chris hughes - bundle theory from a to b

8/6/2019 Chris Hughes - Bundle Theory From a to B

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Mind Association

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Bundle Theory From A To BCHRISTOPHER HUGHES

I

In Dean Zimmerman's dialogue, "Distinct Indiscernibles andthe BundleTheory" (Zimmerman 1997), A starts things off by asserting that sub-stances are nothing but bundles of properties.B objects that the bundletheory of substance is incompatible with the fact that there might havebeen nothing but two intrinsically indiscernible spheres at some distancefrom each other.If thatpossibility hadbeen realised,B holds, therewouldhave been two differentsubstances with the exact same bundle of proper-ties. So if that possibility had been realised, there would have been sub-stances that could not be identified with the bundle of their properties.This is incompatiblewith the bundle theory of substanceas B understandsit, since the bundle theory so understood is not just a claim about whatactually existing substances actually are, but a claim about what it is forsomething to be a substance.

A does not deny that if there could have been a symmetrical universecontaining intrinsically indiscerniblepairs of substances, then the bundletheory is in trouble. But he does not accept that therecould have been. Ashe sees it, therecould have been a universe with nothing in it but a spherea certain distance from an intrinsicallyindiscerniblesphere.But in such auniverse,he thinks, therewould not be two differentspheresin two differ-ent places; there would be one sphere wholly present in each of two dif-ferentplaces (at the same time). While this may seem a bizarremove, it isnot an unnaturalone for A to make, given his assumptionsthat substancesare bundles of properties,and thatpropertiescan be wholly present in dif-ferentplaces at the same time.B then objects thatA cannotcountenancethe possibility of a symmetri-cal world containing contingently indiscernible entities (since nothing iscontingently indiscernible from itself). A agrees, but expresses doubtabout whether this last possibility is a genuine one.Mind, Vol. 108 . 429 . January 1999 ? Oxford University Press 1999


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Bundle Theory From A To B 151NH+ is "between" a pair of circular cross-sections of NH+ having thesame area as each other.Again, though,this is a propertyof spheresratherthan hemispheres.3

The worry raised hereconcernshemispheres and spheres,but it could bestatedin more general terms. Say that a shapes includes a shapes 'if what-ever has shapes has a (properormaximal) partthat has shapes'. It seemsat least initially plausible that the following are conceptual truthsaboutshapes: that shapes include other shapes (e.g. spheres include hemi-spheres), and thatif a thinghas a shape, its shapeis the shapeof the largestregion of space it fills.A mustholdthatat least one of these claims is at mostcontingently true. Indeed,he is committed to denying the necessity of thesecond claim, since he holds that the bi-located sphere in Max Black'sworld is spherical,even though the largest region of space it fills is not.4

Here is a related worry: according to A, there is a world w in which ahemispherical thing-that is, a hemisphericity-including bundle of prop-erties just barely overlaps itself. Now consider a different world w' inwhich a bundle of exactly the same properties exists, but is mono-located.A would have to say that the Oustbarely self-overlapping) hemisphericalthing in w and the (mono-located) hemispherical thing in w' are intrinsi-cally indiscernible. (That is, he would have to say that the hemispherical

3A referee has brought it to my attention that the argument ust sketched pre-supposes that a sphere has hemispherical parts; this presupposition might be de-nied by someone who rejects the doctrine of arbitraryundetached parts. It seemsclear enough that if something is spherical, it must have hemispherical parts, butthis is not the place for me to defend this claim. In any case, even if A could avoidcountenancing hemispheres with centers, by refusing to countenance undetachedhemispheres, he would still be committed to centreless spheres. (Thereis no pointp and distance d such thatp is inside A's allegedly bi-located sphere, every pointat distance d is occupied by some part of thatsphere, and no point at any distancegreaterthand is occupied by any partof thatsphere.)

4If the shape of a multi-located object is not the shape of the largest region ofspace it fills, what is it the shapeof? A might say that it is the shape of the smallestregions of space in which the object (and not just some part of the object) ispresent. Then he could say that the (largest) bi-located object in Black's world isspherical, in spite of the fact that it is centreless, and has other geometrical prop-erties one might have thought incompatiblewith sphericity.But suppose, as seemsplausible, thatthere are possible worlds in which largerextendedregions of spacearemade of smallerextended regions of space, which are made of still smaller ex-tended regions of space, and so on ad infinitum, but no region of space is made ofunextended points. Suppose furtherthat in one of those worlds, a bunch of prop-erties are instantiateduniformly throughouta spherical region of space in such away that-as I would describe things-the universe contains a perfectly uniformspherical object at its center,and nothing else. Where P1 ... Pn .. are the proper-ties thatA supposes constitute the object at the center of the universe, no regionof space will be the smallest region of space in which those properties are found.So, A would have to say, no region of space is the smallest region of space inwhich the object is present. If an object's shape is the shape of the smallest re-gion(s) in which it is present, the object in question won't have any shape at all!


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152 Christopher ughesthing in w has all the same intrinsicpropertiesat w as the hemisphericalthing in w' has at w'.) But how can this be? The thing in w has all of itscircularcross-sections on the inside (at w); the thing in w'does not (at w').So the thing in w and the thing in w'are discerniblewith respect to a prop-erty having all one's circular cross-sections on the inside thatcertainlydoes not look like an extrinsicproperty.If a property s extrinsic,then things could be duplicates, even though they are discernible withrespect to thatproperty.And how could two things be duplicates, if oneof them has all its circular cross-sections on the inside, and one does not?

III

As we have seen, A does not concede that substances in a symmetricalworld could be contingently indiscernible. Be that as it may, he cannotvery well deny that a universe could be contingently or temporarily sym-metricalor non-symmetrical.This will turnout to commit A to some veryunwelcome consequences.

Considera sphericaluniverse that has always been and will always bequasi-symmetrical. The universe consists of two enormous and almostintrinsically indiscernible galaxies. The only intrinsic differences thereare between the two galaxies arise from the fact thatin one half of the uni-verse-but vanishingly close to its centre-there is a tiny unattachedpar-ticle that has no counterpartn the other half of the universe.Since the oddparticle out pulls harder on things closer to it, the stars and planets in itshalf of the universe have slightly different shapes thanthe stars and plan-ets in the other half.The symmetry-breakingparticle might have been (throughout ts exist-ence) at the exact centre of the universe, ratherthan, say, a femtometeraway from it.5If that had been the case, the universe would have been per-fectly symmetrical.ForA intrinsicindiscernibilityin a symmetrical worldentails identity.So A seems committed to saying thatif the quasi-symmet-rical universe just described had existed, the following counterfactualwould have been true: if the particleone femtometer away from the centreof the universe had instead been (permanently)at the centre of the uni-

'This seems obvious enough to me. But for the purposes of the argument,it isenough to suppose that,insteadof therebeing a (symmetry-breaking)particleonefemtometer away from the center of the universe, there could have been one al-most exactly like it, permanentlyat the center of the universe. This will commit Ato its being true at the quasi-symmetrical world that, if instead of there being a(symmetry-breaking) particle one femtometer away from the center of the uni-verse, there hadbeen one almost exactly like it, permanently at the universe's cen-ter, then there would only have been half as many stars as thereactually are.


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Bundle Theory From A To B 153verse, there would have been only half as many stars as there actually are.But how could a minuscule difference in the location of a particle-onethat isn't part of any stars, and has only a negligible effect on the stars'intrinsic and relational properties-make such a big difference to howmany stars there are?

Now consider a possible universe that is perfectly (bilaterally) symmet-rical at time t and at every time before t. The universe in question is notdeterministically symmetrical: at some time later than t a symmetry-breaking particle might suddenly come into existence. Suppose that thiswill in fact happen shortly after t, and that after it does, there will betwenty billion stars(and ten billion pairsof almost indiscernible stars). Wemay ask A: how many stars are there in the universe at t?

A might say that, in as much as the universe is perfectly symmetricalthroughtime t, at t there are roughly ten billion (bi-located) stars (give ortake the stars thatwill come into or go out of existence between t and thetime the symmetry-breaking particle appears). But if there are only tenbillion stars at t, and there are twenty billion after the appearance of thesymmetry-breakingparticle, then at least ten billion starsmust come intoexistence when the particle makes its appearance.6And the particle'sappearance surely does not have such dramaticconsequences. (It changesthe intrinsic and relational properties of already existing stars, but it doesnot result in the production of new ones.)

So A will have to say, as B and I would, that at t there are already(roughly) twenty billion stars. In that case he will have to say unlike Bandmyself that how many stars there are now could depend on whethera tiny symmetry-breaking particle will appear tomorrow,or a year fromnow, or a million years from now. This is hardto believe. He will also haveto say that whether or not the stars are bi-located now could depend onwhether or not symmetrywill be brokena million years hence. This too ishard to believe.

Problems not unlike the ones just set out arise for philosophers whothink that (i) if personal fission takes place, there were two persons allalong (even before the split), and (ii) if personal fission might have takenplace, but does not actually take place, then there was just one. Again, itseems distinctly odd to say that how many persons there are now, or

6A referee has pointed out to me that I am presupposing here that stars arecounted by identity.A might count stars in such a way thatbefore the appearanceof the symmetry-breaking particle, every star is bi-located, but there are stilltwenty million or so stars, because one star gets counted as two if it is in twoplaces. This move would allow A to say that the number of starsdoes not doublewhen the symmetry-breakingparticle appears; but it would not allow him to saywhat seems clearly true: that when the symmetry-breaking particle appears, nostars come into existence.


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154 ChristopherHugheswhether a certain person shares a body with anotherperson, could dependon what a brainsurgeon might or might not do ten years from now.

A defender of the account of fission just sketched might respond thatthe initial oddity of these consequences of her view can be dispelled, oncewe appreciatethatpersons are composed of temporal stages or segments,and distinct persons can share an initial temporal segment, in much theway that distinct roads can share an initial spatial segment. So just aswhether or not one road or two roads startin a certain town may dependon what happens elsewhere (whether or not what looks like one road intown splits outside city limits), whether or not we have one person or twonow may dependon whathappensin the future(whetheror not what lookslike one person now will split). Before fission does or does not take place,we have one initial person-segment, which will turn out to be an initialsegment of one or two persons.

In a similar vein, A might say that before the symmetry-breakingeventdoes or does not takeplace, we have ten million or so initial star-segments(that is, initial segments of "astralbundles"),each of which will turnoutto be the initial segment of one or two stars (of one or two astralbundles)depending on whether or not symmetryis actuallybroken.

Whateverthe'merits of the view thatstars have temporal parts,and thatdifferent starscan share a temporalpart,it does not seem a view thatA canconsistently hold. For he thinks that stars are bundles of universals, andthat universals arewholly present in each of their instances. If universalshave temporal parts, they arenot wholly presentin each of theirinstances.Suppose that roundness has temporalparts.Then some temporal partsofroundnessexist only before oronly afterthis (round)penny does. So sometemporal partsof roundness are not presentin this penny.But if some tem-poral parts of roundness are not present in this penny, roundness is notwholly presentin this penny. (Compare: f partof me is not in the kitchen,I am not wholly in the kitchen.)

If, however, universals do not have temporal parts, and substances arebundles of universalsandnothingbutuniversals,it is hard to see how sub-stances could have temporal parts.Supposingthatsubstances are made ofnothing but universals, universals lack temporal parts, and substancesnevertheless have them, seems like supposing that galaxies are made ofnothingbutstars,stars lack temporalparts,and galaxies nevertheless havethem. In either case, where would the temporal parts come from? Howwould they get there?


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BundleTheoryFromA ToB 155IV

At this point we might wonder whetherA would not be at least as well asoff denying outrightthe possibility of symmetricaluniverses. If he did, hewouldn'thave to classify ashemispheresthingsthat ook morelike spheres,orclassify propertieslike havingall of one 'scircularcross-sections on theinside as extrinsic. Nor would he be committed to the (at least initiallycounterintuitive)view that a materialobjectcouldbe (wholly) intwoplacesat once. Moreover,he could dismiss the difficulties raised in ?111on thegrounds that no possible worlds are contingently or temporarilysymmet-rical ornon-symmetrical.True,atheoryaccording towhich it is impossiblefor there to be nothing but a sphere here and an intrinsically indiscerniblesphere thereis not very accommodatingto untutored ntuition. But it is notthat much less accommodating to untutored intuition thanA's version ofthe bundle theory,according to which it is impossible for there to be justone spherehere, and anotherintrinsically indiscernible spherethere.In fact, though, the version of the bundle theory that rejects the possi-bility of a symmetrical universe faces what might be called the problemof counterfactual entanglement in a different form. On that version, itwon't turnout that (in certainquasi-symmetrical or symmetricalworlds)facts about how many starsthere arenow, andwhere, arecounterfactuallyentangled with facts about the occurrence of future symmetry-breakingevents. But it will turn out thatany bundle'sbeing instantiatedhere is notcompossible with its being instantiated here,andno otherbundle'sbeinginstantiated anywhere. This incompossibility will give rise to counter-factual entanglements different from but every bit as counterintuitiveasthe ones that follow from A's version of the bundle theory.The moral would seem to be that those who identify substances withbundles of immanent universals will have to regard as counterfactuallylinked states of affairs thatare intuitively counterfactually ndependentwhetheror not they countenance the possibility of symmetricaluniverses.At least, they will have to do that if like A they concede that intrinsi-cally indiscernible things in a symmetricaluniverse could not be distinctbundles of properties.7

Departmentof Philosophy CHRISTOPHERHUGHESKing's College LondonStrandLondon, WC2R2LSUK7Thanksto the Editorandto a pairof anonymousreferees for theirhelpful sug-gestions.


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156 ChristopherHughesREFERENCES

Zimmerman, Dean W., 1997: "Distinct Indiscemibles and the BundleTheory".Mind, 106, pp. 305-9.

chris hughes - bundle theory from a to b

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