it must constitute some bundle or another. In order to constitute a bundle, that relation just needs to join further relations. Indeed, constituting a bundle is nothing but joining further relations. Thus, by constituting bundles, relations turn out to depend on their own joining further relations. But consider now the relation of joining. Joining is something that must be bundled together with the relations partaking in it. Thus, some further relation of joining is required. A regress may begin. To avoid this regress, one may try to take joining as an internal, mutual dependence relation holding between the bundled relations, following a strategy developed by Simons (1994). But this would run against the Aristotelian desideratum. Indeed, on this view, relations depend for their existence on their joining further relations in bundles. But joining further relations in bundles now turns out to depend on the former relations. Thus, by transitivity, relations only turn out to depend on themselves for their existence—contra the irreflexivity of dependence.

  39. Alvarado (2020: 304) defends a view in the neighbourhood. According to him, Platonic relational tropes act as nodes in structures.

  40. Ainsworth (2010) suggests a version of ontic structuralism that admits of both monadic properties and relations.

  41. See for example Saunders (2003, 2006), Muller and Saunders (2008), Muller and Seevinck (2009) and Muller (2011a, 2015). For some criticisms of this strategy, see McKenzie (2014b).

  42. I cannot consider here the phenomena of spontaneous symmetry breaking in micro-physics. Such phenomena lead to the reduction of the number of symmetries within a certain group, thus introducing non-symmetry. But I wish to make two quick remarks. First, the reduction of the number of symmetries within a certain group is still not enough to account for the fact that certain non-symmetrical relations are in place. True: when a certain symmetrical relation R is not there anymore, it has to be replaced with some non-symmetrical relation R’. Yet, the underlying symmetrical relation R need not ground which among all of its possible directions or orders R’ gets. Secondly, this entails that the non-symmetrical relation R’ depends only in part on the underlying symmetrical relation R. And this runs against the project of reducing the former to the latter. On symmetry and symmetry breaking, see Brading, Castellani and Teh (2017).

  43. In this respect, Castellani (1998) also appeals to space–time coordinates in order to define Galilean particles. A similar move may be made with respect to microphysical objects. However, it seems that, in order to define space–time coordinates and the occupation of the latter, it is necessary to appeal to non-symmetrical relations—at some point or another. For example, the occupation relation itself seems to be non-symmetrical. Muller (2011b) suggests that we could provide distinction conditions for space–time points by appealing to a symmetrical light cone relation. Such a relation is informally defined as follows: two points stand in the light cone relation if and only if there is some point inside one light cone but outside the other (light cone) of these points. When two space–time points stand in that relation, they are distinct. When they do not, they are identical. However, in order to define the light cone relation, we actually need to appeal to non-symmetrical relations between points and light cones. Indeed, points are taken to be in light cones, whereas light cones are not taken to be in points. Moreover, the fact that such relations may be applied in different ways to different points seems to presuppose an underlying distinction between points themselves.

  44. At any rate, this sixth constraint, dealing with the non-fundamental, seems to be less demanding than the other constraints.

  45. See Williamson (1985). In this case, E1 and E2 would be the following relational instances involving R and distinct conventions C1 and C2: R’s possibly getting its positions assigned according to convention C1; R’s possibly getting its positions assigned according to convention C2.

  46. One may object that E1 and E2 actually play slightly different explanatory roles. For E1 only explains W1, whereas E2 only explains W2. Moreover, E1’s being distinct from E2’s is taken to explain W1’s being distinct from W2. Thus, E1 and E2 together explain the distinction between W1 and W2. Right. However, the need to explain W1 and W2 is an ad hoc one and it is only motivated by the acceptance of this strategy. On alternative ways of dealing with non-symmetrical relations, we may dispense with such a need. Or we may satisfy it without invoking E1 and E2. Another, more radical possibility consists in claiming that the distinction between W1 and W2 entirely hinges on ourselves, on our minds. This solution does not explain the non-symmetry of R. Moreover, it does not explain why certain relations such as R can be legitimately conceptualized in two distinct ways, whereas other relations (i.e., symmetrical ones) cannot—or need not.

  47. Though Bader (2020: 36) assigns grounding roles to the relata of symmetrical relations, so that what he claims is prima facie incompatible with relationism.

  48. The numerical distinction of objects is troublesome as well. That x and y are numerically distinct objects may well depend on R’s being irreflexive. And something analogous may be claimed with respect to R’, y and z. However, what makes it the case that x is numerically distinct from z? It can only be the following, complex fact: that R is distinct from R’ and R(x,y) and R’(y,z) and not-R(y,z) and not-R’(x,z) and not-R’(x,y) and not-R(z,x) and not-R(z,y). Or, alternatively, it is the following totality fact: that R(x,y) and R’(y,z) are all the facts there are. In both cases, it seems that negative facts must be introduced at the fundamental level in order to account for the numerical distinction between x and z. More on negative facts in Paolini Paoletti (2014).

  49. I am grateful to Francesco Orilia, Matteo Morganti and one reviewer for their helpful comments. This study received financial support from the Italian “Ministero dell’Istruzione, dell’Università e della Ricerca”, as part of the PRIN-2017 Project “The Manifest Image and the Scientific Image” (prot. n. 2017ZNWW7F).

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Paolini Paoletti, M. Relationism and the Problem of Order. Acta Anal 38, 245–273 (2023). https://doi.org/10.1007/s12136-022-00513-4

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