NAMES, POSSIBLE WORLDS AND PARTICLE STATISTICS
As we have indicated, by initially introducing sub/super-scripts in our description of an assembly of quantum particles, it may appear that we are labelling and hence naming them. The problem, of course, is that applying a permutation shuffles these names between the particles in such a way that we cannot tell which label 'belongs' to which particle. Let us begin with the claim that all that names do is refer to individuals and they have no meaning over and above that reference. How does this claim fare in the quantum context? Here is an argument that suggests it fares rather badly.
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In Naming and Necessity, Kripke introduces his account of rigid designation and possible worlds by way of an elementary example from probability theory. He asks us to imagine throwing a pair of dice and considering the possibilities for the way the dice may land.
[No] school pupil [would] receive high marks for the question 'How do we know, in the state where die A is six and die B is five, whether it is die A or die B which is six? Don't we need a "criterion of transstate identity" to identify the die with a six-not the die with a five-with our die A?' The answer is, of course, that the state (die A, 6; die B, 5) is given as such (and distinguished from the state (die B, 6; die A, 5)). The demand for some further "criterion of transstate identity" is so confused that no competent schoolchild would be so perversely philosophical as to make it. The 'possibilities' simply are not given purely qualitatively (as in: one die, 6, the other, 5). If they had been, there would have been just twen 949h71j ty-one distinct possibilities, not thirty-six. 43
Thus he insists that the above possibilities are just abstract states and not 'complex physical entities' composed of 'phantom' counterparts (as in Lewis's account of possible worlds), by noting the absurdity in asking for criteria of 'transstate' identity to identify which of the dice in an abstract state are identical with one of the actual die. Such states-possible worlds-are stipulated, rather than 'viewed from afar'. However, as Maidens has pointed out, Kripke has just stipulated his way into a commitment to classical Maxwell-Boltzmann statistics! 44
Let's consider the above passage in more detail. Maidens suggests that the Kripkean account offers us two things. 45 Firstly, the rigid designators "A" and "B" enable us to stipulate worlds as different one from another. Second, the fact that the worlds can be so stipulated explains the observed statistics. Putting these together, we have an argument that rigid designation leads to classical statistics and the failure of such statistics, given QM, leads to the possibility of a form of modus tollens against rigid designators. 46 Thus we appear to have a case where the physics can rule out a particular metaphysical view of proper names. As we shall now try to spell out, the case is not quite as cut and dried as it might seem.
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Maidens draws on the work of Dalla Chiara in order to
articulate the above argument. 47 Thus she notes that if we
consider a single particle in a single state, such as an electron in a state of
spin 'up', it seems natural to read the formalism in subject-predicate form: 
translates
as 'the appropriately labelled or named particle has the property represented
by being in the appropriately labelled state'. Standardly, we would then assign
appropriate denotata to the names and appropriate extensional interpretations
to the predicates. We would also, standardly, invoke the Fregean 'Principle of
Compositionality' which holds that the truth-value of expressions such as the
above is 'composed' of the truth functions of the separate parts; in other
words, in order to determine whether the expression is true or false, we need
to be able to determine whether it is true or false that the object has the
property predicated of it and, crucially, whether the object has been correctly
named in the first place. As Dalla Chiara puts it, ". one has first to identify
the denotatum of the name .". 48 But it is precisely
this latter identification which is problematic in QM,
and thus compositionality fails, or so it is claimed.
Consider the superposition formed by a pair of electrons and
the spin states 'up' and 'down': 
.
In this case, we can assert that 'there is one electron which has spin up', but
not 'this individual has spin up': there does not appear to be any way
of 'picking out' the individual which has one name, rather than the other. 49
The conclusion is that,
There is no trans-world identity. In this situation the meaning of "rigid designator" becomes very fuzzy. Anyway, the term seems useless". 50
Returning to the Kripkean example, if we try to think of a possible world containing only such a superposed state of two particles it is hard to see how swapping the labels would be equivalent to stipulating a new possible world. Swapping labels in this case seems to merely re-describe the same world and suggests that the labels are in this case not functioning as rigid designators in Kripke's sense.
However, this conclusion can be resisted. We shall offer a detailed account of Dalla Chiara's and Toraldo di Francia's approach below, but let us consider first of all how the above situation differs from a classical example. Imagine a world containing two indistinguishable classical particles which are individuals and suppose the description of this world only has rigidly designating names for these indistinguishable individuals. Swapping the names in such a description also appears to generate a description of the same possible world, but here the names were rigid designators by hypothesis and hence such examples cannot count against Kripke's notion. However, Maidens, Dalla Chiara and Toraldo di Francia might point out that in the classical case the particles could be 'picked out' in principle, whereas in the quantum situation they cannot, because they are in a superposition. Therefore, appearances to the contrary, swapping the labels in the classical case should be taken as generating a different possible world and the asymmetry between this and the quantum case remains. Of course, one can question this assertion that the particles can be picked out in principle, particularly since it is precisely such symmetric worlds which have been presented as counter-examples to the Principle of Identity of Indiscernibles.
We recall, however, that at least one form of the Principle, namely PII(1), can be sustained in the classical domain, and if we are willing to accept some form of substantivalist view of space-time, such that the particles can be said to possess different spatio-temporal properties even in this symmetric world, then it would seem we should conclude that swapping the labels leads to a different possible world. With PII violated in the quantum case, this option is ruled out (and even Saunders' version of the Principle does not allow us to say which particle has which label). Thus the issue depends on our understanding of such symmetric worlds and it all comes down to whether the above world containing a quantum superposition is sufficiently different from a classical symmetric world, such that in the former, but not the latter, a permutation of the particle labels cannot be said to yield a different possible world. If it is not sufficiently different-at least not in the relevant sense-then the conclusion that the particle labels cannot act as rigid designators is problematic.
Secondly, consider the claim that the Principle of Compositionality requires us to first identify the denotatum of a name. Our concern is that this claim implicitly conflates distinguishability with individuality. What compositionality is about is the epistemological issue of ascertaining the truth value of, typically, subject-predicate sentences. In order to do so in the cases considered, one clearly has to distinguish the individuals concerned but the fact that one cannot do this in the case of the superposition above does not imply either that one cannot regard the objects as individuals or that they cannot be named. The epistemology does not dictate the metaphysics.
Of course, the metaphysics may be regarded as bizarre, as we have already noted. What would have to be claimed is that we have a situation involving
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named individuals but we cannot, even in principle, say which individual has which name. In effect, the superposition hides or 'veils' the individual objects. Is there a theory of names which can accommodate such a bizarre situation? What about the Descriptivist view of names, or particle labels, according to which they are regarded as reducible to definite descriptions? Maidens claims that ". insofar as particulars can be named, it is in virtue of their possessing qualitative thisness", 51 where 'thisness' is taken to be, not irreducible, but dependent on the properties and relations of things. However, quantum particles cannot possess such qualitative thisnesses, because of the entanglement represented by superpositions such as the above (that is, because we cannot say which electron has which property; ibid.). In other words, as Maidens points out, the Descriptivist approach won't work, since the descriptions in this case will be identical (and we recall that this is why the Principle of Identity of Indiscernibles fails, in even its weakest form). Nevertheless, the descriptivist can at least explain why: entities in such superposition states just don't admit of uniquely distinguishing descriptions. Maidens' conclusion is worth quoting in full:
If we accept that absence of qualitative thisness explains the problems we see with failure to be able to attach names to these particles in any way which enables us to pick out the objects denoted, we have a powerful argument for Lewis's claim that representation de re supervenes on qualitative characteristics. Names may function rigidly, but this is in virtue of features of the world which metaphysics and physics can help us to examine . It is not that a consideration of the workings of names within our language alone suffices to enable us to draw metaphysical conclusions. 52
Here the view is made explicit that the referential function of names is to be understood solely in terms of 'picking out' the objects named. And on this understanding, the labels attached to quantum particles would indeed be meaningless. But absence of qualitative thisness-which is just another way of phrasing the non-classical indistinguishability of quantum particles-need not imply a lack of such referential function, as we indicated in the introduction to this chapter. To this extent, the quantum case need not be seen as providing any sort of argument for Lewis's claim regarding de re representation; indeed, one might regard such a claim as begging the question at issue.
Clearly, then, any view which allows the labels to have a referential function, even in situations of descriptive equivalence, will restore their meaning. Let's consider some of the alternatives.
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As we have just indicated, and as we recall from Chapter 4 it is the apparent identity of descriptions in the above cases which provokes the failure of PII. However, as we also noted, this failure has been resisted by van Fraassen, for example, through an appeal to 'empirically superfluous' factors which serve to distinguish and hence individuate the particles. Could such factors be regarded descriptively as forms of names? The nature of the factors involved is dependent on the statistics. Fermions are regarded as individuated by their 'value' states which, unlike the 'dynamic' states, need not be the same for every member of an aggregate. We can assign different value states to distinct particles, in the sense that for any two particles, some observable has different values (and not that there is a single observable with a different value for each particle). 53 With bosons, however, the same dynamic and value states will be assigned to all members of the aggregate and so genidentity is appealed to, where this is regarded not only as 'empirically superfluous' but also, unlike the fermion case, not describable in quantum mechanical terms. 54 The difference, then, is that with fermions, the individuating factor is describable in quantum mechanical but not empirical terms, whereas with bosons it is describable neither theoretically nor empirically.
This gives a two-fold view of particle labels, depending on the statistics: 55 for fermions, the labels can be understood in descriptive terms, where the description is empirically inaccessible; for bosons, the labels cannot be reduced in this way, unless the description is taken to include spatio-temporal factors. This may seem metaphysically uneconomical, 56 particularly as the particles are
end p.217
still regarded as indistinguishable, of course, and so the gap remains between the metaphysics of naming and the epistemology of distinguishing. As we shall note, this gap is faced by all such accounts which appeal to factors over and above those that can be empirically described. Furthermore, it is our contention that, because of this gap, a non-standard semantics is required, even if the particles are still regarded as individuals.
We may thus save a form of the Descriptivist account, but what about the Causal theory of names? This faces the difficulty that the crucial component of this account, namely the existence of some kind of causal chain connecting the use of a name with its referent, does not appear to be supported by quantum mechanics. As van Fraassen points out,
[h]owever obscure the notion of causal chain may be, this view of reference would seem to preclude differential naming of two photons in the same state-since entering into distinct causal chains would surely distinguish them in a way that quantum mechanics does not recognize. 57
There is also an issue concerning baptism: on this view, we recall, the referent of a name is established either by ostension or via some distinguishing description. However, ostension is clearly ruled out and descriptions are problematic in QM, as we have just seen. One might argue that in a measurement-when an electron hits a scintillation screen, for example-we can provide such a description using spatio-temporal properties, but of course the ability of such a description to distinguish is only fleeting: as soon as the electron enters into a superposition once again it is gone. 58 Nevertheless, one might want to press the case here and insist that since it is precisely in such measurement situations that we are led to conceive of the particles as individual objects to begin with, there is a kind of 'pseudo-' or 'mock' baptism, on the basis of which names can be ascribed. Of course, immediately outside such situations the possibility of keeping track of which particle has which name or label is lost and, as we have seen, there can be no causal chain.
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Alternatively, we might combine aspects of the Causal and hybrid views to yield, again, a form of baptism. We recall Donnellan's suggestion that when it comes to fictional names, the relevant story in which the name appears substitutes for a 'baptism'. 59 Perhaps the theoretical context of QM can serve a similar function, particularly if we follow Gracia's point that in such a 'baptism' the name is associated with a particular individual as that individual and not with a particular description. We can then, perhaps, entertain a kind of 'theoretical baptism' in which we assign names to individuals whilst setting up the quantum formalism. That we then lose the possibility of saying which name is tied to which individual after we construct the state-function of the assembly is strictly irrelevant to this aspect of naming. What it is relevant to is the distinguishing aspect, of course, but this is invoked, on Gracia's view, only with regard to how we learn to use names. Since we are not concerned with this in physics-we don't use names in the practices of either classical or quantum physics, but only descriptions (we shall return to this point below)-there are no obstacles to using names to refer and to baptize. This may seem only the shallowest of baptism ceremonies but unfortunately it's the best we can get in this context.
Of course, in all these cases where names are granted some referential function, the gap between metaphysics and epistemology yawns wide. It is at this point that one may feel that the former should be more closely tied to the latter; this is a legitimate feeling, our point is simply that we are not driven by the physics to give up this particular package of named individuals.
Returning to the passage from Kripke, what about the point that he has tied his act of stipulation too closely to classical statistics? There is a straightforward response to this. 60 As we mentioned above, constraints may be imposed on what we can imagine when it comes to possible worlds. We recall the example given in the Leibniz-Clarke correspondence, when Leibniz asserts that although we can imagine a situation in which there are two indistinguishable individuals, such a situation is not a genuine possibility being contrary to God's will. A similar tack might be taken on stipulation; indeed, as we have already noted, Hacking makes a similar move in his attempt to save PII from the standard Blackian two-globe counter-examples: "In arguing that in a certain possible world there exist two distinct but indistinguishable objects, bland assertion is not enough. There must be argument". 61 Thus, when it comes to Kripke's example, we might insist that 'cold naked stipulation' 62 is not enough and that we must apply a form of stipulation dressed up with what we have discovered about the actual world in the form of quantum statistics; that is, the answer in the probability example is not given a priori but only on the basis of our understanding of what the actual world is like.
Of course, an obvious concern here is that invocation of the actual world in this manner smacks of the view (associated with Lewis) in which assessments are made of the 'closeness' to the actual world of possible worlds containing counterparts to individuals in the actual world. 63 But giving an account of which possible worlds are physically possible in this way still isn't discovery. What is essential and attractive about Kripke's approach is the idea that possible worlds are stipulated, rather than 'viewed from afar'. Where he went wrong was in choosing the analogy of a pair of dice and their possible states and then claiming that the latter are just 'given as such'. In a sense they are, for objects which obey Maxwell-Boltzmann statistics; for other kinds of objects the set of permissible states will be different and fully clothed stipulation is required to ensure we end up with the 'right' set. 64 What is important is to avoid having to specify criteria of counterparthood and we see nothing here that compels us to do that. Kripke himself invoked an aspect of the actual world in drawing on the dice example; his mistake lay in failing to note the other possibilities that exist in this context. 65
There is one final problem to be dealt with. We recall the point that it is the stipulation of possible worlds based on rigid designation which is taken to explain the statistics of dice. If we are attempting to save rigid designation by insisting on constrained stipulation, then we appear to have lost the possibility of explaining the statistics. Indeed, the relationship has now been reversed, with the appropriate statistics feeding into the constraints on possibility. Can we find an alternative explanation? Not surprisingly, we think we can, but it means giving up on the approach which insists that the explanation of the statistics of possible outcomes lies in counting possible worlds, where one makes note of those which are qualitatively indistinguishable yet distinct. 66 According to the particles-as-individuals package, quantal particles may be regarded as (named) individuals subject to certain initial conditions which
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impose restrictions on the set of states accessible to them. It is this which accounts for the statistics. Of course, an explanation might be demanded of the initial conditions themselves. At this point, as we indicated in the previous chapter, one could simply dig one's heels in and insist that this is simply the way the world is. This alternative does at least have the virtue that it meshes with our formal practice, where we begin by labelling the particles and states. 67 We should, perhaps, re-emphasize what we have said before: we are not insisting on the particles-as-individuals package but at least it is not ruled out as a metaphysically viable alternative.
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