1. Introduction

The fundamental intuition underpinning scientific realism is expressed by the so-called no-miracle argument (NMA; Putnam Reference Putnam1975, 73), according to which the success of science is to be explained in terms of the (approximate) truth of scientific theories.Footnote ¹ Standard object-oriented realism has it that successful theories are (approximately) true descriptions of individual objects that exist mind-independently and of their properties. The pessimistic metainduction (PMI) on the history of science (Laudan Reference Laudan1981), however, threatens to sever the link between success and truth by pointing to past scientific theories that were successful to some extent but are now considered false.

Structural realism (SR) attempts to reestablish the connection between success and truth by pointing to the structural continuity that exists between (some parts of some) subsequent theories across theory change. SRists propose that we take (preserved—perhaps via some correspondence principle) structure as the (approximately) true part of such theories. Epistemic structural realism (ESR; Worrall Reference Worrall1989) intends this as an epistemological position, to the effect that we can be realists about whatever is described by the (preserved) mathematical structure of our theories. Ladyman (Reference Ladyman and Zalta1998) introduced instead ontic structural realism (OSR), according to which structure is not only all we can be realist about but also all there is.

In the past decade or so, the latter idea has been developed further and has become increasingly fashionable. On the one hand, OSRists have argued that (1) it is possible to conceive of the world in structural terms, as there is nothing that remains unaccounted for when one subscribes to a structuralist ontology. On the other hand, OSRists have also contended that (2) scientific realists should endorse OSR, as a careful consideration of the best available scientific theories lends stronger support to OSR than to other noninstrumentalist positions.

The discussion of 1 has occupied most of the literature, and it appears fair to say that criticisms aiming to show that the proposed ontology is unworkable do not cause too much trouble for OSRists. Relations—and, consequently, structures—can be primitive (Mertz Reference Mertz2003), and a plausible structural reconstruction of persistence, change, and causality can be provided (French Reference French2003). Moreover, the claim being put forward (in the great majority of cases, at least; see Tegmark [Reference Tegmark2007] for an exception) is not that the world is a mathematical structure and, thus, that charges of conflating the mathematical and the physical (Cao Reference Cao2003) are off the mark. As for the objection that OSR applies only in a very limited field, it has also been answered—by extending OSR to domains other than physics (Ladyman and Ross Reference Ladyman2007; Kincaid Reference Kincaid2008; Ross Reference Ross2008).

However, much less has been said about 2—that is, about the justification for OSR. To fill this gap, it is essential, first of all, to analyze the relationship between ESR and OSR.

2. The Relationship between ESR and OSR

One may be inclined to believe that ESR is a stronger claim than OSR on the basis that it requires commitment both to structure—that is, relations—and to individuals (possibly, with monadic properties) bearing those relations. Worrall (Reference Worrall1989) does indeed echo Poincaré (Reference Poincaré1905/1952) in claiming that relations are all we know but that individual objects, which ‘Nature will hide forever from our eyes’, exist in addition to relations. However, ESR is a purely epistemological thesis concerning the preservation of structure across theory change and its usefulness for avoiding the PMI. And the Worrall-Poincaré line of thought follows from an adherence to common sense, which is natural if one refrains in this way from asking metaphysical questions. In other words, ESR does not rely in any way on a ‘positive’ ontological commitment to the existence of objects.Footnote ²

On the other hand, supporters of OSR have argued that since the basic assumption underlying SR is that we can know structure only, we should adopt a structuralist ontology if only not to create an unacceptable gap between epistemology and metaphysics. However, setting aside the fact that—to repeat—the realist does not need to say anything about metaphysics at all, it is essential to notice that the elements preserved across theory change are (or, at least, might be) different from those invoked by OSRists. The former are whatever properties (not necessarily limited to polyadic relations) are described by the mathematical structures that get preserved across theory change. The latter are, instead, genuine relations, and of a special kind (as we shall see in more detail shortly): those that play essential roles in defining specific theoretical descriptions of things, independently of previous theories (this will become clearer in what follows). In fact, that the epistemic element and the metaphysical element (may) play distinct roles is something that at least some OSRists openly acknowledge (French Reference French2006, 173). Moreover, even assuming that structural preservation suggests a structuralist ontology of the kind envisaged by OSRists, the former is not a sufficient basis for the latter—for filling the alleged gap between epistemology and metaphysics exclusively on the basis of contingent facts about what got preserved in the history of science may well lead one to ignore important metaphysical elements. In addition to the historical evidence of continuity pointed at to neutralize the PMI, therefore, a consideration of the metaphysical import of our best current theories is also required if the move from the epistemological to the metaphysical level is to be made.

As things stand, then, it seems fair to claim that OSR is in fact stronger and more committing than ESR. This is because OSR amounts to a conjunction of (i) an epistemological claim of preservation of structure across theory change (the ‘core’ structural realist thesis aimed to defuse the PMI) plus (ii) a form of eliminativist metaphysics that is an independent addition to i in the sense of being justified independently of the evidence coming from the history of science.Footnote ³

3. The Argument from Underdetermination

In the early years of OSR, the argument provided in support of its eliminativist metaphysical component, mainly by French and Ladyman (Ladyman Reference Ladyman and Zalta1998; French and Ladyman Reference French and Ladyman2003), was based on an alleged underdetermination in the ontological interpretation of nonrelativistic quantum mechanics. It can be reconstructed as follows:

1. 1. The existence of compelling reasons and of a valid alternative is a necessary requisite for the modification of entrenched metaphysical beliefs.

2. 2. Our entrenched metaphysical view of the material world is object based.

3. 3. Postulating objects as fundamental entities leads to a problematic metaphysical underdetermination (between individual objects and nonindividual objects) in the ontological interpretation of quantum mechanics—which is a fundamental theory in current physics, and certainly one that realists need to take into account.

4. 4. A structuralist reconstruction of the quantum domain, according to which objects are not fundamental, is possible.

5. 5. A structuralist reconstruction of material objects gets rid of the underdetermination mentioned in 3 and, thus, satisfies 1.

6. ∴ There are compelling reasons for adopting a structuralist metaphysics.Footnote ⁴

Premise 2 is uncontroversial, and premise 4 has been assumed to be unproblematic in this article. As for premise 1, it appears quite sensible and at least one respected OSRist does openly accept it (French Reference French2006, 177). What about the other premises?

The claim in premise 3 has to do with the fact that quantum particles have features that make them strikingly different from classical particles and the paradigmatic individual objects of everyday life. They do not obey the Leibnizian Principle of the Identity of the Indiscernibles (PII), as they can have all the same properties,Footnote ⁵ and they are ‘indistinguishable’—that is, very roughly, while there are two ways in which two coins can be one heads-up and the other tails-up, there is only one way in which two fermions can be one spin-up and the other spin-down. It allegedly follows from this either that particles are nonindividuals—they do not have well-defined identitiesFootnote ⁶—or that they are individuals whose individuality is not analyzable in terms of qualitative features (and is provided, instead, by bare particulars—‘haecceitates’ or what have you) and whose statistical behavior is due to some specific nonclassical aspect of the relevant domain.Footnote ⁷ The nonindividuality option appears naturally to explain the impossibility of individuation via description or direct reference and the peculiarity of quantum statistics (‘no identities to be permuted’). The individuality view, on the other hand, agrees with common sense and with the ontological presuppositions that hold true in the classical domain.

According to OSRists, there are no conclusive arguments in favor of either option (rather, there are problems on both sides), but the metaphysical dilemma can be dissolved altogether by opting for a structuralist perspective that posits relations, not objects, as fundamental.Footnote ⁸ However, consider again the two metaphysical ‘packages’ just identified. To be sure, each one of them meshes better with some specific metaphysical theses about objects, properties, and identity conditions than with others. And, indeed, it is equally uncontroversial that there is no way to choose one package, with its related set of metaphysical theses, rather than another exclusively on the basis of the available data. But this is not a problem for the typical metaphysician. For, far from expecting to be able to extract well-defined metaphysical theses from the best-available scientific descriptions of things, the typical metaphysician (I contend) always anticipates that this is normally not the case and that other factors will have to be brought to bear. As a matter of fact, the typical metaphysician starts from metaphysical views—arrived at on mostly a priori grounds—and evaluates how these fare with respect to a range of considerations, including, but not reducing to, an assessment of how those views fit with the input coming from the actual world. In view of this, it seems fair to say that in the case under scrutiny, metaphysicians (at least those who have clear opinions about the constitution of material objects and the individuation of those objects) would simply disagree with the claim that there is a problematic underdetermination. An ontological account of the relevant domain, they would argue, can be provided in the framework of either one of the two object-based ontologies—one just needs to be clear about the assumptions used to do this (and the consequences of each interpretation).Footnote ⁹

A sensible reply to this is that a priori considerations never provide us with firm grounds for choosing one set of assumptions over others, and so we can (and should) only do metaphysics a posteriori, so dismissing traditional metaphysical arguments altogether. That this is what OSRists think is suggested by the fact that in the extant formulations of the argument under consideration, OSRists just state that there are different object-based accounts of the particles’ nature and do not engage a critical examination. The problem with this reply, though, is that the OSRist claim being assessed is simply that standard object-oriented realism, based as it is on traditional metaphysical presuppositions, meets with an insurmountable problem of underdetermination when it comes to interpreting quantum mechanics. At no point are methodological considerations about what counts as ‘proper’ metaphysics brought into play.

In light of all this, it appears legitimate to reject premise 3 above. But let us accept that premise for the sake of argument. At least two interrelated questions are left outstanding: Is not the structuralist option also underdetermined by the available evidence? Why exactly should one think that it provides a way out of the underdetermination being pointed at?

As for the first question, perhaps the thought is that the structuralist view is not a third option but, rather, a sort of ‘synthesis’ of the individuality package and the nonindividuality package (see n. 8). That this is not the case, however, appears quite clear: both the individuality and the nonindividuality views are based on objects and monadic properties (possessed by or constituting the former) as fundamental; consequently, relations do not constitute a ‘common core’ shared by the two. Moreover, if a synthesis is what one is looking for, there are a large number of properties that are shared by the two accounts and about which a realist can be realist without also taking a stance regarding the nature of objects in general—certainly without being led to take only relations seriously.Footnote ¹⁰

For what concerns the second question, OSRists often say that one should reconceptualize the quantum domain in terms of physical structures as primitives, from which objects ‘emerge’ as relational ‘nodes’ (French Reference French2006, 183). But (even) if objects emerge, do we not have to account for their (non-)individuality anyway? Compare this with mathematical structuralism. Even once each element, say, in the structure of natural numbers is defined purely structurally, every natural number has definite identity conditions. Therefore—at least relative to one's assumptions about what being an individual exactly means—one is in a position to state whether natural numbers are individual or nonindividual objects. What about physical objects? The only reaction available to OSRists seems to be to regard such objects as entirely ‘epiphenomenal’ and, thus, as not requiring (or permitting) any metaphysical elucidation. This is enough to suggest that it is far from clear that structuralism is the most natural and least costly solution to the (alleged) problem of underdetermination. In light of this, one may legitimately put premise 5 into doubt. More generally, there are grounds for contending that the argument for OSR that is based on the (alleged) underdetermination of metaphysics by nonrelativistic quantum mechanics is unsound and, thus, cannot constitute the basis for a compelling justification of OSR.

4. The Argument from the Primacy of Relations

If the arguments presented in the previous section are correct, merely ‘negative’ considerations against other forms of realism (based on the alleged shortcomings of those alternatives with respect to the interpretation of physical theory) are not sufficient for a persuasive justification of OSR. Consequently, the OSRist will have to provide direct, ‘positive’ support for his or her structuralist ontology. This leads us to the critical assessment of a second argument for OSR that can be found in the recent literature.

It has been contended (Saunders Reference Saunders2006; Muller and Saunders Reference Muller and Saunders2008; Muller and Seevinck Reference Muller and Seevinck2009) that quantum particles are not discernible on the basis of the ‘canonical’ versions of PII—which only quantify over monadic properties—but are, in fact, discerned ‘weakly’ by nonsupervenient, irreflexive, and symmetric relations such as ‘has opposite spin to’ and, consequently, via some Leibnizian principle that takes relations of this type into account. At least once one accepts that metaphysically genuine relations need not be reducible to monadic properties or depend on the existence of already well-defined relata, such weak discernibility of quantum particles entails that the nonindividuality option above is untenable. This, in turn, may seem to mean that the underdetermination is broken and, as a consequence, that OSR is undermined. However, Muller (Reference Muller2011) contends that only the first conjunct of this latter claim is true: for, objects that are only weakly discernible depend entirely on relations for their identity and that such relationals fit the structuralist picture perfectly well. In fact, Muller argues, the ‘discovery’ that quantum particles are relationals is very good news for the OSRist. This is the case, of course, provided that not only the identity-determining factors but all properties are shown to be (reducible to) relations.

It does not come as a surprise, then, that a structuralist analysis of all physical properties has been undertaken by several philosophers, with the aim of showing that objects and monadic properties are ‘idle’ and play no role whatsoever in physical theory and that, consequently, there are good reasons for believing that nothing exists over and above structure.Footnote ¹¹ Notice that, quite importantly, what must be shown for this argument to be effective is not only that all properties of things depend on things other than those exemplifying them (i.e., that no property is intrinsic) but also that—more strongly—every property is a relation.

OSRists customarily quote or mention historical figures such as Cassirer, Born, Weyl, and Eddington as authoritative exponents of the view that objects coincide with the identification of invariants with respect to the mathematics relevant to the theory and then connect these historical remarks to more theoretical considerations (French Reference French, Butterfield and Pagonis1999, Reference French and Ladyman2003; Ladyman Reference Ladyman, Ross, Spurrett and Collier2009, sec. 4.1). Muller (Reference Muller2011), for example, argues that the (allegedly) monadic and intrinsic (essential) properties of quantum particles are, in fact, invariants of the symmetry groups that define the qualitative features of quantum mechanical systems and are, consequently, reducible to the relations that constitute those groups (see also Castellani Reference Castellani and Castellani1998 and French Reference French2000). Others (Kantorovich Reference Kantorovich2003; Lyre Reference Lyre2004) argue in analogous fashion that in gauge quantum field theories objects are secondary to structure because symmetries are fundamental in the constitution of fields. In general, OSRists interpret the mathematical nature of physical theory and the fact that all physical properties must be ‘extracted’ somehow from symmetries and invariants that can be traced in the formalism of the theory as clear signs that the things described by the theory and their properties are themselves reducible to the relations that define such symmetries and invariants.

Now, whether or not this way of drawing metaphysical consequences from features of the language that we use to describe things is considered acceptable—a complex issue we will not discuss here—it seems undeniable that the claims made by OSRists in the present context are considerably unclear. What does it mean, exactly, that objects and properties are/reduce to invariants or that symmetries are ontologically prior to objects?

As a matter of fact, it looks like an important distinction is overlooked (or consciously ignored) here between the formal definition of general, abstract properties, on the one hand, and the concrete property-instances that exist in the material world, on the other hand. Indeed, the claim, say, that objects and properties can be picked out via the identification of invariants across transformations in the groups that define the relevant theoretical structure seems to rest on a fatal conflation of these two elements. When one focuses on invariants and the like, one moves at a high level of abstractness, involving the ‘general properties of the general properties’, so to put it, of types of things. Object-tokens and property-tokens can certainly not be ‘found’ there. For instance, one can say (with Weyl) that all quantum numbers are indexes characterizing representations of groups, but while this provides the basis, for instance, for distinguishing fermions and bosons at the abstract theoretical level, it does not in any way ground a reduction of the actual properties of an actual fermion or boson, which (perhaps with the exception of spin) simply are not the immediate referents of those indexes. Thinking otherwise would be like, say, expecting the actual causal features shared by colored material things to be reducible to the general features shared by abstract concepts and words such as ‘redness’, ‘greenness’, and so forth.Footnote ¹²

Note that the difference involved here is a difference of category: on one side, there are the properties of the abstract, formal structures used to describe the physical world and, on the other side, the properties of concrete things. Consequently, it will not do for the OSRist to just claim that the specific property-instances of specific actual objects can be extracted via a structural analysis of the theoretical apparatuses employed for describing individual physical systems,Footnote ¹³ for although that would (perhaps) deflate the general/particular distinction, there would still be a gap between the concrete and the abstract.

The only remaining option for OSRists is to refuse the request for philosophical analysis on the basis that there is no need to explain how the physical is to be extracted from the abstract. But this can mean only either that (i) the physical is eliminated and abstract structure is directly invested with the role of ontologically fundamental entity or that (ii) the abstract and the concrete are indeed distinct but, nonetheless, the specific way in which they are related is sufficiently graspable for OSR to be compelling without further elaboration.

Option i amounts to a form of realism about mathematical, not physical, structure (for something going in this direction, see Tegmark [Reference Tegmark2007]). Besides having been ruled out at the outset here, such a view is certainly a minority view—and one that is more revisionary than one would hope among OSRists themselves. As for option ii, it seems to be the view underlying, for instance, Ladyman and Ross's refusal to say anything about what makes a structure physical rather than mathematical (Reference Ladyman2007, 158). However, such a refusal will hardly appear motivated to those not already convinced by OSR. To be sure, any revisionary thesis bears the burden of proof, that is, needs to be supported by explicit arguments when it comes to a comparative assessment.

Nor is the case for OSR made any stronger by a further consideration of contemporary physics. Muller, for example, mentions results related to relativistic quantum field theories (the ‘Casimir effect’—showing that the physical vacuum contains no particles but is not devoid of physical activity—as well as existing proofs to the effect that both the number and the localizability of particles become frame dependent in a relativistic context) to conclude that objects really find no room in our best science anymore and that we should, consequently, make do with relations only. However, to what extent do these results put into question the notion of an object rather than ‘just’ the concept of a classical (i.e., well-localized, etc.) object? And is structure the only—or, at any rate, the most obvious—alternative? Or, consider space-time physics: while the hole argument and related considerations certainly represent a problem for the naive substantivalist, it is far from generally agreed that a structuralist understanding of space-time is the most plausible option in view of them. In conclusion, then, the argument for OSR based on the (alleged) priority of relations over objects and monadic properties—witnessed by contemporary physics—can also be deemed unsatisfactory.

From this and what was said in the previous section, it can be concluded that both arguments provided so far in support of OSR are unconvincing. In fact, once they are appropriately disentangled and analyzed, it can be seen that several considerations are often run together based on the erroneous feeling that they complement and strengthen each other. This gives the wrong impression that a full-blown argument for OSR has been provided. To the contrary, OSR may well be a possible realist position, but it is far from clear that it has been supplied with a compelling justification and, therefore, that it truly is the most forceful option available to the scientific realist.