Skip to main content
SpringerLink
Log in

Against relationalism about modality

  • Published:
Philosophical Studies Aims and scope Submit manuscript

Abstract

On a highly influential way to think of modality, that I call ‘relationalism’, the modality of a state is explained by its being composed of properties, and these properties being related by a higher-order and primitively modal relation. Examples of relationalism are the Dretske-Tooley-Armstrong account of natural necessity, many dispositional essentialist views, and Wang’s incompatibility primitivism. I argue that relationalism faces four difficulties: that the selection between modal relations is arbitrary, that the modal relation cannot belong to any logical order, that to explain how the modal relation can relate properties of different adicities additional ideological complexity has to be introduced, and that not all modal constraints are relational. From the discussion, I will extract desiderata for a successor theory of modality.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data availability

The author has no data availability to declare that is relevant to the content of this article.

Notes

  1. As most relationalists do not aim to account for logical modality, I will correspondingly ignore it here.

  2. Thanks to a couple of referees for suggesting this discussion.

  3. An exception is Tugby’s grounding theory of powers (see esp. pp. 11198–11201 Tugby 2021).

  4. There are also conceptual varieties of modal primitivism: some modal concepts are conceptually primitive. I am not engaging with them in this paper. Thanks to a referee for suggesting that I clarify matters here.

  5. I suppose a relationalist may coherently reject both ontological and ideological primitivism, by claiming that \(\mathcal {M}\) is not fundamental, but that modality goes ‘just as deep as \(\mathcal {M}\) goes’, so to speak. I will not further explore this option—my arguments apply all the same. However, see footnote 10, below, for a minor caveat.

  6. In the latter case, though, Lewis’ objection to the DTA account (p. 366 (Lewis, 1983)) would be more appealing: the objection being that the relation’s connection to modality cannot simply result from its name. Relationalists may respond that their relation need only be specified by what it does: by its theoretical role (Schaffer, 2016). In this dialectic, ideological primitivism seems to fare better: the connection to modality is simply that \(\mathcal {M}\) is defined by modality. However, it’s been argued (Romero, xxx) that essence cannot explain modality if essence is defined by modality, and I’d think an analogous objection could be posed to this sort of relationalism.

  7. There are several views on the relation between properties and powers: one is that properties are powers, so that the relation is identity (Heil, 2003); another is that properties have their powers intrinsically related to them, perhaps by essential constitution (Bird, 2007; Yates, 2013); yet another is that properties ground their powers (Tugby, 2021).

  8. Relationalism so understood, its opposing views would reject either of 1, 2 or 3, above. But I take it that the main opposites of relationalism would claim that the modal status of a state is not explained by a relation: it is either not explained by anything else, or it is explained by something which is not a relation.

  9. Wang speaks here of primitive ‘notions’, which could perhaps suggest that her theory works at some conceptual level. That impression would be erroneous; her theory is an ontological theory about the modality of non-notional facts, see Sect. 5 of her paper, for example. Thanks to a referee for pointing out the need of this clarification.

  10. As I said in footnote 5, above, I suppose a relationalist may reject both ideological and ontological primitivism, claiming that \(\mathcal {M}\) is a derivative entity, and that modality derives from \(\mathcal {M}\)-states. For such views, this objection loses some of its bite—but not all. The charge of arbitrariness in the selection of ontology and/or ideology is particularly pressing when applied to the fundamental, but it is also a problem even if the ontology and/or ideology in question is not fundamental. In general, arbitrariness is a defect of a theory.

  11. I am very thankful to a referee for this reply.

  12. Admittedly, not every aspect of Sider’s view fits comfortably with relationalism, as he takes the fundamental to be a-modal. However, in discussing relationalism, we are assuming that modal primitivism is well-motivated; further, it is unclear whether Sider’s rejection of fundamental modality fits coherently with (1) his own meta-metaphysics (Torza, 2017) and (2) fundamental physics, which is modal (e.g. Hofer-Szabò et al., 2020).

  13. I thank a referee for this reply.

  14. Here, I’m oversimplifying Wang’s account, as she uses properties under variable listings. This detail is not relevant for this section.

  15. A referee suggested that \(\mathcal {M}\) need not obtain between properties of different orders, as relationalism can rule out properties of different orders applying to the same thing ‘by fiat’. However, even assuming that philosophers can decree metaphysical reality to be as they see suit, this would entail abandoning the explanatory aims of relationalism, as the modal relatedness of those properties would not be explained by \(\mathcal {M}\).

  16. Some believe that predications like 2–5 are ill-formed, while some believe that they are merely false (cf Linnebo & Rayo, 2012); either option comports with my diagnostic here.

  17. I am indebted to a referee for suggesting that I discuss these possible responses.

  18. Skiba (2021b) proposes first-order tropes and second-order universals, so mixed views are not completely new.

  19. (p. 823 Jones 2018) considers using a many-sorted language to rule out predications of locative language to properties in a first-orderist setting, but this is different.

  20. I am indebted to a referee for discussion of this case.

  21. It may flow from the Fregean assumption of a ‘mirroring principle’, see (Textor, 2010; Valdivia, 1984, 2015).

  22. See (Magidor, 2009) for a related discussion.

  23. These statements should be complicated in a variety of ways, but my basic point remains mutatis mutandis Dixon’s pocket theory generalises slots to pockets, but these are also modally defined: see p. 196 and p. 206.

  24. Gilmore poses this as a possible objection to slot theory, but acknowledges that ‘In the end, this objection may be correct’ (p. 195), although he argues that the brute necessities that slot theory requires may be reasonable and independently motivated.

  25. The formulas are invariant under uniform substitution of variables (p. 547 Wang, 2013), but the point is not about the variables, but about the coordination that they need to represent.

  26. I am indebted for the following suggestions to an anonymous reviewer.

  27. This is only a necessary condition. Another is the correspondence between the functor ‘c’ and ‘\(\exists\)’, which motivates Turner’s (Sect. 6 Turner, 2011) argument that ‘c’-statements in PFL are as committing as ‘\(\exists\)’-statements in FOL. I do not require Turner’s metasemantic principle (*) (p. 17 Turner 2011), the major premise in his argument, for my argument; I am not relying on such a generalisation, but on what the relationalists could use PFL for. For discussion of Turner’s (*) principle, see Diehl (2018).

  28. Note that \(\textbf{B}\) is a frame-dependent property, which does not affect the argument here.

  29. The Lorentz force law:

    $$\begin{aligned} \textbf{F} = q\textbf{E} + q\textbf{v} \times \textbf{B} \end{aligned}$$

    defines the electromagnetic force \(\textbf{F}\) on a particle of charge q with velocity \(\textbf{v}\) perpendicular to a magnetic field \(\textbf{B}\) in the presence of an electric field \(\textbf{E}\).

  30. For example, (p. 531 Purcell and Morin 2013) note that, although matter is actually such that the magnetic field is solenoidal, it could also not be. Given this contingency, solenoidality cannot be part of \(\textbf{B}\)’s nature. (p. 242 Griffiths 2013) notes that the existence of magnetic monopoles ‘remains an open experimental question’. But if it were part of \(\textbf{B}\)’s definition that it is solenoidal, such a definitional fact could not be refuted by experiment.

  31. I owe this point to a commentary of a referee for a relevantly similar case.

  32. For example, an anonymous referee suggested that the necessity that a property be invariant may be accounted for by the fact that being-the-property-P-in-a-situation-S entails being-the-property-P-in-a-situation-T(S), where T is a symmetry transformation.

  33. For example, (p. 80 Weinberg (1987)) suggests the possibility that ‘at the deepest level, all we find are symmetries and responses to symmetries. Matter itself dissolves, and the universe itself is revealed as one large reducible representation of the symmetry group of nature’. (p. 14256 Gross (1996)) notes that ‘Einstein’s great advance in 1905 was to put symmetry first, to regard the symmetry principle as the primary feature of nature that constrains the allowable dynamical laws.’ And Wigner (cited by (p. 64 Lange (2017))) said that for the conservation laws ‘which derive from the geometrical principles of invariance it is clear that their validity transcends that of any special theory’. The possibility that the symmetry constraints are ontologically fundamental has been explored in metaphysics, see e.g. French (2014) and Schroeren (2021). Of course, differentiable symmetries correspond to conservation laws by Noether’s theorem.

References

Download references

Funding

This study was funded by the Instituto de Filosofía at the Pontificia Universidad Católica de Valparaíso through a DI Postdoctorado 2023 project.

Author information

Authors and Affiliations

  1. Pontificia Universidad Católica de Valparaíso, Viña del Mar, Chile

    Carlos Romero

Authors
  1. Carlos Romero
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The author confirms sole responsibility for the whole study.

Corresponding author

Correspondence to Carlos Romero.

Ethics declarations

Conflict of interest

The author has no competing interests to declare that are relevant to the content of this article.

Ethics approval

The author has no ethics approval to declare that is relevant to the content of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

Here, I explore the question whether three influential views—Bird’s, Vetter’s, and Yates’—which are officially defined by means of certain syntactical operators, should be counted as cases of relationalism.

1.1 Bird

According to (p. 45 Bird 2007), the fundamental natural properties are potencies: properties with a dispositional essence. And the dispositional essence of a potency P is defined by a formula of this form:

DEp:

\(\Box (Px \rightarrow D_{(S,M)}x)\)

where ‘\(\Box\)’, the operator of metaphysical necessity, governs a formula meaning: if any possible x is P, then x is disposed to manifest M under the stimulus S—where the disposition is necessarily equivalent to the familiar counterfactual analysis (p. 43). But Bird explicitly takes his formalism to represent a manifestation relation:

Dispositional monism is the view that all there is to (the identity of) any property is a matter of its second-order relations to other properties. [...] In dispositional monism the second-order relation in question is the relation that holds, in virtue of a property’s essence, between that property and its manifestation property—which we will call the manifestation relation. (p. 139 Bird (2007))

We see that, while the theory is syntactically presented by means of operators, these pieces of syntax are interpreted in terms of relations. Bird’s theory is a case of relationalism.

1.2 Vetter

Vetter’s view (Vetter, 2015) is defined with a syntactical operator, ‘POT’, which expresses potentiality:

POT must therefore be a predicate operator which takes a predicate—specifying the potentiality’s manifestation—to form another predicate, which can then be used to ascribe the specified potentiality to an object. [p. 145]

Then, formally, if F is an n-ary predicate and \(t_1, \ldots , t_n\) are terms,

$$\begin{aligned} \text {POT}[F](t_1, \ldots , t_n) \end{aligned}$$

is a well-formed sentence, meaning that the objects \(t_1, \ldots , t_n\) have the (joint) potentiality to F. Vetter’s view is that potentiality-ascriptions like the above can be used to explain modal facts.

First, I hope we can agree that operators and formulas are syntactic devices: whatever metaphysical flesh they have must be in their intended interpretation. One may, for example, want to say that a modal syntactical operator refers to a modal operation (this was an example offered to me by a referee), but then one must say how operations are to be defined. In the standard, set-theoretical setting, operations are relations (see e.g. p. 11 (Jech, 2003)): ‘An n-ary operation on X is a function \(f: X^n \rightarrow X\)’; of course, every function is a relation). One might have another notion of ‘modal operation’ in mind, but it is clear that specifying it requires a theory—which leads to my point. Syntax is not enough: we need an interpretation, if we are to be presented with a metaphysical theory.

Back to Vetter. Although, ultimately, a simplification (p. 96), she accepts as approximately true that potentialities are individuated by their manifestation conditions. Vetter argues that they are definitely not individuated by a pair of a stimulus and a manifestation. This takes us to the question of what is a potentiality.

And I don’t think that the answer to that question is obvious. Ignoring the distracting nuance, assume that potentialities are individuated by their manifestation properties. But are potentialities properties? Yes: ‘Potentialities are, moreover, properties of individual objects’ (p. 145 Vetter, 2015). But the potentiality is not its manifestation condition: ‘Potentialities are potentialities to...’ (ibid.)—there is something more. There must be, because we need to have a modal ‘oomph’ that makes a potentiality be a modal entity, the truthmaker of possibility ascriptions and a graded or determinable possibility (p. 95).

Vetter’s formalism suggests that potentialities are constituted by whatever is represented by the operator ‘POT’. I can see three possible interpretations of this.

One is that Vetter thinks of potentiality as Anjum and Mumford (2011, 2018) think of tendency: as a primitive mode in which states can obtain. Another possibility is that potentialities are monadic properties of facts: \(\text {POT}[F](t_1, \ldots , t_n)\) iff that \(F(t_1, \ldots , t_n)\) is possible to some degree. If either of these options is true, potentialism is not a relationalism but a monadicism. However, these ideas do not make it true that potentialities are properties of individual objects.

But if we take the formalism and the interpretational clues at face value, it would seem that potentialities are constituted by the POT-operation on manifestation conditions. If so, potentialism is a kind of relationalism: there is a modal relation, denoted by the operator ‘POT’, relating properties to objects that have potentialities with those properties as manifestation conditions. A potentiality would be a property like being able to walk, constituted by the property of being walking, related to the subject of the potentiality by POT. Some of what Vetter says in her 2015 book seems consistent with this relationalist framework, like:

I have a potentiality to walk; I have no potentiality to lay eggs. Thus I am differently related to the property of walking than I am to the property of laying eggs. [...] the contrast is between having and lacking a potentiality. [p. 151]

Also, responding to Giannini and Tugby (2020), she says that (p. 215; my emphasis Vetter, 2020):

The Aristotelian picture I suggest is one on which objects, by being some way or another, ground their properties. But they do not ground them one by one. Rather, on the dispositionalist picture, we can think of properties as nodes in a vast network held together by the manifestation relation.

While she accepts that this description has a ‘metaphorical nature’ (ibid.), she stands by it.

1.3 Yates

Yates presents two theories (p. 26 Yates 2013):

  1. Orthodox Dispositional Essentialism (ODE)

    The individual essence of P is a set of dispositions it bestows in virtue of its nature, and which no other property bestows.

  2. Finean Dispositional Essentialism (FDE)

    The individual essence of P is a set of Physical laws that are true in virtue of its nature, and which aren’t true of any other property.

Now, Yates’ ODE is clearly a relationalist view: properties are necessarily linked by their essence to dispositions, and properties and other properties are modally linked through the manifestation relation that constitutes dispositions. What about FDE?

In FDE, the individual essence of a property is directly given by a law. Sometimes, from those laws, ‘certain disposition-defining subjunctive conditionals’ follow (p. 29 (Yates, 2013)), and ‘It’s natural to identify the dispositions a Physical property bestows essentially as those that are derivable [...] from laws true in virtue of its nature’. However, crucially, ‘FDE entails neither that every Physical property essentially bestows dispositions, nor that those that do have dispositional individual essences’ (p. 30). This would seem to entail that Yates’ FDE is a mixed view: partly relationalist, partly essentialist. However, I think it is ultimately purely essentialist (as was, seemingly, pointed out to Yates by a referee: footnote 61): the fundamental modal posit is the essence of a property, and laws get to be necessary by being essential to properties (through an essentialist explanation like that investigated by Glazier, 2017). From these necessary facts, certain subjunctive conditionals follow, but their modal status would seem to be completely explained by the necessity derived by the essentiality in question. (Some reject that necessity can be explained by essence, e.g. (Leech, 2018; Romero, 2019); I will not discuss this issue here.) So, I count FDE not as a relationalist, but an essentialist view.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Romero, C. Against relationalism about modality. Philos Stud 180, 2245–2274 (2023). https://doi.org/10.1007/s11098-023-01981-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11098-023-01981-z

Keywords

Search

Navigation