STEVEN FRENCH and JAMES LADYMAN
REMODELLING STRUCTURAL REALISM: QUANTUM PHYSICS AND THE METAPHYSICS OF STRUCTURE
ABSTRACT. We outline Ladyman’s ‘metaphysical’ or ‘ontic’ form of structural realism and defend it against various objections. Cao, in particular, has questioned the view of ontology presupposed by this approach and we argue that by reconceptualising objects in structural terms it offers the best hope for the realist in the context of modern physics.
1. STRUCTURAL REALISM – THE EPISTEMIC FORM
Accommodating ontological change in science is a fundamental and longstanding issue in the philosophy of science. The fact that there has been ontological discontinuity across theory-change forms the basis of the so-called ‘pessimistic meta-induction’ which lists occurrences of such changes in the history of science and concludes, inductively, that it is very likely that the ontology of our currently accepted theories will also undergo radical revision (Laudan 1981). This is then presented as undermining scientific realism. However, we need to be careful about the form of realism the argument supposedly affects. Presumably it has to be a form of realism which insists that we can ‘read off’ ontology from current science – and in particular, physics – and thus come to some conclusion as to how the world is. An important issue then – to which we shall return – is how this term ‘ontology’ should be understood. There is a general type of response to the above concerns that has recurred through the history of the philosophy of science and which is basically structuralist in nature.1 It constitutes the heart of Worrall’s attempt to defuse the pessimistic meta-induction by insisting that, with regard to these shifts in ontology, ‘[t]here was continuity or accumulation in the shift, but the continuity is one of form or structure, not of content’ (Worrall 1996, 157).2 This forms the basis of his epistemic version of ‘structural realism’ (SR) which, in our view, has reinvigorated the realist-antirealist debate. It is ‘epistemic’ because the central claim is that all that we know is this ‘form or structure’, whereas the ontological content, although retained, is unknowable. Worrall’s remark raises two fundamental questions: Synthese 136: 31–56, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands.
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(1) how are we to appropriately characterise this structure? (2) how are we to characterise (ontological) content? We will consider each in turn. 1.1. The Nature of Structure The principal historical example that Worrall draws upon – the theory of light – is suggestive but also misleading. He argues that, although conceptions of the nature of light have changed through history, from an ontology expressed in terms of corpuscles to one of waves, to – we would add – wave-particle duality and that of a quantum field (however we are to understand that, something to which we shall return below), the mathematical equations describing it have not been abandoned but have been incorporated into successive theories, culminating, classically, in Maxwell’s theory of electro-magnetism which is then taken to be subsumed into quantum electrodynamics. The example can be misleading precisely because it has led to the impression (expressed to us on several occasions) that SR is wedded to a consideration of explicitly mathematical theories only and cannot offer much comfort to the realist when it comes to (qualitatively expressed) biological theories, for example. However, this is simply not the case. Mathematical equations represent one component of theoretical structure but non-mathematical, qualitative aspects can also be represented through the resources of logic and set theory. Thus, within the so-called Received View of theories a syntactic form of SR was given by Maxwell who argued that the ‘cognitive content’ of theoretical terms was exhausted by the structure, expressed – crucially – by the well-known Ramsey sentence of the theory. Unfortunately, tying SR to the ‘Ramsification’ of theories in this way means that it cannot, in fact, capture the continuity of structure beyond the empirical level. This is because, as English has shown, any two Ramsey sentences that are incompatible with one another cannot have all their observable consequences in common (English 1973). Hence, on this approach theoretical equivalence collapses into empirical equivalence. Since any form of realism must allow for a separation of the former from the latter, this result is disastrous for the attempt to construct a viable form of SR. There is another more fundamental reason for thinking that this or indeed any other purely epistemic form of structural realism is not adequate for the task for which it was introduced, and this is that any purely epistemological modification of standard realism seems to leave the problem of ontological discontinuity across theory change untouched. The Ramsey sentence of a theory may be useful to a concept empiricist because it shows how reference to unobservables may be achieved purely by
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description, but this is just because the Ramsey sentence refers to exactly the same entities as the original theory. If the meta-induction is a problem about lack of continuity of reference then Ramsifying a theory does not address the problem at all.3 For Worrall the motivation for adopting structural realism is just the need to respond to the pessimistic meta-induction. While we share the desire to articulate a form of realism that can account for theory-change, our understanding of structural realism is also informed by the need to provide an ontology that can dissolve some of the metaphysical conundrums of modern physics, and also the need to have a conception of how theories represent the world that is compatible with the role of models and idealisations in physics. Others who have expressed a commitment to structural realism, such as Simon Saunders and Michael Redhead seem to have a similarly broad motivation. Now of course it is not clear that structural realism can satisfy all of these needs but in our view it is worthwhile trying to develop a view that can simultaneously accommodate all the problems besetting scientific realism in the light of contemporary physics and a faithful account of its history and practice. In a recent defence of epistemic SR, Worrall has also adopted the Ramsey sentence method of representing structure and appealed to the classic distinction between theoretical terms and observational terms in an effort to defeat the so-called ‘Newman’ problem (Worrall 2000). Put briefly, this states that for any collection of things of a given cardinality, the claim that there exists a particular structure, expressed in terms of the relevant relations, defined over this set, is true merely as a matter of logic (see, for example, the discussions in Demopolous and Friedman (1995) and Psillos (1999, 63–65)). This appears to reduce structuralism to a trivial thesis. Our intention here is not to enter into the voluminous debate surrounding this problem but simply to point out that Worrall’s approach is thoroughly embedded in the so-called syntactic view of theories that adopts first-order quantificational logic as the appropriate form for the representation of physical theories.4 We will not rehearse our reasons here, but we consider this approach to be deeply flawed, not only because of its inadequacy in reflecting scientific practice, but also because of the pseudoproblems that arise once one has adopted it. So for example, the Newman problem is obviated if one does not think of structures and relations in first-order extensional terms. One of us (Ladyman 1998) has suggested an alternative descriptive framework for SR, namely the ‘semantic’ or modeltheoretic approach to theories. Through the work of Tarski, Beth, Suppes, van Fraassen, Suppe and others, the latter has developed into a powerful tool for the structural representation of theories. The recent extension of
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this approach to incorporate ‘partial structures’ allows it to capture, in a natural fashion, both the relationships that hold between theories, horizontally as it were, and those that hold vertically between a theory and the data models. The technical details have been given in numerous other publications so we shall just note here that such structures incorporate an element of openness within the representation of theories via the introduction of so-called ‘partial relations’ (see Mikenberg, da Costa and Chuaqui 1986). With regard to inter-theory relationships partial structures can capture precisely the element of continuity through theory change that is emphasised by the structural realist (see da Costa and French 1993). In particular, it offers the possibility of accommodating examples of such continuity that have been described as ‘approximate’ or partial. Thus Worrall refers to the shift from Newton to Einstein, from classical to relativistic mechanics, and suggests that ‘. . . there is approximate continuity of structure in this case’ (op. cit., 160).5 Worrall continues, ‘[m]uch clarificatory work needs to be done on this position, especially concerning the notion of one theory’s structure approximating another’ (ibid. 161).6 We would like to suggest that the partial structures approach has contributed to this clarification by indicating how such inter-theoretical relationships can be represented by partial isomorphisms holding between the model-theoretic structures representing the theories concerned. Case studies from high-energy physics (French 1997) and the London and London theory of superconductivity (French and Ladyman 1997), interpreted within this approach, refute the claim that the semantic approach is somehow incapable of representing these relationships.7 Concerning intra-theoretical relationships, partial structures allow us to capture these relationships downwards from the theoretical models to the data models – and, in particular, the idealising moves that are made in this progression – and also upwards, from the physical theory to the mathematical (French and Ladyman 1998). We shall not say more about this aspect here but it is important to recall that with respect to the introduction of partial isomorphisms and homomorphisms, such set-theoretical relationships hold only between the mathematical structures and not between such structures and ‘the world’ itself (French and Ladyman 1999). The realist representation of the relationship between theories and the world must be sought elsewhere, perhaps in a notion of reference appropriate for a broadly structuralist metaphysics. Our overall claim at this point is that the partial structures form of the semantic approach offers a general account of theoretical structure that extends beyond the mathematical equations and thus represents an appropriate formal framework for SR.8
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1.2. The Structure of Natures Let us now consider the second of the above fundamental questions. How is this notion of ‘content’ to be explicated? Worrall famously draws on a historical precedent for his epistemic form of SR in the work of Poincaré, who wrote that theoretical terms ‘. . . are merely names of the images we substituted for the real objects which Nature will hide forever from our eyes. The true relations between these real objects are the only reality we can ever obtain’ (1905, 162). Now, as Domski has emphasised, Poincaré may not be the most suitable forefather to claim for this version of SR, given his Kantian inclinations and rejection of truth as the aim of science (preprint).9 If theoretical content is cashed out in terms of the nature of ‘real objects’, understood in a Kantian sense, then the realist side of SR may be radically transformed, at the very least. As we shall see, Kant makes a number of appearances in structuralist considerations of the implications of modern physics. Psillos (1999, 155–157), in his critique of SR, and defence of ‘standard’ (non-structural) realism offers an alternative understanding of the ‘nature of real objects’. He argues that this ‘nature’ should be understood solely in terms of the ‘basic’ properties of the objects together with the equations that describe their behaviour. Any talk of natures over and above this, he claims, is reminiscent of talk of medieval forms and substances, which were decisively overthrown by the scientific revolution. The above understanding of ‘nature’ is thus essentially structural and there is no more to ‘natures’ over and above this structural description. Hence, he claims, the distinction underpinning epistemic SR collapses, fatally undermining the position as a whole. Now, this is an interesting line of argument but the central claim is contestable and the conclusion can be viewed as actually supporting an alternative form of SR rather than undermining it altogether. First of all, let us consider the claim that the understanding of ‘natures’ in terms of forms, substances and the likes was overthrown by the scientific revolution. This represents a rather conservative view of the history of science which historians of both science and philosophy would reject. In particular, let us focus on what many would take to be one of the more notable achievements of 19th and 20th century science, namely the rise of atomism. How was the content of atomism cashed out? Or, equivalently, how was the ‘nature’ of atoms understood? Briefly and bluntly put, atoms were understood as individuals where the metaphysical nature of this individuality was typically explicated in terms of substance or, more usually in the case of physicists at least, in terms of the particles’ spatio-temporal location. Thus, one of the most prominent and ardent defenders of atomism, Boltzmann,
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incorporated such an understanding of the nature of atoms in terms of their individuality in Axiom I of his mechanics. The content of atomism was thus cashed out explicitly in terms of the metaphysical nature of atoms. Similarly, and a lot more recently, Redhead has characterised the difference between standard realism and SR as the difference between the questions, ‘what is a field?’ and ‘what are the equations which govern its behaviour?’ (Redhead 1995, 18). The first can only be fully answered by appealing to such metaphysical natures and typically discussions have centred around the alternatives of describing a field in substantivalist terms and describing it in terms of sets of properties instantiated at space-time points. Crucially, as Redhead emphasises, this answer is not exhausted by the answer to the second question. (We shall return to these points below.) Furthermore, as one of us has insisted (Ladyman 1998), standard realism without such ‘natures’ is nothing more than an ersatz realism which draws on the plausibility of a structural description of theoretical objects whilst backing off from SR proper. Indeed, Psillos’s argument may undermine the epistemic form of SR, which holds that all we can know is structure with the ‘real objects’ hidden forever from our scientific gaze,10 but supports an ontic form which reconceptualises the objects themselves in structural terms (Ladyman, ibid.). 2. STRUCTURAL REALISM – THE ONTIC FORM
Let us begin, again, with Worrall who writes, ‘[t]he structural realist simply asserts . . . that in view of the theory’s enormous empirical success, the structure of the universe is (probably) something like quantum mechanical’ (Worrall op. cit., 163). If we consider this most successful of our (mature) current theories in metaphysical terms, then we discover a kind of metaphysical underdetermination in that the physics is compatible with a view of quantum objects as non-individuals – in the sense, as typically expressed, that they have ‘lost’ their identity – and also with a view of such objects as individuals (French (1989, 1998); see also Huggett (1997) and van Fraassen (1991)). In this case, the (standard) realist is unable to give a full answer to the parallel question to Redhead’s above, namely ‘what is a quantum object?’, where a ‘full’ answer will involve the metaphysical nature explicated in terms of such fundamental categories as individuality, identity, etc. Van Fraassen rightly sees this as a challenge to standard realism (and it is regrettable that the standard realist has not seen fit to respond11 ) expressing his conclusion as a waving ‘good-bye to metaphysics’ (op. cit., 480–482), leaving the field clear for constructive empiricism.
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However, a realist alternative can be constructed. The locus of this metaphysical underdetermination is the notion of an object so one way of avoiding it would be to reconceptualise this notion entirely in structural terms. The metaphysical packages of individuality and non-individuality would then be viewed in a similar way to that of particle and field in QFT, namely as two different (metaphysical) representations of the same structure. One way of explicating the relevant structure in mathematical terms is through group theory12 and Castellani, for example, has begun to explore the ontological representation of the fundamental objects of physics in terms of sets of group-theoretic invariants by Weyl, Wigner, Piron, Jauch and others (Castellani 1998). This would leave no unknowable objects lurking in the shadows, as it were and it would retain a sense of objectivity understood structurally, of course, which could still satisfy the ‘mind independence’ requirement of realism in general (we shall return to consider this shortly).13 Escaping the clutches of the above metaphysical underdetermination provides one motivation for an ontic form of SR, although it is not the only one (Ladyman op. cit.).14 Nevertheless, there are further issues to be dealt with, some of which arise in Cao’s discussion and defence of SR.
3. ONTOLOGY VS . STRUCTURE ?
Like Worrall and other defenders of an epistemic form of SR, Cao sets up a dichotomy between ‘ontology’, or ‘natures’, on the one hand and ‘structure’ on the other, and characterises us as being anti-ontology. However, as should now be clear, we would not characterise our views that way nor do we see any such dichotomy. Rather, we regard the ontic form of SR as offering a reconceptualisation of ontology, at the most basic metaphysical level, which effects a shift from objects to structures. Now, in what terms does such a reconceptualisation proceed? This hinges on our prior understanding of the notion of an ‘object’ which has to do, as we have indicated, with the metaphysics of individuality. Given the above metaphysical underdetermination, a form of realism adequate to the physics needs to be constructed on the basis of an alternative ontology which replaces the notion of object-as-individual/non-individual with that of structure in some form. Let us be clear: we are not ‘anti-ontology’ in the sense of urging a move away from electrons, elementary particles etc. and towards ‘observable structures’ or the S-matrix or whatever; rather, we urge the reconceptualization of electrons, elementary particles and so forth in structural instead of individualistic terms.
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Now, Cao alludes to some of this in his consideration of ontology. He talks of it, for example, in terms of ‘basic existence’ and we would agree that realism should involve reference to what ‘really’ exists. The issue, as we’ve just tried to indicate, is how that which we take to ‘really’ exist is metaphysically conceived. Cao then goes on to say that ontology is that which has ‘real and autonomous existence’, in the sense that it is not dependent on anything external to it. This seems a little ambiguous: on the one hand, it seems he is making the standard realist move – indicated above – of insisting that that which ‘really exists’ is mind independent; on the other, the idea of something not being dependent on anything external is a very Scholastic way of characterising an individual. We think that many ‘standard’ realists do understand ontology in terms of individual objects but of course – unlike Cao – they haven’t learnt the lessons of quantum physics. If we acknowledge the individuality/non-individuality underdetermination then we’re going to have to come up with a different understanding of ontology. The question then is whether, without objects we can still retain a form of objectivity capable of satisfying the realists’ demand for mind-independence. This is a question that many structuralists have grappled with; as Cassirer put it, ‘[w]e are concerned not so much with the existence of things as with the objective validity of relations; and all our knowledge of atoms can be led back to, and depends on, this validity’ (Cassirer 1936, 143). Cassirer, of course, had another, neo-Kantian agenda but it may be worth exploring the possibility of detaching his account of objectivity from this programme, particularly as he was so clearly aware of, and thought it important to accommodate, the implications of quantum mechanics for the metaphysics of objects. Thus Cassirer begins with the claim that in classical mechanics objectivity rests on the spatio-temporal persistence of individual objects. He writes that ‘ “[o]bjective” denotes a being which can be recognized as the same in spite of all changes in its individual determinations, and this recognition is possible only if we posit a spatial substratum’ (ibid., 177). ‘The entire axiomatic system of classical mechanics’, he continues, ‘is based on this presupposition’ (ibid.). As well as the examples he gives, this presupposition features in Boltzmann’s axioms as noted above. It forms the basis of the ‘world-view’ of classical (particle) physics in which we have individual objects possessing at all times well-defined properties and traversing well-defined spatio-temporal trajectories. Furthermore, as we all know, it is this world-view that is overturned by quantum mechanics (at least under the orthodox interpretation).15 Now we cannot say that the particles unambiguously possess definite properties at all times, even beyond measurement interactions, or that they travel along well-defined
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trajectories. It is at this juncture that Cassirer asks a pair of crucial questions: ‘. . . what are these electrons whose path we can no longer follow? Is there any sense in ascribing to them a definite, strictly determined existence, which, however, is only incompletely accessible to us?’ (ibid., 178). In answering these questions, Cassirer makes the fundamental demand of the ontic form of SR, namely that we take the ‘conditions of accessibility’ as ’conditions of the objects of experience’. If we do that, then ‘. . . there will no longer exist an empirical object that in principle can be designated as utterly inaccessible; and there may be classes of presumed objects which we will have to exclude from the domain of empirical existence because it is shown that with the empirical and theoretical means of knowledge at our disposal, they are not accessible or determinable’ (ibid., 179). There are no epistemically inaccessible objects laying behind the structures which we can know. What is an electron then? Not, Cassirer insists, an individual object (ibid., 180). If we want to continue to talk, in everyday language, about electrons as objects – because we lack the logico-linguistic resources to do otherwise (we shall return to this point below) – then we can do so ‘only indirectly’, ‘. . . not insofar as they themselves, as individuals, are given, but so far as they are describable as “points of intersection” of certain relations’ (ibid.).16 And this relational conception of an object is pure Kant: ‘All we know in matter is merely relations . . . but among these relations some are self-subsistent and permanent, and through these we are given a determinate object’ (Kant, in Cassirer ibid., quoted on p. 182) Charge, typically understood as an intrinsic or state-independent property of particles is just such a ‘self-subsistent and permanent relation’ but as Cassirer points out, in an acute rebuttal of the assumption made by the ‘standard’ realist, ‘. . . the constancy of a certain relation is not at all sufficient for the inference of a constant carrier’ (ibid.). The permanence of charge justifies our regarding the electron, say, as a ‘determinate object’, where the scare quotes indicate that the sense is that of an entity prior to reconceptualisation in structural terms, but it is does not justify what Cassirer calls the ‘substantialization and hypostasis’ of the electron in the sense of an entity which is not so reconceptualised. Charge, like the other intrinsic properties, features in the relevant laws of physics and according to Cassirer, what we have here is a reversal of the classical relationship between the concepts of object and law (ibid., 131–132): instead of beginning with a ‘definitely determined entity’ which possess certain properties and which then enters into definite relations with other entities, where these relations are expressed as laws of nature, what we now begin with are the laws which express the relations in terms of
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which the ‘entities’ are constituted. From the structuralist perspective, the entity ‘. . . constitutes no longer the self-evident starting point but the final goal and end of the considerations: the terminus a quo has become a terminus ad quem’ (ibid., 131) Objectivity, therefore, is determinable through law, which is prior to it17 (ibid., 176) and the boundaries of law mark the boundaries of objective knowledge (ibid., 132). Cassirer saw these developments in physics as confirming a neoKantian epistemology (Werkmeister 1949, 777) according to which the laws of physics – in particular those of quantum mechanics and relativity theory – provide the sole basis for our integration of experience. In this integration, a crucial role is played by the ‘principle’ of causality, regarded not as a proposition pertaining to events themselves, but, rather, ‘. . . a stipulation concerning the means through which things and events are constituted in experience’ (ibid., 789). As such, the principle is not undermined by quantum mechanics; indeed, Cassirer insists, understood as a demand for strict functional dependence, the essence of causality remains untouched (op. cit., 188). The significance of quantum physics for epistemology lies precisely with the above consideration regarding the nature of objects. It is at precisely this point, where the neo-Kantian expresses the constitutive role of laws in experience, that the structural realist departs. Of course, she then owes us an account of these laws which, furthermore, will serve to distinguish her position from that of the constructive empiricist. We shall not pursue such an account here, except to note that one of us has begun to make progress in this direction (Ladyman forthcoming). There are two further points arising from Cassirer’s discussion which we would like to highlight. The first concerns the comparison this discussion engenders between physical concepts and mathematical ones. Cassirer talks of a ‘characteristic connection’ as well as a ‘characteristic contrast’ here (op. cit., 195–196). The connection lies in the implicit definition of mathematical concepts – such as a point or line – in structural terms, such that the relations determine and ‘completely exhaust’ the meaning of the concepts. ‘Likewise’, he writes, ‘concepts like atoms or electrons fully share the logical character of these geometrical concepts. They do not admit of an explicit definition but basically can only be defined implicitly. In this respect there is no difference between the material point and the mathematical point’ (ibid., 195). On the other hand, mathematical and physical concepts differ in the manner of the constitution. The former are regarded by Cassirer as constructs which are ‘created’ via the system of axioms they have to satisfy. The latter, on the other hand, must ultimately ‘save the phenomena’ (and at this point Cassirer does indeed cite Duhem) and thus
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they must be both ‘stable’, in the sense that at least some of their content is retained, and also ‘flexible’ in that they can always be ‘reoriented’ and tested by experience. (It is this aspect of stability that structural realism focuses on, of course, whereas the flexibility and openness of scientific developments can be represented via partial structures.) Of course, Cassirer’s characterisation – particularly of mathematics – can be contested but the point we want to note is that the structural dissolution of physical objects leads to a blurring of the line between the mathematical and the physical. The second point pertains to the above reversal of the relationship between structures and objects. How – it might be asked – can the former be regarded as primary and in some sense prior to the latter, when structures – understood as a system of relations – can only be defined in the first place in terms of objects – the relata? If the structural realist cannot answer this question, then the whole metaphysical project threatens to come undone.
4. STRUCTURE AS ONTOLOGY
This question forms the kernel of an objection to the ontic form of SR which has been voiced to us by Redhead (in private discussion): If structure is understood in relational terms – as it typically is – then there needs to be relata and the latter, it seems, cannot be relational themselves. In other words, the question is, how can you have structure without (non-structural) objects? Here the structuralist finds herself hamstrung by the descriptive inadequacies of modern logic and set theory which retains the classical framework of individual objects represented by variables and which are the subject of predication or membership respectively (cf. Zahar (1994)). In lieu of a more appropriate framework for structuralist metaphysics, one has to resort to a kind of ‘spatchcock’ approach, treating the logical variables and constants as mere placeholders which allow us to define and describe the relevant relations which bear all the ontological weight.18 The same approach can be followed in the interpretation of physics: we see, on a scintillation screen for example, bright flashes of light – individual flashes – and this fact seems to support a metaphysics of individuality for quantum objects. On the basis of such observable phenomena we then try to carry over our metaphysics of individuality which is appropriate for the classical domain, but then the way particle permutations are treated in quantum mechanics is quite distinct from classical physics and the above metaphysical underdetermination arises. Thus, we have a metaphysical package of (individual) objects to which the mathematical and physics of quantum theory is applied and which undermines that very
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package we started with. From this perspective, the objects play only a kind of heuristic role (see French (1999)), allowing us to apply the (classical) mathematics and hence getting us up to the (group-theoretical) structures as it were, but once we’re there the objects can be dispensed with. Since Worrall has already appropriated Poincaré, it is interesting to note that the latter adopted a very similar approach in his 1898 Monist paper:19 there he defends a group theoretic approach to geometry and tackles the objection that in order to study the group it first needs to be constructed and cannot be constructed without matter, by insisting that ‘the gross matter which is furnished us by our sensations was but a crutch for our infirmity’, which serves only to focus our attention upon the idea of the group.20 However, Cao’s principal objection to the ontic or ‘metaphysical’ form of SR seems to turn on the case of Gell-Mann. His argument can be summarised as follows: ontic or metaphysical SR is either – in the weaker version – similar to, or – in the stronger version (and its not entirely clear which he’s pushing here) – identical to the view of Gell-Mann in the 1960s. Since the latter blocked the deeper exploration of the existence of quarks and, it is suggested, was ultimately detrimental to the further development of physics, the former should be rejected also. Now this seems to be a rather peculiar kind of ‘guilt by association’ argument. First of all, there might be a disanalogy with regard to Gell-Mann’s generation of ‘observable structures’: of course, since these are the current algebras, ‘observable’ is being used in the physicists’, rather than, say, the constructive empiricist’s, sense, but still a proponent of SR might insist that the kinds of structures we place as ontologically primary are profoundly unobservable. Secondly, and more importantly, there is a disanalogy between the above view of objects as heuristic and Gell-Mann’s – the above is motivated, as we have indicated, by metaphysical concerns with our conceptualisation of objects in terms of individuality, and Gell-Mann’s has to do with bootstrapping and anti-fundamentalism and possibly anti-realist concerns. Thirdly, what this has to do with is the difference between science and the philosophy of science. It is always tricky when the former is used to support or attack the latter – clearly there has to be some relationship, if our philosophy is to be in any way practice based, but when it comes to a philosophical position such as realism, how much weight should one put on a case of a scientist who was or was not a realist? Feynman, for example, seems to have been an anti-realist – does that fact undermine realism? Or is it outweighed by all the physicists who were realists? Likewise, does the Gell-Mann example constitute a falsification of metaphysical SR or is it inductively outweighed by the likes of Eddington, Weyl, Wigner, Born and others? Granted that philosophy of science should accommodate
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scientific practice, pointing to particular examples of scientists adopting or rejecting certain philosophical positions, together with whatever consequence are engendered, does not constitute a philosophical argument for or against any of those positions. Finally, one could be anti-Gell-Mann, as it were, and accept the development of quarks as a profoundly important and fruitful episode in the history of modern physics, yet still be a structural realist by arguing that however the quarks themselves are described in physical terms, they can be philosophically conceptualised or ontologically reduced, in structuralist terms. The general point is that because the structural realist believes that theories tell us about the structure of the world and not just about what we actually observe, structural realism motivates, or at least does not undermine, the desire of researchers to penetrate beyond the latest level of structure, as much as scientific realism does. Now in his paper Cao appears to prefer the position which takes structure to be ontologically derivative (although, as we shall see below, he has been read as supporting a position that is closer to ours). Here again the question arises: how is one to understand, metaphysically, these ‘ontologically primary constituents’? If one adopts the position of the ‘epistemic’ structural realist then one runs into all the problems previously laid out in Ladyman (1998) and, specifically, one opens oneself up to the sort of attack that Psillos makes. In particular, as Cao indicates, there is the issue of our knowledge of these constituents. He states that ‘. . . the question concerning the exact nature and characteristics of the hidden entity can only be answered empirically’, but surely it cannot, if this status is truly metaphysical and the ‘exact nature’ concerns the entity’s individuality or lack thereof. Again there seems to be a confusion between the physicist’s conception of these objects and the philosopher’s. If all the ‘observable’ (in the physicist’s sense) properties of an object can be represented in structural terms, then what is the nature of the ontological residuum? One way to tackle this question is via Kant, and as we’ve indicated Kant seems to be lurking in the shadows in much of this discussion.21 But one can’t defeat Kant, as presented in the quotation Cao gives, by insisting that experimental developments will render observable that which is unobservable (imagine what the constructive empiricist would have to say about that). Surely, by ‘object in itself’, Kant did not mean the object as conceived of by physicists – the latter is not the ‘ding an sich’ but rather the ‘erscheinung’.
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5. THE IDENTITY THESIS
Returning to the arguments against the ’Identity Thesis’ we think each can be responded to. First of all, like Psillos, Cao insists that the mathematical structure can’t exhaust the ‘content’ of an entity, but it is not clear how this content is to be cashed out. As we have indicated, insofar as it is set opposed to ‘structure’, where the latter is taken to embrace all the scientific properties of things, it has to do with some sort of innate ‘objectness’ of the object. But that, as we’ve indicated, is fatally underdetermined by the physics itself. It is further suggested that a structuralist perspective would blur the differences between classical and quantum mechanics but this is not clear to us at all. As Cao himself indicates, some structures do get carried over, albeit in modified form, such as Poisson brackets – and here Saunders, for example, has addressed the ‘heuristic plasticity’ of such structures (Saunders 1993) – but clearly there are vast structural differences. Consider the example touched on, namely quantum statistics: the difference between classical and quantum statistics in terms of the nature and role of permutations was something that Weyl, for example, regarded as absolutely fundamental and indicative of a profound metaphysical difference with regard to the nature/content of the entities represented. Furthermore, as Cao acknowledges, the differences can be pinned down using further structural means. As for the two options presented, we would of course reject the dichotomy of the first as somehow anti-realist. The example of Stein here is illuminating: what he was trying to do, as we understand it, was to try to find an alternative to the substantivalist/realist and relationist/anti-realist options by shifting focus from a broadly Aristotelian substance plus predicates approach to a broadly Platonist structural one (cf. Dorato forthcoming). Regarding the second option, and the epistemic use of structures to ‘know’ an entity, what is the sense of ‘know’ here? If an entity is not dissolved into structure (and in that dissolution one may still have knowledge, so we don’t see an explicit opposition here) what is left over? Secondly, Cao argues that the Identity Thesis implies that there will be a change in our conception of an entity whenever our structural knowledge changes. In one sense, this is an aspect of a perfectly general point which any form of realism must tackle. The ontological changes illustrated by Laudan are of course precisely what led Worrall to propose (epistemic) SR in the first place. More importantly, perhaps, why should the existence of ‘accumulations and modifications’ lead to constant revolutions? At best there seems to be a rather odd notion of revolution at work here; at worst it seems a completely unwarranted step. That there are often
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profound and deep reaching changes within the ‘higher’ theoretical parts of our theories is surely something which realists of all persuasions and anti-realists have to accommodate in one way or another. Surely no-one would deny that our conception of the electron, for example, has changed from J. J. Thompson’s time to today. The anti-Kuhn point is that there are commonalities and cumulativity through such changes. The structuralist point is that what is preserved/accumulated can be understood in structural terms. Presumably Cao would want to insist that there is something else, something non-structural that is also preserved, but again the question arises, what is that? Essentially our response here is that anything that can be presented to resist the Kuhnian argument, the structural realist can buy into, if she wants, but where it is insisted that there is some object over and above the common structures retained through theory change, the structural realist rejects such an insistence on the grounds that the only non-structural understanding of the nature of such objects is metaphysical and unwarranted by the physics itself.22 For these reasons, we deny that the Identity Thesis leads to absurdity. Cao further suggests that a consequence of rejecting the Identity Thesis is that we must distinguish between mathematical and physical structures. This is quite problematic, of course. The idea that mathematical structures have only a relational existence suggests a kind of mathematical antirealism but its not clear what it means. Suppose, for example, one were a structural Platonist (or a Platonic structuralist), one would surely wish to maintain that mathematical structures have an absolute existence. Let’s grant that physical structure exists – what is it? Is it just a description of the properties of entities? This leads to epistemic SR again. What makes these properties physical and not mathematical? That they’re the properties of an entity? Again, we come back to the same old question – what is that (individual or non-individual)? If the entity is dissolved/reconceived then all we have is the structure and at this level the distinction between the mathematical and the physical may become blurred, as we indicated above. Of course, what the structure is, remains an open question: a Kantian will have one answer, a phenomenologist another. Neither will appeal to a structural realist who wants to save a sense of objectivity involving significant mind-independence, unless their accounts can be appropriately detached in the manner we have indicated.23 Some of us might say, the ‘world-structure’ just is and exists independently of us and we represent it mathematico-physically via our theories. Bearing in mind that structural realism is supposed to be realist enough to take account of the no-miracles argument, and in particular the record of successful novel predictions which some theories enjoy, there is a minimal
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metaphysical commitment that we think structural realism ought to entail. This is that there are mind independent modal relations between phenomena (both possible and actual), but these relations are not supervenient on the properties of unobservable objects and the external relations between them, rather this structure is ontologically basic. This is enough to make structural realism distinct from standard realism but also from constructive empiricism. From this metaphysical thesis there follow plenty of realist methodological and epistemic implications but, we hope, no unsustainable beliefs in the specific ontologies that are employed to help us grasp the structure of the world according to particular theories. 6. THE ONTOLOGY OF QFT
It should come as no surprise that the kinds of structuralist moves we have outlined here have also been powered by the development of field theory. Cassirer, again, argues that the metaphysical view of the ‘material point’ as an individual object cannot be sustained once we make the transition to field theory (op. cit., 178). He offers a structuralist conception of the field: The field is not a “thing”; it is a system of effects (Wirkungen), and from this system no individual element can be isolated and retained as permanent, as being “identical with itself” through the course of time. The individual electron no longer has any substantiality in the sense that it per se est et per se concipitur; it “exists” only in its relation to the field, as a “singular location” in it. (ibid.)
However, the description of the field as ‘a system of effects’ raises the ‘how can we have structures without objects?’ question in a new guise: how can we have an effect without a something which is doing the effecting? The issue here is the same as that discussed above, namely that of coming up with a thorough-going structuralism which avoids that which is ontologically non-structural. The problem is that in contemporary accounts, fields are local in the sense that field quantities are attributed to spacetime points (or, taking into account quantum effects, space-time regions). Again, a form of metaphysical underdetermination arises here with the physics supporting both the view of fields as substances whose properties are instantiated at space-time points (or regions) and the view of fields as nothing but properties of those space-time points (or regions). The former option re-introduces a non-structural substantiality, whereas the latter shifts the focus to space-time. Understanding this in substantival terms again brings a non-structural element back into play, but the standard relationist interpretation threatens to generate a circularity. One possible way out of the dilemma, of course, is to explore a structuralist understanding of space-time itself.24 Such a move was famously anticipated by Stein,
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as Cao notes, and more recently Dorato has attempted to flesh out some of the details (forthcoming). As he puts it, To say that spacetime exists just means that the physical world exemplifies, or instantiates, a web of spatiotemporal relations that are described mathematically (ibid., 7)
Thus spacetime has objective existence, but not as a substance, and as structural it captures all the features that make relationism so attractive. However, from our perspective, there is a fly in the ointment: Dorato insists that, . . . to the extent that real relations, as it is plausible, presuppose the existence of relata, then spatiotemporal relations presuppose physical systems and events . . . . (ibid., 7; author’s emphasis)
Now, Dorato does acknowledge that we may avoid the supervenience of such relations on relata by adopting a form of Armstrong’s ‘bundle’ theory of individuals, but it is not clear whether such a move eliminates all non-structural elements. Indeed, he earlier remarks that ‘. . . spacetime points can only be identified by the relational structure provided by the gravitational field’ (ibid., 3; author’s emphasis). This, of course, throws the issue back to the field theorists and Dorato agrees with Cao in his review of the latter’s book (Cao 1997; Dorato 1999), that the existence of spatio-temporal relations must be underpinned by the existence of the gravitational field, understood as a ‘concrete’ and hence, presumably, non-structural, entity.25 However, there is some ambiguity here, as Dorato identifies Cao as an ontic structural realist, particularly when he denies that the structures postulated by field theories must be ‘ontologically supported by unobservable entities’ (Cao 1997, 5) and writes that, . . . while structural relations are real in the sense that they are testable, the concept of unobservable entities that are involved in the structural relations always has some conventional element, and the reality of the entities is constituted by, or derived from, more and more relations in which they are involved. (ibid.)
Dorato comments that, ‘[i]n this respect, entities postulated by physical theories are to be regarded as a web of relations, not presupposing substance-like entities or ‘hangers’ in which they inhere’ (op. cit., 3). In his paper, however, Cao appears to want to distance himself from our form of SR, as we have seen. Thus, he is clearly, and rightly, concerned about the differences between classical and quantum field theory but it is not at all clear why these can’t be explicated structurally. That structuralism illuminates the commonalities and so offers the possibility of a response to the Kuhns and Laudans of the world, doesn’t mean that
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it makes the differences between theories invisible. Surely it is wrong to maintain that ontic or metaphysical SR can’t accommodate or reveal the differences between Maxwell, Lorentz, Schrodinger, Dirac, Tomonaga, t’Hooft and so on. After all, the central differences between classical and quantum mechanics may be thought of as given in the difference between the structure of classical state space and Hilbert space. Furthermore, and crucially, given the rejection of particles as the basic ontology in QFT, it seems to us that the sort of developments Cao very nicely charts provide powerful support for the metaphysical SR programme. In particular, he asks about the reality of quantum fields and responds that the concept of a field is used to generate the field equations which describe the structural aspects of ‘these hypothetical entities’ and to ‘extract’ the concept of particle which are the ‘observable manifestations’ of the same hypothetical entity. But then, thinking once more of Redhead’s questions above, what is this ‘hypothetical entity’, over and above the structural aspects? What is it, metaphysically? Here, again, we face the metaphysical underdetermination noted above. Now, as we have said, the constructive empiricist responds to this by waving good-bye to metaphysics but what is the realist going to do? Again, its an ersatz form of realism that can’t answer – in these terms – the question, what is the field? SR has an answer – the field is the structure, the whole structure and nothing but the structure. The thought here is that we can’t describe the nature of the field without recourse to the mathematical structure of field theory. Similarly, if asked to present the ontology of the world according to general relativity one can present the apparatus of differential geometry and the field equations and then perhaps go on to explain the topology and other characteristics of different models of them. There is nothing else to be said and in either case, presenting an interpretation that allows us to visualise the whole structure in classical terms is just not an option. Of course, we agree entirely that our theoretical claims regarding this structure are only partial – accommodating that partiality is precisely what the partial structures programme was developed to handle. So finally and ultimately, we feel there could be more agreement than disagreement between us, once it is clear what is meant by an ‘entity’ or ‘object’. We agree entirely with what Cao says towards the end about the objectivity of our claims regarding the field but unless one can say what it is, over and above its relational properties and appearances, then we would insist that it is not just our knowledge which has a structural character but, metaphysically, the very field itself. We shall end with an invitation: cast off your (entity) realist inhibitions and come join us in the world of structure!
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ACKNOWLEDGEMENTS
Bits and pieces from this paper have been presented in a variety of places, including a symposium on philosophy of science, Lima, Peru 1997, the annual meetings of the British Society for the Philosophy of Science, Oxford 1997 and Sheffield 2000, and a meeting of the Belgium Society for the Philosophy of Science, Brussels 1999. We are grateful to the participants at all these meetings for their criticisms and suggestions but we would particularly like to thank Otávio Bueno, Anjan Chakravartty, Mary Domski and Stathis Psillos for all their helpful remarks. Finally, we would like to thank Tian Cao for his comments on earlier papers of ours and for his kind invitation to contribute to this issue.
NOTES 1 For an illuminating discussion of the history of structuralism, especially as it appears in
the views of physicists, as well as a critique of modern forms of structural realism, see van Fraassen (forthcoming). 2 Thus this form of SR is tied to a ‘cumulativist’ approach to science and the emphasis on the retention of structure can also be found generally among defenders of such an approach. Heinz Post famously offered a political analogy for these shifts in science: although the government (ontology) might come and go, the civil service (structure) remains broadly the same (Post 1971). (We might say ‘it doesn’t matter who you vote for, the structure always gets in’.) 3 These matters are discussed in more detail in Ladyman (1998). 4 The claim is that if observational terms are introduced, the relevant Ramsey sentence becomes falsifiable and triviality is avoided. 5 Post refers to this case as an example of what he calls ‘inconsistent correspondence’, since classical mechanics agrees only approximately with the relativistic form, in the sense that the latter asymptotically converges to the former in the limit and the former asserts a proposition which only agrees with the latter in that limit (1971, 243). For further discussion, see Pagonis (1996). 6 Bueno has suggested that allowing for approximate correspondence may fatally weaken SR since it apparently grants that there may be structural losses, in which case a form of pessimistic meta-induction may be reinstated (private discussion). This is an important point. However, the problem is surely not analogous to that the realist faces with ontological discontinuity since the realist is claiming that we ought to believe what our best scientific theories say about the furniture of the world in the face of the fact that we have inductive grounds for believing this will be radically revised, whereas the structural realist is only claiming that theories represent the relations among, or structure of, the phenomena and in most scientific revolutions the empirical content of the old theory is recovered as a limiting case of the new theory. Another way of dealing with Bueno’s point would be to insist that not all structures get carried over, as it were, but only those which are genuinely explanatory. We could then avail ourselves of Post’s historically based claim that there
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simply are no ‘Kuhn-losses’, in the sense of successor theories losing all or part of the explanatory structures of their predecessors (op. cit., 229). 7 In our view the supposed independence of models from theory is much exaggerated. For example, the recent collection edited by Margaret Morrison and Mary Morgan (1999) contains numerous references to the idea that models are ‘autonomous agents’. Taken literally this claim seems absurd; since models don’t do anything they can’t be agents. However, we take it that it is meant to suggest that models have a sui generis role in scientific practice, and that their development is often independent of theoretical considerations. Of course, it is quite correct to point out that in general models cannot be simply deduced from theories together with background assumptions. On the other hand, it is quite wrong to suggest that it is the norm for the development of models to be entirely independent of theoretical matters, and indeed the case of the development of the London and London model of superconductivity cited by Morrison and Suarez in their papers in the above volume is one for which we have shown in detail that theoretical considerations played an important role (French and Ladyman 1997; see also da Costa and French, 2000). 8 Lloyd has, of course, represented biological theories via the semantic approach and it would be interesting to adapt the partial structures form to such theories as well. 9 She offers the early Schlick as a more suitable candidate. 10 Cf. Russell: ‘. . . although the relations of physical objects have all sorts of knowable properties, . . . the physical objects themselves remain unknown in their intrinsic nature . . . ’ (1912 32–34). 11 If the realist refuses to be drawn on the metaphysics at least at the level of individuality versus non-individuality then how are we supposed to make sense of the impact of quantum mechanics? 12 The importance of group theory in the development of structuralism in general deserves further historical analysis. It obviously played a crucial role in epistemological reflections on geometry (we shall refer to Poincaré’s invocation of groups below) and its introduction into quantum mechanics by Wigner and Weyl extended and deepened this role still further. Eddington, for example, was quite explicit when he wrote, ‘What sort of thing is it that I know? The answer is structure. To be quite precise it is structure of the kind defined and investigated in the mathematical theory of groups’ (Eddington 1939, 147). 13 It would not satisfy Psillos’ mind independence requirement since that is framed in terms of ‘mind independent natural kind structure’ (1999; our emphasis). It is through the introduction of such non-structural natural kinds, Psillos claims, that the Newman problem can be sidestepped. However, even if we grant the cogency of such a view of natural kinds, when we turn to our best theory as the source of such kinds, we find that they are ultimately structural in nature. Thus, one of the most fundamental natural kind divisions is that between fermions and bosons, expressed, as is well-known, in terms of anti-symmetric and symmetric state functions for the assembly of particles respectively. The latter distinction is expressed group-theoretically, and hence structurally, of course. Furthermore, Wigner’s well known classification of the unitary representations of the Poincaré group allows the different ‘kinds’ of elementary particles – characterised in terms of their invariant properties – to be associated with such irreducible representations (see Castellani op. cit., 183–184). 14 One might wonder if this is a sufficiently strong motivation for ontic SR. Thus, Chakravartty has suggested that our metaphysical underdetermination of individuality and non-individuality is analogous to the kind of relatively innocuous metaphysical underdetermination we encounter at the level of everyday objects – whether they should be
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conceived of in terms of substances, for examples, or as mere bundles of properties – which, he insists, the realist is not obliged to resolve (private email). Hence, he argues, although the realist should not simply refuse the constructive empiricist’s challenge on this point, it is not necessary to suspend one’s realist commitments until the problems have been solved. However, there are important disanalogies between ‘everyday’ objects and unobservable ones. First, we have access to tables and chairs in experience so if someone asks us what we believe in we can just point to them, say, but in the case of unobservables the content of belief in them is exhausted by their theoretical description – if that underdetermines their metaphysical nature then our belief is empty. Furthermore, in the case of observable things we have a choice as to what philosophical account of individuality to choose from, but in the case of unobservables it is more basic than that – we can’t say whether quantum particles even are individuals or not. And if we have no basis in the physics for the application of a such a basic metaphysical category then its not clear what precisely is the content of our realism. 15 Bohm’s interpretation might be thought to restore the classical sense of objectivity, with its particles travelling along well-defined trajectories. However, apart from their spatial properties, it is not clear that the particles can be said to unambiguously possess their other (intrinsic) properties, such as mass for example, which are ‘shared’, in a sense, with the quantum potential; for further discussion of the non-classical metaphysics of the Bohm interpretation, see Bedard (1999). 16 Eddington also took the implications of quantum physics for particle individuality as motivating his version of structuralism (op. cit., 124–128). Thus he argues that quantum mechanics implies that the ultimate particles are ‘identical structural units’; hence ‘. . . all variety originates in the structure and not in the elements out of which the structure is built’ (ibid., 135). We know only the structure of the universe (ibid., 142) and this structural knowledge can then be ‘detached’ from the knowledge of the entities forming the structure (ibid., 143). It is interesting that both our motivations above – structuralism as a response to theory change and as a response to modern physics – can be found in Eddington’s comments (ibid., 152–153). With its emphasis on the entities out of which the structure is built or formed, this may appear to be a form of epistemic structuralism. However, Eddington then goes on to talk of the elementary particle as a ‘product of analysis of [the] group structure (ibid., 164) and then argues that these particles are not essential to the existence of the structure. In a remark indicative of something akin to what we have called the ‘ontic’ view he states that ‘[i]n our new point of view the relation comes first’ (ibid., 166), where he identifies the relation to the whole structure (called, unattractively, the ‘uranoid’) as the state, giving rise to what appears to be the occupation number approach found in quantum field theory. There is more to say, of course, about Eddington’s structuralism and about its relationship to his much-derided ‘quantum numerology’ (ibid., Chap. XI). Just to pursue the history a little further, Born argued vehemently against Eddington’s over-emphasis on theory (he considered the latter’s ideas to be a ‘considerable danger to the sound development of science; 1943, 2) and urged that due consideration be played to the role of experiment. The reason we mention Born in this context is that here too a structuralist element creeps in: drawing on the analysis of sense impressions offered by Gestalt psychology, Born argued that ‘. . . the ‘shapes’ of physical things are the invariants of the equations’ (ibid., 12) and that these have the same kind of objective reality as any shape of more familiar things (see also Born (1956, 163)). Cassirer also approached the results of Gestalt psychology from a group-theoretical perspective in his (1944). There is clearly further work to be done unravelling the historical connections here.
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17 It is interesting that Cassirer sees this move as not only removing the ‘dark nucleus’
of the unknowable object laying behind the laws but also as introducing a welcome and fruitful openness to the determination of ‘entities’, according to which they become ‘determinable without limit’ as our knowledge increases. 18 There are clearly analogies with structuralism in the philosophy of mathematics. 19 We are grateful to Mary Domski for bringing this to our attention. 20 Which, for Poincaré, is to be understood in Kantian terms since we bear that idea in ourselves. 21 For an explicit reintroduction of the Kantian approach in the contemporary context, see Mittelstaedt (1998). 22 There is a further issue raised by Bueno: what is the nature of our understanding of these structures themselves? If this is itself structural, then we appear to be caught in a regress; but if it is non-structural, then we appear to have undermined our thorough-going structuralism. We are tempted to respond by making a distinction between the ontology and the description of that ontology. Our claim is that the most appropriate ontological ‘picture’ of the world, given modern physics, is that of the world as structural. This ontology can then be described, mathematically, at the level of the physics itself, using group theory, and set-theoretically, at the level of the philosophy of physics, in terms of partial structures. Of course, both of these modes of representation – group theory and set theory – presuppose distinguishable elements, which is precisely what we take modern physics to urge us to do away with. If we’re going to take our structuralism seriously, we should therefore be appropriately reflective and come up with thorough-going structural alternatives to group theory and set-theory. Weyl, for example, seems to have perceived the implications of the introduction of group theory for the foundations of that theory itself in his discussion of ‘aggregates’ in Appendix B of his (1949). Krause can be seen as continuing this line of work in his attempt to construct a ‘quasi-set theory’ (Krause 1992) but, of course, insofar as this is based on objects which do not have well defined identity conditions, it represents a formalisation of one side of our metaphysical underdetermination, rather than a structuralist attempt to avoid it altogether. What is needed is the construction of a fundamental formalisation that is entirely structural; we shall leave this to future works or future (and cleverer) philosophers. Returning to Bueno’s point, if we were to come up with such a set theory without sets (of objects), we would still have to talk about the structures involved and this would mean setting down identity conditions for them, for example. However, even if these conditions can only be expressed in non-structural terms, we would argue that this is only an expression of our descriptive limitations and does not undermine our ontology. And if we can give a structural understanding of structure, then the regress is surely that which afflicts any such philosophical description – it is not a regress at the ontological level. (Bueno himself offers an empiricist approach to structure which attempts to retain the crucial elements of Ladyman’s form of SR but in a thoroughly empiricist context; see Bueno (1999).) 23 This is not to say that either the Kantian or phenomenologist are anti-realists of the stripe that typically feature in the realism-antirealism debate. 24 See also Auyang (1995), who, interestingly, continues the Kantian tradition in her approach to quantum field theory. She proposes a view of space-time according to which it is absolute, in the sense that it is presupposed by the ‘concept’ of individual things, but not substantival, and structural but not relational, in that the relations involved are only ‘implicit’ (ibid., 138). It is the space-time structure that keeps ‘events’ numerically distinct. The events are entities in an interacting field system (ibid., 129) which are identified by a
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parameter, x, of the relevant base space in a fibre bundle formulation, and divided into kinds via the appropriate group (ibid., 130–132; note, with regard to Psillos’s invocation of natural kinds, that here again the kinds are entirely structural). Events are thus individuated structurally within ‘the whole’ and the conceptual structure of the world as a field is represented by a fibre bundle (ibid., 133). Returning to the nature of space-time, Auyang is clear that neither the space-time structure, nor the event structure should be given ontological priority: ‘[t]he event structure and the spatio-temporal structure of the objective world emerge together’ (ibid., 135). Shorn of its Kantian epistemology, this might provide the through going structuralist analysis of quantum field theory that the metaphysical structural realist could appropriate; we shall leave such appropriation to another work. 25 Dorato gives a version of the Redhead argument here: ‘I don’t know how one can attribute existence as a set of relations in an observable or unobservable domain without also requiring that these relations be exemplified by non-abstract relata, namely the field itself, to be regarded as a new type of substance, radically different from the traditional, Aristotelian ousia’ (1999, 3; his emphasis). That Dorato is inclining towards a form of epistemic structural realism is clear from his insistence that, although we often identify physical entities via their relations, ‘epistemic strategies for identifications should not be exchanged for ontological claims’ (ibid.). The latter claims obtain their warrant from the sorts of lab-based practices that support entity realism and Dorato argues that structural realism needs entity realism to be plausible (ibid., 4; see Morganti, preprint, for further details). However, these practices crucially involve or depend on causal relations and given this, there is nothing in the practices themselves that particularly tells against structural realism and in favour of entity realism. Indeed, causal relations make up a fundamental feature of the structure of the world and the ontic structural realist can simply take such practices and insist they reveal the dissolution of physical objects into structures, including causal ones (cf. Chakravartty 1998). Van Fraassen (op. cit.) has similar concerns in the context of Fock space: all that there is cannot merely be the structure of this space, he insists, because then there would be no difference between a cell being occupied and a cell being unoccupied. Our response runs along similar lines to the above: that our theory talks of occupation numbers does not imply that what is occupying the cell must a non-structural object, individual or not. As Auyang says, ‘To say the field is in a state |n(k1 ), n(k2 ), . . . > is not to say that it is composed of n(k1 ) quanta in mode k1 and so on but rather n(k1 ) quanta show up in an appropriate measurement’ (Auyant op. cit., 159). And what actually ‘show up’ are the causal properties which for us, as we’ve just said, are just further aspects of structure.
REFERENCES
Auyang, S.: 1995, How is Quantum Field Theory Possible?, Oxford University Press, Oxford. Bedard, K.: 1999, ‘Material Objects in Bohm’s Interpretation’, Philosophy of Science 66, 221–242. Born, M.: 1943, Experiment and Theory in Physics, Dover (rep. 1956). Born, M.: 1956, Physics in My Generation, Pergamon Press, New York. Bueno, O.: 1999, ‘What is Structural Empiricism? Scientific Change in an Empiricist Setting’, Erkenntnis 50, 59–85. Cao, T.: 1997, Conceptual Development of 20th Century Field Theories, Cambridge University Press, Cambridge.
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Cassirer, E.: 1936, Determinism and Indeterminism in Modern Physics, Yale University Press (1956). Cassirer, E.: 1944, ‘Group Concept and Perception Theory’, Philosophy and Phenomenological Research 5, 1–35. Castellani, E. (1998), ‘Galilean Particles: An Example of Constitution of Objects’ in E. Castellani (ed.), Interpreting Bodies: Classical and Quantum Objects in Modern Physics, Princeton University Press, Princeton, pp. 181–194. Chakravartty A. (1998), ‘Semirealism’, Studies in History and Philosophy of Modern Science 29, 391–408. da Costa, N. C. A and S. French: 1990, ‘The Model-Theoretic Approach in the Philosophy of Science’, Philosophy of Science 57, 248–265. da Costa, N. C. A. and S. French: 1993, ‘Towards an Acceptable Theory of Acceptance: Partial Structures and the General Correspondence Principle’, in S. French and H. Kamminga (eds.), Correspondence, Invariance and Heuristics: Essays in Honour of Heinz Post, Reidel, Dordrecht, pp. 137–158. da Costa, N. C. A. and S. French: 2000, ‘Theories, Models and Structures: Thirty Years On’, Philosophy of Science; Supp. Proceedings of the 1998 PSA 67, S116–S127. Demopoulos, W. and M. Friedman: 1985, ‘Critical Notice: Bertrand Russell’s The Analysis of Matter: Its Historical Context and Contemporary Interest’, Philosophy of Science 52, 621–639. Domski, M.: preprint, ‘The Epistemological Foundations of Structural Realism: Poincaré and the Structure of Relations’, paper given to the Research Workshop of the Division of History and Philosophy of Science, University of Leeds, Leeds. Dorato, M.: forthcoming, ‘Substantivalism, Relationism and Structural Spacetime Realism’, Foundations of Physics. Dorato, M.: 1999, ‘Cao on Substantivalism and the Development of 20th Century Field Theories’, Epistemologia 22, 151–166. Eddington, A.: 1939, The Philosophy of Physical Science, Cambridge University Press, Cambridge. English, J.: 1973, ‘Underdetermination: Craig and Ramsey’, The Journal of Philosophy 70, 453–462. French, S.: 1989, ‘Identity and Individuality in Classical and Quantum Physics’, Australasian Journal of Philosophy 67, 432–446. French, S.: 1997, ‘Partiality, Pursuit and Practice’, in M. L. Dalla Chiara et al. (eds.), Structures and Norms in Science: Proceedings of the 10th International Congress on Logic, Methodology and Philosophy of Science, Reidel, Dordrecht, pp. 35–52. French, S.: 1998, ‘On the Withering Away of Physical Objects’, in E. Castellani (ed.), Interpreting Bodies: Classical and Quantum Objects in Modern Physics, Princeton University Press, Princeton, pp. 93–113. French, S.: 1999, ‘Models and Mathematics in Physics: The Role of Group Theory’, in J. Butterfield and C. Pagonis (eds.), From Physics to Philosophy, Cambridge University Press, Cambridge, pp. 187–207. French, S.: forthcoming, ‘The Reasonable Effectiveness of Mathematics: Partial Structures and the Application of Group Theory to Physics’, Synthese. French, S. and J. Ladyman: 1997, ‘Superconductivity and Structures: Revisiting the London Account, Studies in History and Philosophy of Modern Physics 28, 363–393. French, S. and J. Ladyman, J.: 1998), ‘A Semantic Perspective on Idealisation in Quantum Mechanics’, in N. Shanks (ed.), Idealization IX: Idealization in Contemporary Physics:
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Pozna’n Studies in the Philosophy of the Sciences and the Humanities, Rodopi, pp. 51– 73. French, S. and J. Ladyman, J.: 1999, ‘Reinflating the Semantic Approach’, International Studies in the Philosophy of Science 13, 103–121. Huggett, N.: 1997, ‘Identity, Quantum Mechanics and Common Sense’, The Monist 80, 118–130. Krause, D.: 1992, ‘On a Quasi-Set Theory’, Notre Dame Journal of Formal Logic 33, 402–411. Ladyman, J.: 1998, ‘What is Structural Realism?’, Studies in History and Philosophy of Science 29, 409–424. Ladyman, J.: 2000, ‘What’s Really Wrong with Constructive Empiricism? van Fraassen and the Metaphysics of Modality’, British Journal for the Philosophy of Science 51, 837–856. Laudan, L.: 1981, ‘A Confutation of Convergent Realism, Philosophy of Science 48, 19–49. Mikenberg, I., N. C. A. da Costa, and R. Chuaqui: 1986, ‘Pragmatic Truth and Approximation to Truth’, Journal of Symbolic Logic 51, 201–221. Mittelstaedt, P.: 1998, ‘The Constitution of Objects in Kant’s Philosophy and in Modern Physics’, in E. Castellani (ed.), Interpreting Bodies: Classical and Quantum Objects in Modern Physics, Princeton University Press, Princeton, pp. 168–180. Morgan, M. and M. Morrison (eds.): 1999, Models as Mediators, Cambridge University Press, Cambridge. Morganti, M.: preprint, ‘Structural Realism and Experimental Realism: A Possible Realist View of Scientific Knowledge’. Pagonis, C.: 1996, Quantum Mechanics and Scientific Realism, Ph.D. thesis, Cambridge University Press, Cambridge. Poincaré, H.: 1905, Science and Hypothesis, Dover (1952). Post., H. R.: 1971, ‘Correspondence, Invariance and Heuristics’, Studies in History and Philosophy of Science 2, 213–255. Psillos, S.: 1999, Scientific Realism: How Science Tracks Truth, Routledge, London. Redhead, M. L. G.: 1995, From Physics to Metaphysics, Cambridge University Press, Cambridge. Redhead, M. L. G.: 1999, ‘Quantum Field Theory and the Philosopher’, in T. Cao (ed.), Conceptual Foundations of Quantum Field Theory, Cambridge University Press, Cambridge. Russell, B.: 1912, The Problems of Philosophy. Saunders, S.: 1993, ‘To What Physics Corresponds’, in S. French and H. Kamminga (eds.), Correspondence, Invariance and Heuristics: Essays in Honour of Heinz Post, Reidel, Dordrecht, pp. 295–325. Van Fraassen, B.: 1991, Quantum Mechanics: An Empiricist View, Oxford University Press, Oxford. Van Fraassen, B. C.: forthcoming, ‘Structure: Its Shadow and Substance’, in P. Ehrlich and R. Jones (eds.), Reverberations of the Shaky Game: Essays in Honor of Arthur Fine, University of Chicago Press, Chicago. Werkmeister, W. H.: 1949, ‘Cassirer’s Advance Beyond Neo-Kantianism’, in P. A. Schilpp (ed.), The Philosophy of Ernst Cassirer, The Library of Living Philosophers, pp. 757– 798. Weyl, H.: 1949, Philosophy of Mathematics and Natural Science, Princeton University Press, Princeton (1963).
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Worrall, J.: 1996, ‘Structural Realism: The Best of Both Worlds?’, in D. Papineau (ed.), The Philosophy of Science, Oxford University Press, Oxford, pp. 139–165 (originally published in Dialectica (1989), 43, 99–124). Worrall, J.: 2000, ‘Miracles and Models: Saving Structural Realism?’, paper given to the Annual Meeting of the British Society for the Philosophy of Science, Sheffield. Zahar, E.: 1994, ‘Poincaré’s Structural Realism and his Logic of Discovery’, in G. Heinzmann et al. (eds.), Henri Poincaré: Akten des Internationale Kongresses in Nancy. Steven French Division of History and Philosophy of Science School of Philosophy University of Leeds U.K. E-mail:
[email protected] James Ladyman Department of Philosophy University of Bristol U.K. E-mail:
[email protected]