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