www.methodejournal.org

Categorical Structures and theMultiple Realisability Argument

Vassilios Livanios

Department of Philosophy and History

of Science, National and Kapodistrian

University of Athens (Greece)vlivan@phs.uoa.gr

Pages: 141 – 166

Keywords: categorical structures; multiple realisability; de re modal representation; worldbound tropes;property counterpart theory

Abstract

Perhaps the most compelling argument against the possibility of fundamental categorical struc-tures is the Multiple Realisability Argument (MRA). According to it, the proper account ofthe de re modal representation of categorical structures implies the multiple realisability oftheir causal/nomic roles, a fact that prima facie has unpleasant epistemic and modal conse-quences. In this paper, I examine some recently proposed responses to MRA and find themwanting. I then suggest an alternative response and argue for its adequacy. The suggestedresponse is based on two assumptions: first, that the actual fundamental structures are world-bound tropes and, second, that the appropriate account of their de re modal representation isa properly articulated version of property-counterpart theory.

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1 Preliminaries

The debate concerning the proper account of the de re modal representation ofthe fundamental features of the world is currently very popular. Two are the dom-inant views: according to the first, the Dispositionalist View (henceforth DV), thede re modal representation of fundamental properties and relations is completelydetermined by their actual causal/nomic roles. While according to the second, theRadical Non-Dispositionalist View (RNDV, for short), the actual causal/nomicroles of properties/relations are completely irrelevant to their de re modal rep-resentation.1 Along with this debate in the metaphysics of properties, a secondtraditional one persists and divides property theorists; it is the debate about thedispositional/categorical distinction. Some philosophers (neutral monists) holdthat the distinction concerns not two distinct kinds of fundamental features butonly two ways of describing2 the one and only kind. Others (property-identitytheorists) allow categoricality and dispositionality to be ontological characteris-tics of the fundamental features of the world; yet they deny that they are distinctand identify them. Finally, according to a third view (the one I prefer) the dis-positional/categorical distinction is ontological and concerns two distinct kinds offundamental features. Although the two core issues of the aforementioned debatesare clearly distinct, it is traditionally supposed that DV fits exclusively to the dis-positional “side”,3 while RNDV to the categorical one (call this supposition, theI(ntimate) R(elationship) assumption).

Recently, a new version of the debate between dispositionalists and categorical-ists has arisen within the context of Ontic Structural Realism (OSR henceforth).As it is well known, according to OSR (either in its eliminative or moderate form),the fundamental entities of the world are structures. In particular, according toeliminative OSR, fundamentally, all there is to the world is structures. Objectsare at best ontologically dependent entities which must be structurally reconcep-tualised. 4 In contrast to eliminative OSR, moderate OSR allows for the existenceof both objects and structures; in that case either the ontological dependence ismutual5 or not,6 (Esfeld & Lam 2011, Esfeld & Sachse 2011). It is a common belief

1The definition of RNDV leaves room for two different approaches. RNDV-ists should ei-ther identify one or more non-qualitative (in the sense of being completely independent fromcausal/nomic roles) factors as the ground for the de re modal representation of fundamental features,or regard the latter as a primitive fact.

2Neutral monists claim that the dispositional/categorical distinction concerns the different predi-cates we use to refer to properties.

3I use this vague term in order not to beg the question against neutral monists and property-identity theorists.

4For a recent defence, see French (2010).5See, for instance, Esfeld (2004).6According to Esfeld & Lam (2011) the distinction between objects and relations (that consti-

tute structures) is not ontological but conceptual. Hence, the issue of the (mutual) ontological

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among OSR-ists that it is fundamental physical theories that shift the focus from ametaphysics of monadic intrinsic properties to a metaphysics of relations. Physicaltheories, however, do not tell us whether the structures are categorical or disposi-tional. Hence, the metaphysical debate concerning whether the fundamental struc-tures are powers to bring about certain effects (Esfeld & Sachse 2011, p. 47),7 orontologically irreducible, primitive, non-modal entities which by themselves bringabout nothing (Lyre 2012, p. 176).

In most of the extant literature on OSR, there is a certain kind of vaguenessconcerning the intended meaning of the term “structure” and the associated properontological account of structures. The debate between categorical vs. dispositionalfundamental structures is not an exception to this. I am not an advocate of OSRand so I do not think that I have to take up the burden to provide a persuasiveontological account of what a fundamental structure really is. Nevertheless, thevery nature of the debate I wish to participate sets some limits to the possible on-tological alternatives in this context. As far as I can see, for the debate to makesense, we have to conceive the fundamental structures in a certain manner. First,we should avoid any notion of structure as concerning second-order, formal prop-erties of relations. Such an abstract (in the logico-mathematical sense) notion refersto structures that lack physical content and cannot properly be characterised as ei-ther dispositional or categorical. So, as a first step, fundamental structures must beconceived as concerning first-order relations with a specific physical interpretation.The next step is to clarify how a fundamental structure is ontologically ‘related’ tothese physical relations. Two options come to my mind: first, a fundamental struc-ture can be understood as a network of physical relations among objects (see, forinstance, Esfeld (2004), where the objects in question do not possess an identityindependently of the relations in which they stand). Second, it can be conceivedas a holistic, “structural” property constituted by these relations and instantiated(if it actually does) by relational systems of particular objects. In both ontologicalinterpretations fundamental structures are taken to be relationally constituted en-tities. As far as I can see, however, there is a crucial (for the purposes of this paper)difference between them. A network of relations can be consistently construedas a concrete8 entity, even in the case where no concrete objects are relata of the

dependence is ill-posed. This view recognises the existence of genuine objects (and in that sense is amoderate form of OSR) and regards relations as ways (modes) in which objects exist.

7For some philosophers – see Esfeld (2009) – the modal character of dispositional structures isintimately related to their causal efficacy. That is why they use the term “causal structure” as (almost)synonymous to the term “dispositional” structure.

8There is no need here to make explicit any criterion under which the abstract/concrete distinc-tion is drawn. As we’ll see below, what matters for the purposes of the paper is that we have (in thepresent context) cogent reasons to classify fundamental structures as properties and not objects. Theissue of whether one should, in turn, conceive properties as abstract or concrete entities is minorfor the goals of the paper. And not just for the present paper; in my view, the verdict on that issue

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relations (see, for instance, Mertz’s (1996, pp. 76 – 78) proposal of ontologicallyconstructing concrete objects on the basis of hierarchies of networks of relationinstances). Yet, I think we have (in the context of the present discussion) three rea-sons to think of fundamental structures as properties. First, at least in the context ofmoderate OSR, fundamental structures can be causally efficacious and “shareable”9

by distinct relational systems of objects. This dual role, however, is traditionallyascribed to properties.10 Second, as I will point out in section 2, thinking of struc-tures as (holistic) properties can help us to understand how a powerful argumentagainst RNDV which is initially formulated in a non-structuralistic context can bealso applied mutatis mutandis to the case of fundamental structures. Finally, sincethe general debate between categoricalists and dispositionalists concerns the natureof properties, the whole discussion about the categorical/dispositional character offundamental structures presupposes that the latter must be conceived as properties.For all the above reasons, I take the structure-as-a-holistic-property interpretationas the most appropriate one in the context under discussion.

Of course, there are several difficulties besetting the above suggestion. One ofthem concerns the way to understand (in a consistent with the proposal manner)the distinction between eliminative and moderate forms of OSR. My suggestionis that the eliminative/moderate OSR distinction may be understood (at the on-tological level) as the distinction between instantiated and uninstantiated holisticproperties. Moderate OSR, in contrast to eliminative OSR, can be plausibly inter-preted as claiming that the actual fundamental structures are always instantiated byrelational systems of particulars in the actual world. To be more specific, I take therelational systems under consideration to be groups of particular objects with cer-tain physically interpreted relations (constituting the relevant structures) holdingamong them. Since moderate OSR-ists often embrace an ontological interdepen-dency view between objects and structures, the objects which constitute the afore-

seems to be insignificant even more generally, provided that we confine the discussion in the contextof trope theory. Trope theorists have found serious obstacles to articulate an adequate account of thedistinction and justify the attribution of an abstract character to tropes. Given that the traditionalcriteria of abstractness based on non-spatiotemporality, causal inefficacy and asymmetric ontologicaldependence fail in the case of tropes (the last criterion fails in those versions of trope theory accord-ing to which tropes are the building blocks of the universe), trope theorists have frequently turnedto epistemic accounts of abstractness (for instance, an abstract entity is one which is the referent ofan idea resulted from the mental process of abstraction) which, however, cannot account for theabstractness of tropes associated with the fundamental fields of physics and spacetime. All that castsdoubt to the belief that abstractness is an essential feature of fundamental tropes and so (in a sense)relieves the pressure of giving an account of the abstract/concrete distinction (at least in order tojustify the appeal to trope theory).

9I put the word “shareable” in quotes because if fundamental structures are tropes they cannotliterally be shareable by distinct relational systems.

10As I shall remark in the sequel, eliminative OSR-ists might also follow this view by consideringthe fundamental structures as uninstantiated (by relational systems of particular objects) properties.

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mentioned relational systems should not be uni-directionally ontologically depen-dent on structures; otherwise, one may claim that eliminativists, who have recentlyintroduced an ontologically “thin” account of objects which are uni-directionallyontologically dependent on structures (French 2010), can also allow the fundamen-tal structures to be instantiated by the relational systems. It is interesting to notethat the above proposal does not work if it is assumed that eliminative OSR holdsnecessarily; for in that case there is no possibility of instantiation of any fundamen-tal structure. I do not think, however, that there exist cogent reasons to hold thateliminative OSR is necessarily true. Eliminative OSR-ists hold that no fundamen-tal structure is actually instantiated by relational systems of objects. Their view,however, is mainly based on the findings of the contemporary physical theories ofthe actual world and so is most plausibly justified as a contingently holding one.Therefore, I cannot see why eliminative OSR-ists should reject the instantiabilityof fundamental structures.

A second difficulty concerns the plausibility of the suggestion that the funda-mental structures are physically interpreted holistic properties belonging to theontological inventory of the actual world. It is a controversial issue whether, forinstance, the gauge symmetry structures appearing in the Standard Model havea physical interpretation, though they are currently considered as fundamental.11

Most possibly, a detailed form of the suggested ontological account will raise anumber of other objections that need to be met. But as I have already said, I amnot a proponent of OSR and, so, the task of the present paper is not to defend anyversion of this ontological view against all objections. The suggested brief formu-lation of an ontological account of fundamental structures is all I need to set thestage for the whole discussion to take place.

The main aim of the present paper is to defend the possibility of RNDV; tothat extent, the arguments that follow are largely independent both of the IR as-sumption and the preferred account of the categorical/dispositional distinction.Yet, for all those that might want to espouse the IR hypothesis and, furthermore,follow my preferred view on the categorical/dispositional distinction,12 a defenceof the possibility of RNDV is in effect a defence of the possibility of existence ofcategorical fundamental features, distinct from the dispositional ones. If successful,it would be a significant contribution to one of the central debates in metaphysics;namely, the debate concerning whether all fundamental features of the actual world

11For instance, I take Lyre’s (2010) suggestion that the fundamental U(1)-structure of the world isexemplified by charge conservation as an attempt to provide a physical interpretation to this gaugesymmetry structure.

12 These philosophers must therefore insist that DV is the proper account of the de re modalrepresentation of any member of the class of the fundamental dispositional properties/relations,while RNDV is the appropriate account of any member of the distinct class of the fundamentalcategorical ones.

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are dispositional or not. For, arguing for the possibility of the existence of cate-gorical fundamental features is the first step towards the refutation of the thesis ofdispositional monism. (The second step is, of course, to argue for the actual ex-istence of fundamental categorical properties/relations.) Furthermore, besides itssignificance in the aforementioned debate, the upshot of the paper can also be usedby those philosophers that reject that there are two kinds of fundamental featuresin the world (that is, neutral monists and property-identity theorists) to supporttheir own views. For example, for neutral monists, a defence of the possibility ofRNDV might justify their claim that there are two distinct ways of de re modal rep-resentation of the fundamental properties/relations and not only one. While in theproperty-identity theoretical context, a defence of the possibility of RNDV mightbe considered as a defence of the possibility of categoricality of each fundamentalproperty/relation.13

The roadmap of the paper is this: I start out in section 2 by presenting what Ithink is the most compelling argument against the possibility of categorical featuresin general (and categorical structures in particular); the Multiple Realisability Ar-gument (MRA). Then, I proceed in section 3 by examining some extant responsesto MRA (due to Holger Lyre and Georg Sparber). After showing that those re-sponses are for various reasons inadequate, I present in section 4 my own responseto MRA. The final section is devoted to some objections to my response and therelevant replies.

2 A Structuralistic Version of the Multiple RealisabilityArgument

All participants of the debate concerning the existence of dispositional and/orcategorical fundamental features of the world embrace the IR assumption and sothink that strong arguments against RNDV are also arguments against the existenceof actual categorical features. Even a brief survey in the relevant literature clearlyindicates that for most of them the major argument against RNDV is the so calledMultiple Realisability Argument (MRA). The original version of MRA is formu-lated in a non-structuralistic context and refers to fundamental natural non-holisticmonadic properties (in Lewis’s version, instantiated by point-sized particulars orspace-time points). Following Lewis (2009), let us assume that a true and completefinal theory ought to deliver a true and complete inventory of those fundamen-tal properties that play an active role in the actual world. That inventory willeventually omit two kinds of fundamental properties; first, following Lewis’s ter-minology, idlers, which are fundamental properties instantiated within the actualworld but play no active role. And second, aliens, which are fundamental prop-

13Granted, of course, the exclusive intimate relationship of RNDV to categoricality.

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erties that are instantiated at other possible worlds but not within the actual one.Consider now, following Hawthorne (2001), the Ramsified lawbook of our world.Here are the instructions to construct the lawbook; take all the actual laws andconjoin them. Replace then each property-name appearing in the conjunction bya distinct variable and, finally, prefix each variable by an existential quantifier.14

Consider in turn the n-tuple of fundamental properties which is the unique ac-tual realization of the Ramsified lawbook. We can get a different n-tuple either bypermuting15 the members of the original one or by replacing any member of thelatter with an alien or an idler. Assuming Combinatorialism, that new n-tuple is apossible realization of the lawbook and, given RNDV, a distinct one. Thus we havemultiple realisability of the lawbook.

According to the advocates of DV, the above-mentioned multiple realisabilityhas unpalatable consequences. The one I shall not discuss here is the so called Hu-mility and it is epistemic; arguably, given the previous assumptions, we have inprinciple no epistemic access to which n-tuple of possible properties is the actualone.16 In this paper, I shall focus on the other unpleasant corollary of the multi-ple realisability; the one concerning the acceptance of the previously mentioneddistinct metaphysical possibilities. As far as I know, there are at least three claimswhich purport to explain the kind of uneasiness (and the associated difficulty)emerging from admitting those possibilities as genuinely metaphysical. Accordingto the first of them, it is counterintuitive to accept possible worlds at which funda-mental properties have swapped roles. For instance, it seems difficult to accept thatthere is a possible world at which the property of mass has swapped causal/nomicroles with the property of electric charge. According to a second claim, we shouldembrace a sparse modal ontology and reject the existence of possible worlds, suchas those “emerging” from the multiple realisability of the actual lawbook, thatare causally/nomically indiscernible from the actual one. Finally, there is a thirdreason which has considerable importance in the context of science-informed meta-physics. It is true that scientific theories largely describe the causal/nomic roles ofthe actual fundamental features. Given that science-informed metaphysics appealsmainly to the findings of the mature, most successful, scientific theories to shedlight to a number of metaphysical issues, it seems that invoking possible worlds thatdiffer, for instance, just by permutation of the fundamental properties, is againstOccam’s Razor; we just do not need this extra metaphysical baggage in order to

14After constructing the Ramsified lawbook, the causal/nomic role of each fundamental propertyis given by the open sentence that results by dropping the existential quantifier prefixing the variableassociated to the property under consideration.

15It is important to note that the relevant permutation concerns the fundamental properties quarelata of the causal/nomic relations included in the lawbook; it is not a permutation of propertiesamong the places defined by the pattern of their instantiation (of course, if one follows the Lewisianview about the nomic relations, the two options are intimately related.).

16For instance, besides Lewis (2009), see also Whittle (2012), Locke (2009) and Langton (2004).

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make sense of the world.Proponents of dispositional/causal structures make use of an analogous argu-

ment to argue against the existence of fundamental categorical structures.17 Yet,in order for a proper structuralistic version of MRA to be formulated, fundamen-tal structures should be conceived as properties that can be permuted within therelevant structuralistic lawbook. I suggest (on behalf of the dispositional OSR-ists) that this can be done following the ontological interpretation of structuresas holistic, “structural” properties constituted by physical relations among objectsand instantiated (if they actually do) by whole relational systems of these objects.Granted the viability of this ontological suggestion (a controversial assumption,given the difficulties presented in the previous section), dispositional OSR-ists mayproceed and formulate a structuralistic version of MRA. They just have to replacein the aforementioned formulation the term “property” with the term “structure”and point out that, in the structuralistic context, the lawbook of the world includesthe totality of nomic relations between structures.18 To give an example, providedthat the spatiotemporal metric structure is a fundamental one, the structuralisticlawbook should contain Einstein’s equations which express the nomic relation be-tween metric structure and the distribution structure of the energy-matter of theworld. After formulating the new version of MRA, dispositional OSR-ists mayproceed and draw attention to the aforementioned unpalatable consequences ofthe multiple realisability. For instance, they may stress the difficulty to accept thatthere is a possible world at which the metric spatiotemporal structure has swappedcausal/nomic roles with the structure of quantum entanglement.

In what follows, I am not going to challenge the viability of the suggested on-tological interpretation of structures. I’ll also assume that at least one of the threeobjections against the metaphysical possibility of the RNDV-worlds constitutes agenuine worry that needs a proper response for the RNDV to be viable. Givenall that, I’ll proceed to offer a plausible solution to the difficulty from MRA. Butbefore doing that, one point must be clarified. One might wonder why the whole

17See, for instance, Esfeld & Sachse (2011).18The structuralistic reformulation of MRA is based on the assumption that the available units for

free recombination required by the argument are whole structures construed as holistic properties.We may conceive those structures as possessing an intrinsic nature ‘emerged’ from their constitutiverelations. A problem might however arise when we attempt to determine the identity of structuresthemselves in structuralistic terms. A possible way out for the OSR-ist is to determine the identityof each fundamental structure via its relations to the other fundamental structures, but I am not surethat that strategy can be successful (consider the akin difficulties for the identity-determination ofmonadic dispositional properties). In any case, the identity difficulty is a problem for the disposi-tional OSR-ist who appeals to MRA as an objection to categoricalism, not for my suggested solution.In order to provide a solution to the MRA difficulty, I presuppose that the latter is a well-posed prob-lem in the structuralistic context. Otherwise, this major argument against categoricalism cannot getoff the ground in that context. I would like to thank an anonymous referee for this interesting point.

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discussion takes place in the OSR-context. After all, multiple realisability (andits bad consequences) arises in any context (structuralistic or not) which is basedon the assumption that the fundamental features of the world (or, at least, someof them) are categorical. Hence, it is a problem for realism about any categoricalfeatures and not just for categorical ontic structuralism.19 Of course, a plausiblemotivation for discussing MRA in the structuralistic context would be the beliefthat the reformulated argument posits extra or particular challenges for the ad-vocate of RNDV. My motivation, however, is not based on that conviction; it isbased instead on my belief that the whole discussion on the de re modal represen-tation of the actual fundamental features should take place within the context of ascience-informed metaphysics. Hence, even granted that MRA raises difficulties forthe categoricalism about monadic properties in the traditional context of object-oriented metaphysics, it is important to show that the MRA difficulties can be metin the context of OSR, since the latter is (despite my qualms) a serious ontologi-cal view which is (arguably) based on the findings of the most recent fundamentalphysical theories.20

3 Responses so Far

It is time now to take a closer look at the existing responses to the difficultyfrom MRA, formulated by two adherents of categorical structuralism.

3.1 Inevitable RNDV?

A first response, presented (but not embraced) by Holger Lyre (2012, p. 178), issimply to bite the bullet and claim that RNDV though problematic is neverthelessinevitable. This claim seems prima facie implausible; yet, it can be supported onthe basis of the following scenario presented by Psillos (2012, p. 177, properlymodified to fit in the structuralistic context): consider, for instance, a world w1

with two fundamental structures S1 and S2 acting in tandem to generate a certaincausal/nomic profile R. Suppose further that, at w1, S1 or S2 taken individuallydo not have any further causal/nomic role. Consider also another world w2, atwhich a single fundamental structure S has R. w1 and w2 are intuitively distinctpossible worlds because, by stipulation, contain a different number of fundamentalstructures. For the advocate of DV, however, those worlds are identical. Hence, if

19This point is important as regards the dialectic of the debate in the context of OSR because itclearly shows that the adherent of dispositional structuralism does not bring a novel argument thattargets specifically the existence of categorical structures. It by no means, however, undermines thestrength of MRA; for, if in the general context the consequences of the multiple realisability are asbad as dispositionalists claim, the specific case of categorical structures falls prey to them as well.

20A strategy akin to the one presented in the sequel can be applied in order to meet the MRA-difficulty in the case of fundamental (non-structural) properties. For details, see Livanios (2014).

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she wants to have an adequate theory of possibility that accommodates all genuinemetaphysical possibilities, she must go beyond causal/nomic roles by admittingextra metaphysical factors which are role-independent.

Lyre thinks (as I do) that the above response is inadequate; firstly, because ul-timately it does not show how to avoid the bad corollaries of RNDV. Secondly,because it is based on an argument which is indifferent between fundamental prop-erties and structures. Consequently, it cannot give to the categorical structuralistthe privilege of being the only one among categorical realists21 who manages torespond to the multiple realisability challenge. I agree with the first reason, andthat is why in the sequel I shall present my own response which aims precisely towhat Lyre points out. But I find his second reason unpersuasive; for an adequatereply to the multiple realisability argument does not have to support the superi-ority of structuralism. After all, OSR is not the only metaphysical view whichis (arguably) supported by the scientific findings and so, even in the context ofscience-informed metaphysics, it is desirable to have a response to MRA difficultycompatible with any context that allows for the existence of fundamental categor-ical features of any kind. Regardless of the previous remarks, the response underconsideration is inadequate because, though it undermines DV, it does not showthat RNDV is unavoidable. For the acknowledgement of role-independent factorsis consistent with a form of moderate NDV according to which causal/nomic rolesco-ground the de re modal representation of fundamental structures.

3.2 PISIW to the rescue?

Lyre (2012, pp. 178 – 179) presents and embraces a response to the problemfrom multiple realisability that presupposes the claim that OSR in general (andcategorical OSR22 in particular) is based on the Principle of Identity of StructurallyIndiscernible Worlds (PISIW). Here is a reconstruction of his argument:

(1) According to PISIW, all possible worlds that differ just by a permutation ofsome actual fundamental properties instantiated by particular objects, or thereplacement of the latter by aliens or idlers, are identical.

(2) OSR in general (and categorical OSR in particular) is based on the PISIW.

(3) Premises (1) and (2) imply that categorical OSR rejects the existence of dis-tinct possible worlds that differ just by a permutation of some actual funda-mental properties or the replacement of the latter by aliens or idlers.

21To avoid misunderstandings, I use the term “categorical realist” as referring to realists about theexistence of any fundamental categorical feature.

22According to the categorical OSR, the fundamental structures of the actual world are categorical.

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(4) RNDV, however, implies the existence of the aforementioned distinct worldsand the multiple realisability of the causal/nomic roles of the fundamentalstructures.

∴ Hence, categorical OSR rejects RNDV and its consequences; there is no mul-tiple realisability (and its associated difficulties) in the context of categoricalOSR.

The controversial premises of the above argument are (1) and (2). Lyre, followingLewis (2009, pp. 209-210), presents premise 1 as the relevant definition of PISIW;and he also regards premise 2 as a consequence of the fact that OSR is the view thatthe world exists up to structural isomorphism. Yet, in the ontic structuralistic con-text of Lyre’s argument, the fundamental entities of the world are structures and so,according to my view, the definition of PISIW should be properly modified. In par-ticular, PISIW should insist on the identity of all possible worlds that differ just bya permutation or replacement of the actual fundamental structures, ontologicallyconstrued as holistic properties constituted by physical relations between particu-lar objects and instantiated by relational systems of those objects. Taking that claimas the proper definition of PISIW in the context under consideration, we can showthat premise 2 is not true according to all versions of OSR (in particular, it is nottrue according to the categorical version).

To illustrate that, let us first examine the possible relationships between fun-damental structures and their causal/nomic roles. According to a strong disposi-tional essentialist account of structures, the latter have causal/nomic roles whichare their individual essences. In that case, the identity of roles entails the iden-tity of structures. According to a more liberal dispositional account of structures,however, fundamental structures are characterised by essential causal/nomic roleswhich nevertheless are not their individual essences. That means that there can ex-ist two distinct dispositional fundamental structures having the same role. Hence,the identity of roles does not entail, in that case, the identity of structures.23 Fi-nally, according to a categorical account of structures, the latter have no essentialfeatures related to their causal/nomic roles. Fundamental structures can swap roles,and so, different structures might be characterised by the same role (and the samestructure might have different roles).

Let us now assume, for the sake of the argument, that we are OSR-ists. We canthen embrace any of the previously mentioned accounts. For the argument to be

23Bird (2007, p. 72) vividly presents (in the case of properties and their powers) the motivationthat leads dispositionalists to embrace the strong form of dispositionalism: “. . . just as essentialismaims to give an account of what laws are, it may also aim to account for the nature and identityof, at least, fundamental properties. That is, not only are the powers of a property essential to thatproperty, they are the essence of the property-they constitute what it is to be that property. Thusidentity of powers entails identity of property.” A similar motivation exists for the fundamentalstructures and their causal/nomic roles.

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sound, premise 2 must be true. Hence, in order to show that the argument is notsound, it suffices to show that premise 2 is false, i.e. that according to at least oneversion of OSR PISIW need not be true. Indeed, this is the case for the categoricalversion of OSR. Since, according to premise 2, categorical OSR is based on PISIW,categorical OSR-ists should embrace PISIW. Recall, however, that, in the contextunder consideration, PISIW refers to the permutation or replacement of the fun-damental structures. So, the crucial question is: should categorical OSR-ists acceptthe truth of PISIW thus defined? Surely, they may allow, for instance, the existenceof possible worlds instantiating the actual causal/nomic roles but differ from theactual world just by a permutation of the fundamental structures. But why do theyhave to identify all those worlds? Certainly the latter have the same structures butnevertheless differ about which fundamental structure plays which role. To insist onthe identity of those worlds a categorical OSR-ist must ignore a difference which,according to her favorite view about de re modal representation (i.e. RNDV), is agenuine modal distinction.24 Things get worse when we consider possible worldsthat differ from the actual just by a replacement of an actual fundamental structureby an alien one. For in that case the categorical structuralist (which is also an ad-herent of PISIW) should identify worlds characterised by the same causal/nomicroles but populated by different fundamental structures. To conclude, the adop-tion of PISIW offers an adequate solution to the multiple realisability difficulty;PISIW, however, (in its proper for the discussion under consideration form) is ill-motivated in the context of categorical OSR. Hence, categorical realists cannotavoid the consequences of the multiple realisability simply by following OSR.

3.3 Inappropriate RNDV?

Let me now turn to an alternative response presented by Lyre in his 2012. Hereis a reconstruction of the relevant argument:

(1) Categorical structures are particular entities.

(2) Particular entities are worldbound.

(3) RNDV is an account of the de re modal representation of physical featuresthat requires their transworld identity.

∴ RNDV cannot be regarded as the correct account of the de re modal repre-sentation of categorical structures.

24The argument presupposes the transworld existence (and identity) of the actual fundamentalstructures. PISIW-ists cannot plausibly embrace the worldbound existence of the structures on painof identifying possible worlds populated by different structures (e.g., the actual world and a possibleworld populated by counterparts of the actual fundamental structures).

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Given that (according to the MRA) RNDV is a problematic account, the aboveconclusion indicates that the existence of categorical structures does not raise anyserious difficulties (at least, as far as their de re modal representation is concerned).

On my view the really problematic premise of Lyre’s argument is the third.Lyre follows the lead of Robert Black who in his locus classicus (Black 2000) claimsthat RNDV (quidditism in his terms) is consistent only with the literal transworldidentity of natural properties. This is a widely-held assumption based on a coreintuition according to which RNDV requires that there are worlds which are suchthat a property that fills a certain causal/nomic role in some of them fills a differentrole in others. And that can be held only if the property exists in all worlds underconsideration. But that is too quick. Unless we give some good reasons against theimplementation of counterpart theory in the case of properties, RNDV-ists mayclaim that a fundamental natural property can be de re represented in a possibleworld by having a counterpart in that world. Of course, the plausibility of thatclaim depends inter alia on whether RNDV-ists can address the general objectionsagainst the counterpart theory of natural properties. But as far as I can see, thiscan be done (see the relevant discussion in section 5). So it is not true that RNDVis an account of the de re modal representation of fundamental natural properties(and more generally, of fundamental natural features) that requires their transworldidentity. Hence, premise 3 is false and Lyre’s second argument is unsound.

3.4 Sparber’s ways of relating

In his 2009, Georg Sparber defends a Humean version of moderate OSR. Ac-cording to his account, fundamental structures are holistic non-localised complexsystems constituted by first-order, physically interpreted, relations relating objectswhose identity is entirely constituted by their structural relations.25 The identity-dependence of objects (which lack any intrinsic property) on the structural rela-tions they enter into implies that the latter are metaphysically necessary de re con-nections between objects. That fact, however, does not disagree with the Humeancharacter of Sparber’s proposal because in his theoretical framework objects arenot entirely distinct existents.

Sparberian fundamental structures are categorical in the sense that they haveno inherent modality; in particular, they have no disposition to enter into second-order causal/nomic relations with other structures. Their causal/nomic relationsare metaphysically contingent and (within Sparber’s unorthodox Lewisian frame-work) supervene on the contingent arrangement (that is, the spatiotemporal distri-bution) of all fundamental, non-localised structures (2009, p. 174).

25On Sparber’s view, fundamental structures need not be global (for instance, two electrons in anentangled state is a fundamental structure).

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Sparber’s defence of a consistent Humean moderate OSR is systematic and de-tailed and there is no room in this paper to do justice to his various arguments. Iwould rather focus on one aspect of his proposal which I think can be the groundfor a prima facie adequate response to the MRA difficulty. He insists that the funda-mental structures, though categorical, do not possess primitive transworld identity.On the contrary, the way fundamental structures relate objects (more correctly:the way the constitutive relations relate their relata) constitutes their essence andthe latter is the relevant ontological feature that grounds their de re modal repre-sentation. It is important to emphasise that, according to Sparber, those essencesare not defined by the structures’ dispositions. For instance, it is not its causalpowers (if any) that ground the de re modal representation of the spatiotempo-ral metric structure, but the specific way that that structure relates its objects (i.e.spatiotemporal points).

It is evident that the multiple realisability objection cannot arise in this context.Due to the suggested essence of the fundamental structures, the causal/nomic rolesof the latter cannot be multiply realised.26 So, it seems that the appeal to Spar-berian essence of relations (and structures) provides an adequate response to theMRA difficulty. Yet, I have two objections that make me to consider it as an unsat-isfactory solution to the problem. The first objection concerns its very consistencywith RNDV. According to Sparber, the suggested essence is not a quiddity-like on-tological factor inaccessible to science, but rather a ‘qualitative’ one described byscience itself (2009, p. 198). But, since the scientific findings are most often re-lated to the causal/nomic roles of the fundamental entities they describe, it is notclear whether this essence is actually independent from the causal/nomic roles ofstructures. Consequently, it is not clear that Sparber’s proposal is consistent withRNDV according to which the actual causal/nomic roles of the fundamental fea-tures of the world are completely irrelevant to their de re modal representation.

The second objection emerges from the limited application of Sparber’s pro-posal. Even if we grant him the consistency of his account with RNDV, the prob-lem remains that his solution presupposes the core tenets of his preferred versionof Moderate OSR and so cannot provide the desired solution within the context ofthe eliminative categorical OSR.27 It might be objected that the applicability to theeliminative OSR context should not be a desideratum simply because eliminativeOSR is not a viable view any way. I think, however, that the issue concerning the

26Of course, we must assume that the way structures relate objects constitutes their individualessence; otherwise, the possibility of swapping structures with the same essential way of relatingobjects arises again.

27A modified version of Sparber’s account (in which talking about objects has been replaced bytalking about “object-places”) might work in the context of eliminative OSR. Yet, my previous objec-tion related to the inconsistency with the core tenet of RNDV is still valid even in this hypotheticalproposal.

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viability of the eliminative OSR is not settled and, consequently, I take as a draw-back of Sparber’s account that it is based on premises that beg the question againsteliminative OSR.28

4 An Alternative Response

In order to provide an adequate solution to the MRA problem, I suggest thatwe start by making an assumption which Lyre also makes but uses in an erroneous(according to my view) way. In particular, I propose that we endorse the followingview:

X The fundamental structures of the world are worldbound tropes.

To support that first assumption we have first vindicate the view that funda-mental structures can be particular properties and then that, qua tropes, can beworldbound entities. Let me start with the former view. I’ve previously arguedthat in the context under consideration the actual fundamental structures shouldbe conceived as properties. Given that, the metaphysician has two available op-tions; she may ontologically interpret structures either as universals or as tropes.Although there is no unanimously accepted account of how the relevant distinc-tion can be drawn, I would here suggest to draw it in terms of multiple-instantiationcapability; that is, though both universal properties and tropes are instantiable en-tities, only the former are capable of multiple instantiation in distinct relationalsystems. The criterion surely works in the context of moderate OSR according towhich there are fundamental objects and relations between them (i.e. relational sys-tems) and fundamental structures must be ‘shareable’ and modally laden propertiesof distinct structurally similar systems.29 It can also do its work in the context ofeliminative OSR, provided that the latter is not necessarily true (recall, from 1, myreason to think of OSR as a contingent metaphysical view). Now, if the OSR-ist

28Sparber himself justifies his preference to Moderate OSR by presenting arguments against twointerpretations of the “no-relata” claim of eliminative OSR (2009, pp. 164-167). According to him,the first interpretation (that is, there is a fundamental level consisting of relations without relata)commits the eliminativist to a Platonic conception of fundamental relata-less structures. The secondinterpretation (that is, there is no fundamental level and there exist relations all the way down), asSparber sees it, is incompatible with the metaphysical principle of composition. Discussion of myobjections to his arguments is beyond the scope of this paper.

29Moderate OSR-ists insist that the fundamental structures are causally active and confer to theirbearers causal powers that do not supervene on the causal powers of the properties of their relata(otherwise, moderate OSR would turn into a version of causal structuralism). So, pace Psillos (2012,p. 172) and Busch (2003, p.221) who find this view mysterious, moderate OSR-ists hold the view thatfundamental structures are genuinely causally efficacious. For instance, Esfeld & Sachse (2011, p. 53)claim that structures are causally efficacious by enabling the objects that stand in their constitutiverelations to produce taken together certain specific effects.

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insists that distinct systems (in this world or in other possible worlds) may liter-ally share the same structure, structure-properties should be conceived as universalsand not particulars. If instead she holds that each structural trope can characterise(again in the actual world or in other possible worlds) just one relational system,then structure-properties should be conceived as tropes.30

Given the huge complexity of the issues related to the controversy betweenuniversalists and tropists, we cannot plausibly expect to have a knockdown argu-ment in favour of one of the previously mentioned views. Yet, as far as I can see,the plausibility of the trope interpretation is significantly increased if we take intoaccount the arguments against the existence of structural universals which purportto show that there is a considerable difficulty in getting an isomorphism betweenrelational systems and the alleged structural universals they instantiate (for a briefreview of this discussion, one that emphasises the relevance to the present context,see Psillos 2012, pp. 178 – 184).31 Of course, given the vast literature on the topicand the number of arguments in favour of structural universals we cannot plausiblyclaim that the issue is settled. But for the present purposes, it suffices to say thatthe trope-interpretation of the fundamental structure-properties is a consistent andplausible ontological construal which is also a part of the flourishing metaphysi-cal project of trope theory. Those facts, I think, provide an adequate justificationfor considering it as possibly true and consequently using it as a premise of thesuggested solution to the MRA difficulty.

The hypothesis of worldboundedness is not a novel suggestion in metaphysics.Lewis (1986b) famously argued for the worldbound existence of particular concrete

30According to my view, two distinct relational systems are intraworldly structurally similar if theirtropes are primitively similar. This claim accords well with the view that most trope theorists thinkas the most plausible one; namely, that particularity and individuality of, as well as the resemblancebetween, tropes are primitive. It might be objected, however, that the plausibility of the primitivistaccount of similarity is lost when we turn from the monadic tropes of particulars to the structuraltropes. It seems that we have an adequate reductive account of the similarity of structural tropesin terms of the 1:1 correspondence needed for their isomorphism. As far as I can see, there can betwo reasons to adopt a primitivist account in the structuralistic context. First, since by definitionisomorphism presupposes an 1:1 correspondence between the relata and the relations of two distinctstructures, it is not clear how it could be applied in the eliminativist (OSR) context where (arguably)the constitutive relations of the fundamental structures have no relata. Second, the very notionof isomorphism, qua indifferent to the nature of the constitutive relations of the structures, is toopermissive to capture what is intuitively similar among a number of fundamental structures.

31For instance, Lewis’s 1986a objections to structural universals applies equally well to this case(with the proviso, of course, that the problematic identical constituents of the structural universalsare all relation-universals). Both in Lewis’ example of the methane and the case of an appropriatelyselected fundamental structure, we have a structural universal with a number of identical constituent-universals and we are in trouble to provide a proper and illuminating account of the relationshipbetween the structure of the universal and the structure of the relational system that instantiates it(for an actual example of such a structure, consider the case of the metric structure and its constitutivemetrical relations which many of them can be identical).

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objects to avoid the absurdity that one and the same object may and may not haveany of its accidental intrinsic features. His argument, however, does not work inthe case of particularised properties since the only intrinsic features that any allegedtransworld fundamental natural property could have are its “nature” (whateverone think it is) and perhaps a (distinct from the nature) non-qualitative individ-uating factor and both of them can hardly be considered as accidental features ofthe property. A more promising argument in the case of tropes is based on ananalogy between the temporal and the modal repeatability. Based on that analogyone may claim that temporally non-repeatable entities can be plausibly regardedas non-repeatable across possible worlds as well. Now, according to a plausibleversion of trope theory, tropes are spatially and temporally non-repeatable and so(following the previous line of thought) they may be regarded as worldbound en-tities. The modal/temporal analogy, however, is not universally accepted and sothe hypothesis about the worldboundedness of tropes remains controversial. Nev-ertheless, and regardless of whether the previous argument succeeds, I am aware ofno arguments against the worldboundedness of tropes that cannot be answered (seeLivanios (2014) for a discussion of two relevant objections). Given that, and justlike the previously examined trope-interpretation, the worldboundedness hypoth-esis is a consistent and viable view which can be used as a premise of my proposedresponse to MRA.

What can we gain by considering fundamental structures as worldbound enti-ties? As I have already noticed, we cannot follow Lyre’s route and insist that world-boundedness is incompatible with RNDV. On my view, categorical structuralismis related to RNDV regardless of whether we conceive fundamental structures asworldbound or transworld entities. RNDV can be construed as the appropriatetheory of de re modal representation for any categorical feature, be it the inhab-itant of only one possible world or many.32 Yet, the crucial difference betweenthe two options (worldbound vs. transworld) is that only according to the for-mer RNDV does not imply the multiple realisability of the causal/nomic roles ofstructures and its bad consequences. The assumption about the worldboundednessof fundamental structures seems to dissolve the problem arising from the multi-ple realisability. It renders the multiple realisability scenario literally impossible;there is no possible world in which we can permute the actual fundamental struc-tures while keeping the causal/nomic roles intact simply because there is no worlddistinct from the actual one in which the structures under consideration literallyexist. For the same reason, there is no possible world distinct from the actual onein which we can replace an actual structure with an alien or an idle one.

32Notice that what I say here does not commit me to the truth of the IR assumption. RNDV maybe related to categorical structuralism but not exclusively. Furthermore, construing RNDV as thecorrect account of the de re modal representation of categorical features does not preclude thinkingof it as the appropriate account of any feature (categorical and dispositional alike).

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The worldboundedness hypothesis, however, does not provide by itself a plau-sible response to the MRA objection. The main reason is that it dissolves the prob-lem only by forbidding any kind of modal judgment about the possible behaviorof fundamental structures and, consequently, totally ignoring the intuitions behindthe multiple realisability scenario. In order to fix this lacuna, we have to introducean appropriate theory of de re modal representation of fundamental structures; atheory that respects the worldbound character of the fundamental structures andprovides the means to make sense of the multiple realisability problem. This the-ory, by definition, cannot be the transworld identity one. So we arrive at thesecond main assumption of my suggested solution:

X The appropriate framework for the de re modal representation of fundamen-tal structures is the counterpart theory.

RNDV-ists in general (and categorical structuralists in particular) may claim thata fundamental structure can be de re modally represented in a possible world byhaving a counterpart in that world.

Given the previous core assumptions, I now present the four premises of mypreferred RNDV-friendly version of the counterpart theory that can provide a so-lution to the multiple realisability problem. In what follows, I assume that a pro-ponent of RNDV has identified one or more non-qualitative ontological factors asthe ground for the de re modal representation of a fundamental structure S. I re-fer to that ontological factor (s) – which is, by definition, completely independentfrom the causal/nomic role of S – simply as “the non-qualitative factor (s) of S”.

An RNDV-friendly version of the property-counterpart theory for fundamen-tal structures

(1) The fundamental structure-tropes and their second-order features (which arealso tropes) are worldbound entities.

(2) Each member of the class of worldbound counterparts that corresponds toany given fundamental structure-trope S exemplifies a counterpart(s) of thenon-qualitative ontological factor(s) of S.

(3) Any actual fundamental structure S is de re represented in a possible worldby having a counterpart in this world which exemplifies a counterpart(s) ofthe non-qualitative ontological factor(s) of S.

(4) The relation holding between the worldbound (second-order) non-qualitativeontological factors is modally primitive; that is, there is nothing that can de-termine which worldbound (second-order) ontological factors belong to theclass of counterparts of the ontological factor(s) of S.

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The four assumptions taken together clearly provide an RNDV-friendly solutionto the multiple realisability problem. By accepting the worldboundedness of thefundamental structures, the suggested version renders the multiple realisability sce-nario literally impossible; and by being a kind of counterpart theory (more pre-cisely, a kind of property-counterpart theory), it certainly allows modal judgmentsabout the possible behavior of fundamental structures. Furthermore, it is consis-tent with RNDV because it acknowledges only non-qualitative factors as the solegrounds of the de re modal representation of the fundamental structures.

What are the advantages of the suggested solution? First, I take it as a virtueof the proposal that it leaves room (as it should) for the possibility of a mixed ac-count of de re modal representation according to which the grounds of the latterare role-independent and role-dependent ontological factors. This mixed accountmay (under certain conditions) do justice to the modal intuitions that ground Psil-los’s scenario. Of course, such an account may face other problems, but I take itas an advantage of my proposal that, in giving a way out to RNDV-ists, it doesnot rule out a possibility that certainly exists. Even granted the success of Psil-los’s argument, RNDV is not unavoidable and my solution respects that. Second,there is nothing that hinders the application of the proposal in the context of elim-inative OSR. Of course, this application presupposes the existence of uninstanti-ated structure-tropes and surely some metaphysicians may be reluctant to acceptthat. Recall, however, that only properties/relations can be characterised as cat-egorical/dispositional and given that eliminativists do not allow the existence offundamental concrete ontologically independent objects, there is simply no (onto-logically independent of structures) entity which can instantiate the fundamentalstructure. Finally, for all those (like me) who have qualms about the excess use ofessentialism in meeting difficulties in various philosophical fields, it is a merit ofthe suggested response to the MRA challenge that is anti-essentialist; namely, thatit does not invoke any kind of (individual) essence (not even a non-dispositionalone, as Sparber does).

5 Objections and Replies

In this final section, I discuss some possible objections to my account. Accord-ing to the first one, my suggestion looks like an ad hoc construction formulatedto save RNDV from a major argument against it. I do not think, however, thatthis true, because my solution to the MRA problem results naturally as a con-sequence of metaphysical assumptions (worldboundedness of properties, a specificversion of property-counterpart theory that abandons resemblance as a ground ofthe counterpart relation) which are internally consistent and independently mo-tivated. Though there is no room here for a systematic defence of any of those

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assumptions, I shall briefly respond to the objection that one of them, property-counterpart theory, is an implausible view. Surely, the counterpart theory of prop-erties is not a fashionable view amongst the participants of the categorical/ dispo-sitional debate. As far as I can see, there are two main reasons for that. The firstone concerns the alleged lack of motivation for adopting the counterpart theoryin the property-context. Those philosophers that put forward this reason againstthe counterpart theory insist that the latter introduces unnecessary and unmoti-vated complications in the modal representation of properties. According to thesecond reason (Locke 2012), the appeal to counterpart theory beyond the level ofindividuals generates an infinite regress that must stop somewhere by assuming thetransworld identity of some relevant feature. For instance, if we ask “what is itfor two counterparts to ‘share’ a property P?”, the proper counterpart-theoreticanswer is “the first must have P and the other a counterpart of P”. But what inturn makes one property a counterpart of another? Suppose we posit a secondorder feature of properties to ground the counterpart relation at this level. If weask “what is it for two property-counterparts to ‘share’ this second order feature?”,the proper counterpart- theoretic response is “the first must have this feature andthe other a counterpart of it”. One may continue and ask “what makes one sec-ond order feature a counterpart of another?”. If she posits a third order feature toground the relevant counterpart relation, she engages in an infinite regress. Accord-ing to Locke (2012), since the appeal to transworld identity theory is inescapable,we should think of that theory as the proper account of the de re modal represen-tation of all levels of natural features. Elsewhere (Livanios 2014) I respond to bothof these objections to the implementation of counterpart theory in the property-context. So, I shall not present any details here. Suffice it to say that, pace the firstreason and due to the flexibility of the counterpart account, it can be shown thatalmost all property theorists (opponents and proponents of dispositional essential-ism, property-identity theorists) may invoke the counterpart theory to deal withproblems emerging from their accounts.33 Furthermore, as regards the second ob-jection, we can stop the infinite regress by assuming that the counterpart relation

33Two examples to illustrate the point: a) Property-identity theorists may appeal to counter-part theory to explain how a fundamental natural property can be both dispositional and non-dispositional. Within the counterpart-theoretic framework, each fundamental natural property mayhave two distinct counterpart relations grounded on different ontological factors (a causal/nomic roleand a non-qualitative factor such as a quiddity). b) Proponents of a moderate form of DV (accordingto which the actual causal/nomic role of a natural property is essential to it but not its individualessence) may appeal to counterpart theory to accommodate the possibility of distinct natural prop-erties having the same causal/nomic role with an actual one. Transworld-identity theory precludesthat possibility because distinct properties cannot be identical to one actual property. Counterpartrelations, however, need not be 1:1 and, so, distinct natural properties can be counterparts of a singleactual natural property.

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at some level34 is primitive. That is, by taking the fact that some higher-order fea-tures are counterparts of others as a modal brute fact. Following this option, wecan deny that counterpart theory of properties presupposes the transworld identitytheory. It just presupposes, like all theories, the introduction of some primitives.

This latter remark leads naturally to the second objection to my response thatI want to discuss here; the one concerning the primitive character of the coun-terpart relations. Recall that my proposed account remains faithful to the tenetsof counterpart theory even at the level of the second-order features of the funda-mental structures. In contradistinction to Lewis’s original theory, it insists on theworldboundedness of the ontological features that ground the de re modal repre-sentation. Hence, it makes use of counterpart relations between those features.But crucially (in order to stop Locke’s regress) it regards those relations as primi-tive. The objection is that this assumption seems prima facie implausible (see, forinstance, Lewis’s qualms about primitive counterpart relations (1986b, pp. 229 –230)). Recall however (see also fn. 30) that, according to the most plausible ver-sions of trope theory, the intraworld resemblance between tropes is primitive. Isee no obvious reason not to extend this view to cover the transworld resemblanceof tropes as well. Given that this resemblance is (according to counterpart theory)the relation holding between the counterparts, I see no obstacle in claiming thatthe counterpart relation between tropes can be plausibly construed as primitive.It might be objected, first, that the primitive account of intraworld similarity ofstructural tropes is not preferable because there is a more plausible reductive ac-count in terms of isomorphism. I have already met this objection (see fn. 30).Secondly, it might be objected that my conclusion about the primitive transworldsimilarity is plausible only for the qualitative tropes of objects and its extension tothe case of non-qualitative, second-order, features of structures is not justified. Butgiven that the controversial issue is whether the counterpart relation is primitiveor not, I do not see how the distinction qualitative/non qualitative can justify adifferent treatment for each case. For I do not claim an analogy with an internalrelation of similarity between tropes which, according to one definition, obtains invirtue of the intrinsic qualitative natures of tropes. I rather appeal to the primitiveaccount of similarity of tropes which is not supposed to obtain in virtue of anyqualitative nature. If we are justified to think of a counterpart relation betweenqualitative tropes as primitive, we are equally well justified to think the same fora counterpart relation between non-qualitative tropes. Hence, second-order non-qualitative worldbound tropes can be plausibly related to their counterparts by aprimitive relation.

Thirdly, my account of the de re modal representation of fundamental struc-34On my preferred view (see in the sequel), this happens at the level of the non-qualitative, second

order, ontological features of the fundamental structures.

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tures, qua ontological one based on primitive non-qualitative counterpart relations,may raise objections related to the created gap between the modal epistemology andthe ontology of structures. According to my view, we lack any qualitative means(that is, means related to causal/nomic roles) to decide which entities are counter-parts of the actual structures. It is a brute, primitive modal fact. This is a generalobjection that targets any primitivist account of modal representation. I claim,however, that the acknowledgement of this ontology/modal epistemology gap is aprice we have to pay. On my view, Psillos’s (modified for our purposes) scenarioshows that if we want to have an adequate theory of possibility that accommo-dates all genuine metaphysical possibilities, we should step beyond causal/nomicroles and admit role-independent second-order ontological factors as grounds forthe de re modal representation of fundamental structures. Due to the exclusionof any qualitative aspect, it is impossible to provide any analysis of the (counter-part) relations relating those non-qualitative factors that inhabit different possibleworlds. Hence, the introduction of primitive (unanalysable) counterpart relationsis justified by reasons of theoretical adequacy.

Finally, consider the case of two actual fundamental structures with identicalcausal/nomic roles, or the case of time-dependent swapping of causal/nomic rolesbetween actual structures. Both cases have counterintuitive consequences akin tothe ones presented by the MRA. And in both cases we have to deal with intra-worldphenomena. Can my counterpart-based suggestion accommodate those cases? Theobvious response is that, since RNDV is not a theory concerning the intra-worldidentity (or distinctness) of the actual fundamental features (but an account of theirde re modal representation instead), it is not RNDV’s business to accommodate aputative fact of two causally/nomically duplicate structures of the same world (or,similarly, of two structures that swap their causal/nomic roles in different epochs ofthe same world). Nevertheless, RNDV (armed with the metaphysical assumptionsof my proposal) may deal with the possibility of two distinct structures engagingin those kinds of facts. For instance, two actual distinct structure-tropes with dis-tinct non-qualitative factor-tropes (and different causal/nomic roles) may have inanother possible world two distinct counterparts with identical causal/nomic rolesand distinct non-qualitative factor-tropes (which are the counterparts of the initialfactors and related to them by a primitive counterpart relation). In the same vein,if we allow that an actual fundamental structure may have multiple35 counterpartsin another possible world, RNDV has the means to deal with the possibility oftwo distinct structures swapping their roles in different epochs. In this case, each(of the initial pair) actual structure-trope has (in another world) a multiplicity

35Lewis himself (1986b, p. 230) admits the possibility of multiple counterparts in one worldto accommodate haecceitistic possibilities without the introduction of distinct possible worlds thatdiffer non-qualitatively.

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of epoch-and-world-bound counterparts characterised by distinct non-qualitativefactor-tropes (which are the counterparts of the initial factors and related to themby a multiplicity of primitive counterpart relations).

To sum up: RNDV is not a popular account of the de re modal representa-tion of the fundamental features of the world mainly because it seems to implythe multiple realisability of their causal/nomic roles which has annoying epistemicand modal consequences. Given the traditionally assumed intimate relationshipbetween RNDV and categoricality, the multiple realisabilty problem casts doubton the existence of fundamental categorical features in general. In this paper, I’vesuggested a way out for the RNDV-friendly OSR-ist on the basis of two assump-tions: first, that the actual fundamental structures are worldbound tropes and,second, that the appropriate account of their de re modal representation is a prop-erly articulated version of property-counterpart theory. The combination of thesesuppositions render the multiple realisability scenario literally impossible, while atthe same time preserving the modal intuitions/judgements that make it intelligi-ble. I’ve also pointed out that my response has some merits, among which is itsapplicability within both eliminative and moderate OSR contexts.

Of course, the current defence of RNDV in the structuralistic context doesnot show that it is superior compared to DV. The issue is far more complicated,especially in the territory of science-informed metaphysics where one has to con-sider both the metaphysical proposals about the modal features of fundamentalproperties/relations and the scientific findings and practice.36 Besides that, it is myconviction that in order to reach a verdict on the debate between DV and RNDV,metaphysicians have to take into account the role of each account in the broaderHumeanism vs. Non-Humeanism discussion. In any case, the present paper showsthat RNDV is (at least) a viable alternative account of the de re modal representa-tion of the fundamental structures. And given the supposed exclusive relationshipbetween RNDV and categoricality, it also shows that a metaphysics that positsfundamental categorical structures is possible.

Acknowledgements

I would like to thank the participants of the workshop Metaphysics of Scien-tific Realism (University of Athens, March 2013) for their helpful comments onan earlier version of this paper. This research has been co-financed by the Euro-pean Union (European Social Fund – ESF) and Greek national funds through theOperational Program “Education and Lifelong Learning” of the National Strate-

36For instance, a DV-friendly OSR-ist may insist that we have to assume that only causal/nomicfactors can be the ontological grounds of the de re modal representation of structures because interalia these factors are all we need in science.

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gic Reference Framework (NSRF) - Research Funding Program: THALIS –UOA-70/3/11604, MIS 375791.

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References

Bird, A. (2007), Nature’s Metaphysics, Claredon Press, Oxford.

Black, R. (2000), ‘Against Quidditism’, Australasian Journal of Philosophy 78(1), 87–104.

Busch, J. (2003), ‘What Structures Could Not Be’, International Studies in the Phi-losophy of Science 17(3), 211–223.

Esfeld, M. (2004), ‘Quantum Entanglement and the Metaphysics of Relations’,Studies in History and Philosophy of Modern Physics (35B), 601–617.

Esfeld, M. (2009), ‘The Modal Nature of Structures in Ontic Structural Realism’,International Studies in the Philosophy of Science 23(2), 179–194.

Esfeld, M. & Lam, V. (2011), Ontic Structural Realism as a Metaphysics of Objects,in A. Bokulich & P. Bokulich, eds, ‘Scientific Structuralism’, Springer, pp. 143–159.

Esfeld, M. & Sachse, C. (2011), Conservative Reductionism, Routledge, New York.

French, S. (2010), ‘The Interdependence of Structure, Objects and Dependence’,Synthese 175, 89–109.

Hawthorne, J. (2001), ‘Causal Structuralism’, Philosophical Perspectives 15, 371–378.

Langton, R. (2004), ‘Elusive Knowledge of Things in Themselves’, AustralasianJournal of Philosophy 82(1), 129–136.

Lewis, D. (1986a), ‘Against Structural Universals’, Australasian Journal of Philoso-phy 64(1), 25–46.

Lewis, D. (1986b), On the Plurality of Worlds, Blackwell, Oxford.

Lewis, D. (2009), Ramseyan Humility, in D. Braddon-Mitchell & R. Nola, eds,‘Conceptual Analysis and Philosophical Naturalism’, MIT Press, pp. 203–222.

Livanios, V. (2014), ‘Radical Non-dispositionalism and the Permutation Problem.’,Axiomathes (24), 45–61.

Locke, D. (2009), A Partial Defense of Ramseyan Humility, in D. Braddon-Mitchell & R. Nola, eds, ‘Conceptual Analysis and Philosophical Naturalism’,MIT Press, pp. 223–242.

Locke, D. (2012), ‘Quidditism without Quiddities’, Philosophical Studies 160, 345–363.

Methode

issn: 2281-0498165 Issue 2

Vassilios Livanios

Lyre, H. (2010), Humean Perspectives on Structural Realism, in F. Stadler, ed.,‘The Present Situation in the Philosophy of Science’, Springer, pp. 381–397.

Lyre, H. (2012), Structural Invariants, Structural Kinds, Structural Laws, inD. Dieks, W. Gonzalez, S. Hartmann, M. Stöltzner & M. Weber, eds, ‘Prob-abilities, Laws and Structures’, Springer, pp. 169–181.

Mertz, D. (1996), Moderate Realism and Its Logic, Yale University Press, NewHaven and London.

Psillos, S. (2012), Adding Modality to Ontic Structuralism: An exploration andCritique, in E. Landry & D. Rickles, eds, ‘Structural Realism: Structure, Objectand Causality’, Springer, pp. 169–185.

Sparber, G. (2009), Unorthodox Humeanism, Ontos Verlag, Frankfurt.

Whittle, A. (2012), ‘On an Argument for Humility’, Philosophical Studies 130, 461–497.

Methode

issn: 2281-0498166 Issue 2