RECENT DEBATES OVER STRUCTURAL REALISM

DANIEL MCARTHUR

SUMMARY. In recent years Structural Realism has been revived as a compromise candidate to resolve the long-standing question of scientific realism. Recent debate over structural realism originates with Worrall’s (1989) paper “Structural Realism: The best of Both Worlds”. However, critics such as Psillos contend that structural realism incorporates an untenable distinction between structure and nature, and is therefore unworkable. In this paper I consider three versions of structural realism that purport to avoid such criticism. The first is Chakravartty’s “semirealism” which proceeds by trying to show that structural realism and entity realism entail one another. I demonstrate that this position will not work, but follow Chakravartty’s contention that structural realism need not imply that scientific knowledge can only be of mathematical structure. I advance from this conclusion to sketch a version of structural realism that is consistent with recent deflationary approaches to the scientific realism question. Finally, I consider a third approach to structural realism Ladyman’s “metaphysical structural realism” which tries to avoid the difficulties of earlier versions by taking structure to be ontologically primary. I show that the deflationary approach to structural realism undermines the rationale behind Ladyman’s approach. Key words: Scientific realism, scientific theory change, structural realism, James Ladyman

1. introduction Originating with Poincar´e (1905) and before, structural realism (henceforth SR) is a view of scientific theory change asserts that equations, that are retained across instances of theory change, pick out relations that are at least approximately true. This, supporters claim, explains why such equations can be successfully retained across an instance of theory change. While SR commits to knowledge of structure, (i.e. the equations that describe relations) it does not commit to knowledge of the nature of the entities in the retained equations. For its supporters, such as Worrall, SR represents a congenial compromise position that accommodates the main argument from the “no-miracles” argument for scientific realism (Worrall, 1989). “No-Miracles” is the thesis that the success of science stands in need of explanation, the explanation being that successful theories are successful because they are, at least, Journal for General Philosophy of Science (2006) 37:209–224 DOI: 10.1007/s10838-006-9022-5

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approximately true. SR’s restrictions on the knowledge of “nature” recognises that much of the constituents of science do not survive instances of theory change. Entities such as “ether” and “caloric” are cases in point. However, SR has been subject to considerable criticism recently, most notably by Psillos (1995, 1999, 2001). Psillos argues that the structure/nature distinction provides an implausible version of nature. Structure and nature form a continuum for Psillos. They are not wholly distinct since much of what one might consider “nature” is expressed by laws that entities obey, laws that come in the form of equations, i.e. structure. For example, part of lights “nature” in several classical theories of light is that it propagates as a transverse wave, but this “nature” is expressed in equations that survived instances of theory change. In this paper, I consider three versions of SR that purport to avoid this difficulty. The first is Chakravartty’s so-called “semirealism.” I demonstrate that this position will not work, but follow one of Chakravartty’s main suggestions, namely his contention that SR need not imply that knowledge can only be of “nature.” I advance from this conclusion to sketch a version of SR that is consistent with what have been described as “deflationary” approaches to the scientific realism question. Finally, I will look at a third approach to SR. This version is Ladyman’s so-called “metaphysical structural realism” which tries to avoid the difficulties associated with earlier forms of SR by taking structure to be ontologically primary. However, I demonstrate that my version of SR undermines the rationale that motivates Ladyman’s account. 2. chakravartty’s s emirealis m In his paper, “Semeirealism” Chakravartty advances the thesis that SR and entity realism entail one another. The two, he contends, fold together into a single position that he calls “semirealism”. I will take issue with this claim. However, I will show that there is some merit in Chakravartty’s notion of semirealism and that suitably reformulated it can help outline a plausible version of SR. Entity realism consists of the thesis that science does provide knowledge of a mind independent reality. It does not follow the strongest realist thesis that claims that science provides complete knowledge of unobservables and their properties. In Chakravartty’s characterisation entity realism divides the properties of unobservables into two types: detection properties and auxiliary properties. The former represents the causal properties of an unobserved entity whereby its existence can be detected. Auxiliary properties, on the other hand, represent other causal properties the entity may have but that are not involved in detection

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(Chakravartty, 1998, pp. 394–395). Entity realism holds that science gives us knowledge of detection properties but not auxiliary properties. While reference to entities, which are referred to by scientific theories, survives instances of theory change, their detection properties will be retained but not necessarily their auxiliary properties. Chakravartty borrows an example from Worrall (1989), the case of the transition from Fresnel’s wave optics to Maxwell’s electromagnetic theory of light, in order to illustrate what is at issue for his reading of entity realism. Fresnel’s wave optics provide a set of equations that describe how (non-polarised) light propagates as a wave at right angles to the direction of incidence. The amplitude of the wave corresponds to the intensity of the light. This aspect of light is retained in Maxwell’s electromagnetic theory, which retains the equations that describe how light propagates. These properties, then, are the detection properties. However, in Fresnel’s theory the intensity or amplitude corresponds with the magnitude of the displacement of particles in the elastic ether. This view is not retained in Maxwell’s theory. Since this thesis is not involved in the detection of light’s wave like behaviour, it can be seen as belonging to the auxiliary properties to which entity realism is not committed (Chakravartty, 1998, p. 396). In his account of SR and its relation to entity realism, Chakravartty characterises it as follows. Science reveals the mathematical structure of reality, mathematical equations are preserved across instances of theory change and express real relations (although nothing of the relata is known) and different ontologies are consistent with any given mathematical structure. SR responds to observations made by Laudan (1984) and others to the effect that many of the constituents of superseded scientific theories (such as ether, caloric, phlogiston, etc.) have not survived to be included in current theory. SR restricts epistemological commitment to structural relations, accepting that the relata might someday go the way of the caloric. SR and entity realism might seem like opposite positions. Entity realism commits to the belief in entities, but accepts that many of their properties may not survive theory change. SR on the other hand, commits to structural relations and avoids commitment to the entities that stand in those relations. However, Chakravartty argues that when entity realism’s conception of “property” is considered more closely, SR and entity realism can be seen to entail one another. Detection properties for entity realism, as we have seen, are those causal laws that are involved in detecting the entity in question. Entities possessing these, in entity realism, can be believed in (following Hacking, 1983). The same is not true for auxiliary properties. However, detection properties are what SR has in mind by structural relations.

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Thus entity realism is committed to the thesis that structural relations are known and survive theory change. Thus, for Chakravartty, entity realism entails SR. Chakravartty also contends that the reverse is true. SR denies that anything can be known about entities (other than the relations that they stand in), it must nevertheless, for Chakravartty, still be committed to the existence of entities. The Structural Realist must believe that something stands in the relations it picks out. As we have seen, in Chakravartty’s view the bare existence of an entity plus some of the laws that it obeys amounts to entity realism. Both views amount to the same position, semirealism. Semirealism for Chakravartty represents a compromise position that avoids what he takes to be the difficulties that plague rival positions on the realism question, especially other versions of SR. One of its key virtues, for Chakravartty, is its ability to avoid the sorts of problems that Psillos raises. Specifically, Chakravartty has in mind the accusation to the effect that SR imports a false distinction between structure and nature, noting that a great deal of “nature” amounts to laws (expressed as equations) that entities obey. Denying knowledge of nature, seen this way, is to render the idea of structure empty. For Chakravartty semirealism responds to this critique by drawing attention to the distinction between detection properties and auxiliary properties. Chakravartty argues that his re-reading of SR, which permits knowledge of at least some nature (in the form of detection properties), avoids the accusation that SR holds an implausible and false distinction between structure and an unknowable-in-principle nature. Nevertheless, some difficulties attend Chakravartty’s thesis that entity realism and SR entail one another. The reason for this can be appreciated by returning again to SR’s distinction between structure and nature. Chakravartty is quite correct that the structure and nature distinction is only untenable if it supposes that nature refers to an unknowable metaphysical substrate. Chakravartty identifies detection properties as an attractive view of nature. These, for Chakravartty, are retained along with the relations in which the entities possessing the properties stand. However, Chakravartty has failed to take due account of some subtleties in the distinction between structure and nature. Chakravartty, along with Psillos, is correct in the contention that what nature typically refers to are basic properties and laws that an entity obeys. However, such a definition of nature is necessarily not at odds with the standard reading of SR. The main point of Worrall’s SR, is that while equations are retained (as a limiting case or otherwise) across instances of theory change, the referents might not be. No explicit entailment exists about how the natures of the referents are to be defined, only that their definitions might not be retained. Seen this

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way, the distinction that is important to SR is not a distinction, within a theory, between testable mathematical relations and an unknowable “nature” of their terms. Rather the distinction is between various properties that define a term’s nature and particular contexts (i.e. specific equations) in which such terms (perhaps defined in other equations) are related to others. The definition of a term might change, as the definition of amplitude-intensity did in the Fresnel/Maxwell case, but some of the equations in which it is used are retained. So far, this account of the structure/nature distinction is in keeping with Chakravartty’s detection/auxiliary property distinction because the elastic properties of Fresnel’s ether (which, for Maxwell, do not define intensity-amplitude) clearly fall under the rubric of auxiliary properties. A slightly closer look at the same case study displays some shortcomings in Chakravartty’s account. For entity realism, detection properties remain constant across theory change. Chakravartty’s reading identifies these with Fresnel’s wave equations and the means by which they are tested. However, in the account of SR’s distinction between the properties and laws that define a term and the equations in which the term is used, nothing requires that these properties and laws remain across theory change, only some of the relations in which the term is employed. For Chakravartty’s claim that entity realism and SR mutually entail one another to hold water, it is necessary that new properties (auxiliary or detection) that are introduced by the new theory do not revise the conception of the term to the point where it cannot really be said to be the same entity referred to by the old theory. Chakravartty (following Psillos, 1995) denies that the redefinition of intensity falls in the Fresnel/Maxwell case into this category. The point is considerably stretched since the properties of the disembodied field are not at all like the ether (amplitude corresponds to variation in charge strength, not displacement of molecules), to call them the same “entity” is to tax the basic idea of entity realism rather severely. However, I will not dispute the point at length because the idea totally breaks down when contemporary theories of light are considered. Maxwell’s equations do still hold as limiting cases in modern theories of light. However, in modern quantum mechanical theories of light (even as limiting cases) the amplitude-intensity is defined very differently again. This time not as a wave at all, but in terms of the properties of photons (i.e. the probabilities for their detection in a given location and the quantity detected there). This cannot be reconciled to older accounts of intensity at all. To say that properties of the ether and of photons refer to the same entity is to reduce entity realism to triviality by pointing out nothing more than the fact that new theories

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and old all seem to refer to “something”. The point becomes even more telling since one cannot relegate the redefining features of modern theories to dispensable auxiliary status since exactly the redefined features, like intensity relating to photon quantities, have long since passed from auxiliary status to become detection properties. This point does not rule out Chakravartty’s thesis that entity realism entails SR. If an entity’s nature is defined, to a large measure, as Chakravartty claims, then the mathematical structure of detection properties is retained across theory change. However, the reverse is not the case. In the case of intensity-amplitude, even if Chakravartty is able to defend the notion that Fresnel and Maxwell were referring to the same entity the notion cannot to be stretched to cover subsequent instances of theory change. The main problem facing semirealism is that if SR’s central insights are to be taken seriously then a non-trivial role for entity realism is cast into serious doubt. That said, there is much in semirealism that is in keeping with a plausible reading of SR and this is the topic of the next section.

3. a deflationary approach to s tructural realis m One strategy for someone wishing to defend SR is to try to maintain a viable reading of the structure nature/distinction while, at the same time, denying (as Chakravartty suggests) that SR always entails that nothing can be known of nature. One way to proceed is to base such an account on the distinction that I sketched between the definition of a term and the equations in which it is employed rather than on Chakravartty’s distinction between auxiliary and detection properties. Approached this way, SR helps us understand the retention of equations when the definitions of their terms change, but has little to say about how they are to be defined or whether current definitions need be regarded as true. When so characterised, the structural realist account can be seen to be useful in those instances where some mathematical structure is retained after an instance of theory change contexts where the terms of these equations bear quite different interpretation. Such situations are quite common. The Fresnel/Maxwell case is the main example cited. Other examples are easily found. Quantum mechanical accounts of light average out to approximately correspond to the classical equations at macroscopic scales. In this case too, the interpretation of the intensity of light is profoundly re-conceptualised, this time in terms of agglomerations of photons, but Maxwell’s equations still represent limiting cases. Also, the equations of classical physics are retained for practical use in many everyday situations

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even though concepts such as mass are re-defined in contemporary relativistic physics (and not for instance as a conserved quantity). Although I contended that SR is a useful way to interpret such cases, it has little to say about the proper interpretation of the terms in current, unreplaced, and well-confirmed equations. It is reasonable to expect that philosophers and scientists alike will regard the constituents of current theory with variable commitment. This is appreciated by Psillos who notes that it is not the case that “one must believe everything that a scientific theory predicates of the world to an equal degree or, else, believe in nothing but observable phenomena” (Psillos, 1995, p. 44). The deployment of SR to account for the retention of equations and not the current interpretation of their terms is quite consistent with any number of positions with regard to the interpretation of the constituents of current theory. Such a role for SR is consistent with the increasingly popular deflationary approach to the scientific realism question. This view is well summarised by Psillos’ observation noted above. The central point of such a view being that global positions, on the realism question are to be avoided. The correct stance in particular instances being established locally, depending on the details of the situation in question (cf., Sismondo, 1997; McArthur, 2002, 2003 for characteristic presentations of the view). SR is a useful way to regard certain structural constituents in current theory that have been retained from older previously replaced theory. It also provides a useful way to analyse certain instances of theory change where the constituents of a theory are considerably re-conceptualised but at least some mathematical structure is retained. The distinction between the interpretation of a theory’s constituents and the context of their deployment provides a clearer account of the central distinction of SR than the problematic structure/nature distinction that critics like Psillos (1995, 2001) claim it is tied to. Moreover, nothing in that distinction precludes scientists from taking any number of stances with regards to the truth of the definitions of the terms used in the equations (old or new) that make up current well-confirmed theory. Nothing in the structural realist view of theories precludes either a provisionally realist or, say, an empiricist reading of the content of current theory. Some of this content will warrant realist belief and some will not. SR then, must find its place within the pluralist philosophical environment described by deflationary interpretations of science. If my arguments are sound, while not perhaps providing a comprehensive solution to every situation where the question of scientific realism is in some way germane, it provides a useful resource to clarify our understanding of a large body of common situations.

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Such a deflationary approach to SR possesses certain advantages over semirealism. Semirealism, tries to maintain the central plank of entity realism through its contention that subsequent theories refer to the same entity. The claim that SR entails entity realism can easily lead us to loose sight of the central observation of SR: although considerable conceptual disruption takes place in instances of theory change, mathematical structures often (i.e. equations) survive such upheavals. Semirealism leads to a dead end through fruitless efforts to demonstrate that new theories refer to the same entities as those they replace. The deflationary approach to SR accommodates the retention of equations in a more satisfactory manner. This is so because it can retain SR’s main thesis that equations are retained because they represent real relations without at the same time supposing that the terms of those relations refer to the same entities in both the old and new theories. Moreover, this approach can maintain this view while avoiding criticism that it rests on an untenable structure/nature distinction. This is so because it has not rendered our understanding of nature empty through the implausible claim that nothing of it can be known. In fact it permits “nature” to be defined in structural terms as Psillos (1995) has suggested. The contemporary definition of intensity of light, for example, may well employ other equations found in current theory, but this does not alter the fact that intensity still figures in Maxwell’s (limiting case) equations that are retained from the older theory. The deflationary approach is less limiting than semirealism, which always maintains that anything retained must be able to be understood from the perspective of entity realism. However, one could try to resist the deflationary view’s ban on an a priori approach to the realism question by attempting to formulate a workable version of a thoroughgoing structuralism (i.e. denying the possibility of knowing anything of “nature”). Ladyman proposes just this, and has prominently advanced a position recently that takes structure to be ontologically primary. I will address this strategy next and show that its prospects are not promising. 4. ladyman’s metaphys ical s tructural realis m Ladyman presents his position by drawing a distinction between two species SR, “epistemological” and “metaphysical”. Ladyman associates epistemological SR with those versions of SR that date from earlier periods, (Maxwell’s, 1970 or Russell’s). These positions clain that only the structural relations unobservables engage in can be known i.e. nothing can be known of their “nature”. In Grover Maxwell’s case the notion is explicated in terms of a theory’s Ramsey sentence.

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The Ramsey sentence eliminates reference to theoretical terms. Consider a theory T that has been formalised in a first-order language and contains two kinds of vocabulary: T (t1 , t2 , . . . , tn , o1 , o2 , . . . , on ) where (t1 , t2 , . . . , tn ) are theoretical terms and (o1 , o2 , . . . , on ) are observational terms. The resulting reduction from the Ramsey replacement is ∃x1 , ∃x2 , . . . , ∃xn (x1 , x2 , . . . , xn , o1 , o2 , . . . , on ) where the theoretical terms formerly enjoying an interpretation are replaced with existentially quantified bound predicate variables. The Ramsey sentence refers to theoretical entities only through their logical form. It only says “there are some objects properties and relations that have certain logical features” (Ladyman, 1998, p. 412). The resulting view is epistemological structural realism, nothing can be known of unobservables other than the structural relations that they engage in as expressed in a theory’s Ramsey sentence. Serious difficulties attend this view. As Demopoulos and Friedman (1985) point out, any two theories with the same empirical content can be given the same structure (i.e. they have the same Ramsey sentence). Claiming that only structure can be known tells us little of value. In other words epistemological SR amounts to nothing more than a version of strict empiricism, since any two empirically equivalent theories are equally true, and of course supporters of SR, like Worrall (1989), would like to commit to significantly more than this. For Ladyman, SR must find a balance. It must commit to ontologically more than strict empiricism, but it must “stop short” of realist commitment to a theory’s full ontology (Ladyman, p. 415). Ladyman proposes that his “metaphysical structural realism” (henceforth MSR) is the version of SR that can strike this balance. MSR takes structure to be ontologically primitive, where theories are seen as collections of models, not sets of sentences. For Ladyman the criticism that has been directed against epistemological structural realism (whether Maxwell’s or Worrall’s) presuppose the “received” view of theories. That is, it takes them to be sets of sentences. However, following Giere (1985), Ladyman rejects the received view in favour of the so-called “no statement view” and contends that once one takes scientific theories to be collections of models, that can be described by any number of linguistic formulations, SR becomes a more natural option. This is so because the no-statement view emphasises structure, i.e. the structures of the models that comprise a theory (which Ladyman proposes to construe using group theory, cf., 1998, p. 420). Since the various problems that have been identified with SR relate to the versions of it that employ an ontology of objects, properties and relations rather than an ontology of models, Ladyman finds the view attractive (cf., Ladyman, 1998, p. 418). Psillos’ objections to SR, for example,

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attack the distinction between the structure and the nature of objects or entities whose relations to each other have the structure in question. Taking structure to be primitive, i.e. what is real, allows a genuinely realist reading of theory change, while avoiding difficulties that attend the versions of SR that rely on ontologies of objects. That is, it permits SR to capture the main insight of the “no-miracles” argument, where the structure depicted by science is what is taken to be real and all that is real. Moreover, MSR also purports, like all versions of SR, to be able to deal with instances of theory change. It can accommodate, “the continuity of mathematical structure that is found even between theories that differ radically. . .and so would not be confounded by theory change” (Ladyman, 1998, p. 418). MSR has attracted criticism. According to Cao, one objection that can be raised against it is that it can stifle development of more fundamental theories by resting content with current structural understanding (cf., Cao, 2003). Cao also notes that this sort of difficulty has arisen before. For Cao, the decline in interest in S-matrix theory can in part be explained because it, along with Gell–Mann’s purely structural investigations of quarks, had “an unproductive implication of giving up exploring deeper than the level of structures available to us now” (Cao, 2003, p. 12). A closely related objection associates MSR with a version of Platonism that remains at the level of existing structure because it denies the existence of anything else. While I think that French and Ladyman can respond to these objections, their existing rebuttal misses its mark and even undermines MSR to an extent. They reject the accusation of unproductivity by claiming that MSR does not preclude the search for deeper physical understanding. They also deny that it implies, like certain forms of Platonism, that the only real things are mathematical structures. They note, “to describe something using mathematics does not imply that it is itself mathematical” (2003b, p. 75). This answer will not do. On the face of it this answer responds to MSR’s critics by adopting a form of epistemological SR and in fact abandons thoroughgoing structuralism as its critics, such as Cao, suggest it should. However, Ladyman elsewhere (1998) states that MSR denies the reality of object or “nature” beyond structure. Oddly, Ladyman’s response is that structure can nevertheless be distinguished from the mathematics by which it is known. However, this answer leaves MSR open again to Psillos’ objection. Here MSR distinguishes between the representation of structure and its real, non-mathematical, nature, distinct but inexpressible in-itself. But how are we to understand this nonmathematical nature-of-structure? This non-mathematical, yet real, nature-of-structure seems to inadvertently re-introduce the same sort of

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unknowable-in-principle metaphysical nature that Psillos (1995, 2001) has rightly decried. However, A less problematic response to Cao’s objections is available to MSR. Ladyman could try to accommodate the search for objects and causal processes lying behind current structure by advocating the search for hitherto unknown structural relations. Believing in a particular set of structures, and believing that there only are structures, does not imply that one knows all about all the structures that there are. Be this as it may, Cao’s objections do succeed in showing that MSR accommodates fundamental physics practice less naturally than epistemological SR. This is so because much of this practice explicitly stems from an object ontology that seeks new and more fundamental causes and objects on deeper levels than that of current structure (cf., Cao, 2003, pp. 8–12). Additionally, while MSR need not be tied to French and Ladyman’s response to the Platonism objection, the difficulties that attend their response point to serious problems with their view. 5. the inadequacy of metaphys ical s tructural realis m The main feature of MSR is the shift from an object-ontology to an ontology of structure. Ladyman proposes an ontology without entities, of just mathematical relations. Entities, and their properties that are referred to by a theory (i.e. the names of the terms of equations) become just conventional expressions, and they do not refer to things other than the structure of the models that they are employed in. Thus, the plausibility of the position rests on whether or not its ontology, and its “no-statement” interpretation of a theory’s expression of that ontology, makes sense in the last analysis. In this section I will make it clear that it does not. The question I will concern myself with is not with the merits of the no-statement view. I focus on whether or not Ladyman’s particular appeal to it succeeds in making MSR immune to the criticism that he thinks attaches to epistemological SR. Ladyman’s main ambition in taking the no-statement view is to deflect Friedman and Demopoulos’ complaint that the Ramsey sentence version of SR collapses into strict empiricism. And, of course, Ladyman is correct that it is quite possible to maintain the thesis that theories with the same observational consequences can be construed differently in model theoretic terms. However, this point does not really attach to the more recent debates between Worrall and Psillos, since this version of SR does not propose to reduce theories to their Ramsey sentences or to construe SR the way Grover Maxwell proposed. What is currently at issue is whether survival of relations across theory change is best explained by supposing that

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the relations are true (while at the same time remaining agnostic about the characterisations of the relata). In other words, what is currently at issue is whether or not Psillos’ complaints about the distinction between structure and nature can be satisfactorily answered. While Ladyman is anxious to preserve Worrall’s insight, his appeal to MSR is still open to a Psillos-like accusation to the effect that it holds an implausible distinction between structure and nature. French and Ladyman’s contention that structure is ontologically primary is ambiguous in that it can be taken to mean either that nature (that goes beyond mathematical representation) might exist but is not modelled by science, or taken to mean that there is no such nature at all. The response to Cao’s objections that we discussed above seems to imply that they sometimes read their position as taking some form of the former stance, although elsewhere they explicitly espouse the latter view. The former reading is the certainly more problematic of the two. Nevertheless, either reading leads to difficulties. If the former reading is taken, then this leaves Ladyman squarely open to the accusation (as we have already seen) that MSR maintains a false distinction between structure and nature. Scientists, when they refer to an entity’s nature, do not mean some metaphysical substance or essence (in an almost pre-modern sense) that cannot (even in principle) be investigated by science. Light’s transversal character is very much part of its nature, even though this aspect of light is expressed structurally in both old and new theories. I think Ladyman would resist this charge by taking the latter reading of his claim. Following French (1999), he can maintain that no problematic distinction exists between structure and nature because MSR dispenses with nature entirely. However, this approach to MSR is also problematic and Ladyman’s (and French’s) proposals to provide group theoretic accounts of scientific models help little. Group-structure may well be separate from particular domains of individuals, but it is not detached from domains of individuals in general. Indeed, the notion of isomorphism, which is central to the group theoretic construal of scientific models (and especially the retention of structure across theory change), requires the pairing of different domains of individuals. Given this, it is difficult to see how Ladyman and French can maintain a plausible version of MSR (this difficulty has also been noticed by Psillos, 2001). Additionally, moving away from the specifics of MSR for a moment, maintaining an ontological commitment to structure as primary while denying the existence of any nature at all amounts to asserting the existence of relations while denying the existence of relata. This is exactly the same problem that Moore identified in Bradley’s doctrine of internal relations. That is, an infinite regress is created if no distinction of

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any sort can be drawn between relations and relata. Since Ladyman proposes that relations exist without there being any relata, he seems to be in the same position as the supporter of internal relations and the definition of any term will lead to an infinite regress. However, the debate over MSR can be set aside since it is unnecessary for a plausible reading of SR. If the deflationary view I outlined above is adopted, the motivation for Ladyman’s distinction disappears. Ladyman introduces “metaphysical” SR exactly because of what he takes to be the untenability of the claim that although the world really does contain unobservables, only their structure can be known. However, as we have seen, SR, as I claim it should be read, is not committed to this thesis. It is only committed to the thesis that the world’s structure is knowable, and it is silent on whether or not the definitions of the particulars referred to (as distinct from the equations in which they appear) ought to warrant belief. French and Ladyman could, of course, try to counter this criticism by trying to show that the view is nevertheless mandated. This move seems especially appealing because they maintain that only MSR can solve pressing conceptual problems that attend foundational debates in certain of the special sciences. French and Ladyman have, in fact, elaborated MSR in the context of their work on foundational problems in the philosophy of physics. Without straying too much off topic, French and Ladyman’s application of MSR to these debates does warrant some discussion. French and Ladyman deploy MSR in part to solve conceptual problems associated with traditionally realist interpretations of both quantum mechanics and quantum field theory. With regards to traditional quantum mechanics, a standard problem for a realist interpretation concerns the individual identity of quantum particles. As numerous commentators have noted, the physics is quite compatible with both the idea that quantum objects are not individuals and with the sort of individuality that two identical base-balls still possess in spite of being identical (cf., French, 1989; Van Fraassen, 1991). In quantum mechanics then, it can be meaningless, for example, to imagine two identical particles, say electrons, swapping locations but still remaining in the same relation to one another. Although French (e.g. French, 1989) in particular has argued for a reading of quantum mechanics that preserves some notion of individuality, he admits that the physics completely underdetermines the correct interpretation (French and Ladyman, 2003a, p. 36). This, as Van Fraassen (1991) has pointed out, poses a problem for the realist since fully fledged realist metaphysics of quantum objects would need to settle the question. However, for French and Ladyman, MSR prevents this

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situation from opening the ground for constructive empiricism. Either reading of quantum objects involves the same physics, i.e. structural relations, and since MSR claims that there is nothing beyond structure, MSR reconciles the two interpretations. As French and Ladyman note, “the locus of this metaphysical underdetermination is the notion of an object. So one way of avoiding it would be to re-conceptualise this notion in entirely structural terms” (2003a, p. 37). MSR, they claim, is also helpful with the conceptual foundations of quantum field theory. As Huggett (2000) and others have noted, fundamental ontology in quantum field theory has shifted from particles to fields. Again, metaphysical underdetermination prevails in quantum field theory with regards to the nature of the field. A form of underdetermination “arises again between fields as substantival and fields as properties of space time points” (French and Ladyman, 2003b, p. 74). As with objects in quantum mechanics, a fully fledged realist account of quantum field theory must account for the correct interpretation but cannot do so. MSR solves the problem by pointing to unity of structure with regards to the two interpretations. For reading either quantum mechanics or quantum field theory, a standard advantage claimed for MSR over its competitors is that any object ontology will run afoul of metaphysical underdetermination. In making such arguments, the case for MSR is overstated. A realist of Chakravarty’s sort can always claim, as French and Ladyman acknowledge (2003a, p. 50), that such metaphysical underdetermination applies to ordinary large objects, and this is no reason to give up belief in an ontology that includes such objects. However, French and Ladyman contend that for unobservable entities like fields, belief is restricted to theoretical description, which if underdetermined renders our beliefs empty (2003a, p. 50, b, p. 74). This reply misses its mark. Since theoretical description of unobservables also includes what Chakravarty terms detection properties, not all beliefs about metaphysically underdetermined entities turn out to be empty. After all, we have justified beliefs about their experimental interactions. Nothing prevents a supporter of the deflationary view I advocate from making a very similar response. That view sanctions variable commitment to theoretical properties, and experimental interaction through detection properties can be a means of parsing such commitment. While the metaphysical underdetermination of quantum field theory does not rule out other forms of SR, a view that is specifically tied to entity realism is problematic with regards to the controversy over identity of quantum objects. Here it is not just a question of choosing the correct reading, a distinct possibility exists that the notion of individually distinct objects must be given up. This is a difficult situation

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for a realist wishing to globally preserve entity realism as it is typically understood. However, for the deflationary version I advocate, it is no more of a difficulty than the problem of metaphysical underdetermination. Since deflationary SR does not require realist commitment to every unobservable, no presupposed commitment to continuity with objects possessing a distinct identity or individuality exists. Indeed, it is exactly this sort of local suspension of a realist take on unobservables that my position sanctions. A deflationist can perfectly well believe in quantum objects (or not), but doubt they are individuals in the classical sense, or believe in fields but reserve judgement on their complete metaphysical description. Thus, recourse to MSR is unnecessary in this view since underdetermination and even local anti-realism pose no problem. MSR then does not really present any unique solution to any of the conceptual problems in either quantum mechanics or quantum field theory. 6. conclus ion The virtue of the deflationary approach I defend in this paper is not limited to the fact that makes a problematic metaphysical hypothesis such as Ladyman’s unnecessary. It also preserves Worrall’s insight that the retention of equations across instances of theory change is accounted for by SR. It also accounts for the fact that scientists can and do take differing and local stances to the unobservable entities referred to in their currently accepted theories. While this means that SR cannot provide a solution to every situation where the realism question is somehow germane, it is still a very useful tool to understand theory change. In this way SR finds its place within the philosophically pluralist environment that the deflationary stance implies. references Cao, T.Y.: 2003, ‘Structural Realism and the Interpretation of Quantum Field Theory’, Synthese 136, 3–24. Chakravartty, A.: 1998, ‘Semirealism’, Studies in History and Philosophy of Science 29, 391–408. Demopoulos, W. and Friedman, M.: 1985, ‘Critical Notice: Bertrand Russell’s The Analysis of Matter: Its Historical Context and Contemporary Interest’, Philosophy of Science 52, 621–639. French, S.: 1989, ‘Identity and Individuality in Classical and Quantum Physics’, Austalasian Journal of Philosophy 67, 432–446. French, S.: 1999, ‘Models and Mathematics in Physics’, in J. Butterfield and C. Pagonis (eds.), From Physics to Philosophy, Cambridge University Press, Cambridge. pp. 187–207. French, S. and Ladyman, J.: 2003a, ‘Remodelling Structural Realism: Quantum Physics and the Metaphysics of Structure’, Synthese 136, 31–56.

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French, S. and Ladyman, J.: 2003b, ‘The Dissolution of Objects: Between Platonism and Phenomenalism’, Synthese 136, 73–77. Giere, R.: 1985, ‘Constructive Realism’, in P. Churchland and C. Hooker (eds.), Images of Science, Cambridge University Press, Cambridge. pp. 75–98. Hacking, I.: 1983, Representing and Intervening, Cambridge University Press, Cambridge. Huggett, N.: 2000, ‘The Philosophical Foundations of Quantum Field Theory,’ British Journal for the Philosophy of Science 51, 617–637. Laudan, L.: 1984, ‘The Confutation of Convergent Realism’, in J. Leplin (ed.), Scientific Realism, University of California Press, USA. Ladyman, J.: 1998, ‘What is Structural Realism’, Studies in History and Philosophy of Science 29, 409–424. Maxwell, G.: 1970, ‘Structural Realism and the Meaning of Theoretical Terms’, in R. Colodny (ed.), Minnesota Studies in the Philosophy of Science, Vol. IV. University of Minnesota Press, Minneapolis, pp. 3–34. McArthur, D.: 2002, ‘The Methodological Implications of Resolving the Realism Debate’, Science Studies 15(2), 59–78. McArthur, D.: 2003, ‘Reconsidering Structural Realism’, Canadian Journal of Philosophy 33, 517–536. Psillos, S.: 1995, ‘Is Structural realism the Best of Both Worlds?’, Dialectica 49, 15–46. Psillos, S.: 1999, Scientific Realism: How Science Tracks Truth, Routledge, London. Psillos, S.: 2001, ‘Is Structural Realism Possible?’, Philosophy of Science (Proceedings) 68, 13–24. Poincar´e, H.: 1905, ‘Science and Hypothesis’, reprinted in H. Poincar´e (1913), The Foundations of Science, The Science Press, Lancaster. Sismondo, S.: 1997, ‘Deflationary Metaphysics and the Construction of Laboratory Mice’, Metaphilosophy 28, 221–232. Van Fraassen, B.: 1991, Quantum Mechanics: An Empiricist View, Oxford University Press, Oxford. Worrall, J.: 1989, ‘Structural Realism: The Best of Both Worlds’, Dialectica 43, 99–124. Department of Philosophy Atkinson College York University 4700 Keele St. Toronto, ON Canada M3J 1P3 ([email protected])