Alhassanain(p) Network for Heritage and Islamic Thought

7. Bringing Back the Bundle

Thus a further, broad option would be to stick with truth,standardly understood, resisttruthmakers and offer some form metaphysical account in terms of which we ‘recover’ the relevant features we are interested in, in this case, particles, from our base ontology, in this case, structures, or features thereof. There are various routes one might take, but here I shall consider one that has particular relevance in thestructuralist context.

As noted previously, the earlystructuralists , such as Cassirer andEddington , expressed their ontological commitments in terms of opposition to what they saw as the generally acceptedsubstantivalist views of the day. This naturally leads to comparisons with another well-known anti-substantival ontology, namely the so-called’ bundle’ view of objects, according to which the latter are nothing more than bundles of properties (French 2001). Indeed, more recently,Chakravartty (2007) has defended a form of structural realism that holds this view at its core. Specific forms of this view will then vary according to their account of the nature of properties, their instantiation and so forth.Chakravartty prefers adispositionalist account (for criticism and a response see Frenchforthcomingb andChakravartty forthcoming, respectively); others opt for trope-theoretic formulations (Morganti 2009). Whatever form one adopts, some modification will be required when importing it into the quantum context.Standardly the Principle of Identity ofIndiscernibles has been allied to the bundle view as a kind of metaphysical guarantor of thediscernibility of these object-bundles in the absence of substance, which rules out qualitative duplicates, but that Principle faces well-known problems here (see French and Krause 2006, Ch. 4). Again as indicated previously, Saunders’ revival of the Principle inQuinean form may offer a way forward and the consequent inclusion of relations into the bundle, although taking this view away from the originalLeibnizian vision, takes it closer to astructuralist conception, which in turn meshes withChakravartty’s version of the bundle view for example[14] .

The question now is, can this bundle view of objects be allied with an appropriatemereological metaphysics that is consonant, at least, with astructuralist base ontology? Paul’s ‘Mereological Bundle Theory’ (MBT) suggests a positive answer. The key move is to regard ‘our knee-jerk way of thinking about the things physicists describe as “objects” or “particles” as little material-like hunks ofstuff [ as] fundamentally mistaken.’ (Paul forthcoming; see also her contribution to this issue). According to this account, the world is not built from the bottom up, ‘spatio -temporal hunk by spatiotemporal hunk’, as it were. Rather, we are presented with a one category ontology in which the only category is that of properties, with ‘objects’ understood as bundles of these properties and ‘bundling’ conceived of as restricted qualitative composition involving fusion. Thus, Paul writes,

‘My personal preference is for a contingent, purely qualitativemereological bundle theory wherespacetime , as well as everything else there is, is constructed from fusions of properties.’

Earlier bundle theories invoked primitive and hence rather mysterious relations of ‘compresence ’ or ‘concurrence’ to tie the bundle together and form an object. Paul avoids the mystery by understanding bundling in terms of fusion or part-hood, a well-known relation frommereology in general. In particular, fusion is taken to capture the idea that bundling involves thecreation of objects and by restricting the relevant compositionappropriately, the creation of bizarre or generally unwanted objects can be avoided. Everyday objects and those that can bespatio -temporally located in general are effectively created by fusing the relevant properties withspatio -temporal location, where the latter is also understood in property terms, rather than a ‘sui generis entity’ (see op. cit. p. 12). I will return to this aspect shortly butits worth noting here that Paul takes the relationship between property fusion andspatio -temporal fusion to be crucial for understanding how objects can be composed of property parts and also smallerspatio -temporal parts (p. 6). In particular, it is crucial for her view in general that property parts be seen as no different in kind fromspatio -temporal parts – the former are not to be understood as abstract, with the latter as concrete; rather properties, or at least some of them, and in particular those that are everyday objects, are concrete.

This understanding of properties also sheds light on the nature of fusion: it does not somehow produce concrete entities out of abstract ones but rather just creates the one (object) from many (properties). All fusions, on this account, are fundamentally qualitative fusion. Thus,

‘There is no mystery about how material objects are built from smaller material objects while also being built from property parts, because material objects are only built from property parts.’(ibid., p. 9)

What about the individuation of objects on this view and, in particular, the role of the Principle of Identity ofIndiscernibles ? As Paul notes, the alliance of this Principle with the bundle theory depends on accepting the ‘supervenience of identity thesis’ which holds that the ‘identity of x’ reductively supervenes on the qualitative properties of x. But as she says, one could deny this thesis and thus avoid having to adopt the problematic PII. One way of doing this would be to accepthaecceities , primitivethisnesses or suchlike as grounding identity, although that would undermine a crucial motivation for adopting the bundle view in the first place. Alternatively, one could take the thesis to be false on the grounds that identity facts do not supervene on any qualitative properties but simply on the object x itself (ibid., p. 16). As Paul states, this amounts to a form of primitive individuation but one that involves an ungrounded difference and hence avoids a lot of ‘ontologically heavy machinery’. Again, I’ll come back to this point below, butits important to note the motivation here is to accommodate the kinds of symmetries that thestructuralist sets such store by:

‘… the primary ontological choice one must make, given the seeming possibilities of various sorts of qualitative symmetries, is not betweenontologies but between accommodating the possibility of these symmetries or not. Only if one chooses to accommodate the possibilities, must one then choose betweenontologies : between a universe with primitive grounded differences and a multiplicity of categories, or a universe with primitive ungrounded differences and a single category.’ (ibid., p. 19)

However, a well-known problem arises in the current context, as Paul acknowledges, namely the possibility of multiple, qualitatively indiscernible particles at the same location, or, more generally, in the same state (ibid., pp. 21-27). If we reject the attempt to extend Saunders’ approach to bosons, then the existence of n-boson states appears to pose a problem for Paul’s property basedmereology . The solution she suggests is that such states do not have the quantitative structure their name implies: what we have is a property instance of ‘two boson-ness ’, where the latter is an example of what Armstrong called ‘fundamentally intensive properties’, in the sense that they lack structure and cannot be reduced to co-instantiations or co-occurrences of multiple instances of unit properties such as ‘being a boson’ (a well-known example of an intensive property would be ‘being sweet’; ibid., p. 24). Thus, the bundle view can accommodate the above possibility by acceptingstructureless intensive properties and in effect denying that we havetwo, or more, objects in such states – a move that also allows the view to mesh with QFT (ibid., p. 24).

Now, this is an interesting attempt to bring novel metaphysical considerations to bear on issues of identity andobjecthood in quantum physics, and I think it generates a useful comparison withstructuralist views, as I shall briefly discuss below. I also have a number of concerns, however. First of all, it comes at a cost: that of introducing many intensive properties. As Paul notes, Armstrong’s vision of eliminating such properties has to be given up in the face of the above analysis of boson states, but even those who do not share his vision may balk at the inflation of our property ontology that this entails. Of course, the alternative objects-as-distinct-from-properties ontology is likewise vast in terms of the number of items it entertains but at least it presents fewerkinds : the kind ‘boson’, under which fall numerous objects, as opposed to numerous ‘kinds’ of property, such as two-boson-ness , three-boson-ness and so on. Secondly, the denial of internal structure does not sit well with the experimental ‘facts’: we can manipulate such states and obtain what appear to be single particles from them. Of course, between observing the flash on the scintillation screen and asserting the existence of a single particle a number of inferential steps must be laid down, but something needs to be said about how the property instance of ‘two-boson-ness ’, say, can yield an instance of ‘one-boson-ness ’ (perhaps one could say that an operation of ‘de-fusion’ is involved).

Thirdly, and restricting ourselves to QM with QFT left to one side for the moment, Paul’s analysis is explicitly couched in terms of the so-called ‘Received View’ of the implications of QM for identity and individuality (although she herself thinks it is a mistake to think of these implications in these specific terms). She takes permutation invariance to imply that n-boson states, for example, should not be understood as involving multiple indiscernible bosons, but, as indicated above, aspartless intensive properties. However, as is well-known, quantum statistics and permutation invariance in particular is also compatible witha metaphysics of quantum particles – even bosons – as individual objects (French and Krause 2006). Of course, such a view comes at a cost, with regard both to how identity and individuality arecharacterised , and to how we understand quantum states. However, instead of introducing intensive properties, we can regard such states in terms of properties that are non-supervenient (Teller 1986; French and Krause op. cit. Ch. 4), an option that does not seem incompatible with MBT. As for the former cost, Paul would presumably want to advocate an understanding of individuality in terms of ungrounded difference. Here the basis of the difference would be the ‘two-ness ’ or, more generally, ‘n-ness ’ of the state, but again there doesn’t seem to be anything there that would conflict with this view. Alternatively, she could appeal to Saunders’ understanding of PII – for fermions at least – and take this as grounding the particles’ identity. This would involve the inclusion of irreducible relations within the bundle, something that takes this view closer to astructuralist understanding. In either case, one will still be able to accommodate the relevant symmetry represented by permutation invariance without having to accept intensive properties.

Of course, one could reject this latter option and embrace the Received View on the grounds that it meshes better with QFT. As a way of deciding between interpretations of particles inQM I think this is a problematicmanoeuvre (see French and Krause op. cit., pp. 192-197) but Paul’s application of MBT to QFT is certainly suggestive. A standard way of understanding fields in this context is in terms of field quantities instantiated at, or smeared over, space-time regions (for a discussion of possibleontologies for QFT see, again, French and Krause op. cit., Ch. 9). Typically the latter are given some form ofsubstantivalist interpretation, with the former taken to be properties-as-universals possessed by or instantiated in this substance. Taking the field to be a bundle of qualitative andspatio -temporal properties is an interesting step and bears comparison ofAuyang’s structuralist view of physical structure and space-time structure as emerging together as aspects of the world-structure , a view that is also similar toEddington’s (Auyang 1995).

The anti-substantivalist stance that lies behindmereological bundle theory obviously meshes well with structural realism, particularly insofar as MBT offers a one-category ontology in which the distinction between objects (qua bearers of properties) and properties themselves evaporates[15] . Indeed, if the latter include, as they should, relations and non-monadic properties in general, then the distinction between bundle theory andastructuralist ontology likewise evaporates (cf.Chakravartty 2007). Furthermore, the co-occurrence of certain properties lends itself to astructuralist understanding. Paul acknowledges this as a possible worry about MBT: properties, it is claimed, differ from objects in that the former may be co-dependent in ways that the latter are not (op. cit., p. 11). Her response is that the fact of co-occurrence (understood on her view as involving fusion) does not imply ontological co-dependence:

‘It just means that there are certain facts about the universe that result in certain connections: for example, that anything with mass also has extension.’(ibid.)

I think that understanding MBT from astructuralist perspective offers a more robust response: the supposed ontological independence of objects is problematic to begin with.Cashing out this independence in terms of the grounds for identity and individuality leads to the metaphysicalunderdetermination in the quantum context that OSR aims to overcome. Dropping this presumption of independence (derived ultimately from reflections on everyday objects as bits and pieces of matter banging about in the container of space-time) then removes the source of the worry. Furthermore, Paul’s suggestion that these connections can be related to the role of laws can be bolstered by astructuralist understanding of this relationship. Thus she writes,

‘Perhaps these connections are simply contingent facts about how the qualitative profiles of objects are to be completed that are derived in some way from the physical laws of the world.’(ibid.)

As articulated elsewhere (Cei and French forthcoming), thestructuralist reverses the current (mainlydispositionalist ) understanding of the relationship between (intrinsic) properties and laws by taking the latter to have ontological priority as features of the structure of the world, with the former as derivative. On this view, the connections Paul speaks of are precisely those that thestructuralist will want to highlight as physically significant (not perhaps the mass-extension relationship but certainly that between spin and particle kind as given by the relevant statistics, for example). Further connections are expressed by the symmetry principles that play such a prominent role in current physics and which thestructuralist sets at the core of her ontological world-view. As already indicated, the most basic kind distinction between fermions and bosons is captured via symmetry considerations, as represented by group theory.And as is well-known Wigner established the connection between symmetry and the relevantcharacterising properties via the irreducible Hilbert space representation of the (restricted)Poincaré group. In addition there are the so-called internal symmetries, such as that associated withcolour (in quantumchromodynamics ) as represented bySU( 3), which famously underpins the classification of hadrons[16] . Again, the relevant properties thatcharacterise both the kinds and their inter-relationships are connected to the relevant symmetries in such a way that the meaning of a physical quantity such as spin can be understood as deriving from its representation in terms of theeigenvalues of the generators of the relevant group algebras and the (second-order) properties of these quantities is given by the associated structure.

And just to pursue this line a little further, as Paul notes, the ‘flip side’ of her response to the above worry is that it also answers the worry about unrestricted composition since if there are ‘deep’ facts about the co-occurrence of properties there will also be ‘deep’ facts about which cannot co-occur. Thus there will becontingent restrictions on composition on this view. Of course, a little care needs to be taken in understanding the sense of contingency here since on aunificationary view of the progress of science the extent of co-occurrence will spread until we arrive, presumably, at the Theory of Everything on which all (physical) properties are connected.

In this context we might then bring togetherblobjectivism and the bundle theory under thestructuralist umbrella. A ‘global’ bundling of the relevantpolyadic properties will yield the blob as structure of the world, with a ‘local’ bundling of the relevant properties giving us the putative ‘objects’. Of course, there remains the issue of accounting for the complexity of the appearances, either through manners of instantiation, or an appropriate notion ofparthood with restricted composition.

Furtherrmore , on a naturalistic view these ‘deep’ facts will ultimately be physical facts and hence the restrictions on composition will ultimately be read off from the relevant physics. The danger here is, again, that the metaphysics is effectively gutted by the physics and contributes at best some form of label for the relationships that are fundamentally explicated in physical terms. Thus consider again the interesting suggestion of bringing space-time within the remit of MBT, with thespatio -temporal location of physical objects understood in terms of the fusion of ‘physical’ properties withspatio -temporal ones. The notion of ‘fusion’ is carrying all the metaphysical weight here, and explicating it further so as to relieve some of that burden runs the risk of cashing it out entirely in physical terms. Of course, this is a general worry when it comes to the relationship between metaphysics and science, but it has particular bite in this context.

Conclusion: Back to Composition

We recall the Hawley’s suggestion that there will be different answers to the General Composition Question for different sorts of things. Thus we might expect that the answer obtained when it comes to ‘everyday’ objects such as tables and their constituent particles will be different from what we get when we consider particles (as objects) and structures. In the former case, and from a naturalistic stance, we would expect the metaphysics of composition to track the relevant physics. This raises the twin possibilities that there may be little more for the metaphysics to add to thisphysicalist account; and that it may push us towardseliminativism . This may not be as problematic as some seem to think since there are ways in which we can still make statements about these everyday objects without having to incorporate them into our ontology. Of course, some of these ways – such as Cameron’s version oftruthmaker theory – deny the significance of the GCQ to begin with. When it comes to particles and structures, the comparison with identity criteria that Hawley makes with regard to the GCQ again needs to be treated with some care when it comes to quantum particles, at least. Again we recall that there is a fundamental form ofunderdetermination in this context, one response to which is to abandonobjecthood and associated identity criteria entirely, leading to theeliminativist form of OSR. Likewise, from that perspective we should abandon (general) object based composition, for obvious reasons.

Thus taking the Special Composition Question as a constraint, the ‘right’ ontology must provide systematic and general answer to the question: Under what circumstances do several distinct objects compose an object? From the perspective of the view that the latter have a kind of derivative existence, composite objects ‘exist’, but only derivatively so the answer to the SCQ is ‘never’, since there are, strictly, no composite objects. Likewise, according toblobjectivism there is only one concrete particular and no composite objects. So, again, the answer to the SCQ is never, but in this case because there is only one real object. When it comes to simples and truth-makers, acceptance of the existence of the (purportedly) composite object does not bring ontological commitment to such objects. There are no such objects over and above the simples, although we can of course still make statements and utter truths about composite objects – they are, as it were, an ‘ontological free lunch’ (Cameron 2008).Yet again, then, the answer to the SCQ is never, as no collection of objects ever composes and there are no composite objects, just the simples.Mereological Bundle Theory, on the other hand, does allow for composition. Here we have very many objects, since properties count as such, and composite entities will compose according to the nature of the bundling. As Paul insists, this composition is not unrestricted and on a naturalistic approach the relevant restrictions will track the kinds of relationships represented in the physics.

Finally, we can then apply the notions of existential andesssntial dependence to the relationship between structures and objects (see French 2010). Here it is useful to distinguish what can be called,

‘Identity Dependence’:

(ID) ‘objects’ are dependent for their existence on features of the structureiff the identity of such objects is dependent on the structure;

from

‘Constitutive Dependence’:

(CD) ‘objects’ are dependent for their existence on features of the structureiff the constitutive nature/ ‘essence’ of such objects is dependent on the structure.

ID captures what is behind Non-Eliminativist OSR, where the identity of (putative) objects is given in terms of the relevant relations – those exemplified by the singlet state in the case of fermions (Saunders 2006), orspatio -temporal relations in the case of space-time points (Stachel 2002). The worry here is that if the identity, as in weakdiscernibility , of these objects is explained in terms of the relevant relations, then it is derivative upon the latter. In that case, the only grounds for claiming that we retain a notion ofobjecthood at all, even as ‘thin’ as this, is by adopting a particularQuinean reading of ontology off theories, which may be contested. CD, on the other hand, obviously fits withwith Eliminativist forms of OSR and captures the intuition behind the derivative existence of objects on this conception.

All of these moves come with some cost. However, at the very least they can be used to assuage some of the concerns associated with the kind of revisionary ontology that structural realism presents. In particular, we can still say things about everyday objects while maintaining that only elementary particles exist, either by adoptingHorgan andPotrc’s division betweentruth as indirect- and direct-correspondence, or a form oftruthmaker theory with simples. Proceeding down a metaphysical level, we can still say things about elementary particles while maintaining that there are no objects, only structures. How composition looks from thisstructuralist perspective then depends on which of the above metaphysical moves one decides to make and, of course, on the form ofontic structural realism adopted.

According to ‘eliminativist ’ OSR, there are no objects, whether composite or composing, so at first glance the answer to the SCQ would again seem to be ‘never’, but now because there are no composing objects. Even at second glance, as it were, one might reach the same answer: if one thinks of the structure of the world in a monadic fashion, and draws the comparison with ‘the blob’, then again the answer is ‘never’ but now of course the reason is that there is only one ‘object’ (broadly understood), namely the structure, with the requisite ‘manners of instantiation’. Alternatively, one could take the features and aspects of the structure as the appropriate simples on the truth-makers approach and still give the same answer to the SCQ. If, however, one thinks of the structure as a big bundle (and relational too), then the nature of composition, and hence the answer to the SCQ, will depend on which features one is talking about, the nature of the physical relationships and so on.

Non-Eliminativist OSR, with its talk of ‘thin’ objects, may appear to invite consideration of composition, but the worry here is that the ‘objects’ may be too thin to compose. Remember: for fermions we have weakdiscernibility in entangled states, for bosons the situation is more problematic. Of course, if one were to adopt MBT, with Saunders’ revised form of PII, perhaps, the issue would be moot: even thin, the ‘objects’ would be nothing but bundles of properties and composition would proceed along the lines sketched above. Alternatively, as thin as they are, these objects may be robust enough to act as simples without the concerns attendant upon regarding ‘features of structure’ in this way. Such concerns have to do with discerning such features in such a way that we can say they function as distinct simples appropriate for making true the relevant statements – weakdiscernibility may just be enough for that.

At this point, one might well feel that we haveproceeded too far down the level of detail, to the ‘nit-picking’ stage. However, I believe that deploying such metaphysical moves is absolutely crucial if we are to develop forms of realism that are appropriate for current physics.Ladyman and Ross have famously berated the metaphysicians for constructing speculative proposals that at best draw on images of physics that have long since been outdated. More generally, ‘physics-lite ’ metaphysics runs the risk of floating free from any contact with modern science (Ladyman and Ross, 2007 p. 9). On the other hand, metaphysics-lite realism runs the risk of incomprehension and certainly it is not enough to pose a revisionary ontology, whether of wave-functions in configuration space, density operators in space-time, or structures, in whatever form, without articulating that ontology in metaphysical terms. And one of the things I want toemphasise is that, however one views the current state of metaphysical research, it lays out for us an array of tools andmanoeuvres that we can deploy in the service of that articulation.

Less obviously, perhaps, the humility that has to be adopted towards many features of today’s metaphysical views allows these views to be insulated from physics (cf.Ladyman and Ross 2007, p. 22). Consider the question whether the metaphysicians’ simples are individuals or not? Quantum physics can’t answer that, because of theunderdetermination touched on previously. The correct response, I believe, is to reduce the level of humility that has to be adopted, in order to bring these metaphysical views into closer accordance with the relevant physics. Doing this involves reducing the number of unknowable metaphysical facts by reducing the basis for such facts. The obvious example would be the notion of ‘object’: removing that from our pantheon resolves the aboveunderdetermination and moves our metaphysics closer towards modern physics. But to make sense of an object-less ontology, we need to draw on the kinds of moves I’ve sketched here. Talking of wholes and parts and composition in the absence of a consideration of the relevant physics is just armchair metaphysics mongering; but simply pointing to the physics leaves us with just a set of equations, at worst, or at best, a partial interpretation cashed out in crude metaphysical terms that sit uneasily with the physics itself. What I’ve tried to do here is indicate a possible ‘third way’ in which the physics motivates a certain kind of realism and we then draw on the range of options available to help make metaphysical sense of it. This is not the only way to proceed, but proceed we must if we are to construct aphilosophy of physics.

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Notes

5. MetaphysicalManoeuvres

5.1Manoeuvre 1: Revise our Semantics

We could adopt a form of error theoretic approach, according to which the sentence ‘Tables exist’ is understood to be simply false but it is allowed that we can still pragmatically use such sentences. Such approaches can be found in the philosophy of mathematics and ethics and Miller (2010) distinguishes them as follows: one can reject the claim that the relevant objects exist, or one can admit that they exist but deny that they instantiate the relevant properties. Thus, in the philosophy of mathematics one can find forms offictionalism that deny that mathematical objects exist and the statements of mathematics are strictly false. Nevertheless mathematics serves a pragmatic purpose in helping derive relevant conclusions, and the relevant statements can be taken as ‘true-within-the-derivational-context’ or more broadly, within the ‘story’ of mathematics, just as statements about Sherlock Holmes, for example are true within the stories of Arthur Conan Doyle. Likewise, one could insist that ordinary objects do not exist, that all our statements about them are strictly false, but that nevertheless beliefs about such objects serve a pragmatic purpose and the relevant statements can be regarded as ‘true-within-the-narrative-we-construct-for-our-everyday-lives’.

Alternatively, one could adopt something like the error-theoretic account one finds in ethics: there, it is not denied that people exist (at least not typically) but the error-theorist insists they do not have the moral qualities usually attributed to them and hence the declarative statements one finds in ethics are strictly false. Now the argument for such a view depends on the claim that there are no objectively prescriptive qualities (see Miller op. cit. for a nice summary) and the qualities attributed to everyday objects certainly do not seem to be prescriptive. Furthermore, adapting something like this for everyday objects would lead to the bizarre conclusion that there are tables, but they do not possess the properties they are usually taken to have, such as solidity for example. One could certainly maintain that solidity can be reduced to theantisymmetry of the collective wave function, as indicated above, and thus that insofar as it is regarded as more than that, nothing is solid (contraStebbing andThomasson ), but then the table, as an object, would possess neither the properties it is usually said to have, nor those the latter are reduced to, since these are only attributable to quantum particles and their aggregates.

5.2.Manoeuvre 2: Revise our notion of existence, truth and/or ontology

We could account for the appearances – that is, our apparent experience of tables – and maintain the truth of the relevant sentences by introducing some notion of derivative existence, or by deploying a form of truth as indirect correspondence, or by developing the well-known account oftruthmakers . There are undoubtedly other metaphysical tools we could use, but I shall focus on these.

5.2.1.Manoeuvre 2a: Derivative existence:

So, we could maintain that the sentence ‘Tables exist’ is true but take the sense of ‘exist’ here to be derivative. This is not, perhaps, a well trodden metaphysical path to take, given our standard understanding of existence. Although as we shall see, the other two sub-options can be thought of as leading to a form of derivative existence, it is not a metaphysically robust form; that is, when it is introduced in these contexts we are reassured that it is just a way of speaking. A notion of derivative existence that is more than this does not seem to feature prominently in the metaphysicians’toolbox, and for good reason perhaps, since it would require modifications to the standard syntax and semantics associated with the existential quantifier.

However, and interestingly, given thestructuralist theme of this paper,Eddington can be thought of as adopting something like this kind of view in his application of structuralism to the concept of existence itself (French 2003). He rejected ‘‘any metaphysical concept of ‘real existence’’’ (1939, p. 162) and introduced in its place a ‘‘structural concept’’ of existence (1946, p. 266). This followed from his analysis of claims such as ‘‘Tables exist’’ as half-finished sentences, requiring completion instructuralist terms[9] . Thus, atoms and electrons, for example, ‘‘exist,’’ in this derivative sense, since they are analyzed as aspects of structure. The question then is, what about the world structure itself, does that exist? To say that this exists would result in another half-finished sentence byEddington’s lights, for what further structure could the physical structure be a part of?Eddington maintained that this question never actually arises within his epistemology: having described the nature of physical knowledge, understood itself as a description of the physical universe, nothing further is added to our knowledge of it if one were to say ‘‘and the physical universe exists.’’

He then went on to consider the structure of existence itself,characterised as having only two values and thus represented in terms of idempotent symbols (French op. cit. pp. 249-250). Interestingly, this takes him toward the occupation number interpretation of quantum field theory, couched in terms of a group theoretic analysis from which particles effectively emerge. Returning to the issue of the two tables,Eddington was explicit that it was by analyzing existence in this way that one could respond to the concerns of philosophers such asStebbing . Thus to recapitulate, ‘Tables exist’, on this view, must be understood as a half-finished sentence, to be completed by incorporating structure. The full sentence will then be ‘Tables exist within a certain structure’ and in this sense their existence can be understood as derivative.

Interestingly, given the themes of this issue, it seems we can usefully apply this analysis to the quasi-particles of condensed matter physics. These arise from the collective effect of a macroscopic aggregate with an atomic lattice structure, such as a crystal (for a useful analysis, seeFalkenburg , 2007, esp. pp. 243-46). There is a considerable body of theoretical and experimental work devoted to studying such effects, as they may play a crucial explanatory role with regard to certain phenomena. The quantum Hall effect, for example, has been taken to provide compelling grounds for accepting the existence ofanyons , quasi-particles that arise in systems that are confined to only two spatial dimensions and whose statistics differ from either Bose-Einstein or Fermi-Dirac (for an excellent review see Stern 2008). Nevertheless, quasi-particles in general are ‘nothing more’ than excitations of such a lattice which propagate through the structure and interact as if they were ‘standard’ or ‘normal’ particles. Of course, for theontic structural realist, the latter are ‘nothing more’ than nodes in the fundamental structure of the world, but the crucial difference is that both the dynamical properties of quasi-particles and their independence arise from certain approximation procedures applied to the excitations of the relevant collective (Falkenburg op. cit., p. 240). In particular, without the collective, the quasi-particles would not exist; henceFalkenburg refers to them as ‘fake entities’.

5.2.2.Manoeuvre 2b: Tweak Truth:

OnEddington’s view, statements such as ‘Tables exist’ cannot be taken as either true or false, since they are incomplete. Taking such statements to be non-truth-apt might be seen as forcing too radical a revision of our standard semantics, so an alternative would be to continue to take them to be true, but explicate truth in something other than the standard correspondence sense.Horgan andPotrc canvas just such a view in theirdefence of what they call ‘austere’ realism, which also eliminates ‘everyday’ objects, but on the grounds that they appear to be vague and since ontological vagueness is impossible, they must be removed from our ontology qua objects (Horgan andPotrc 2008; see alsoHorgan’s contribution to this issue). The extension of this argument to the objects of ‘scientific’ ontology may be blocked by the lack ofsorites susceptibility in such cases (Darby 2010), which would render their realism considerably less austere. However, what is important for my purposes here isHorgan andPotrc’s use of contextual semantics. Thus they write:

‘Numerous statements and thought-contents involvingposits of common sense and science are true, even though the correct ontology does not include these posits. …

Truth for such statements and thought contents is indirect correspondence.’ (Horgan andPotrc 2008, p. 3)

Note that they accept that tables, for example, are not to be included in our ‘correct ontology’ but we can continue to utter statements about them and regard these statements as true, but with truth understood not in terms of correspondence along the usualTarskian lines, but in that of indirect correspondence. This is understood as semantic correctness under contextually operative semantic standards (ibid., p. 370, in terms of which the relevant statement is made true not by sometruthmaker but ‘… by the world as a corporate body …’ (ibid.). Thus the claim ‘There are tables’ is true, in the ‘indirect correspondence’ sense, under the contextually operative standards governing ‘ordinary’ usage. However, these are not the standards appropriate for the context of ‘serious ontological enquiry’. If we designate in bold those posits which feature in this enquiry, then ‘There are tables’ is true but there are no tables. In particular, ‘There are tables is true, under the contextually operative standards governing common usage and ‘There are no tables’ is true, under the much rarer semantic standards that apply to ‘direct correspondence’, where this involves the standardTarskian account of truth. The typical reaction of many to the elimination of objects can then be dismissed as a competence based performance error (ibid., p. 122).

Even if we were to accept that ‘scientific’ objects are vague and can also be eliminated, there may be more than one outcome of ‘serious ontological enquiry’ compatible with austere realism.Horgan andPotrc survey and dismiss two broad and potentially viable austereontologies (Ch. 7): ‘snobjective non-compositionalism ’, which includes only non-vague, perfectly precise simples and no composites; and ‘snobjective universalism’, which allows ‘snobjects ’ to compose unrestrictedly. Three variants of the first are considered: those that countenancesnobjective ‘non-regions’ – that is precise objects that are notspatio -temporal regions – those that involvespatio -temporal points only (‘snobjective pointillism’) and those that involve both. The first and third are ruled out on the grounds that the only candidates for such precise objects are elementary particles and these, they claim, are more like clouds than billiard balls. Hence they count as vague and can be dismissed. Here, as elsewhere in current metaphysical discussions, we find the argument depending upon a rather crude semi-classical framework. As it turns out,a metaphysics of individual ‘snobjects ’ can be made compatible with quantum physics (see French and Krause 2006), although so can alternative accounts, of course.

With ‘snobjective pointillism’ eliminated on the grounds of the problems it would cause for the instantiation of mental properties, it is ‘universalistsnobjective regionalism’ that is left as the main contender toblobjectivism . Here considerations of ‘deep ontological parsimony’ are brought into play: we should treat as few features of our metaphysics as actual and ontologically basic as we can. Sinceuniversalist snobjective regionalism yields a compositionally unrestricted plethora ofspatio -temporal regions, all of which are actual and ontologically fundamental,Horgan andPotrc takeblobjectivism to be preferable on grounds of parsimony. Their conclusion, then, is that there can be only one concrete object – the ‘blobject ’ – about which statements are true in the standard correspondence sense.

There are two things to note. First, this obviously yields a radically minimalist ontology in one sense, although asHorgan andPotrc point out, theblobject manifests considerablespatio -temporal structural complexity and local variability. I shall briefly return to this below. Secondly, although this is an interesting way of resolving our dilemma, it raises an obvious worry about the context dependence of this notion of truth (whichHorgan andPotrc acknowledge).Korman (2008) argues that it leads to a form of relativism with regard to the content of the relevant statements: suppose Julie is in our ‘everyday’ context, and Kate is in that of ‘serious ontological enquiry’. Each utters the sentence ‘tables exist’. According toHorgan andPotrc , Julie said something true (but in the indirect sense) and Kate something false (in the direct sense). However, if the content of the sentence is invariant across context in the way thatHorgan andPotrc appear to suggest (op. cit. section 3.5), then,Korman insists, the truth and falsity of that content must vary withcontext, and relativism results. However, the examples thatHorgan andPotrc consider – that cover both diachronic and synchronic meaning change – all involve differences governed by the relevant standards, whether those of direct or indirect correspondence. In the case of Julie and Kate, we have different standards brought into play (we recall that on this view truth is just semantic correctness, under operative semantic standards), rather than simply different contexts, and hence the possibility of relativism is denied. Instead what we have is precisely whatHorgan andPotrc are seeking to capture, namely the elimination of tables, as objects of serious ontological enquiry, whilst maintaining the truth (in the indirect sense) of our everyday statements about tables. That is not relativism. Nevertheless, one might still feel uneasy about tampering with truth in this way, so let us consider a further option that retains truth as we know and love it but introducestruthmakers .

5.2.3.Manoeuvre 2c: TryTruthmakers

The final option we shall consider retains both our standard understanding of existence and the standard interpretation of truth in terms of direct correspondence but urges us to reconsider what it is that makes statements such as ‘Tables exist’ true.

According to theQuinean view of ontological commitment, with its famous slogan of ‘to be is to be the value of a variable’, we should be committed to those things that lie within the domain of the quantifiers if the relevant sentences of the theory are to be held as true. This is now perhaps the most widely held view about determining ontological commitment. However, it is not without its problems. First of all it requires an appropriate regimentation of the theory concerned such that the relevant variables are made manifest. Secondly, andrelatedly , the mode of regimentation may itself bear on this issue of ontological commitment – the debate over whether a form of ‘thin’ individuality can be ascribed to quantum particles and a weak form of the Principle of Identity ofIndiscernibles sustained depends, in part, on not only differences as to the formal framework chosen for the regimentation but also whether that such regimentation is a prerequisite for such commitment to begin with (see French and Krause 2006, Ch. 4). Thirdly, the metaphysician may find theQuinean criterion operates on too high a level to address the ontological questions she has in focus. Thus, returning to the Special Composition Question,Quine’s approach is of no help in helping resolve the debate between theuniversalists who think that every collection of things composes something, and the nihilists who hold that none do (Cameron 2008, p. 4). And this is because the relevant variables in our regimented theory will pick out ‘things’ at the level of tables, dogs and electrons, rather than composite parts; that is, it applies at too high a metaphysical level. Of course, some might well insist that it is at precisely this level that our ontological commitments should lie and that thinking of theQuinean commitment in this way reveals what is problematic about such metaphysical debates as those between the universalist and nihilist – namely that, in theseQuinean terms, they are ontological empty. I’m going to leave that issue to one side because my concern here is to indicate how some of themanoeuvres developed by the metaphysicians can be put to use in the context of astructuralist view of the part-whole relationship.

So, according to the alternative ‘truthmaker theory’, the ontological commitments of a theory are not whatever is referred to by the variables of an appropriately regimented theory, but are just those things that have to exist in order to make the relevant sentences of the theory true. Now, on the standard understanding of this account, thetruthmaker for the claim ‘x exists’ is always x (see, for example, Armstrong 2004), and thus in the case of ‘Tables exist’, we must be committed to the existence of tables. However, one can modify this approach in order to shift ontological commitment elsewhere:

‘I think one of the benefits oftruthmaker theory is to allow that <x exists> might be made true by something other than x, and hence that ‘a exists ’ might be true according to some theory withouta being an ontological commitment of that theory. ‘(Cameron 2008, p. 4)

When it comes to the debate regarding SCQ, Cameron points out that this has mainly focused on the issue of whether we need to take as true sentences referring to complex objects, with the attendant commitment to such objects. Cameron sees this as completely wrong-headed:

‘serious ontological questions are being decided by linguistic facts; whether we are committed to complex objects is being decided by whether or not sentences concerning them can be paraphrased away into plural quantification over simples. What’s wrong, in my opinion, is theQuinean idea that we have to resist the literal truth of ‘there are tables’ if we want to avoid ontological commitment to tables.’ (ibid., p. 5)

Thus the idea here is to retain truth (à laTarski ) for such sentences but avoid an inflationary ontology by taking the constituent objects themselves to make it true that there is a sum, or composite, of those objects. What makes the sentence ‘Table exist’ true are whatever we take the fundamental constituent objects of tables to be: molecules, atoms, elementary particles, table parts, whatever. Metaphysicians employ a generic term to cover those objects which are fundamental in the sense that they themselves have no proper parts – they call them ‘simples’, which is perhaps unfortunate because in some cases these fundamental elements of our ontology will not be simple, at least not physically. However, bearing that point in mind, I shall use the term here.

Cameron offers a range of responses to criticisms of his view and indicates its benefits with regard to various metaphysical issues but here I shall simply note two things: first, it is clearly no contradiction on Cameron’s view, even on adisquotational view of truth, to maintain that ‘Tables exist’ but deny any ontologicalcommittment to tables (ibid., p. 6)[10] . What we are committed to when we utter such a sentence is whatever it is that makes it true, and on Cameron’s view that would the relevant metaphysical simples. Secondly, although this approach may appear to mesh with the idea of derivative existence, the suggestion that tables exist in such a sense is just a way of talking, for what really exist, and all that really exist are the relevant metaphysical simples (ibid., p. 7).

So, we can accept that ‘Tables exist’ is true but refrain from any ontological commitment to tables, because ‘Tables exist’ is made true by the relevant ‘simples’ (arranged table-wise, one might say, although the notion of ‘arrangement’ here will have to be fleshed out using the relevant physics, in particular the Pauli Exclusion Principle – or, better, theantisymmetrisation offermionic wave-functions). This line on our dilemma retains the literal (and non-contextual) truth of sentences and captures the thought that what we should really befocussing on, in setting out our fundamental ontology, are not tables, chairs, and so forth, but the fundamental entities of which they are composed.

Now there are well-known worries about metaphysical simples – whether they must be understood as point-like, for example, or can be extended. More significant for this discussion is the concern over whether they must be broadlyspatio -temporal, in the sense of beinglocalisable in space-time. This raises obvious difficulties if the relevant simples are taken to be quantum particles (so, can a photon be a simple?) and brings into the picture something that that is not prima facie a simple and may be subject to analysis itself, namely thespatio -temporal background (certainly thestructuralist will want to give this a particular interpretation). But in this context at least I see no reason why we cannot release simples from such a (spatio -temporal) constraint and allow them to be the kind of ‘building block’ from which one constructs space-time, elementary particles and so on. This should become clearer when we considerstructuralist simples below.[11]

6.Ontic Structural Realism and the Elimination of Particles (as Objects)

Having canvassed variousmanoeuvres that we might adopt when faced with our dilemma regarding tables, let us now consider a similar dilemma regarding particles: theontic structural realist insists that all there is, is structure and quantum objects are at best re-conceptualised , or even eliminated altogether, depending on which variant is chosen. This yields two forms of our dilemma: following the example of high energy particle physicists we may wish to assert that ‘particles exist’, yet according to theontic structural realist, either there are no particles (as objects) at all, or at best they are metaphysically ‘thin’ with their identity cashed out in relational terms[12] . Here we seem to have something similar to the table example – from thestructuralist perspective particlesas objects do not exist but we still want somehow to accommodate talk of them. In particular, we want to accommodate statements such as ‘Particles exist’, or ‘Particle x exists’, while acknowledging that fundamentally or ultimately, they are merely aspects of structure and hence do not[13] . Again, it seems, we can deploy the metaphysical tools used above.

Thus theEddingtonian approach would allow us to continue to assert that ‘Particles exist…’ (expressed in the ‘practical language of elementary particle dynamics’) but insist that we must understand this in the structural sense of existence ; that is, the sentence must be understood as incomplete, with its completion articulating the claim that particles only exist as aspects of structure.

Or we could understand ‘Particles exist’ as (contextually) true in the indirect correspondence sense but false in the context of ‘serious ontological enquiry’; that is, there are no particles (as objects), just structure or aspects thereof.

Or we could take ‘Particles exist’ to be (literally) true but maintain that what makes the sentence true are not particles as objects; that is, thetruthmakers are structures or aspects thereof (arranged, to put it one way, ‘particle-like’).

In this last case (which has the advantages of retaining our standard understanding of truth, the relevant metaphysical simples obviously cannot be particles-as-objects, or their metaphysical correlates. One could followQuine (1976) in his assertion that physical objects have metaphysically withered away under the glare of quantum mechanics, leaving only space-time points. The latter would then be our ‘simples’. However, this depends on a particular understanding of quantum mechanics as requiring particles (qua objects) to be non-individuals, a requirement that, ironically, the application ofQuine’s own criterion of ontological commitment in support of a ‘thin’ notion of object shows can be resisted (Saunders 2006; French and Krause 2006, Ch. 4). This latter notion is itself astructuralist one (see French andLadyman forthcoming), and whether one builds one’s structural realism on this directly or takes it as comprising one horn of the metaphysicalunderdetermination that has also been taken to power OSR, one might be inclined to understand the ‘simples’ themselves instructuralist terms.

Two further broad options then present themselves: one can take the relevant ‘features’ of structures as acting as the appropriate ‘simples’ ortruthmakers . These features will obviously not be the kind of thing that metaphysicians may have in mind, where they typically think of this notion in broadly ‘atomic’ terms. Here they will include symmetry principles and fundamental laws and the truth-making relation will be reversed of course, insofar as it is not objects and properties that make true law statements and the like, on this view, but rather the laws, and symmetries, that ground the properties andbehaviour of the putative objects (for discussion of this reversal, seeCei and French forthcoming). Nor will these simples bespatio -temporal, unless one views the physical structure with all its features as sitting in or contained by space-time. It has long been part of thestructuralist programme to incorporate space-time within this ontology (French andLadyman forthcoming;Auyang 1995), and the structure of the world has been taken to include space-time structure, although the details of that inclusion are waiting on a viable theory of quantum gravity (Rickles and French 2006),

Alternatively, one might want to say that there is only one ‘simple’, namely the structure of the world in all its glory, considered as a single entity. This invites obvious comparisons withblobjectivism . The problem now is that faced by all forms of monism: how to account for the apparently manifest complexity and variety of ‘the appearances’. AsHorgan andPotrc note, one cannot say that physical magnitudes, in all their huge variety, are instantiated byparts of the blob, since strictly speaking, it has no parts. Instead, they refer to ‘manners of instantiation’, in the sense that the blob itself instantiates in a certain manner (and, in particular, in aspatio -temporally local manner) the relevant properties and relations (op. cit., p. 169). However, there is the obvious concern that this metaphysical move is merely parasitic upon (and therefore adds nothing to) the account offered by physics with regard to the relationship between the physical correlate of the blob (the quantum field, say; see Healey forthcoming) and the relevant physical magnitudes. More acutely, perhaps, the notion of a ‘manner of instantiation’ remains obscure.

If the idea of structure, of features of structure, functioning as metaphysical simples is less than compelling, then there are further options that one might consider.