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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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