looking forward, not back: supporting …...1 looking forward, not back: supporting structuralism in...
TRANSCRIPT
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LookingForward,NotBack:SupportingStructuralisminthePresent
KerryMcKenzie
Abstract
Theviewthat the fundamentalkindpropertiesare intrinsicpropertiesenjoysreflexive
endorsementbymostmetaphysiciansofscience. Butonticstructuralrealistsdenythat
there are any fundamental intrinsicproperties at all. Given that structuralistsdistrust
intuition as a guide to truth, and given that we currently lack a fundamental physical
theorythatwecouldconsultinsteadtoordersettletheissue,itmightseemasifthereis
simplynowhereforthisdebatetogoatpresent.However,Iwillarguethatthereexists
anas-yetuntappedresource forarguing foronticstructuralism–namely, theway that
fundamentality is conceptualized in our most fundamental physical frameworks. By
arguingthatphysicalobjectsmustbesubject tothe ‘Goldilock’sprinciple’ if theyareto
countasfundamentalatall,Iarguethatwecannolongerviewthemajorityofproperties
definingthemasintrinsic.Assuch,onticstructuralrealismcanberegardedastheright
metaphysicsforfundamentalphysics,andthatthisissoeventhoughwedonotyetclaim
toknowpreciselywhatthatfundamentalphysicsis.
Keywords: Ontic structural realism, quantum field theory, fundamentality, property
metaphysics.
1.Introduction
Taking Ladyman’s seminal 1998 paper to mark its contemporary inception, ontic
structural realism (OSR) has nowbeen lurking as a philosophical position for the best
part of two decades. Seeming both promising as a response to the master argument
against scientific realismanda fittingmetaphysic forquantumphysics, thisperiodhas
seenvibrantdebateconcerningOSR’scentralcontentionthatitisstructure,notobjects,
that is ontologically fundamental. Butwhile thosedebateshavewithout questionbeen
informativeandilluminating,severalpiecesofthestructuralistpuzzleremaintobeput
intoplace.Inparticular,itseemsthatstructuralistswillneedtosaysomethingaboutthe
fundamentalkindproperties if it is togainmore converts. For if there isone thing that
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unitesthemoremainstreammetaphysiciansofsciencethatOSRstandsopposedto,itis
theprevailing intuition that the fundamentalkindpropertiesare intrinsic in character;
fundamental intrinsicpropertiesofany sort, however, are anathema to structuralism.1
Of course, structuralists are likely to object at this point thatwhat anyone’s intuitions
regarding matters of fundamental ontology happen to be are wholly irrelevant to
metaphysics. OSRis,afterall,anavowedlynaturalisticandself-consciouslyrevisionary
thesis,andstructuralistswillholdthatweneedtolookattherelevantphysicsifwewant
todevelopadefensiblemetaphysicsofit.However,suchamoverunsintothedifficulty
thatwedonotcurrentlytakeourselvestoknowwhatthetrulyfundamentalkindsare–or
at thevery least,wedonot takeourselves tohavea truly fundamental theoryof them.
Giventhatwethereforeseemtolacktheonetheorythatcouldbeinvokedtoadjudicate
onthematterofwhatfundamentalpropertiesarelike,itseemsthatstructuralistsmust
either sit on their hands until we have that fundamental theory, or baldly reject the
receivedintuition;eitherway,itseemsunlikelythattheywillsucceedinpersuadingthe
unconvertedanytimesoon.
Inthispaper,Iwanttoarguethatsuchpessimism,whileunderstandable,isnevertheless
mistaken: OSR need neither be regarded as false, nor as something to be put on ice
indefinitely. The reason for this is that, although it is true that we lack a truly
fundamental theory of the properties that OSR’s sights must be trained on, we do
neverthelesspossessaframeworkforthinkingaboutsuchtheoriesthatcanplausiblybe
regardedasfundamental.Thisistheframeworkofquantumfieldtheory(QFT).Crucially
for structuralism, this framework suggests that thekindproperties thatwill feature in
any fundamental theory,whatever itmaybe, cannotplausiblybe regardedas intrinsic.
Assuch,IwillarguethatamajorstumblingblocktoOSRcanbeovercometoday,andina
thoroughlynaturalisticfashion.
1See, e.g. Ladyman andRoss (2007), p. 131: ‘talk of unknowable intrinsic natures andindividualsis idleandhasnojustifiedplaceinmetaphysics…[T]hereareobjectsinourmetaphysics but they have been purged of their intrinsic natures, identity, andindividuality,andtheyarenotmetaphysicallyfundamental.’
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Inmoredetail,thelayoutofmyargumentwillbeasfollows.InSection2Ioutlinewhat
commitmenttoOSRinvolves,andemphasizethat(a)itisathesisaboutthefundamental
inparticular,andthat(b)itseemstoprohibitobjectsfromhavingfundamentalintrinsic
properties.2 In Section 3 I present how the case for OSR is typically made in the
literature, and emphasize that the widely-held intuition that the fundamental kind
propertiesareintrinsichasbeentakentorenderOSRunfeasible.InSection3Iconsider
how structuralists might get around this problem, given that we currently lack the
appropriately fundamental theory of physics that could be appealed to in the hope of
settlingtheissueintheirfavour:myproposalwillbethatwecanusetheframeworkof
QFTtoprobesuchtheoriespriortoourbeingacquaintedwiththem. InSection5Ishow
that the constraintsQFTplaces on fundamental theoriesmeans that fundamental kind
propertiescannotberegardedasintrinsic,onthegroundsthatthefundamentalityofthe
properties involved has implications for the existence and non-existence of objects
distinctfromthebearer.Section6istheconclusion.
Myaim,then,istoshowhowQFTandtheconceptoffundamentalityembeddedwithinit
presentsonticstructuralistswitharichnewresource–a resource thatallows themto
denythatfundamentalkindpropertiesareintrinsicquafundamentalproperties. Itwill
doubtlessalreadybeclear,however,thatthefullarticulationoftheargumentisgoingto
beratherinvolved,andIshouldcomeoutandsayrightattheoutsetthattheargumentto
beoutlinedhereisatbestasuggestivesketch. Itstentativenessowespartlytothefact
that thereremaina fewpurelykinematicpropertiesnot touchedby theargument,and
partly to the fact that some relevant mathematical methods required to understand
fundamentaltheories intheir fullgeneralityawait furtherdevelopment. Myconclusion
willthereforenotbeacategoricalclaimthatOSRistrue,butrathertheweakerandmore
tentative one that everything we know about physics is pointing in that direction.
Nevertheless, this lackof anythingdefinitive to sayat thispointneednotbe seenas a
criticism:onthecontrary,onecouldinterpretitasshowingthatOSRremainsanongoing,
active, and exploratory research programme marching in step with the progress of
physics.2SeethoughqualificationsonthisclaiminSection4.
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2.OSRasaFundamentalityThesis
Whileithasanumberofdifferentarticulations,atitscoreOSRisaproposalconcerning
what is ontologically fundamental to this world. As the name suggests, the position
proposes that the mantle of fundamentality, at least in the actual world, belongs to
structureandstructurealone. Thuswhilecontemporarystructuralistsaretypicallynot
so radical as to claim that there are no objects simplicter, their proposal is that the
categoryofobjectshastoberegardedasontologicallysecondarytothatofstructure.To
quote Ladyman, they hold that “relational structure is more ontologically fundamental
thanobjects”,andforbrevityletthisbethe‘coreclaim’ofOSR.3
Itisclearthat,asafundamentalitythesis,OSRneedstoworkforthemostfundamental
objects if it is toworkatall.ThuswhileOSRistshaverecentlyelaboratedonwhatOSR
has to offer to the special sciences, it must nevertheless be the case that the most
fundamentalobjectsofphysicsareamenabletostructuralistanalysis if thepositionisto
standup.Infocusingitscoreclaimonthefundamentallikethis,OSRechoestheoverall
trendinmetaphysicsawayfromtheorizingaboutordinaryobjectsandtowardsthetask
of ‘limning fundamental structure’ – a project also engaged in by leading analytic
metaphysiciansoftheday,suchasTedSider,JonathanSchaffer,andL.A.Paul.Butwhile
OSRists take themselves to be distinguished from theirmore analytic counterparts by
theirmore naturalistic approach, they have been criticized for being less explicit than
theyastotheirconceptionofontologicalpriority,andhaveoftenbeenguiltyofslipping
andslidingbetweennon-coextensiverelationswhenspellingouttheirclaims.4Another,
perennialcriticismofitisthathowstructuralfeaturesaresupposedtobedistinguished
from non-structural features is likewise left somewhat imprecise. Clearly, however,
3LadymanandRossopcit.,p145.ItmightbeobjectedthatwiththischaracterizationIamequatingOSRwithitsradicalversion,whileOSRalsoadmitsamoderateversion.ButI leave the question ofwhether the considerations below lend support to one form ofstructuralismattheexpenseoftheothertoanotheroccasion.4Seee.g.Hawley(2010).
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withoutsomesuchdistinctionwecannotevensayofwhatitisthatistobegracedwith
fundamentalstatus.
InordertoclarifyOSR’scoreclaimthatstructureismorefundamentalthanobjects,then,
wemust clarify both how ontological priority is conceived and also what it is that is
meantby‘structure’.Soasnottogettooboggeddowninthedetails,Isuggestthatwedo
the following. Withregardtoontologicalpriority,wewill followChakravartty inusing
therelationof identitydetermination toexpress it:notonly is thisarelation frequently
invoked in the literature, but also one that may be argued on general metaphysical
groundstobeanaptrelationforstructuralism(thoughIshallnotargueforthathere).5
Assuch,totheextentthatthefundamentalityclaimdefinitiveofOSRdoesnotgothrough
withrespecttoidentitydetermination–thatis,totheextentthattheidentitiesofobjects
turnoutnottobedeterminedbystructures–wewilltakeitthatitthatOSRdoesnotgo
through simpliciter. Regarding the contrast between structure and non-structure, I
propose that we be somewhat liberal do not demand that structuralists must give
necessary and sufficient conditions for what counts as an ‘object’ andwhat counts as
‘structure’beforeweagreetoexaminethewarrantfortheirthesis;forplausibly,allthat
needstobeshownforOSRtogothroughisthatentitiesordinarilytakenasparadigmsof
fundamental objects can be shown to be secondary to entities ordinarily taken as
paradigms of structures.6 With respect to the first category, it seems that there is no
better candidate than fundamental particles, and as such our focus will be on those.7
With regard to the second category, we will here follow Maxwell and take structural
5IdiscussthisfurtherinMcKenzie(inpreparation).6Partof the reason it seems folly tome togivenecessaryand sufficient conditions forobjecthood isbecause theconcepthasevolvedsomuchover thehistoryofphysics–ahistorythatisofcourseitselfalargepartofthestructuraliststory.7Note thatmy argumentwill go throughwhetherwe speak of particles or directly ofquantumfields.Ishouldsaytoothatspacetimepointsaretakenasanother–perhapstheonlyother–candidatefor ‘fundamentalobject’;butsinceit ishardtothinkofwhattheanalogy of fundamental kind properties would be for these entities, it is likely thatstructuralismwill be easier to secure in the spacetime case. (See Ladyman and Ross(2007),Section3.2fordiscussionofit.)
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features to be ‘those that are not intrinsic’, 8 where we will understand intrinsic
properties somewhat intuitively as thatmaybepossessedbyan entity independently of
whattherestoftheworldislike.9Assuch,intrinsicpropertiesarethosepropertieswhose
possessionneitherdemandsnorprecludes the existence of any object distinct from the
beareroftheproperty. Giventhischaracterizationofstructuralfeatures,itfollowsthat
relations between and extrinsic properties of objects will qualify as numbering among
them. Andwhile one could object that there are intrinsic features of objects that also
qualifyasstructural–compositionalstructurebeingtheobviousexample–itmuchless
clearthatfundamentalobjectscouldhavesuchfeatures.Ourfocushereisonjustthose
objects,andwewilltakeitasgiventhattheycannot.10
8ThisquoteisfromMaxwell(1970),p.188:whilehewasanearlyadvocateofepistemicstructuralism–but one can find the sameequationof structuralismwith thedenial ofintrinsicnaturesintheOSRcanon,e.g.LadymanandRoss(cf.footnote1).
9ThusWeathersonandMarshall(2012)takeitthat‘athinghasitsintrinsicpropertiesinvirtue of the way that thing itself, and nothing else, is’; similarly, for Dunn (1990),‘Metaphysically, an intrinsic property of an object is a property that the object has byvirtueof itself,dependingonnoother thing’ (p.178).While theexistenceof theminorindustry inmetaphysicsdedicatedtodefining intrinsicalitysuggests that thiscouldusesomesharpeningup,Iwillbecontenttorestwiththisinformalcharacterizationinwhatfollows.Onereasonforthisisthattheby-nowstandardformaldefinitionofLangtonandLewis(1998)isfarfromidealinthiscontext:foronething,theiranalysismakesappealto perfectly natural properties,which for Lewis are both fundamental and intrinsic bydefinition–preciselythatwhichthispaperdenies.
10Afficionados of ‘group structural realism’ will rightly object at this point that I amsimply ignoring the claim that even intrinsic features of fundamental objects may beaccounted for structurally – namely, by utilizing the symmetry structures that are socentral to contemporary physics theories (see, e.g. Ladyman and Ross Section 3.3).Though regrettably this issue demands a far fuller discussion than I can give it here,sufficetosaythat–despiteonceholdingthisviewmyself(seee.g.McKenzie2012)–Inolonger think that it works. To see this, it suffices to note that althoughwe know thesymmetries of, eg, the Standard Model, many of the kind properties definitive of theparticlesinitareneverthelessfreeparameters. Thussymmetrystructuredoesnot–atleastnotingeneral–determinethefundamentalkindproperties.(Onecanatmostsaythat theydependon such features; but I no longer regard dependence as a relation ofpriority. I discuss this a little further in McKenzie (in preparation).) It is howeverpossiblethatthissituationmaychangewithfurtherdevelopmentsofphysics,andindeed
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Puttingeverythingtogether,then,forusanefforttodefendOSR’scoreclaimwillconsist
aneffort to show that theidentitiesof fundamentalobjectsaredeterminedexclusively in
terms of relations and extrinsic features. An obvious corollary is that no recourse to
intrinsic properties will need be made in specifying the identities of fundamental
particles.
I propose, then, that if we are to establish OSR then this is what we must try to do.
Worryinglyforstructuralists,however,ithasbeenclaimedthatthisispreciselywhatwe
cannotdo, for intrinsicproperties ineliminablyenter into identitiesat the fundamental
level. In particular, has been claimed that the fundamental kind properties that sort
particles intospeciesare intrinsicproperties,andthat theseareproperties thatcannot
beleftoutoftheinventoryofidentifyingproperties.11Inthenextsection,Iwillgivejust
enoughofanoverviewoftheworkthatidentitydeterminationhasdoneinOSRtobring
outtheproblemofintrinsics.Afterthat,Iwillconsiderthedifficultiesthatstructuralists
faceingettingaroundtheproblem,beforeproposinganewandmorepromisinglineof
attack.
3.IdentityDeterminationandtheArgumentfromIntrinsics
Onenicefeatureoftheidentity-basedapproachtostructuralismisthatitappliesbothin
the context of spacetime theory and in quantum mechanics – the two mainstays of
philosophyofphysics.Inthespacetimecontext,thepurporteddeterminationofobjects
byrelations issupportedbytheholeargument ingeneralrelativity,sincethissuggests
that primitive identities for spacetime points subjects physics to form of a priori
indeterminism.12 In the quantum context, the argument is premised on the fact that
quantumunlikeclassicalparticlescannotingeneralbedistinguishedfromothersofthemanyphysicistshopethatthiswillbethecase.Nevertheless,thatobservationisclearlyoflittleuseindefendingstructuralismtoday.
11Sincekindpropertiesarecommonbothtoquantumfieldsandtheirassociatedquanta–thecorrespondingparticles–itdoesn’tmatterformypurposeswhetherweregardthefundamentalobjectsofphysicsasparticlesorfields.Iwillmostlystickto‘particle’.12See,forexample,LadymanandRossop.cit.,Section3.2.
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sametypebyspatiotemporallocationortrajectory.13Furthermore,whensuchparticles
become entangled with others, none of the particles in the resulting state can be
distinguishedfromtheothersthroughempiricalmeans.Thusunlesswearetopostulate
problematic ‘primitive thisnesses’ to ground the numerical diversity of entangled
particles, all that remains that can play this role are the features of the entanglement
relation itself. Fortunately, however, at least in the case of fermions – the basic
constituentsofmatter–onecanappealtosuchfeaturestoperformthisrole.Forinthe
case of entanglement between two fermions – two electrons, say – the relations may
genericallyberepresentedas
!!(| ↑! | ↓! −| ↓! | ↑! )
It is clear that if in this relationwe replace a label ‘1’ with a label ‘2’, (or vice versa,
understanding ‘or’ as exclusive), the relation disappears, thus establishing that the
relation is irreflexive. Since it follows from this that no one object can stand in this
relation to itself, we see that there are grounds for saying not only that the particles
involved are distinct, but also that it is a feature of the relations between them that
underwritesthisdistinctness.Sincefactsaboutanentity’sdistinctnessfromotherthings
clearly qualify as facts about its identity, and since (I have claimed) facts about
determination of identity should be taken to track facts about priority, these
considerations about individuation are often presented as sufficient to secure ontic
structuralismaboutquantumphysics.14
Whiletheseargumentsconcerninghowobjectidentitiesaredeterminedbystructureare
central planks of the structuralist scheme,many objections have been pitched against
them.Foronething,itisatleaststrangethatwhileinthespacetimecasetheargument
aims to show there are no haecceities, the analogous argument in the quantum case
13See,e.g.ibid.,Section3.1.14Seeespecially ibid.,p.138. Note thatentanglementbecomesevenmorepervasive inquantum field theoretic regimes (seee.g.Lam(2013),particularlySection2). As such,theconclusionsregardingtheroleofentanglementinsecuringthediversityofsame-kindquantumsystemswillcarryovertotheQFTcontexttobediscussedbelow.
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seemstohavethemsimplyruledoutbyfiat.15Foranotherthing,itisessentialtophysics
that bosons be countable (for example, when confirming quantum field theories via
scattering experiments, inwhich thenumber of photonsproduced canbe crucial); but
theargument,at leastasoutlinedabove,seemstogive thewronganswer forbosons.16
However,themostsalientobjectionforpresentpurposesisthatbyclaimingvictoryon
thebasisofthesearguments,itseemsthatOSRaspiresonlytogivingastructuralaccount
of thenumericaldiversityof fundamentalparticlesofagivenkind. Suchanaspiration
clearlytakesforgrantedthatparticlesaresortedintokindsinthefirstplace.Butthese
facts about whatmakes particles particles of a given kind, as opposed to particles of
anotherkind,seemtoconstitutejustascrucialanaspectoftheidentitiesofparticlesas
factsabouttheirdistinctnessfromothersofthesametype.Clearly,therefore,something
needs to be said by the structuralist about their interpretation of fundamental kind
properties. Alarmingly for structuralists, however, the view that these properties are
intrinsic properties is very much the received view in metaphysics. Since we have
identifiedstructuralfeaturespreciselywith‘thosethatarenotintrinsic’,thisclearlydoes
not bode well. Indeed, things look so bad it would be easy to suspect from the
comparativepaucityofdiscussiononthisissueintheOSRliteraturethattheyhavebeen
notsomuchoverlookedasstudiouslyignored.17
HereishowChakravarttyputstheproblem.
[L]etusgrantforthesakeofargumentheretheorthodoxinterpretationaccording
to which quantum particles have relations that cannot be analyzed in terms of
anythingintrinsic.Wouldthisdemonstratethattheidentitiesoftheseobjectsare
15Thisisnotthecaseinallstructuralists’hands:StevenFrench,forexample,partlypremiseshisstructuralismonthefactthathaecceitiescannotberuledoutapriori(seee.g.French1998).ButFrenchisanexceptionhere,especiallynowthatJamesLadymannolongerbaseshisstructuralismontheunderdeterminationargument.16AtleastasIunderstandthepresentationinSaunders(2003);seeHuggettandNorton(2014)foramuchfullerdiscussion.17Hereagain Iemphasize,as Ididat footnote10, thatstructuralistshavehadthings tosayaboutkindproperties.Butitiscertainlythecasethatstructuralistshavesometimesspokenasiftheaboveconsiderationsregardingdiversityareinthemselvessufficienttoestablishtheposition,andChakravarttyisrighttoprotestthatthatismuchtoohasty.
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extrinsic, in the manner suggested by the ontological priority thesis of non-
eliminativeOSR?18
Theanswer,Isuggest,isno.Inorderfortheappealtoextrinsic[properties]inthis
contexttoofferanysupporttonon-eliminativeOSR,itwouldseemthatoneofthe
twofollowingconditionsshouldobtain.Eitheritshouldbethecasethatnot just
some, but all properties of the particles described by quantum theory are
extrinsic, or it should be the case thatwhatever intrinsic properties the theory
doesattributetothemdonotdeterminetheiridentity.[…]Butneithercondition
obtains. While some properties are described by quantum theory in terms of
relationsofentanglement,othersarenot.Massandcharge,forexample,arestate-
independent intrinsic properties of subatomic particles, whose attribution thus
violatesthefirstconditionthatallpropertiesbeextrinsic…[T]hefactremainsthat
whereveroneappliestheconceptofaparticle,thetheorypresentsdescriptionsof
whatappeartobeintrinsicpropertieswhichareconstitutiveoftheiridentity.19
TheviewthatChakravarttyreportsinthispassageiscertainlynotidiosyncratic:itisso
well-entrenchedthatitprobablydeservestobecalledthe‘receivedview’inmetaphysics.
His fellowdispositionalessentialistBird, forexample,statesthat ‘no-onehassuggested
that charge, rest mass and spin are not intrinsic’, and indeed the same policy on
fundamentalpropertiesissharedevenbytheirHumeanrivals(mostobviously,Lewis).20
Butifmetaphysiciansasdividedonvirtuallyeveryotherissueofscientificmetaphysics
canneverthelessagreeontheissueofintrinsicality,thenstructuralistshadbettergivean
impressive argument as to why the view is wrong. Let this objection that the
intrinsicalityofthesepropertiesforeclosesOSRbethe‘argumentfromintrinsics’.Since
OSR is the thesis that no identity-determining features of fundamental objects are
intrinsic in character, the argument from intrinsics throws the gauntlet firmly at the
structuralists’feet.
18By‘non-eliminativeOSR’,ChakravarttymeansanyformofOSRinwhichobjectsaretakentoexistbuttakentobenon-fundamental19Chakravartty(2012),p.204.20Bird2007,p.125;e.g.Lewis1983,p.357.
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4.TheStructuralistDilemmaandANewStrategy
Structuralists therefore need to find a way of rebutting the argument from intrinsics.
What,then,aretheytosay?Nodoubt,structuralistswillbequicktopointoutthatwhile
it is certainly the case that kind properties like charge and mass are ‘commonly
regarded’21as intrinsic–while itmayevenbethat ‘no-onehassuggested’thattheyare
not intrinsic,at leastno-one failing toself-identifyasa structuralist– remarkably little
argumentforthisclaimisevergiven.22Butiftheintrinsicpropertiesarethosethatcan
behadevenbya lonelyobject, thengiventhatwewillobviouslyneverencountersuch
objectsitisjustveryhardtosaywhetherthesepropertiesareintrinsicornot–inmuch
thesamewaythatitisdifficult,asMachnoted,tosaywhatwouldhappentoabucketin
anemptyuniverse.23Giventhis,ratherthansimplybackingdownbeforetheintuitions
thatmetaphysiciansmayhappentoshareonthematter,thestructuralistwilllikelyinsist
thatwhatwemustdo–indeed,allwecando–islookatwhatasuitabletheoryofphysics
hastosayaboutit,anddefertothat.
Butifthat’stheplan,thenstructuralistsfaceaproblem.Thisproblemisthat,asalready
underlined, OSR is ultimately a fundamentality thesis, butwe do not take ourselves to
possessatrulyfundamentaltheory.Assuch,wedonottakeourselvestohaveatheory
that would definitely answer the question of whether or not we can regard the
fundamentalkindpropertiesasintrinsicornot.ThuseventheStandardModelofparticle
physics(describingtheinteractionsofquarks,leptons,andgaugebosons),whilewithout
doubtthemostfundamentaltheorywehavebeenabletoproducetodate,isnevertheless
notthoughtnottobetrulyfundamental–partlyonaccountofitsfailuretoincorporate
gravity,itssurfeitoffreeparameters,andsuspecteddivergenceinthehigh-energylimit.
21Cf.Esfeld2014.22Theclosestoneseemstoget istheargumentfromdispositionalthattheirpostulatedintrinsicalityisnotinconsistentwiththeirassumeddispositionalnature.Seee.g.Birdopcit.23SomeofthedifficultiesinvolvedinjustifyingtheclaimthatthepropertiesofphysicalobjectsareintrinsicaregiveninSlaterandHaufe(2009),Section4.
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As such, it cannot definitively answer the question of whether the fundamental
propertiesareintrinsic;andifitisn’tqualifiedthenitishardtoseewhatis.Giventhis,it
seemsthatstructuralistsmustsimplysitontheirhandsuntilatrulyfundamentaltheory
comesalongthattheycanciteinsupportoftheirargument.Butthatmaybealongtime
incoming–assumingitwilleverhappenatall.
The defence of OSR at this point therefore seems to have run into the ground. While
structuralists face an uphill struggle in talking metaphysicians out of an intuition,
apparentlyuniversally shared, concerning fundamentalkinds, theywant for the theory
that they can appeal to in order to try and settle the issue in their favour.What Iwill
propose here, however, is that contrary to appearances structuralists need not simply
downtoolsfornow,fortheremaybeathirdwayofdefendingOSRthatreliesneitheron
intuitiontradingnoronourpossessionofatrulyfundamentaltheory.Whatmakesthis
third way possible is that, while we lack such a theory, we do nevertheless have a
frameworkfortheoriesthatmaywellbefundamental.Thisistheframeworkofquantum
fieldtheory.24WhatitmeanstocallQFTaframeworkandnotsomuchatheory(despite
thename)isthat,whenwethinkofatheoryinphysics,wethinkofasetofobjects,such
asfieldsandtheirassociatedparticles,andalawoftheirinteraction;QFT,ontheother
hand, constitutes a set of principles that constrain any theory that claims to describe
relativistic quantum systems.25 As such, this framework can be used to define an
unlimited number of different theories, depending on the fields whose behaviour we
wanttomodelandtheinteractionswepostulatebetweenthem.ThecrucialclaimthatI
will make here is that whenwe reflect upon the constraints that the QFT framework
placesonfundamentaltheoriesinparticular,weseethatthereisactuallypositivereason
todenythatthefundamentalkindpropertiesareintrinsic–atleastinthevastmajority
ofcases.26Thisisbecausetheirverystatusasfundamentalkindpropertiesturnsoutto
24On the notion of theories as contrasted with frameworks for theories, see Shimony(1987),p.209.25For example, that any lawmustbeLorentz invariant, that the statesofQFT systemsmustsuperpose,andsoon.26OSRistsofcourseneedsittobethecasethatnofundamentalpropertyisintrinsic,andweshallseemyargumentdoesnotapplytoquiteall.Moreonthistofollowpresently.
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behighlysensitive towhatotherkindsexist in theworldbesides thekind inquestion.
As a result, we should regard the fundamental level as populated not by fundamental
objectswith intrinsicnatures,but ratherwithobjectswhoseverystatusasfundamental
enmeshestheminarichnexusofdependencestooneanother.Itshouldbenoted,then,
thatsincemyclaimisthatthefundamentalkindpropertiesareextrinsicquafundamental
properties,theargumenthasnothingtosayaboutworldsinwhichthosekindsexistbut
are not fundamental – on the (highly) questionable supposition that such worlds are
possible. But since it is givinganaccountof the fundamental inparticular thatOSR is
concernedwith, the fact that thesepropertiescannotberegardedas intrinsicwherever
theyoccurasfundamentalpropertiesshouldbegoodenoughforit.
InthenextsectionofthispaperIwilltrytomakegoodonmyclaimthatfundamentality
conceptualizedàlaQFToffersanewlineofsupporttostructuralism. BeforeIdothat,
however, I need to make a few qualifications and disclaimers. The first of these
qualificationsisthat,aswillalreadyhavebeennoticed,Ihavealreadyslippedinthatmy
argument,althoughhighlygeneral,willapplyonlyto ‘thevastmajority’of fundamental
properties.Thereasonforthisqualificationisthat,whileanyparticleinQFTmusthave
some value of spin and parity (as a consequence of the symmetries of Minkowski
spacetime), my argument will not apply to these properties. This is because my
argumentappliesonlytothosepropertiesthatareassociatedwithacouplingparameter
in the Lagrangiandefining the theory: these are anyproperties throughwhichparticles
interact with other particles, as well as the property of mass.27 The value that the
parameter takes determines the strength of the interactions involved or the effective
massoftheparticlerespectively.28Spinandparity,ontheotherhand,arenotassociated
with coupling parameters, and while there is reason to think that these are the only
propertiesthatarenottouchedbytheargumentIwillnothazardherewhatOSRshould
sayaboutthem.Nevertheless,itremainsthatmyargumentwillseeoffthevastmajority
27We can think of the Lagrangian as just anotherway of expressing the lawof naturereferredtobythetheory.28Masshasthisstatuseveninanticipationofaquantumtheoryofgravitationbecauseitmay in a sensebe regarded, in theQFT context, as encoding the interactionsof a fieldwithitself.Seee.g.Susskind(2012)foraqualitativedescription.
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of the properties cited by OSR’s critics, clearing the way for us to focus on these last
aspects.29
A further limitation topoint out is thatmy argumentwill not be conclusive evenwith
respect to those properties that it succeeds in applying to. The reason is that, in the
approachIpropose,thefundamentalityofpropertiesistobeconceivedofintermsofthe
fundamentalityofthetheoriesinwhichtheyoccur;butpreciselywhatfeaturestheories
musthavetoqualifyasfundamentalissomethingnotyetunderstoodinitsfullgenerality.
Myargumentwillapplyonlytotheclassoffundamentaltheoriesthatwedounderstand–
namely,theasymptoticallyfreetheories.Butsuchtheoriesareonlyasubsetoftheclass
of asymptotically safe theories – where ‘asymptotically safe’ is just another word for
fundamental QFTs. While the features of asymptotically free theories are ratherwell-
understood, thegeneral featuresof the remaining theories arenotknownatpresent –
indeedtheyaredifficulteven‘toimagineorinvestigate’.30Itisthusunderstandablethat
myargument focusesonlyonthe formercase,but thisstrategyobviouslyrunstherisk
thatmyconclusionswillnotholdwhenwegeneralizeout.However,thereasonthatthe
features of the more general class are not known is because the interrelationships
betweenthecouplings in these theories are so involvedand so complex that theorizing
aboutthemprovesmathematicallyprohibitive,atleastbymethodscurrentlytohand.It
wouldthusinmyopinionbeverysurprisingiftheholismthatIwillclaimismanifestin
therestrictedclasswerenotpresentinthemoregeneralone–indeedsurprisingifnot
stillmorepronounced.Nevertheless,forthemomentthatremainsmerespeculationon
mypart.
AfinalpointtounderlineatthisstageisthatmyargumentisgoingtoassumethatQFTis
indeeda fundamental framework for theories,so thatwehavereasonto thinkthat the
fundamental level can indeedbedescribedwithin it.What is certain is thatQFT isour
29Imightpointout too thatby focusingprimarilyon interactionproperties I am innowaybeggingthequestion, for–asdispositionalessentialistshavelongbeenatpainstopoint out – the mere fact that a property is an interaction property does nothing toundermineitsintrinsicstatus.Ireturntothispointbelow.
30Wilczek(1999),p.2;Kang(1975),p.11.
15
mostfundamentalframeworkforphysicsatpresent,atleastthatweareabletosubmitto
empiricaltest;thereismoreoverincreasingoptimismaboutitbeingatrulyfundamental
framework,owingtoagrowingsensethatitisonlytechnicalobstaclesthatstandinthe
wayofaquantumfieldtheoretictreatmentofgravity.31Nevertheless,sincemyargument
dependsonspacetimehavingthecontinuousstructurethatithasinQFT,andsincesome
(speculative) new physics frameworks deny this, the truth of my conclusions is
vulnerable to change as physics develops. Fundamentality is in that sense a highly
theoreticalconcept.However,Itrustthatthoseofanaturalisticoutlookwillnotseethis
asnecessarilyacriticism,asopposedtosimplypartofwhat itmeanstodonaturalistic
metaphysics.
Withthosequalificationsandclarificationsinplace,letmeproceedtotheargument.
5. The Strategy Implemented: Supporting Structuralism in the Present via
FundamentalityConstraintsinQFT
Myaim, then is to show that thekindpropertiesdefining the fundamental particles of
physics are not intrinsic, and – to repeat – the properties I am focusing on are the
propertyofmassandthepropertiesthroughwhichobjectsinteract:letuscallthelatter
the ‘interaction properties’.32 Having already said a little about what I’ll intend by
‘intrinsic’,itremainstosaysomethingabouthow‘fundamentalkindproperty’shouldbe
understood.
Since the aim of the game here is to show that the properties defining fundamental
objectsarenotintrinsic,itseemsnatural(wereitnotsoalready)todefine‘fundamental
kindproperty’asoneofthepropertiesthatsortthefundamentalobjectsintokinds.But
doing so just shifts the problem of defining ‘fundamental kind property’ to defining
‘fundamentalobjects’, and inany relativisticquantum theory– that is, in anyquantum
fieldtheory–thisisnotoriouslydifficulttodo.Inparticular,giventhatinthesetheories31Onthis,seePercacci2009.32Themostfundamentalinteractionpropertiesweknowofarecharge,weakisospinandcolourcharge,butitislikelythatatsomeofthesearenottrulyfundamental.
16
even(whatareregardedas)pointparticlescandecayintootherparticles,anyattemptto
define fundamentality inmereological terms seems a hopeless enterprise. Partly as a
result of this, it is now standard to regard a fundamental particle as one whose field
appearsdirectlyinafundamentalLagrangian–that is,aparticlewhoseinteractionsare
specifiedbyafundamentallawofnature.33Weshouldthereforeregardthefundamental
kindproperties as theproperties that sort theobjects evolving in accordancewith the
fundamental laws of nature into kinds. In so doing, we use the fundamental laws to
definethefundamentalkindproperties.
Tofindoutwhetherthesepropertiesareintrinsic,then,itappearsthatwemustconsult
thefundamentallawsofphysics,lookatthefieldsandparticlesinthem,andseewhatthe
theory has to say about their metaphysical features (of course in tandem with some
appropriatemetaphysicaltheory).Butifthatisthecase,thenitseemsthatweareback
at theproblemwestartedwith–namely,our lackof fundamental theory. However, to
drawthisconclusionwouldbeoverlookthefactthatwhilewemaylackknowledgeofthe
fundamental lawsofnature,wecanhazardthattheyaccordwithquantumfieldtheory.
AsIwillargue,thisfactallowsustoidentifygenericfeaturesthatanyfundamentallaw
must satisfy, making it possible to make substantive metaphysical claims concerning
fundamentalproperties,eventhoughweremain inthedarkrightnowastowhatthose
propertiesare.34
Letusthenturntothosegeneric features. Thesimplebutcrucial insight is that, inthe
QFTframework,tocallalawfundamentalistomakeaquitespecificpredicationofit:itis
to affirm, at the very least, that the law staysmathematically consistent in the limit of
infiniteenergy.Wedoafteralltakeprobingstructuresathigherandhigherenergies–or,
equivalently, shorterandshorterdistances– to correspond toprobingmoreandmore
fundamentalregimes,andthecontinuityofspacepresupposedinMinkowskispacetime
entails that the energy range that is available tobeprobed is inprinciple infinite. We
might thus follow Huggett and Weingard in saying that theories valid in the infinite
33See,e.g.Heisenberg(1975);Weinberg(1996).34Modulothecaveatregardingkinematicalpropertiesmadeabove.
17
energylimitare‘continuumcompatible’.35Butalthoughthisconditiononafundamental
lawiseasytostate,statingwhat lawsmustbe liketoactuallysatisfy it isamuchmore
difficultendeavor,assumingthatthelawsdescribeanyinteractions.36Whatwedoknow
isthatcontinuumcompatibilityisanextraordinarilystringentrequirement–somuchso
that there is a general feeling in contemporary particle physics that if we can find a
theoryoffundamentalentitiesthatsatisfiesit,thenwehavefoundthetheory,andsoan
actual fundamental lawof nature. Part of the reason it is sohard towrite down laws
satisfying continuum compatibility is that the coupling parameters that appear inQFT
Lagrangians – to repeat, those associated with the masses of particles and the
interactions between them – change their values as the energy is scaled up, in a way
describedbytherenormalizationgroupequation.37Thusresultsinthepropertieswhose
magnitudesaregivenbythevaluesofthesecouplings–suchastheparticle’smassand
charge–becominglikewisescale-dependent.38Sincegenericallywecanexpectfunctions
todivergeastheirargumentsdo,wecanexpectthemassorstrengthof interactionsof
particles inanarbitraryquantumfield theory to likewisediverge in the limit–making
thetheorythattheyoccurinmathematicallyill-definedtoo.Thusaminimalconsistency
conditiononanyfundamentalQFTisthatallofitscouplingparametersstayfiniteinthe
infinite-energylimit. Thosetheoriesforwhichallcouplingsremainfinitearesaidtobe
‘asymptoticallysafe’.Theoriesforwhichallofthecouplingsnotonlystayfinitebutalso
have the special feature of tending to zero in the limit are known as theories that are
‘asymptoticallyfree’.
As alreadymentioned, however, the only theories we are able to get a grip on at the
moment are those that are asymptotically free. While the lack of generality is
unfortunate, there is nevertheless now a great deal that we can say about the35HuggettandWeingard(1995).36Iwillconsiderhowtheexistenceoffreetheoriesimpactsuponmyconclusionsbelow.37Seee.g.Ryder(1996),p.325.38Thus,forexample,thechargeonanelectronincreaseswithenergy,andthemassofaquarkdecreases.Thuswhatwerefertoas‘the’chargeonanelectronisreallyjustthevalueofthecouplingconstantmeasuredine.gThomsonscatteringexperimentsatverylowenergy.Seee.g.Maggiore(2009),Section5.9.
18
asymptoticallyfreecase. Themostimportantthingweknowisthatanyasymptotically
freetheoryhastobearenormalizablelocalgaugetheory:thatis,itmusthaveaformthat
it is invariant under the transformations of a gauge symmetry group, and contains no
non-renormalizable terms.39 For present purposes,we do not need to know precisely
whatthesetermsmean:however,whatwedoneedtoappreciateisthat–andsomewhat
amazingly – this requirement gives us a recipe for uniquely pinning down the laws of
nature.Inalittlemoredetail,itgivesusarecipeforpinningdownthelawsofinteraction
pertaining to fundamental constituentsofmatter – that is, the fundamental fermions–
givenaspecificationofwhatthesefermionsare.Forexample,supposewearehanded6
quarks – that is, particles that carry colour in addition to somedeterminatemass and
spin. Thenourknowledgethatthelawappropriatetotheseparticlesmusthavealocal
gauge symmetry if it is to be fundamental determineswhat the form of that law is: a
renormalizabletheorywithgaugegroupSU(3)istheuniquetheorywiththisproperty.40
Crucially, armedwith this informationone cangoonand show that, in addition to the
kinematic terms describing the quarks’ free motion, the law must contain a term
describingthequarksinteractingwithaspecificsetofbosonsthroughacouplingconstant,
g.Moregenerally,wheneverweascribefundamentalinteractionpropertiestofermions,
the requirement of local gauge invariance implies that they couple through those
propertiestoasetofbosons,withthestrengthofthecouplingmeasuredbyacoupling
constantfeaturingintherelevantLagrangian.
This requirement that asymptotically free theories have to be local gauge theories has
profoundimplicationsforthepossibilitythatwemayactuallydiscoverthefundamental
laws of nature, given empirical information concerningwhat fundamental kinds there
39See e.g. Wilczek op cit.. It must furthermore be a non-Abelian gauge theory, whichmeansthatthebosonswillcarrythesamechargesthroughwhichthefermionsinteractwitheachotherandwiththebosons.40HereIassumethatquarkcolourstateshavethestructure,inallpossibleworlds,ofthefundamental representation of SU3. The fact that the canonical discussions of themetaphysicsofpropertieshave focusedmoreor lessexclusivelyonclassicalpropertiesmeansthatIcannotsimplycitesomeauthoritativefigureinsupportofthisclaim. Fornow,sufficetosaythatIcannotimaginehowsomeonecoulddenyit;nordoesitbegthequestionathand.
19
are.Butithasequallyprofoundimplicationsfortheintrinsicalityofthepropertiesofthe
particles that feature in those theories. These implications may be divided into two
classes:firstly,thoseconcerningtherelationshipoffermionstobosons;secondly,those
concerning the connections between all types of particles with (other) fermions. The
first class of implications is easy to state: it is that any interaction property had by a
fundamentalfermioncannotberegardedasintrinsic,becausethepossessionofanysuch
property requires the existence of bosons. That is, since fundamental particles are
particles whose fields appear in fundamental Lagrangians, and since the laws of
interactionforfundamentalfermionsrequiretheexistenceofgaugebosons,thosebosons
are needed in order for there to be fermions thatwe can designate as fundamental at
all.41Thusitcannotbesaidthatthefundamentalinteractionpropertiespartlydefinitive
of fundamental fermionsare intrinsic incharacter:onthecontrary, theirverystatusas
fundamentalbringsinitstrainentitiesdistinctfromthemselves.
Onaccountoftherelationshipthatfermionswiththesepropertiesmuststandintothe
correspondinggaugebosonsiftheyaretobefundamental,then,wearenolongerableto
regardmanyof thepropertiesof fundamental fermionsas intrinsic – inparticular, the
interaction properties. However, this is not the only reason why considerations of
fundamentality undermine the intrinsicality of the features defining fundamental
particles.Afurtherreasonisthat,whilelocalgaugeinvarianceisanecessaryfeatureof
anyfundamentallaw,itisinitselfinsufficient:foriftherearetoomanytypesoffermions
includedinthelawthenthefundamentalityofthatlawislost.Thereasonbehindthisis
thatthebehaviorofthecouplingsinalocalgaugetheoryissensitivetohowmanykinds
(or ‘flavours’)of fermionsexist in the theory, in suchaway that (at least someof) the
41StevenFrenchandImadetheargumentthatinteractionpropertiescannotbeintrinsicbecauseoftheirrelationtogaugebosonsinFrenchandMcKenzie(2012).ThatargumentwascriticizedbyLivanioshowever,onthegroundsthatthisrelationcouldbecontingent(see Livanios 2012, p. 32). This argument of the present paper improves on thatargument, in that itexploits the fact thatwearenotconsideringchargesimpliciter,butcharge qua fundamental property. It is the extra constraints placed on propertiesfeaturinginfundamentaltheoriesinparticularthatlinkschargetogaugebosons.
20
couplings will diverge if there are too many of them.42For example, in the case of a
theorywithalocalSU3gaugesymmetry,suchasQCD,thenumberofquarktypesinthat
theorymustbeno greater than16 the theory is tobe valid to arbitrarilyhigh energy;
otherwisethecouplingassociatedwithcolourwilldivergeinthelimit,andthelawwith
it.43 And, to repeat, since a fundamental particle is one whose field appears in a
fundamentalLagrangian, it followsthatwecannotsaythatthefundamental interaction
propertiesofanygivenkindareintrinsic,becausetheirverystatusasfundamentalkind
properties depends on there not being toomany other kinds in theworld besides the
kindinquestion.Moreover,whilealessobviousroutetointrinsicalitythanthelast,this
approachismoreextensiveinitsreach. Thisisforatleasttworeasons. Foronething,
theargumentappliesjustasmuchtothepropertiesofbosonsastothoseoffermions:the
colourchargeonagluon,say,willceasetobecapableofbeingregardedasfundamentalif
thereare17ormorefermiontypesinhabitingtheworldalongsidethegluon,justasthe
colourchargeonanygiventypeoffermionwillsufferthesamefate.Butfurthermore,the
argumenthas implications forourability toregard thepropertyofmassas intrinsic in
additiontotheinteractionproperties.ThisisbecausethemassesofparticlesinQFTare
also functions of the energy, and the renormalization group equation describing the
couplingparametercorrespondingtomassisafunctionoftheallcouplingspresentinthe
theory.Asaresultofthis,ifthecouplingsdivergewecanexpectthemasstodivergeas
well.Soforbroadlythesamereasonsasbefore,itseemsthatwecannotregardparticle
masses as intrinsic in any straightforward sense either: we simply cannot postulate
fundamentalparticlesandpredicatemassofthemwithoutkeepinganeyeonwhatother
particles inhabit theworldalongside theparticle. As such,we cannot say thatmass is
bothafundamentalkindpropertyandintrinsicatthesametime.
42Thus, asWilczek puts it, ‘One finds that only nonabelian gauge theorieswith simplemattercontent,andnonon-renormalizablecouplings,satisfythiscriterion(opcit.,p.3);similarly for Ho-Kim and Yem, ‘theories of non-Abelian gauge fields and fermionmultiplets are asymptotically freeonly if the theorydoesnothave toomany fermions’(1998,p.278).(p.535).
43One can see this from looking at the renormalization equation governing the colourcoupling:seeforexampleHo-KimandYemopcit.,equation15.83(p.535).
21
Wehaveseen,then,thatgivenhowfundamentalityisconceivedofinphysicswecannot
considereitherinteractionpropertiesorthepropertyofmassasintrinsicinanythinglike
theusualsense.Withoutthegaugebosonstosupplementthefundamentalfermions,the
interactionpropertiesofthelattercouldnotqualifyasfundamental;toomanyfermions
inthepicture,ontheotherhand,willroballparticlesof fundamentalstatus. Whatwe
have arrived at, then, is a sort of ‘Goldilock’s principle’ governing the fundamental
particle kinds:akindcanonlyqualifyas fundamental if thereareotherkinds inhabiting
theworldalongsideit,solongastherearenottoomany.44The fundamental levelof the
world,then,seemsnotmadeupofentitieswiththeirown‘intrinsicnatures’:eachmust
besensitivetothetotalityofwhatelseexistsinordertobefundamentalatall.
Itmightbeobjectedatthispointthatallthishasbeenderivedfromtheassumptionthat
thefundamentalkindspartakeinlawsof interaction. Foritisinteractionsinparticular
thatmake it difficult to define laws that staywell-defined in the limits appropriate to
fundamentallaws,andwhichresultintheconstraintsonmattercontentexpressedbythe
Goldilock’sprinciple.45Butonecouldobjectthatthefundamentalkindsthatwefindin
this world can all feature in lawswithout interactions – specifically, the laws of free
motiontowhichinteractiontermsareaddedwheninteractionlawsarewrittendown.As
such,onecouldarguethatalthoughthequarks(forexample) that feature inourworld
might need the relevant gauge bosons in order to interact, they could quitewell exist
withoutthem–namely,inworldsinwhichtheyundergonointeractionatall.Andsince
thereareworldscontainingonlylonequarks,albeitofnecessityfreequarks, itmustbe
possibletoregardthepropertiesoffundamentalobjectsasintrinsicafterall.46
However, it seems tome that this objection does not succeed, for at least a couple of
reasons.Firstofall,weknowthatthefundamentalobjectsinourworldareasamatter
of fact interacting – otherwisewe couldnever knowabout them (indeedweourselves
44IowethisnicephrasetoDavidBrink.45Notethatthesuppositionthatthefieldsinvolvedareinteractingdoesnotinitselftellagainstintrinsicality.Forquantumfieldtheoryadmitslawscontainingonlyasinglefieldinteractingwithitself–although,bytheabovearguments,weknowthatnosuchlawcanberegardedasfundamental.46ThisobjectionhaslikewisebeenraisedbyLivaniosopcit.,pp.33-4.
22
wouldn’texistatall). Andweknowfromthefactthattheyareinteractingthatsomeof
their properties are scale-dependent. It strikesme that an object in a world without
interactions–andassuchanobjectwhosepropertiesarenotscale-dependent–cannot
reasonably be said to count as a duplicate of an object whose properties are scale-
dependentinthewaythatactual-worldobjectsare.Forthisreason–andalthoughdoing
so is commonplace in philosophy of physics – I think we must be extremely cautious
about drawing conclusions about the metaphysics of actual-worldly objects based on
claimsaboutworldsdescribedbyfreetheories.47Butinanycase,the(putative)factthat
anobject could existwithout someotherobject, suchas a gaugeboson, existing isnot
sufficient to make its properties intrinsic: it must in addition be the case that its
possessingthosepropertiesdoesnotprecludetheexistenceofotherobjectsalongsideit.
But we know that the presence of fundamental objects with colour prohibits the
existence of toomany fermions in anyworlds inwhich those objects interact. And it
seemstomethatthefactthatthereareprohibitionsonwhatcanexistalongsidecoloured
objectsinevensomesubsetoftheworldsinwhichtheyexist–namelythesetofworlds
withinteractions–isincompatiblewiththesuppositionofitsintrinsicality.
In sum, then, wemay say that contra Chakravartty, Bird, and seemingly almost every
othermetaphysicianof scienceoutwith structuralism, the fundamental kindproperties
cannotbe regardedas intrinsicafterall. InsofarasOSR is the thesis that fundamental
objectslackintrinsicproperties,then,itisleftstandingtall.
8.Conclusion
The main argument of this paper has been that the concept of fundamentality as
understoodinQFToffersarichnewresourcefordefendersofonticstructuralism.Itisa
resource thatallowsstructuralists toattack theargument fromintrinsics inadvanceof
thetrulyfundamentaltheorythat,primafacie,onewouldhavethoughtwouldbeneeded
todenytheforceoftheiropponents’intuitions.However,asIhavetakenpainstonote,
47Onthispoint,seealsoBaker2013,Section3.
23
the argument is not yet conclusive. For one thing, I have considered only the class of
fundamental quantum field theories that arewell-understood at present – namely, the
asymptotically free theories – and while these considerations surely count at least as
evidence for the conclusions I have drawn, it nevertheless may well be that the
fundamentallevelisnotdescribedbyatheoryinthisclass.ForallthatIhavespeculated
thatsimilar–perhapsyetmoreexaggerated–conclusionswillholdinthemoregeneral
case,thatremainsaspeculationonmypart.Anotherlimitationisthatthereseemtobe
propertiesthatarenottouchedbymyargument,namelythepurelykinematicproperty
of spin and parity. Most significantly of all, perhaps, I have proceeded as QFT is a
fundamentalframework;butQFT’scapacitytoincorporategravityverymuchremainsto
beseen.
Nevertheless,itseemsclearthattheargumentsofthelastsectionarestronglysupportive
ofonticstructuralismanditsdenialoffundamentalintrinsicproperties.Ithereforehope
tohave shown that the conceptof fundamentality itselfpresagesa structuralist future,
even though we still look forward to discovering what exactly the fundamental
constituentsoftheworldare.
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