The Ins and Outs of Counterfactual Switching

The Ins and Outs of Counterfactual Switching1

Paul TellerUniversity of California, Davis

1. The problem and the program for this paper. Kripke, in explaining how heunderstands talk of possibility and explaining why there is no problem of “tran-sworld identity” wrote the following about the possible cases we entertain whenwe roll two dice:

Nor should any school pupil 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 whichis six? Don’t we need a ‘criterion of transstate identity’ to identify the die with asix—not the die with a five—with our die A?” The answer is, of course, that thestate~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 soconfused that no competent schoolchild would be so perversely philosophical asto make it. The ‘possibilities’ simply are not given qualitatively....If they had been,there would have been just twenty-one distinct possibilities, not thirty-six.~1992,pp. 17!

Yet it seems to a number of us that problems connected with quantum sta-tistics and with the interpretation of space-time give powerful reasons to revisitthis evaluation of the qualitative way of counting possibilities. The presentpaper reviews these problems, reviews our understanding of the referentialapparatus needed for discussing these issues, clarifies the close similarity andimportant differences between the two problems, and then sorts through theavailable ways for dealing with the problems and their implications for Kripke’sclaim. The result will be a broad comparative survey of these issues whichwill, along the way, also provide a strong conclusion about the labels used invirtually all presentations of conventional many-particle quantum mechanics:There is nothing remotely label-like about the way these “labels” can be inter-preted in the theory.

NOÛS 35:3~2001! 365–393

© 2001 Blackwell Publishers Inc., 350 Main Street, Malden, MA 02148, USA,and 108 Cowley Road, Oxford OX4 1JF, UK.

365

To set ideas, I give a miniature of the problems, to be expanded later afterI have reviewed the needed tools.

If we toss two fair coins we expect four possible outcomes: Both heads,both tails, coin 1 heads and coin 2 tails, and, finally, 1 tails and 2 heads. Onthe assumption of the same probability for each case, we get chances of 104each for two heads and for two tails, and 102 for one head and one tail. Butfor certain “quantum” coins the observed statistics are 103, 103, 103, just whatone would expect if there were not four but three equiprobable cases, describedqualitatively as two heads, two tails, and one occurrence of each, heads andtails.

The space-time problem begins with Leibniz’s indiscernibility argumentagainst the Newtonian supposition that space is a substance, a collection ofconcrete particulars at which physical objects can be located. Consider the pos-sible case, exactly like the actual world except that all objects and events havebeen moved over by three units. More specifically, suppose the world to bedescribed by a coordinate system, so that we have an x, y and z coordinate todescribe each point in space. At every time, where in the actual world an objector event is located at~x,y,z!, in the alternate possibility the same is located at~x13,y,z!. Relational critics reject this alternative as a merely “verbal” and nota genuine possible alternative distinct from the real world. With no qualita-tive difference in the two cases described, the distinction is claimed to beillusory.

Both problems can be put in terms of a claimed excess of at least appar-ently possible cases, suggested by applicability of the tools of reference. Theseunwanted cases arise by what I will callcounterfactual switching. In bothproblems we have names—number-labels of “quantum coins” and number-coordinates of space-time points. In both problems we suppose that there areidentity bearing things, the coins or the space-time points, to which these namesrefer, and that reference is constant across possible cases. Finally in both prob-lems we get descriptions of the problematic possible cases by supposing shiftsof ALL the properties and relations pertaining to one object of reference fromthat referent to another, so that the new case is utterly indiscernible from theoriginal. The only difference in the cases is taken to be the identity of theunderlying bearers of properties and relations.

2. Some background: Counterfactual cases, identity, and labels.So far Ihave talked in terms of “possibilities” and “possible cases”. I want to take asneutral a stance as I can as to how these are to be understood. I start from thefact that we freely use counterfactual statements, such as that if Tom had stuckto his diet he would have lost five pounds and that Tom might have weighedfive pounds less than he in fact does. I will speak about the language so usedas providingcounterfactual contexts, so that counterfactual contexts them-selves are taken to be set by, or to be essentially dependent on, language. Inturn I take such locutions to describecounterfactual circumstancesor counter-

366 NOÛS

factual cases, which we also callpossibilities, possible circumstances, or pos-sible cases. I will use these expressions as stylistic variants. Where I can, Iwill make no assumptions about what these possibilities are or how they areto be understood, intending my conclusions to be compatible with as wide arange of more specific analyses as I can manage. In particular many describesuch counterfactual or possible cases in terms of “possible worlds”, whichsome, in turn, understand metaphorically and some literally. In particular, therelevance of Lewis’s views will come in for careful examination.

Since names and identity also play a central role, let’s spell out their rele-vant features and interconnections.2

Since counterfactual switching works by wholesale reassignment of proper-ties, the relevant means of reference must not be constrained by properties ofthe referent. That is, our difficulties arise by use of what is known asdirectreference.3 To emphasize this I will henceforth speak of the relevant referringterms aslabels. When one manages to single out an object of reference, bywhatever means, one can stipulate that henceforth a given label will have thatobject as its referent, whatever properties that object might have. The objectmay exist at different times, and if so the label can be used to pick it out as itexists at those times. The object might exist in different counterfactual cases,and again, if so, the label can be used to pick it out in those cases. At this pointI need take no stand as to whether objects endure through time or exist in dif-ferent possible cases. Butif there are such cross-temporal or trans-world exis-tents, a label functions to pick out, at those other times and in those other cases,exactly the object to which it was originally assigned. This is a simple conse-quence of the original stipulation and the application of identity to the object.

It is worth noting that labels can function similarly even when no specificobject is initially singled out for stipulative association. This happens whenwe use labels to argue generally. For example I might begin an argument thus:Anyone accused of a crime has a right to a fair trial. Suppose that John Doehas been accused of burglary....In this context there is no one person to whom‘John Doe’ refers. Instead we are considering collectively what is true when‘John Doe’ refers, first to this person and then to that one. Under each one ofthese suppositions, ‘John Doe’ functions like a label in exactly the same wayas does a label successfully introduced by attachment to a specific individualwhich has been specifically picked out.

In the following we will also need the fact that when the devices of quanti-fication are applied, in argument or in description, whatever is in the range ofthe variables must be supposed to be things to which strict identity applies.This can be seen by applying the considerations of the previous paragraph, ormore straightforwardly by noting that for each value of a variable appearingin a quantifier, one supposes constancy of reference for each occurrence ofthe variable bound by that quantifier. But constancy of reference just meansthat the various occurrences of the variable pick outthe samereferent, whichpresupposes that strict identity applies to that referent.


We can clarify the close connection between identity and labelability by not-ing that, in a sense, identity and labelability are equivalent. In principle, any-thing, and so anything with identity, can be labeled. This can happen whenevera thing is picked out for stipulative association with a label, and it happensindirectly whenever an object falls in the domain of a quantifier occurring ina general statement. Conversely, whenever there is a label, applicability of strictidentity has been presupposed. The function of a label is to pick outthe samereferent on each occasion of use. But to talk of “the same referent” just is topresuppose application of strict identity, that the object of reference on twooccasions are strictly, numerically identical. Consequently, given the nature ofidentity and the function of labels in a language, when one applies, so doesthe other.

3. The problems of quantum statistics and the hole argument.Virtually everytext and discussion of the conventional quantum mechanics of many particlesystems proceeds by supposing that each particle can by considered to be theobject of reference of a numerical label: They consider a system composed ofparticle 1, 2, . . . . n.4 In addition, it is supposed that each particle is susceptibleto possessing any of the observable~or detectable! properties attributed by thetheory to the kind of particle in question. This tempts one to offer the follow-ing gloss on realistic situations exemplified by the following special case withthe same form as the initial example of the quantum coins.

Suppose we have a box which we have prepared to contain exactly two par-ticles.5 In the initial state of the system each particle is described as being def-initely confined to the box but to have no determinate position within the box.The situation is completely symmetric with respect to the two particles: Eachhas a completely uniform and independent probability to be found, on measure-ment, anywhere within the box. We install a measurement set up which willexamine both the right half and the left half of the box and report the numberof particles found in each half. If we take the particles to bear labels, so thatwe can describe the situation in terms of the observed location of particle 1and particle 2, we are lead to expect there to be four possible outcomes: 1and 2 on the right~1R & 2R!, 1L & 2L, 1R & 2L, and 2R & 1L. The counter-factual switching which yields the 3rd and 4th cases depends on the assump-tion of constancy of reference across counterfactual context, and on theassumption of freedom to reassign properties wholesale to the particles. Addi-tionally assuming the possibilities to be equiprobable6 we expect a probabil-ity of 104 for each possibility. But the observed statistics are 103 each for bothon the right, both on the left, and one particle on each side, it not being speci-fied which one.

On the face of it, application of the tools of reference and the possible casesgenerated by counterfactual switching gives too many possible cases: We wouldbe better off with the possible cases described qualitatively in just the waythat Kripke disparaged. Standard quantum theory deals with this problem by

368 NOÛS

requiring so called symmetrized and antisymmetrized states, which I willexplain below. The problem with appealing to this standard solution is that,as I will argue below, although the symmetrized and antisymmetrized statesare expressed using notation which looks like labels, there is no sensible wayto interpreted these “ersatz labels” as referring expressions when they are usedin describing the states in question. Consequently, we have a pressing prob-lem with the interpretation of quantum theories: Is there any way in whichthe labels, introduced asprima facie referring expressions, can be so inter-preted consistent with the unexpected but well confirmed facts predicted byquantum theory?

This is what makes comparison with the problem of excess possible casesin space-time theories particularly attractive. For in the latter cases there are anumber of solutions to the problem which one might hope to apply to the quan-tum cases. One of our important conclusions will be that such applications allfail. This will force us to take up the physicists’ solution in terms of the sym-metric and antisymmetric states, which, as I mentioned will also yield the con-clusion that the labels cannot be understood as standard referring expressions,consistent with the quantum facts.

Let’s turn to the space-time case and the contemporary generalization ofLeibniz’s indiscernibility argument, the so called “hole-argument”.7 Supposethat instead of moving everything over, we took a little spatial volume of unitradius and reassigned all its physical contents to locations closer to the center.We do this smoothly, so that objects at the edge of the volume retain theiroriginal locations. As we consider points closer to the center the displace-ments get larger. Then, halfway to the center, the displacements fall off again,until at dead center there is no displacement at all.8 Of course, in this exam-ple, the possible case considered looks radically different from the real world.Objects in the volume are distorted in shape and moved around relative to eachother and relative to objects outside of the volume.

But now think of the spatial points as concrete individuals which them-selves bear relations of spatial distance to each other. And suppose that thedistance between two spatial points is not a matter of necessity, so that, giventwo spatial points, we can consider an alternative possible case in which thepoints themselves bear different spatial relations to one another. Now con-sider a possible case like the one just described, but in which, additionally,the spatial distances between the points themselves are altered exactly to com-pensate the reassignment of physical objects and events to spatial points. Thus,for example, let p0 be the spatial point at the center of the volume and p1 andp2 points which, in the real world, lie on a radius at distances, respectively, of102 and 104 from the center. In the new possible case a point object which, inthe real world lies at p1, is relocated to p2; but p2, and so the point objectrelocated at it, are both assigned a distance of 102 from p0. So, just as in theoriginal Leibniz cases, the supposed possible and real cases “look” exactlyalike.


In classical theories, distance relations were taken to hold essentially betweenspatial points, thought of substantively. But in the framework of general relativ-ity, space-time separation—the metric—becomes a variable of the theory. If oneframes general relativity in terms of substantially conceived space-time pointsthe theory appears to countenance alternative possible cases like the one justdescribed, except the volume, or “hole” is a four dimensional space-time volume.

The problem in general relativity can be given a simple formulation by useof coordinate systems which constitute a systematic way of labeling the space-time points with 4-tuples of numbers. We ordinarily think of coordinate sys-tems, such as Cartesian coordinates, as functioning by appeal to relations—typically distances from a reference point or origin. But since general relativitywill make distance relations one of the variables of the theory, it uses quitearbitrary assignments of numbers to points, limited only by some simple con-tinuity requirements to insure that “neighboring” points be represented by num-bers close to each other in value.

Given a coordinate system, we can specify a case or a description of oneway the world might be by giving an assignment of physical objects, events,and fields to space-time points by making the assignment to the 4-tuples ofcoordinate numbers which name the points, along with a specification of thedistance relations between the points again as described by the coordinate num-bers. Given such a description, the same case is redescribed by performing acoordinate transformation, by systematically reassigning numbers to points.Such a coordinate transformation is called apassive transformation. Thedescription after such a transformation looks very different from the originaldescription, but it is simply an alternative description of the same case whichwe get by relabeling the points with new number labels, or coordinates.

But given such a coordinate transformation, one can perversely reinterpretit as anactive transformation. Where before we supposed that all things stayedat the same physical places, and the distance relations between the places allremained fixed, while only the names of the places changed, we now supposethat everything gets moved around in ways exactly described by the reinter-preted passive transformation. Instead of thinking of the new association ofnumbers and physical objects, events, and fields as no more than a set of newnames for the places, we now take the numbers to retain their original signifi-cance as names of the places, and instead regard the redescription as character-izing new locations for physical objects, events, and field values and correlativenew distances between the space-time points. The idea here is similar to whatone gets by starting with a simple change in units for the mass of objects, sayfrom grams to kilograms, and then reinterpret it as an actual change in themass of all physical objects, with corresponding adjustments in forces and otherphysical quantities in which mass enters as a dimensional quantity.9

Finally, from the fact that a passive coordinate transformation involves nochange other than the names of where things are, it follows that after reinter-pretation the active transformation involves no change other than the way every-

370 NOÛS

thing is “painted” onto the completely undetectable space-time points. Allrelations among physical things, including the distance relations—anything thatone might be able to detect, however indirectly—remain the same before andafter the active transformation.

Leibniz rejected such alternatives for a combination of theological reasonsand appeal to a principle of sufficient reason. Today some find such a surfeitof possibilities unacceptable because it violates some formulations of determin-ism: The facts outside such a hole are consistent with all kinds of rearrange-ments within the hole, no matter how small the hole might be.10 For my ownpart, I find this multiplicity of alternatives unacceptable simply because it vio-lates what I will callsanitized operationalism.11 The only difference in the casesis taken to be the identity of the underlying bearers of properties and rela-tions. It is not just that we cannot in practice make observations which wouldselect from among such alternatives. The way the theoretical framework hasbeen set up, the theoretical framework itself, and so any theory using thisframework, tells us that in principlenothingwould count as an observation ordetection, no matter how indirect, which would discriminate among such alter-natives. In so far such a theoretical framework appears to be burdened withexcess metaphysical baggage, not needed for any account of the world.

The two problems, quantum statistics and the hole argument, have much incommon as to how the excess possible cases arise: They both work by what Ihave calledcounterfactual switching.12 In both problems we have names—number-labels of quantum particles and number-coordinates of space-timepoints. In both problems we suppose that there are identity bearing things, thequantum particles or the space-time points, to which these names refer, andthat reference is constant across possible cases. Finally in both problems weget descriptions of the problematic possible cases by supposing redistributionof ALL the properties and relations pertaining to one object of reference fromthat referent to another. In the space-time case the shift occurs between theactual case and various alternative possibilities, and in the quantum case theshift is between a multiplicity of apparently possible ways in which one andthe same observational outcome could occur. In the space-time case the multi-plicity is objectionable because it violates sanitized operationalism—it counte-nances differences which make no difference in an extremely strong sense. Thequantum case faces the same problem, and in addition runs afoul of observedquantum statistics.

This analysis of how the problem arises immediately provides a rough typol-ogy of how one might bar the excess possible cases. Given the use of labels,one might question the individuation of possible cases by questioning the con-stancy of reference across counterfactual contexts. Or one might question theassumed free redistribution of properties. Or, in a final related pair of options,one might, conservatively, give up the assumption that what appear to be labelsreally have referents, or, radically, try somehow to compromise the role thatidentity is clearly playing in this little drama.


The differing demands of analysis of possible cases and of our two prob-lems compromise the neatness of this typology. The following sections sortthrough these complications

4. Can we eliminate the excess possible cases by denying constancy of labelreference across counterfactual contexts? I have stated our problem in termsof the function of labels, which attach by stipulation to a fixed object of refer-ence.13 Given this direct reference formulation, constancy of reference acrosscounterfactual contexts could only fail where the objects of reference failedto exist. This could happen because, for the subjects under consideration, therereally are no objects of reference—where we think labels have attached to ref-erents, this is an illusion. This “no-referent” option gets its own section below.Or the labels might in fact attach to referents, but these referents might failto exist in the relevant counterfactual circumstances, however we finallyunderstand counterfactual contexts and the counterfactual circumstances theydescribe. This second option in turn divides. Counterfactual circumstancesmight be understood in some way in which they “contained” no possible objectsof reference at all. Or they might be understood as containing possible objectsof reference, but not the ones to which the relevant labels have been attached.

Assume that counterfactual contexts are somehow understood so that anykind of putatively referring terms occurring in such contexts have no refer-ents at all. This would require a theory of counterfactual contexts which wouldaccommodate such an asymmetric treatment of putatively referring expres-sions, and I have no idea of what such a theory would look like. Furthermore,I take it to be implausible in the extreme that such an account could workwith any generality, because it is hard to see how such an account would treatdispositions. To say of something actual thatit is fragile is to say, among otherthings, that ifit were struck, it would break, or would be likely to break. Thiswould appear to require a referent for the original referring term in the coun-terfactual context. This problem is really extremely general, inasmuch as most,and I think all properties have a dispositional side to them. To attribute a massof one kilogram to a thing is, among other things, to attribute to it the disposi-tion to accelerate at the rate of one m0sec2 subjected to a total force of onekg-m0sec2. To attribute triangularity to an object is to attribute counterfactualoutcomes to possible measurements of the angles. And so on.

So I drop the option of referents in indicative, no-referents in counterfac-tual contexts, pending presentation of such a theory.

Finally, one might suppose that terms generally have referents in and outof counterfactual contexts, but in counterfactual contexts our stipulatively intro-duced labels, literally understood, fail to refer to their original referents becausethe actual objects to which they have been stipulatively attached fail to existin the counterfactual circumstances described by the counterfactual contexts.Counterfactual contexts would then have to be understood as somehow reas-signing referents to our labels. While this option may also seem implausible,

372 NOÛS

especially in view of the facts about dispositions mentioned just above, wehave a finely detailed realization of this idea to consider—Lewis’s counter-part theory.

On Lewis’s account there are alternative possible worlds constituted by col-lections of concrete individuals such that no thing exists in more than one pos-sible world. In his terminology, there is no “overlap”. A prospective solutionto our problem that supposed a change of referents across counterfactual con-texts would require only no overlap in referents of the terms in question, whileLewis requires no overlap at all. This difference from Lewis’s position is ines-sential to the present argument, so I will streamline exposition and assimilatethe “no relevant overlap” position to Lewis’s position of completely disjointworlds.

How does counterfactual reference work on such a theory? For example, ifwe say, “Humphrey might have won the election” we generally take our-selves to be saying something about the actually existing man, Humphrey.14

Lewis agrees that “...it is Humphrey himself...who might have been different,who might have won the presidency....The controversial question is how hemanages to have these modal properties.”~1986, p. 198! Lewis answers thatto have a modal property is to be represented in alternative possible worldsas having the corresponding indicative property; and that a thing can be repre-sented as having a property in a world by a distinct object, operating as a rep-resentative, existing with that property in the alternative world:

Humphrey may be representedin absentiaat other worlds, just as he may be inmuseums in this world. The museum can have a waxwork figure to representHumphrey....Another world can do better still: it can have as part a Humphrey ofits own, a flesh-and-blood counterpart of our Humphrey....By having such a part aworld representsde re, concerning Humphrey—that is, the Humphrey of ourworld....—that he exists and does thus-and-so.~1986, p. 194!

Lewis calls such a representative acounterpart, and counterfactual refer-ence works by literal reference to counterparts.15 So, for example, to say thatHumphrey might have won the election is to say that there is some other pos-sible world with a Humphrey counterpart whodoeswin a counterpart elec-tion in that world.

Counterparts are determined by similarity. For something in another possi-ble world to constitute a counterpart of Humphrey in this world, the alterna-tive object must be similar, in the relevant respects and to the relevant degrees.What counts as relevant similarity is not fixed but is determined by contextand interests of speakers and their audiences.

Jeremy Butterfield deploys this counterpart theory to eliminate the surplusof hole-alternative possibilities.16 We presume substantivalism about space-time points: The points are things to which we can refer. On counterpart theory,the space-time of an alternative possible world is composed of an entirely dis-


tinct population of such space-time points. In making counterfactual compari-sons, relevant similarity determines which space-time points in an alternativeworld function as the counterparts of given space-time points in the actualworld. In the “hole alternative” the relevant similarity is clearly the wholenetwork of metrical relations and relative placement of physical bodies, events,and fields. Thus the counterpart of a space-time point in the actual world willbe an otherworldly point with exactly the same metrical features and other rela-tions. If we now consider a hole alternative world, the points to which thingsare “relocated” will be exactly the counterparts of the points at which thingswere originally located. So a hole alternative would leave each thing at~thecounterpart of! exactly where it was to begin with. No difference is described.

Let us see whether description in terms of Lewis’s counterpart theory like-wise restricts the number of possible cases in quantum mechanics. Supposethat in the actual world we have prepared a box with two Bosons, 1 and 2,each with completely indeterminate position, and a measurement apparatus setup to detect the number of particles in the right and in the left side of thebox, all as described in section 3. We consider a possible world similarlyarranged, but in which the measurement apparatus has been triggered anddetects one particle in the right and one in the left side of the box in that world.Now, which is the counterpart of the real particle 1 and which the counter-part of the real particle 2? It makes no difference. We can chose arbitrarily.There are also, of course, two further otherwise similar worlds in one ofwhich two particles are detected in the right, and one in which two particlesare detected in the left side of the boxes in those worlds. If in addition wesuppose that there are no qualitatively duplicate alternative possible worlds itlooks like we’ve got just what we need: three possible outcomes for the actu-ally unperformed measurement of the location of the particles in the actualbox.

The counterpart maneuver works for the hole argument17 but not for theexcess quantum mechanical possible cases. To get a viable account of possibil-ities Lewis is forced to take possibilities to be, not just possible worlds, butalso alternative ways of drawing the counterpart relations to a given possibleworld. For example~1986, p. 231! Lewis considers two possibilities in bothof which he is one of identical twins, but in one of which he is the first born,in the second, the second born. To make these out as two distinct possibilitiesLewis supposes one possible world with very Lewis-like identical twins andtakes as one possibility what we get by taking the first born twin to be hiscounterpart and as a second possibility what we get by taking the second bornto be his counterpart. Any other way of getting these as alternative possibili-ties would call, not only for more possible worlds, but for a mysterious non-qualitative counterpart relation, and would anyway fail to prune the unwantedpossibilities in our coin case.

Thus counterpart theory fails, after all, to prune the possible cases whichare in excess for quantum theories. One might suggest falling back on the pos-

374 NOÛS

sible worlds instead of the possible cases as that over which the probabilitydistribution is characterized. But so doing would be to abandon the labels asgenuinely referring expressions, just what I am claiming the facts of quantumstatistics force us to do. At this stage of the discussion we are seeing whetherthe facts of quantum statistics can be reconciled with use of labels as genu-inely referring expressions.18 Doing so requires that when, in a given case wehave two Bosons labeled ‘1’ and ‘2’, the probabilities for where these Bosonswill be found be understood as probabilities for findingtheseBosons, not someothers. Working within the framework of Lewis’s counterpart theory thisrequirement in turn is spelled out by application of the counterpart relation.Counterpart theory interprets Humphrey’s having various modal properties interms of counterparts of Humphrey having the corresponding indicative prop-erties in other possible worlds. Likewise, a counterpart theoretical interpreta-tion of the probabilities for what will happen to Bosons 1 and 2 will be interms of distributions over possibilities involving counterparts of 1 and 2. Tointerpret in terms of possible worlds not characterized in terms of counter-parts for 1 and 2 would be to abandon the interpretation of ‘1’ and ‘2’ as refer-ring labels in discussions of probabilities of what will happen tothem, or atleast to abandon the counterpart theoretic approach to such treatment.19

There is one more wrinkle to iron out in this argument. What about the alter-natives, Bosons 1 and 2 both on the right and both on the left? Don’t each ofthese also divide into two possibilities, corresponding to the two ways of draw-ing the counterpart relation to Bosons 1 and 2 in the actual world? We wouldthen have a total of 6 possibilities and so would recover the statistics of quan-tum theory after all! But consider: In the event that a measurement actuallyresulted in 1R & 2L, there would be an unactualized possibility, that of 2R &1L. But in the event that a measurement actually resulted in 1R & 2R, whatwould be the corresponding unactualized possibility? The purported distinc-tion between possibilities in this case would be an artifact of how we drawthe counterpart relation, not a fact about the Bosons. In a sense there are, onLewis’s counterpart theory, two possibilities; but, unlike the case of 1R & 2Lvs. 2R & 1L, it is built into the theoretical framework that if one possibilityoccurs, so does the other. So, the two “possibilities” falling under 1R & 2Rmust be counted together.20

It is important to see why the quantum mechanical case does but the holeargument does not succumb to the problem I have been describing. In bothcases the problem originally arises by counterfactual switching, the cir-cumstance that we get alternative possibility by wholesale reassignment of anindividual’s properties to a distinct individual. Counterpart theory blocks coun-terfactual switching by denying overlap, that is by denying that, strictly speak-ing, any individual exists in more than one possible world. The work of identityacross possible worlds is done instead by the counterpart relation. When theindividuals are in fact individuated each by a unique collection of propertiesand relations, as space-time points surely are in the real world, the counter-


part relation uniquely picks out the needed counterpart in the relevant alterna-tive possible worlds. But the two Bosons in the box have no such individuatingproperties. Consequently the counterpart relation fails to pick out the neededcounterparts uniquely, and the unwanted surfeit of possibilities returns. Roughlyspeaking, where Leibniz’s identity of indiscernibles in fact obtains, the individ-uating properties get us the right range of possible cases. But where individu-ating properties are not available, the scheme collapses.

5. Can we eliminate the excess possible cases by denying the free redistri-bution of properties to individuals across counterfactual contexts? With the realworld’s irregularity in the metric, space-time relations among the space-timepoints fully suffice to individuate them. We have seen how Butterfield appliesthis fact to Lewis’s counterpart metaphysics to eliminate the offensive holealternative possibilities. Tim Maudlin~1989, 1990, 1993! also resolves the holeproblem by using exactly the same fact but deployed with an entirely differ-ent metaphysics, which he calls metrical essentialism.

Maudlin starts with his reading of Aristotle on substances, according towhich an individual substance cannot be stripped, even in thought, of its formor essential properties. Maudlin applies this Aristotelian metaphysics to thespace-time points, taking their form, or essential properties and relations, tobe exactly their metrical relations. Consequently one can write down the math-ematics which seems to express a reassignment of metrical relations and rela-tions among bodies and fields to new space-time points as in a hole-alternative.But such a revised verbal description has no application to the world of possi-bilities: The space-time points to which new metrical relations have been ver-bally assigned simply don’t have those metrical properties and relations, andthis by necessity based on their essences as Aristotelian individual substances.Thus a hole alternative is at best a verbal but not a real possibility, in the sameway as are a “square-circle” or a “lifeless person”. One is much more sen-sibly advised to interpret verbal hole alternative descriptions as alternativedescriptions of the one fixed possibility. This is pretty obviously the readingto put on physicists’ use of the relevant space-time redescriptions.

Where Maudlin’s scheme eliminates the unwanted possibilities generated bythe hole argument, his maneuver fails as badly as Butterfield’s did in applica-tion to the unwanted quantum possible cases, and at bottom for the same rea-son. Both schemes appeal, though in very different ways, to the real world’sirregularities in the metric, irregularities which provide a unique signature ofspace-time properties and relations that serve to individuate the space-timepoints and that can then be enlisted in the job of individuation, using eitherthe counterpart or the Aristotelian metaphysics. In the quantum case there isno analogous unique signature to play the same role: The two Bosons in theactual box are described as being in exactly the same state.21

6. Haecceities. We have been examining attempted cures for excessive coun-terfactual switching. The ones considered so far proceeded by reexamining the

376 NOÛS

individuation of counterfactual cases or possibilities, either by examining ref-erence across counterfactual contexts or by appeal to essential properties andrelations. We now turn to a family of approaches that study the problem moredirectly from the point of view of reference and identity.

Counterfactual switching requires that the identity of two~or more! thingssomehow stays fixed even though ALL properties and relations are exchanged.Some have thought that the required pinning down of identities works by dintof each thing having, in addition to all its qualitative properties and relationsin any ordinary sense, its ownprincipium individuationiscalled ahaecceity.On this presumption one might think to solve our problems by rejectinghaecceities.

Haecceities are supposed to be non-qualitative characteristics or principlesof things which explain their identity independently of all their properties andrelations. Adams~1979! presents what might be thought to be the same or asimilar idea as the “primitive thisness” of an object. Adams explains primi-tive thisness of a thing very simply as the~non-qualitative! “property of beingthis thing” ~p. 5–6!. I suggest that this idea can be taken with strong or withweak intent. On the strong formulation the “property of being this thing” mightbe held to be some non-qualitative property which does explanatory work,explaining the object’s identity. On the weak formulation, talk of a thing’s prim-itive thisness is no more than an alternative way of talking about the fact thatstrict identity applies to the thing. Indeed, as I have elaborated in section 2,talk aboutthe thing, something we could label as ‘a’, is inseparable from theapplication of strict identity.22

I trust that talk of the applicability of strict identity is clear enough. Talkabout any stronger version of primitive identity or haecceities is obscure inthe extreme. But no matter. Applicability of strict identity, and the concurrentavailability of directly referring labels, is all we need to get counterfactualswitching. So we can forget about haecceities in any stronger sense. Gettingrid of them would change nothing as long as strict identity still applies.23

7. Compromising direct reference and identity: the no-referent option.Sincewe describe counterfactual switching by using labels, one might attempt tododge the problem of excess counterfactual cases by rejecting the labels. Thismove can’t work by itself. As long as we admit the existence of identity bear-ing objects to be counterfactually switched, the counterfactually switched pos-sibilities are out there whether we refrain from discussing them or not. Inaddition, we often use labels to many good effects. Consequently this approachcould only work by reinterpreting labels as functioning in some way other thanby unmediated reference to identity bearing objects.

The resulting “no-referent” option could take a stronger or weaker form. Inthe weaker form we suppose that the relevant labels do not refer because thereis no subject matter, or at least no subject matter to which the labels refer indi-vidually. Instead we take the labels to function indirectly, for example by


describing the instantiation of properties and relations by things to which thelabels themselves do not refer. Or the labels might function to describe thedisplay of properties and relations which occur without there being any instan-tiating subject matter. On the stronger no-referent option we take use of thelabels to pick out instantiation of properties and relations by some kind of sub-ject matter, but a subject matter which is somehow identity free. This strongerversion still counts as a no-referent option because the labels won’t have spe-cific referents. By a referring label we mean one which is capable of repeatedreference, and what we mean by repeated reference is reference to thesamereferent, hence a referent to which identity applies.

7.1 Reinterpretation of coordinates as something other than labels of space-time points. Coordinate labels identify locations. But what are locations?

Every object and event has some specific location or other. And each loca-tion is a possible location—that is, a “where something is or might be”. Thispair of characteristics of locations sets them out as very like determinables,such asmass. Every physical object has some mass or other. And each massis the mass some object could have. We say thatmassis a determinable, withindividual mass-values, such as 1 kg, 5.78 kg, etc., being properties which arethe determinate values of the determinable,mass. In general, a determinableis a collection of properties such that anything that can have one of the prop-erties in the collection must have exactly one of them. Location is straightfor-wardly interpretable as a determinable of physical objects and events.

But on this interpretation locations, and more specifically space-time loca-tions, aren’t things but properties, properties which objects and events can have!This suggestion was developed in detail in~Teller, 1987!. Unfortunately it alsofalls prey to the hole argument.24 Just as the hole problem arose by reassign-ing metrical relations to the space-time points, substantively conceived, we canreassign metrical relations to the space-time properties in the following sense:To say that a distance relation holds between two space-time location-propertiesis to say that if two physical objects or events had those locations they wouldalso bear each other the named space-time distance relation. Reassigning dis-tance, and more generally metrical, relations among the space-time locationproperties just means reassigning them in the same dispositional sense.

There is a simple way to resolve this defect in the locations-as-propertiesproposal~Teller 1991!: Instead of taking locations be non-relational proper-ties of objects and events, take them to be relational properties, specifically,relations to the physical objects and events which also get moved around in ahole alternative. This is a generalization of traditional relationalism about thenature of space-time.

According to traditional space-time relationalism all the facts about spaceand time are subsumed under the facts about the spatio-temporal relations actu-ally instantiated among physical bodies and events. What I callliberalizedrelationalism expands the basis for analysis to include all instantiated and

378 NOÛS

uninstantiated metrical relations. That is, the facts about space-time are heldall to be subsumed under the facts about spatio-temporal relations that do orcould obtain among actual objects and events or among some actual objectsand events with counterfactual deletions and additions to the world’s actualinventory.25 From the point of view of liberalized relationalism, to refer to alocation is to refer to the relative space-time location property which a bodyor event does or could have, relative to some actual reference bodies or events.We use coordinate systems to refer in a systematic fashion to locations thusunderstood.26

Liberalized relationalism easily avoids the hole argument, which requiredmoving the metrical relations around on something assumed to be indepen-dent of those relations. This device for producing hole alternatives worked ifone presupposed independently existing space-time points or independentlysubsisting non-relational space-time location properties. But if the location-properties are relational, specifically metrical relations to existing bodies andevents, any attempted redescription of the net-work of these relations, preserv-ing the metrical relations themselves and all metrical relations among bodiesand events, leaves us with a description of exactly the same situation withwhich we started.

Liberalized relationalism counts as a no-referent option: We still use thelabels provided by coordinate systems, but we no longer regard these labelsas referring to independently existing space-time points or even independentnon-relational location-properties. Instead we interpret the coordinate labels asa way of talking about actual or merely potential spatio-temporal relationsamong physical bodies and events, much as we use the apparatus of referenceto talk about masses, temperatures, densities, and sizes without explicitly men-tioning the relations to a unit-setting reference object which must be tacitlypresupposed for such a term to pick out a specific value of one of thesedeterminables.27

Liberalized relationalism differs radically in metaphysics from the propos-als of Maudlin and Butterfield, but in a sense it shares their strategy of individ-uating the space-time points with metrical relations. For Butterfield, which pointin another possible world counts as the same as a given point in this world isfixed by the metrical relations. For Maudlin, only one point is allowed to bearcertain metrical relations to other points, namely the point which bares thoserelations essentially. For liberalized relationalism, to talk about a “space-timepoint”—a location—just is to talk about an actual or possible instantiation ofthe relevant space-time relations.

In all three proposals the metrical relations are doing the individuating. Theextent to which one takes the three proposals to be different turns on one’sviews about the trade-off between ontology and ideology. If you take ontol-ogy in a decidedly literal minded way, you will judge the three proposals asentirely different. At the other extreme, if you interpret talk of ontology as nomore than a material mode expression of the same facts which one can put


equally well in the formal mode of an ideology, then you will consider thethree proposals as different expressions of what, at bottom, comes to prettymuch the same strategy.

But we have already seen that no such strategy can work in the quantummechanical case because there is no unique signature of individuating rela-tions which we can enlist in the job of individuation of the Bosons in the pre-measured box.

We are out of options for directly reconciling the function of labels in quan-tum mechanics with the observed facts of quantum statistics. It is time to turnto the physicists’ approach to the problem by imposition of symmetrized andantisymmetrized states.

7.2 Reinterpretation or elimination of labels in quantum mechanics. As wehave seen with the example of the two Bosons in the premeasured box, Bos-ons straightforwardly cannot always be individuated by their properties becausetwo or more Bosons can be in exactly the same state. But according to thefull theoretical description given by quantum mechanics the situation ismuch worse because this description requires something called “symmetriza-tion” of quantum states, which makes it impossible ever to individuate Bosonsby instantiated properties. A short explanation will reward with thoroughunderstanding.

Suppose thatCR~n! andCL ~n! are, respectively, quantum mechanical statefunctions which represent the states in which particle n is R~in the right halfof the box! and in which n is L~in the left half of the box!. A description of astate in which 1 is R and 2 is L would be given by

CR~1!CL ~2!,

allowing for the counterfactually switched description,

CR~2!CL ~1!

Conventional quantum mechanics eliminates the possibility of such counterfac-tual switching, and in the same breath it represents a state with one R particleand one L particle in which “both” particles are in exactly the same state byrepresenting this state as

~a! CR~1!CL ~2! 1 CR~2!CL ~1!

This “superposition” counts as describing “both” particles as in exactly thesame state because exchanging the labels, writing ‘1’ where we saw ‘2’ and‘2’ where we saw ‘1’, we get back the same state description we started with.All states of a collection of Bosons must, according to quantum mechanics,

380 NOÛS

be symmetric in the sense that exchanging any two labels of Bosons leavesthe state unaltered.

Fermions are particles of which there can always beat mostone in a givenstate. This might make one think that Fermions, at least, can be individuatedby their properties. Strangely, this is not so. The theory accomplishes the limitof one Fermion to a state by requiring “antisymmetrization” of state functiondescriptions of Fermions. Each state of a collection of Fermions is written sothat if any two Fermion labels are exchanged in the description, the value ofthe resulting description changes sign. For Fermions, instead of~a! we havethe superposition

~b! CR~1!CL ~2! 2 CR~2!CL ~1!

Writing only antisymmetrized state descriptions for Fermions limits one Fer-mion to a state in the sense that if there were two in the same state, switchingthe labels would reverse the sign of the state function, and the only state func-tion which is its own negative is the identically zero state description: Forexample,

CR~1!CR~2! 5 2CR~2!CR~1! ] CR~1!CR~2! 5 0

~b! is an anti-symmetrized, Fermionic state description, with two Fermionsin different states. But note that this occurs in a strange way. There is no say-ing in this state that Fermion 1 is the R-Fermion and 2 the L-Fermion, or thereverse.~In quantum mechanics the sign of the total state function makes nodifference to any properties recognized by the theory.! There is no specific Fer-mion in this state such thatit is the R and no one such thatit is the L. Thusfor Fermions, every bit as much as for Bosons, and in spite of being limitedto one a state, there is no label-supporting individuation of Fermions by theproperties they might have.28

The quantum mechanical requirement that all states be either symmetrizedor antisymmetrized has severe consequences for the interpretation of thequantum mechanical labels, much more severe, I believe than is usually recog-nized. In description of space-time we can fall back on the uniquely individu-ating metrical relations to protect a substantial metaphysics from the unwantedhole alternatives, in the manner of either Butterfield or Maudlin; or we canappeal to these same individuating metrical relations to execute a no-referentoption which takes the labels implicitly to pick out the actual or possible instan-tiation of the uniquely individuating relational complexes. But because of therequirements of symmetrization and antisymmetrization such individuating qual-itative properties areneveravailable in quantum theories to sustain interpreta-tion of the labels. Thus a no-referent option cannot be executed in anythinglike the way available for descriptions of space-time. How, then, are the labels


to be interpreted as they are used in symmetrized and antisymmetrized statedescriptions?

We could retreat to the formal mode and note that, in effect, what symme-trized and antisymmetrized state descriptions accomplish is to give Carnapianstructure descriptions, or what physicists call occupation numbers. That is, suchstates tell us how many times each complex of properties is exemplified, forexample how many times one’s particle counter will click when examining theright and the left sides of the box. But for this to work we have to resist fall-ing back into the habit of thinking that this is because the labels describe par-ticles, a definite number of which are on the right and the left side respectively.To do so will immediately regenerate descriptions of the problematic alterna-tive possible cases, such as 1R & 2L. Indeed, the full quantum formalismdenies, not just that too many such states occur, but thatno such states everoccur, since they would have to be described by state functions which are nei-ther symmetric nor antisymmetric.

We can, of course, take the interpretation of the labels to be given implicitlyin terms of the occupation numbers. But to do so is to completely give up on think-ing of them as labels in any ordinary sense. Even in the no-referent version devel-oped in terms of liberalized relationalism, the number coordinates are serving topick out specific actually or possibly instantiated places in a relational structure.Because of the complete symmetry required by the descriptions of quantum theo-ries, such theories do not allow anything similar. The labels can be taken to havereceived an implicit interpretation when the symmetrized and antisymmetrizedstates are redescribed in terms of occupation numbers, but this is not to assignthe labels any role in a combinatorial semantics. The labels do not receive anyinterpretation individually. They are labels in name only.

Let us take stock: We started by putting to one side the details of the quan-tum formalism and considered whether the numbers which are presented aslabels in expositions of quantum theories can be understood as functioning aslabels in anything like the ordinary sense. We found that all attempts to do sorun afoul of the facts of quantum statistics. In particular we examined the via-bility of transferring known strategies for avoiding problems which are, in somerespects, analogous in the description of space-time, and we found that all suchattempts fail. We then looked in more detail at how the labels are used in thequantum mechanical formalism and concluded that there they function as akind of tally device to yield occupation numbers, but not in any way as indi-vidually interpreted semantic primitives with the function of individually refer-ring to identity bearing objects.

Of course, the fact that there is no heretofore proposed way of understand-ing the quantum mechanical labels in anything like the way labels are usuallyunderstood does not prove that no such way can be found. But the evidenceis not encouraging. I submit that in presenting quantum theories the use oflabels is misleading, and consequently, at least when clear interpretation is theobjective, we should avoid the labels altogether.29

382 NOÛS

In fact, quantum theories can do just that, executing the no-referent optionin a decisive way by use of a completely label free formalism. The so-called‘Fock space’ formalism30 works straightforwardly by listing the number oftimes attributes, such as R and L, are exemplified.

~CR:n times!~CL : m times!

By eschewing labels altogether the Fock space formalism sidesteps the prob-lem of how to understand the labels individually and avoids misleading oneinto thinking, simply on the grounds of the notation, that the subject mattermust be comprised by identity bearing entities.31

But how, then, are we to understand the subject matter of quantum theo-ries? Some of us toy with a radical alternative: Quantized identity free sub-stance.32 To set the idea, begin with a more ordinary conception of a continuoussubstance which can come in variable amounts. We refrain from thinking aboutany individuatability of subamounts of this substance. It is as if there were afluid, like water in a glass, but no difference to be had by thinking of the fluidportions in the top half and the bottom half as exchanged—we stipulate thatfor this kind of substance, counterfactual switching does not apply to portionsof any body of such a substance. We can put this characterization in the formof a slogan: Such a substance can be measured as to amount but has no partswhich can be counted. There can be more or less of such a substance, but anygiven amount cannot be broken down into smaller amounts which can becounted and thought of as exchanged.

In the quantum case we add quantization—such a substance can be increasedor decreased by amounts only of fixed units. There can be 0, 1, 2, . . .units,called, ‘quanta’, of such an identity free substance, but characterization in termsof a number of units qualifies only as a measure of amount, not as an enumer-ation of discrete entities which could be thought of as exchanged.

The intuitive idea can also be presented with the analogy of money in abank account.33 Suppose that, on Monday, and using a check, Mr. McGoodeposits one dollar in his bank account, explaining to the teller that this is thedollar that his Aunt Lucy gave him for his birthday. On Tuesday, and againusing a check, he deposits a second dollar in his account, as it might be, thedollar he earned on his paper route. On Wednesday he appears at the bank,asking to withdraw one dollar. What is the teller to say if he makes a fuss,insisting that he wants to withdraw the dollar he deposited on Monday, hisbirthday dollar, the one his Aunt Lucy gave him, andnot the one he depos-ited on Tuesday?

In the last paragraph I used expressions, such as “the dollar that his AuntLucy gave him for his birthday,” which have the form of referring terms. Weunderstand such expressions in context. But they cannot be taken to have ref-erents, identity bearing things of which it makes sense to say that one can refer


to thesameitem on two different occasions. I have suggested that, at least inthe context of quantum theories, we can take such locutions as “covering”~tocoin a neutral term! a kind of identity free entity which can come in variousquantized amounts. Such “entities” are not things in any ordinary sense. Onecannot refer to “them” individually. “They” cannot be collected into sets orprovide values of the variables of quantification theory.

Some will hold that any sort of “entity” or “substance” language is entirelyout of place for such a notion. And the money example suggests a more con-servative alternative.34 That Mr. McGoo’s account has two dollars in it, onedeposited on Monday and another deposited on Tuesday, should be under-stood as properties of the bank and its relation to Mr. McGoo in their socio-economic context. On Monday Mr. McGoo’s dispositional state—his creditwith respect to his account in his bank, increased by one unit. On Tuesday itincreased an additional unit. The change of state should, on this view, be under-stood entirely in terms of Mr. McGoo’s ability successfully to obtain goods—oridentity-bearing hard currency—by writing checks. No mysterious “identity freemoney entities” need be supposed.

It’s a bit more awkward to make a similar move in the case of quantumtheories. What has the dispositions? Measuring devices? But a state can occurwhere there are no measuring devices. There doesn’t appear to be much alter-native to simply letting the dispositions be free floating, or saying that “theworld” has the dispositions to reveal the number of cases described by thestates.

Alternatively one could try to reformulate in terms of some kind of prop-erty bundle theory: The entities described by quantum theories are the com-plexes of quantized properties. To the extent that one takes properties to becollections of dispositions, it is not clear whether this alternative differs muchfrom the last. And those who want to understand properties in terms of non-dispositional, manifest characters may find the details particularly difficult tocarry out in this context. If properties are thought of as universals, occurringin their entirety wherever they are instantiated, when we have multiple instan-tiation we will havethe wholeof the universal occurring multiply. This diffi-culty is more acute than when the universal is instantiated by an individuatingsubstance which can do the work of differentiating the separate instantiationsof the whole. On the other hand, if one works up a property bundle theory interms of tropes, one must be careful not to let the tropes themselves carry iden-tity, or the problem inducing identity will be reintroduced.35

Another common response to this problem situation is to insist that we havebeen misled into obscure speculation about some kind of “identity free sub-stance” by misconstruing the subject matter of quantum theories as substanti-val when it is really, at bottom, field theoretic. This becomes clear, the claimcontinues, when we consider quantum field theory. Again the intuitive idea canbe presented with a simple analogy. Imagine that you and I hold the two endsof a rope, pulling to give it a bit of tension. Each of us gives our respective

384 NOÛS

end a little shake, thereby generating two traveling bumps, or waves, whichmove towards the middle, merging briefly in the middle as they pass througheach other and continue on their way. But wait a minute! Do the two bumpspass through each other, or do they reflect off of each other? Do the bumpsretain their “identity” when they merged in the middle? These questions palpa-bly have no answers. These are not well formed questions for waves, asopposed to objects. And likewise for fields more generally. Quantum fieldtheory, it is claimed, is a theory about fields, not objects substantively con-ceived, and the issues about identity, individuation, and counterfactual switch-ing simply do not arise for fields properly construed.

But this attractive option has its drawbacks too. Quantized fields theoriesretain much that is “particle like”. These fields are, first of all, quantized: Theycome in discreet units. In addition, fields as classically conceived are indefi-nitely extended, but quantized fields are susceptible to very exact~though notcomplete! localization. Also the fields carry energy and momentum, inter-related in just the way suggested by theories of substantial matter character-ized by a rest mass.

My own attitude, developed in detail in my~1995, see also my 1996 and1999! is that field and “quantal” construals of the subject matter of quantumfield theory are interderivable, that they work equally well, and they both departin very extensive ways from pre-quantal conceptions of “fields” and “parti-cles”. What seems clear in any case is how extraordinary hard it is to con-strue the subject matter of the theory in terms of objects of reference of labels.What I hope to have added to the discussion here is further reasons for con-cluding that the labels one finds in virtually all presentations of standard quan-tum theories, and throughout the history of the subject, was a profoundly bumsteer.

7.3 The no-referents options for space-time and quantum theories com-pared. For descriptions of space-time we could more easily execute theno-referent option because we had things—ordinary objects and events towhich we can attribute metrical relations and because the relational analogsof locations are, in the real world, unique. Quantum theories fall down in boththese respects, forcing the no-referent option to take on one or another moreradical form. But once formulated we can ask whether a no-referent optionwhich works for quantum theories can be applied to the case of space-time.Continue to think of space-time as a substance, but deny that its parts havestrict identity. Without identity there are no fixed referents on which one candescribe a hole alternative and the counterfactual alternatives evaporate.

The most detailed development of this approach is provided by Hoefer~1996!,36 who distinguishes~p. 24! betweenmanifold plus metric substantival-ism, ~I presume Maudlin’s view!, andmetric field substantivalism.For the first,we start with manifold substantivalism “primitive identity and all” and add theessential possession of a metric to the bare manifold. For the second we “...strip


primitive identity from space-time points: call this view metric field substanti-valism. The focus of this view is on the metric tensor as the real representerof space-time....” Apparently we apply the metrical relations to a manifold ofprimitive identity free “points” analogously to the “quanta” of quantum theo-ries. Again, it would seem that the metric is doing the individuating. If this isa substantivalism of points, it would appear that, as in Maudlin’s view, thepoints have their metrical relations essentially. But the view apparently differsfrom Maudlin’s in that Maudlin endorses strict identity.37

When one asks how the metric is to be applied to “the space-time points”if “they” are free of strict identity Hoefer responds by hanging on to the toolsof reference. At various places~1996, e.g., pp. 18–19! he insists on using thetools of reference in application to “parts” of a subject matter which are freeof strict identity, including indiscernibles. But, as we have noted, identity-freereference would appear to make no sense. By reference we mean referencewhich can be repeated, which means that two occasions of reference are tothe same thing. And without the tools of~quantificational! reference, it is notclear how the metric gets ascribed to identity free manifold points. Ordinarilywe do this mathematical0set theoretically: Let M be a manifold. Let g~x!, forx in M, be a tensor function on M....But if theelements of M are free of strictidentity, it is not clear how to understand this.

Perhaps a better way to try to think of this alternative is to consider thestuff of space-time, as in the case of quantum theories, to be a substance whichcan be measured but not counted, which comes in amounts with no parts. Itdoes not in itself serve to individuate. But it still has the metaphysical func-tion of providing a substratum, a that in which properties and relations getinstantiated. We consider the various instances of metrical relations and con-sider them instantiated by amounts of this identity free substance. Since themetrical relations individuate uniquely the resulting locationsare individu-ated. But the individuation is done entirely by the metrical relations, while thesubstance serves only to provide the that-in-which-instantiation-occurs.

8. Conclusions. I have concluded that the travails of counterfactual switch-ing can be reconciled in the case of space-time with a referential under-standing of the use of coordinate systems: Counterpart theory and metricalessentialism both resolve the problem, if one is willing to pay the accompany-ing metaphysical costs. To my taste liberalized relationalism carries a lightermetaphysical burden, yielding a no-referent way of understanding coordinate-labels which is no more radical than its appeal to possible as well as actuallyinstantiated space-time relations. Perhaps more important is the conclusion thatthe counterpart, metrical essentialist, and liberalized relationalist approachesto the issue have a common strategy in appealing, in their different ways, tothe individuating work of the metrical relations which pertain to the real world.

I have also concluded that these strategies do not carry over to the par-tially analogous problems in quantum theories, and that when we also con-

386 NOÛS

sider the implications of the requirement that all quantum states be eithersymmetrized or antisymmetrized, we should conclude that nothing in quan-tum theories plays any genuine label-like role. The subject matter of quantumtheories then must be understood either in terms of a radically conceived “iden-tity free” ontology, or in terms of non-substantial field concepts, or in termsof the multiple instantiation of properties, but not “in” anything“. Some haveattempted to retool the first approach to the subject matter of quantum theo-ries for space-time, though I would urge that the viable part of this approachis really already captured by liberalized relationalism.

There are a host of interrelated issues which I have not so much as men-tioned. Foremost among them is the worry of reductionism: For example, ifliberalized relationalism as a view about space-time locations works by deploy-ing relations among ordinary objects and events, and if ordinary objects andevents must, ultimately, be understood in terms of quantum theories, doesn’tthe option of liberalized relationalism ultimately have to let go of strict iden-tity of objects in a more radical way than I have so far intimated, leaving allthe work of individuation to be done by complexes of property instantiations?Well, maybe. But I take reductionism itself to be a suspect doctrine. Nonethe-less, whether reductionism stands or falls, working out a coherent cross levelview obviously demands a great deal further work.38

Acknowledging that, and much other additional work left to do, for themoment I have detailed some tentative conclusions and the interrelations of arange of approaches to two intriguing and similar issues in the ontology ofscience. I hope that my map of the conceptual alternatives will help all of usfurther find our way in sorting out these issues. I am sure of only one thing:That we will continue to find that the interconnections run deep among manyof the newest and oldest problems in metaphysics.

Notes

1Many discussions with Michael Jubien have guided my thinking in important parts of thispaper. Two referees have provided extremely valuable comments.

2While some readers will take what follows as going without saying, some appear to haveradically different presuppositions about the tools of reference. See, for example, Hoefer~1996!and Huggett~1999!.

3Whether proper names in natural languages refer directly is besides the point of the presentdiscussion. All that matters here is that directly referring terms can be stipulated in formal lan-guages and scientific theories, and that this is a prima facie viable way to understand the use ofcoordinates in space-time theories and labels in quantum theories.

4The only exception of which I am aware is Merzbacher~1970—see pp. 508ff!. The issue isusually treated very differently in quantum field theory, as I explain later. My impression is thatthe founders of quantum mechanics thought very explicitly of the particle labels as functioningto refer directly to identity bearing objects in the usual sense. The consequence was that they hadto devise an elaborate application of permutation group theory to undo the consequences of postu-lating distinct, labelable and identity bearing objects. While this historical speculation bears much


closer examination, see French~1999, MS pp. 8–17~section entitled “The Role of Group Theoryin Physics”!! in support of this impression.

5The particles must be supposed to be Bosons~e.g., photons or alpha particles!. The distinc-tion between Bosons and Fermions, and the relevance of the distinction will be explained below.

6More specifically, we assume that in cases of equilibrium all accessible states are equallyprobable, an assumption which has proved extremely powerful in the theory of statistical mechan-ics. It is, to be sure, a substantive assumption, and there are alternatives which get the quantumstatistics right without reducing the number of accessible cases. But these alternatives are bur-dened with severe puzzles. On these alternatives particles act as if they were subject to forces~called “exchange forces” in the early days of quantum theory!, forces which do not fit into theoverall theoretical framework in anything like the way all other known forces fit. The overalltheoretical framework is much more attractive if such “exchange forces” can be avoided alto-gether, which is the route taken by contemporary physics. See van Fraassen~1991, ch. 11! andreferences therein for a survey of these issues. Teller~1995, p. 23! presents a brief illustration ofthe force like effect of different statistical assumptions when incorporated into the quantum mechan-ical formalism.

7See Earman~1989, ch. 9! for a thorough discussion, or Teller,~1991, pp. 383–92! for analternative non-technical presentation.

8The displacement of mass points towards the center might, in this example, be given by theformula 102~12r! for 1$ r $ 102 and r02 for 102 $ r $ 0.

9See Teller~1991! pp. 383 ff. where this analogy is spelled out in greater detail.10See Earman,~1989, p. 176 ff.! For a contrary view see, Leeds~1995!. Belot ~1996, pp. 260–

274! provides an acute analysis of some of the relevant literature. I do not myself see the threatto determinism as the central problem.

11I learned the following way of making the point from Richard Healey. The term is mine.See my~1991, p. 367! for an alternative statement.

12The plausibility of free counterfactual switching appears to be endorsed in other contexts,for example in Skyrms~1981! and Armstrong~1989!. Armstrong’s endorsement is qualified—seenote 23 below.

As noted by Rynasiewicz~1996, p. 305; see also his 1994!, the same intuitions that supportthe possibility of counterfactual switching can be applied to call into question the determinate-ness of reference of any putatively referring term of our language, a stratagem which has beendeployed by Quine in arguing for the “inscrutability of reference”, and especially by Putnam inhis critique of “metaphysical realism”. Rynasiewicz suggests that the hole argument is nothingbut an application of this stratagem to the referential apparatus of space-time theories, and thatreservations about the general stratagem should apply to this special application. In outline,Rynasiewicz’s evaluation appears to be this: Start from the premise that the qualitatively indistin-guishable, but distinct possible cases are unacceptable. Then consider the hole argument as anargument from determinateness of reference to such an unacceptable multiplication of possiblecases. But such an argument should be on all fours with any argument in the reverse direction,from the absence of such cases to the “inscrutability of reference” or the failure of “metaphysicalrealism”. So anyone who rejects an argument of the latter form should reject an argument of thefirst kind, and for the same reasons.

I don’t think this is right. As we will see, there are a great many options for blocking the holeargument. It is not at all clear that one need opt for the same basis for blocking the argument inone direction as in the other. In addition, the situation is much more complicated for perfectlygeneral permutation arguments that suggest switching, say,all of Nixon’s properties for those ofsome specific ham sandwich. In the case of such objects there is much more room for debateabout essential properties; and problems of composition further occlude our view of what is goingon. Complicated though they are, the issues are much clearer for the purported objects of ourbasic physical theories, where, in addition, the natural notation facilitates, if it does not positivelyinvite, examination of permutation issues.

388 NOÛS

Finally, some readers will see in a recent article~Huggett, 1999! a claim that counterfactualswitching can be consistently denied.~pp. 22–23! Huggett introduces~pp. 8–10! what he callsG-space, familiar also as a Carnapian state space, individual elements of which are described bystate descriptions provided by specification, for each individual, of which maximal predicate appliesto that individual. Next Huggett appeals to what are in effect Carnapian structure descriptions,which specify how many times each maximal predicate is instantiated; and he takes these todescribe something he calls “Z-~Zeta! or distribution space”~p. 10!. In Carnap’s presentationsstructure descriptions are incomplete descriptions of states in state space, but Huggett appears totakeZ-space somehow to differ fromG-space. Next, a long examination argues, effectively as faras I can see, that classical statistical mechanics, augmented with a diluteness assumption, cannotdistinguish between the appropriateness of state vs structure descriptions. Huggett then writes that“I am tempted to go further here and claim that this is no real difference at all@betweenG- andZ-space#: that this so-called metaphysical difference@haecceitism# is nothing but empty words. Itsimply asserts a difference without giving an account of what it is supposed to be. To say that“this atom” now has this property, and now that, and for this to be saying something substantialpresupposes that something meaningful is being done in the denotation in the different situa-tions...” ~p. 22! However, since Huggett has drawn no putative distinction betweenG- andZ-space,as opposed to the distinction between state descriptions and structure descriptions as, respec-tively, complete and less complete descriptions of the very same states, I fail to see that any dis-tinction has been collapsed. We continue to have states in state space, described completely bystate descriptions and less completely by structure descriptions; and some of the states in statespace are obtained from others by counterfactual switching, that is by simply permuting the indi-viduals. Likewise, on page 23, when Huggett presents some discussion and then concludes that“...this reasoning holds in bothZ- and G-space...” I am unable to follow the argument since nocontrast between the spaces~as opposed to the different forms of description of the same space!has been provided.

13I believe this way of stating these problems to be extremely general, in the sense that anyversion presented with alternate tools of reference can be recast in a direct reference formulation.

14Kripke appears to insist on this, e.g.~1972, p. 49!.15More accurately by quantification over counterparts. This is a point at which it is important

to remember that the referential use of quantificational variables has the same involvement withidentity as does the use of direct reference labels.

16Butterfield, ~1987, 1989a, and 1989b!. Brighouse~1994! likewise appeals to counterparttheory. She takes her account to differ from Butterfield’s, but I believe that a careful examinationof reference to alternative models will show that their approaches are not as different as she main-tains. In any case, the following closer examination of application of counterpart theory will serveto elaborate on Brighouse’s account as well as Butterfield’s.

17Of course, granting Lewis’s extravagant metaphysics, of which I am no fan. In addition, But-terfield’s argument depends crucially on the failure of “overlap” in Lewis’s system, that is on thecondition that each entity exists in only one possible world. I have critically examined Lewis argu-ments against overlap in my~2001!.

18See note 6 for the more careful statement and qualifications.19These considerations really provide a stronger argument that Lewis’s, summarized in the pre-

vious paragraph, for the conclusion that possibilities for an individual must be taken to be possi-ble worlds under the interpretation of a counterpart relation.

20A full treatment of this issue would require more detail than space allows, involving the fol-lowing considerations. First, I am tacitly assuming no determinate and non-overlapping space-time trajectories. If such are assumed, as in a Bohmian interpretation, these will fix the counterpartrelation and everything works out classically. Second, the argument sketched in this paragraphreally involves possible cases which are also possible futures for the actual case. A more detailedstatement would take this into account, showing that a sensible description involves two possiblefutures for 1 and 2 describable as 1R and 2L and 2R and 1L; but only one possible future each


for 1R and 2R and 1L and 2L. Finally, there is an interesting connection between the issues exam-ined in this paragraph and Healey’s “minimal essences” described in footnote 21, below. While Ithere express skepticism about minimal essence outside Lewis’s counterpart framework, in thisframework the idea appears to work out exactly as Healey envisages.

21This is not the place for a full scale critical evaluation of Maudlin’s approach to the space-time case, but here is a brief summary: Many~though not I! take a dim view of Aristotelian indi-vidual substances. In the present case the essential individuating characteristics are not justproperties, but very much relations to things likewise individuated, so the metaphysics is one heav-ily burdened with what some might hold are internal relations of the old idealist stripe. Criticswill differ as to whether these are problems at all, and if so, how severe. There is also a specialawkwardness about Maudlin’s proposal. We do want to say that space-time relations might havebeen deployed differently from the way they in fact occur. Maudlin~1989, p. 550 and 1989, p. 90!responds to this problem by himself interpreting the relevant counterfactuals in terms of counter-parts: To say that I would not be at a different place even if the Earth had been a bit more mas-sive is to say of a non-actual but possible collection of space-time points, individuated by a veryslightly different metric from the one occurring in the actual world, that I~or my counterpart!would have been at the place with individuating metrical relations most like those characterizingmy location in the real world.

In another essentialist maneuver, Healey~1995! evades the hole argument by requiring thatspace-time points satisfy the requirement of “minimal essence”, that a space-time point cannot beusurped by a competitor with exactly the original’s complex of location properties and relations.Among the real possibilities are very different distributions of properties, including those of rela-tive location, to the space-time points; but an alternative description according to which a givenspace-time point inherits exactly the location properties and relations which apply to some otherspace-time point does not describe a real possibility.~p. 302, also footnote 25, p. 315!

When not working within Lewis’s counterpart theory~see note 20 above! I do not find it plau-sible that alternatives which are arbitrarily close to one specified by an actively interpreted holecoordinate transformation should count as real alternative possibilities, but not the hole transfor-mation itself.

Healey argues that “@Minimal Essence# follows from an intuitively plausible conception of thenature of space-time. On this conception it is the place in a certain relational structure that makesp the space-time point that it is. In this respect space-time points are analogous to mathematicalobjects.”~p. 303! But this conception supports if anything, Maudlin’s metrical essentialism, whichHealey sharply distinguishes from his Minimal Essence. In particular, change just a few of a math-ematical object’s mathematical relations, and, we are no longer considering the same mathemati-cal object.

22Pretty clearly Adams intended readers to understand ‘primitive identity’ in the weaker sense,as he says that he wants “the word ‘property’ to carry as light a metaphysical load here as possi-ble.” ~p. 6! Jubien~1993!, p. 45 makes a similar proposal, thought the details of his system leadto a substantially different statement. I have used other terms with the same intent: ‘Label transcen-dental individuality’ in ~Redhead and Teller, 1991! and ‘minimalist haecceities’ in~Teller 1998!.For an extended contemporary discussion of haecceities in the strong sense see Rosencrantz~1993!.

23That identity functions in this way is clearly part and parcel of Kripke’s~1972! overallapproach to modality and identity. I take Kaplan~1975, e.g., pp. 722–23! also to be advocatingthe same understanding of identity and reference across counterfactual contexts in the doctrinehe labels “haecceitism”. By haecceitism Lewis~1986, pp. 221 ff.! means something quite differ-ent: That there are at least two worlds which do not differ qualitatively in any way, but which dodiffer in what they representde reconcerning some individual~1986, p. 221!. Since, on Lewis’sviews, cross world representation of any kind is only by counterparts, and the counterpart rela-tion is set by speakers, I take the qualification concerning representationde re to have no force,so that for Lewis haecceitism comes down to the doctrine that there are at least two qualitativelyindistinguishable possible worlds.

390 NOÛS

Armstrong~1989! draws a distinction, p. 61, between haecceities, which he appears to intendin my weak sense, and haecceitism. While endorsing~weak! haecceities, Armstrong also wishesto endorse what he calls weak anti-haecceitism, which comes down to denying just the sort ofcounterfactual switching which is giving rise to our problematic possibilities. But otherwise heappears to endorse free counterfactual rearrangement of properties to objects of reference. I takethese two positions to be in prima facie conflict: If one’s larger account endorses free counterfac-tual reassignment, what rules out the special case of complete counterfactual switching which givesrise to distinct but qualitatively indiscernible possibilities of just the sort which appear to be prob-lematic? An acceptable account should specify what it is about the limit cases of qualitativelyindiscernible but distinct possible cases which rules them out, while allowing all other instancesof counterfactual reassignment. This is just what authors such as Butterfield, Maudlin, Brig-house, and Healey have tried to do.

24The bad news was delivered by Arthur Fine in a personal note.25Leibniz himself would appear to count as advocating what I am calling liberalized relation-

alism, in view of his characterization that “space denotes, in terms of possibility, an order of thingswhich exist at the same time.”~Alexander 1984, p. 26!. But many contemporary authors want tointerpret relationalism in terms of actually instantiated relations only. The reasons appear to benervousness about the status of possibilities and the worry that if relationalists appeal to merelypossible relations the distinction between substantivalism and relationalism will evaporate. Thelatter worry would appear to be unfounded since, as explained in the next paragraph, liberalizedrelationalism straightforwardly avoids the hole argument, which any straightforward version ofsubstantivalism does not. For narrow construals of relationalism see Friedman~1983, pp. 62–3and 216 ff.!, Sklar ~1974, pp. 169–73!, and Earman~1989, p. 134–6!. See Belot~1996 and toappear! for an exposition and substantive defense of the view that the distinction between substan-tivalism and liberalized relationalism may make a very robust difference to physics.

26My impression is that Wilson~1993, pp. 236–9! is advocating something similar: Physicalspecification requires a physically applicable coordinate system, and ifall the physical content isso specified, the hole argument is avoided, as explained below.

27See Teller~1987, especially pp. 436–44! for a detailed examination of how this works for mass.28Redhead and Teller~1992, p 211 ff.! present this argument in a very general form, which

supposes that the only properties available for individuation are the ones specifically attributedby the theory. van Fraassen~1991, pp. 423–33! shows that one can consistently suppose the fieldof properties applying to particles to be enriched beyond what the theory requires in a way whichindividuates Fermions.

29I reach the same conclusion by an entirely different line of argument in Redhead and Teller~1991! and Teller~1995, pp. 16–36! based on a principle of parsimony according to which weshould eschew descriptions in the formalism which, in principle, can never be realized.

30In practice, the Fock space formalism tends to be used in presentations of quantum fieldtheory, yielding the impression that when this formalism is invoked we have left quantum theoryin favor of quantum field theory. In fact, both theories can easily be presented with the Fock spaceformalism, as was already made clear in Heisenberg’s~1930, pp. 177–82!.

31Again, I suspect that this connection between the notation and assumed ontology is, histori-cally, not accidental. See note 4.

32Redhead and Teller~1991!, Teller ~1995, ch. 2!, and Maidens~1998!.33Schroedinger~1950, p. 114!, ~1957, pp. 212–16!, and Hesse~1996, p. 50! present this analogy.34As suggested to me by Michael Jubien.35Allarie ~1963, 1965! claims that we must suppose identity bearing individuals to enable us

to make sense of numerosity when we have, or just imagine, qualitative duplicates. I take theFock space formalism to show that quantized multiple instantiation of a fixed property complexmakes perfectly good sense without supposing that there are identity bearing individuals whichinstantiate the property complex. In the quantum case, the property complex can include rela-tional as well as non-relational properties.


36See also Maiddens~1998!.37Hoefer uses the term “primitive identity”, as far as I can tell, exactly as I use “strict iden-

tity”. He claims ~p. 15! that Maudlin retains primitive identity while he clearly rejects it.38Readers will find some notes towards this further work in~Teller 1999, pp. 316–323!.

References

Adams, Robert Merrihew~1979! “Primitive Thisness and Primitive Identity,”Journal of Philoso-phy, pp. 5–26.

Alexander, H. G., ed.~1984! The Leibniz-Clark Correspondence. New York: Barnes and Noble.Belot, Gordon~1996! Whatever is Never and Nowhere is Not: Space, Time, and Ontology in Clas-

sical and Quantum Gravity.PhD. Dissertation, University of Pittsburgh.Belot, Gordon~to appear! “Rehabilitating Relationalism.”Brighouse, Carol~1995! “Spacetime and Holes,” in D. Hull, M. Forges and R. M. Burian~eds.!,

PSA 1994, Vol. 1. East Lansing, MI: Philosophy of Science Association, pp. 117–25.Butterfield, Jememy~1987! “Substantivalism and Determinism,”International Studies in the Phi-

losophy of Science, pp. 10–32.Butterfield, Jeremy~1989a! “Albert Einstein Meets David Lewis,” in M. Forbes and A. Fine~eds.!,

PSA 1988 Vol 2.East Lansing MI: Philosophy of Science Association, pp. 65–81.Butterfield, Jeremy~1989b! “The Hole Truth,” The British Journal for Philosophy of Science,

pp. 1–28.Earman, John~1989! World Enough and Space-Time: Absolute versus Relational Theories of Space

and Time. Cambridge, Massachusetts: Bradford Books.Friedman, Michael~1983! Foundations of Space-Time Theories. Princeton: Princeton University

Press.French, Steven~1999! “Models and Mathematics in Physics: The Role of Group Theory,” in J.

Butterfield and C. Pagonis~eds.!, From Physics to Philosophy. Cambridge: CambridgeUniversity Press~MS, p. 49!.

Healey, Richard~1995! “Substance, Modality and Spacetime,”Erkenntnis, pp. 287–316.Heisenberg, Werner~1930! The Physical Principles of the Quantum Theory.London: Dover

Publications.Hesse, Mary~1966! Models and Analogies in Science. Notre Dame: University of Notre Dame

Press.Hoefer, Carl~1996! “The Metaphysics of Space-Time Substantivalism,”Journal of Philosophy,

pp. 5–27Huggett, Nick~1999! “Atomic Metaphysics,”The Journal of Philosophy, pp. 5–24.Jubien, Michael~1993! Ontology, Modality, and the Falacy of Reference. Cambridge: Cambridge

University Press.Kaplan, David~1975! “How to Russell a Frege-Church,”Journal of Philosophy, pp. 716–29.Kripke, Saul A.~1972! Naming and Necessity. Oxford: Blackwell.Leeds, Stephen~1995! “Holes and Determinism: Another Look,”Philosophy of Science, pp. 425–37.Maidens, Anna~1998! “Particles and the Perversely Philosophical Schoolchild: Rigid Designa-

tion, Haecceitism and Statistics,”Teorema, pp. 75–87.Maudlin, Tim ~1989! “The Essence of Space-Time,” in M. Forbes and A. Fine~eds.!, PSA 1988

Vol 2. East Lansing MI: Philosophy of Science Association, pp. 92–91.Maudlin, Tim ~1990! “Substance and Space-Time: What Aristotle Would Have Said to Einstein,”

Studies in the History and Philosophy of Science, pp. 531–61.Maudlin, Tim ~1993! “Buckets of Water and Waves of Space: Why Spacetime Probably is a Sub-

stance,”Philosophy of Science, pp. 183–203.Merzbacher, Eugen~1970! Quantum Mechanics, Second Edition. New York: John Wiley and Sons.Redhead, Michael, and Teller, Paul~1991! “Particles, Particle Labels, and Quanta: The Toll of

Unacknowledged Metaphysics,”Foundations of Physics, pp. 43–62.

392 NOÛS

Rosenkrantz, Gary S.~1993! Haecceity: An Ontological Essay. Dordrecht: Kluwer AcademicPublishers.

Rynasiewicz, Robert~1994! “The Lessons of the Hole Argument,”The British Journal for thePhilosophy of Science, pp. 407–36.

Rynasiewicz, Robert~1996! “Absolute versus Relational Space-Time: An Outmoded Debate?”Jour-nal of Philosophy, pp. 279–306.

Schroedinger, Erwin~1950! “What Is an Elementary Particle?”Endeavour,pp. 109–16.Schroedinger, Erwin~1957! Science, Theory, and Man. London: George Allen and Unwin.Sklar, Lawrence~1974! Space, Time, and Space-Time.Berkeley: University of California Press.Teller, Paul~1987! “Space-Time as a Physical Quantity,” in R. Kargon and P. Achinstein~eds.!,

Kelvin’s Baltimore Lectures and Modern Theoretical Physics, MIT Press, pp. 425–48.Teller, Paul~1991! “Substance, Relations, and Arguments About the Nature of Space-Time”,The

Philosophical Review, pp. 363–97.Teller, Paul~With Michael Redhead! ~1992! “Particle Labels and the Theory of Indistinguishable

Particles in Quantum Mechanics,”The British Journal for Philosophy of Science, Vol.43, pp. 201–18.

Teller, Paul~1995! An Interpretive Introduction to Quantum Field Theory, Princeton UniversityPress.

Teller, Paul~1996! “Wave and Particle Concepts In Quantum Field Theory,” in R. Clifton~ed.!,Perspectives on Quantum Reality. Dordrecht: Kluwer. pp. 143–54.

Teller, Paul~1998! “Quantum Mechanics and Haecceities,” in Elena Castellani~ed.!, InterpretingBodies: Classical and Quantum Objects in Modern Physics. Princeton University Press,pp. 114–41.

Teller, Paul~1999! “The Ineliminable Classical Face of Quantum Field Theory” in Tian Yu Cao~ed.!, Conceptual Foundations of Quantum Field Theory. Cambridge: Cambridge Univer-sity Press, pp. 314–23.

Teller, Paul~2001! “Against Against Overlap and Endurance” in G. Preyer and F. Siebelt~eds.!,Reality and Humean Supervenience: Essays on the Philosophy of David Lewis. Lanham:Rowman and Littlefield, pp. 105–21.

van Fraassen, Bas~1991!. Quantum Mechanics: An Empiricist View. Oxford: Clarendon Press.Wilson, Mark ~1993! “There’s a Hole and Bucket, Dear Leibniz,” in P. A. French, T. E. Uehling,

and H. K. Wettstein~eds.!, Philosophy of Science. Notre Dame: University of Notre DamePress, pp. 202–41.


The Ins and Outs of Counterfactual Switching

Documents

Transcript of The Ins and Outs of Counterfactual Switching