Alhassanain(p) Network for Heritage and Islamic Thought

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.