Relational–SubstantivalDebate
JillNorth
1.INTRODUCTION
Thetraditionalrelational–substantivaldebateisaboutwhetherspace in modernterms,spacetime exists.Thesubstantivalistsaysthatitdoes.The relationalistsaysthatitdoesn’t.Accordingtotherelationalist,allthatexists, inthephysicalworld,arematerialbodiesrelatedtooneanotherspatiotemporally;thereisnofurtherthinginwhichthesebodiesarelocated.
Thisisadebatewithalonghistory.Yetthereisstillsurprisinglylittle agreementnotonlyonwhatistherightanswer,butalsoonhowto understandtheveryquestionatissueandthepotentialanswerstoit and evenonwhetherthereisanygenuinedisputehere.Forexample,wecantry toformulatethedebateinawaythatharkensbacktothetraditional Leibniz–Newtondispute,asthequestionofwhetherspaceexistsasa substantialentity.Butthenwhatitmeanstocallsomethingasubstantial entityisdisputed,sothatitmaystarttoseemlikethetwosidesaresimply talkingpasteachother.
Somepeoplehaveconcludedthatthedebateisnotsubstantive.Perhapsit ismerelyaverbaldisputeaboutwhichthingstocall ‘ space ’ versus ‘ matter ’ , withnoobjectivelycorrectanswertobehad(Rynasiewicz,1996).Others havethoughtthatthedisputehasstagnatedorbecomedivorcedfrom physics.¹Areviewofthehistoricaldisputeanditscentralexamples(Newton’ s bucketandglobes,Leibniz’sshifts,Kant’sglove,aswellasthemorerecent
¹Claimsthatthetraditionaldebateisnon-substantive,unclear,orremovedfrom physics,eitherincertaincontextsoringeneral,canbefoundinStein(1970;1977b); Malament(1976);Horwich(1978);Friedman(1983,221–3);Earman(1989);DiSalle (1994);Leeds(1995);Rynasiewicz(1996;2000);Dorato(2000;2008);Belotand Earman(2001,sec.10.7);Pooley(2013,sec.6.1,7);Curiel(2016);Slowik(2016). Earman(1989)advocatestheneedfora tertiumquid.
holeargument,allofwhichliveonintoday’sdiscussions)mayreasonably suggestastagnateddebate.Eachoftheseaimstoshowthattheopposingside recognizeseithertoofewortoomanyspatiotemporalfactsforthephysics;but therearevariousmaneuvers,wellhashed-outintheliterature,allowingeach sidetoescapethecharge.Relatedly,giventhevarietyofdifferentunderstandingsofthedispute,youmightthinkthatthereisnooverarching,well-posed questioninthevicinity(Curiel,2016).DavidMalamentisnotalonein wonderingwhetherthereisanyclear-cutdisputebetweenthetwosides: “Bothpositionsastheyareusuallycharacterized...areterriblyobscure.After theyarequalifiedsoastoseemintelligibleandnottooimplausible,itishardto retaina firmgrasponwhatdividesthem” (1976,317).Certainlyallofthishints at “thefragilehealthofthesubstantival–relationaldebate” (Belot,1999,38).
Thesearereasonableconcernswhenleveledattraditionalconceptionsof thedispute.Nonetheless,Ibelievethatthereisadebatethatissubstantive, notstagnant,andrelevanttophysics.ThedebatethatIwillpresentisnot exactlythetraditionalone.ButitiscloseenoughinspiritthatIthinkitis thebestwayofunderstandingthatdispute,updatedtotakeintoaccount morerecentdevelopmentsinphysicsandphilosophy.Andonceweframe thedebateinthisway,weunearthanovelargumentforsubstantivalism, givencurrentphysics.Atthesametime,thatconclusioncouldbeoverriddenbyfuturephysics.Aseeminglysubtleshiftyieldssurprisingprogresson alongstandingissuethatmanypeoplefeelhasstagnated.
InSection2,Idiscussanideathatwillplayacentralrole:structurein general,andspatiotemporalstructureinparticular.Iwillarguethat,regardlessofwhetheryouarearelationalistorsubstantivalist,youshouldthink thatthereareobjective,determinatespatiotemporalfactsaboutaworld:you shouldbearealistaboutspatiotemporalstructureinmysense.Thisfollows fromageneralprinciplewerelyoninphysics.(Thetraditionaldebatewas abouttheexistenceofspaceandtimeseparately.Idiscussthequestionof spacetime,orspatiotemporalstructure,updatingthingstothetermsof modernphysics.)InSection3,Iwillarguethat,regardlessofwhetheryou arearelationalistorasubstantivalist,you can bearealistaboutspatiotemporalstructure.Idothisbyframingthedebateintermsoffundamentality andground,notionsthathavegottenlotsofpressrecentlyinmetaphysics. Ishowthatthiswayofputtingthingscapturestraditionalconceptionsof thedispute,whileallowingustoformulatethemostplausible ifnot entirelytraditional versionsofthetwomainpositionsonit.(Although Iputthingsintermsofground,what’smostimportantisthatwemakeuse ofsomenotionofrelativefundamentality.)Finally(Sections4and5),Iput allthepiecestogethertoshowthatthereisapowerfulargumentfor substantivalism,oratleastapowerfulchallengetorelationalism,givenmuch ofcurrentphysics.
Attheend,Ibrieflydiscusshowtheconclusioninfavorofsubstantivalism maychangewithfuturedevelopmentsinphysics.Yethoweverthephysics turnsout,thequestionofrelationalismversussubstantivalismshouldbe settledbymeansofthenewtypeofargumentofferedhere.Hence,ifIam right,thesubstantivityofthedebateissecuredregardlessoffuturedevelopmentsinphysics,whiletheconclusioninfavorofoneviewortheotherwill ultimatelybedecidedbythephysics.
2.SPATIOTEMPORALSTRUCTUREAND THEMATCHINGPRINCIPLE
I’llbeginbyarguingthatboththerelationalistandthesubstantivalistshould positenough,andnottoomany,spatiotemporalfactsforthephysics.As Iwillputit,theybothshouldcountenancethespatiotemporalstructurethat isneededforthephysics.(InSection3,Iturntowhethertheybothcan dothis.)Iarguethatthereisacertainmethodologicalprincipleweareused torelyingoninphysics,evenifitisnotusuallymentioned.Thisprinciple guidesourinferencesfromthemathematicalformulationofatheorytothe natureoftheworldaccordingtothetheory.Ishowbyexamplethatwedo generally,andsuccessfully,relyonthisprinciple.Theconclusionabout spatiotemporalstructurewillfollowfromit.
ConsiderclassicalNewtonianmechanics.Whatdoesthistheorytellus abouttheworld?Newtonthoughtittellsusthatabsolutespace,aspacethat persiststhroughtime,exists.Hearguedthatphenomenainvolvinginertial (unaccelerated)andnon-inertial(accelerated,inparticularrotated)motion revealthis.(Thinkofhisbucketexperimentandthespinningglobes example.)Althoughwenowadaysagreethatthephenomenaindicatea realdistinctionbetweeninertialandnon-inertialmotion,wethinkthat Newtonwaswrongaboutwhat’srequiredtoaccountforthisdistinction.
Intoday’sterms,Newtonwasarguingforsubstantivalismaboutwhatis oftencalledAristotelian,orNewtonian,spacetime.²Thisspacetimehasthe structuretosupportNewton’sideaofabsolutespace,forithasstructurethat identifiesspatiallocationsovertime.Butwenowknow(asNewtondidnot) thatGalilean,orneo-Newtonian,spacetimealsosupportsthedistinction betweenacceleratedandunacceleratedmotion,withoutabsolutespace.
Spellingthisout,AristotelianspacetimehasallthestructureofGalilean spacetime,butitalsohasabsolutespace,oranabsolutestandardofrestor
²NottobeconfusedwiththespacetimethatEarman(1989,sec.2.6)calls ‘Aristotelian.’ IfollowGeroch’s(1978)useofthe ‘Aristotelian’ and ‘Galilean’ labels. ANewApproachtotheRelational
preferredrestframe.Toremindyouofwhatthismeans,thinkofanobserver onaplatformandanotherobserveronatrainmovingwithconstantvelocity relativetotheplatform.Eachobserverfeelsthatheorsheisatrestandthat theotherismoving.Galileanspacetimesaysthatneitheroneis “ correct ” or atrestinanyabsolute,observer-independentsense.Eachissimplyin motionrelativetotheother,andatrestinherownframeofreference. (Thinkofareferenceframeasacoordinatesystemattachedtoanobserver, representingherownpointofview.)AccordingtoanAristotelianspatiotemporalstructure,there is anobserver-orframe-independentfact,from amongalltheobserversinconstantrelativemotion,aboutwhichoneis at rest inanabsolute,frame-independentsense namely,theoneatrestin absolutespace.Forthereisaframe-independentfactaboutwhetheragiven spatiallocationisthesamelocationovertime,sothatanobjectlocatedthere isatabsoluterest.Inotherwords,thereisapreferredrestframe:theone that’satrestwithrespecttoabsolutespace.
Intuitively,anAristotelianspatiotemporalstructurehas more structurethan aGalileanone.Ithasallthesamestructure,plusanadditionalabsolute-space, orabsolute-velocity,structure.Itrecognizesallthesamespatiotemporalfacts, butitalsosaysthattherearefactsabouthowfastanobjectismovingwith respecttoabsolutespace.
Itturnsoutthattheseadditionalfactsarenotneededfor,orrecognized by,thephysicshere.Newton’slawsarethesameinanyinertialframe they are invariant underchangesininertialframe whichmeansthattheycanbe formulatedwithoutmentioningorpresupposingapreferredframe.Sincea preferredframeisn’tneededinthemathematicalformulationofthelaws,we inferthatitdoesn’tcorrespondtoanythingphysicalintheworld.An absolutestandardofrestisn’tpartofthetheory’s,orworld’s,spatiotemporal structure.Thephysicsdoesnotrecognizeobjective,frame-independentfacts aboutwhatvelocityanobjecthas.Conclusion:Aristotelianspacetimehas excess,superfluousstructure,asfarasNewton’slawsareconcerned.It recognizesmorespatiotemporalfactsthanthelawsdo.
Theselawsdorecognizefactsaboutobjects’ accelerations(asNewton argued).ThinkofNewton’ s firstlaw:anobjecttravelswithuniformvelocity unlessactedonbyanetexternalforce.Thislawassumesthatthereisa distinctionbetweenacceleratedandunacceleratedmotion,sinceittells thingstobehavedifferentlydependingonwhethertheyareacceleratingor not.Intermsofspatiotemporalgeometry,thelawassumesadistinction betweenstraightandcurvedtrajectoriesorpathsthroughspacetime,with thestraightonescorrespondingtoinertialmotion,thecurvedonestononinertialmotion.AndGalileanspacetimehasthestructuretosupportthis distinction.Ithasanaffineconnection,orinertialstructure,whichprovides astandardofstraightnessforthesetrajectories.Wemightputitlikethis:this
spatiotemporalstructuresupportsanotionorquantityofabsoluteacceleration butnotofabsolutevelocity—“absolute” notinNewton’ssense,whichassumes theexistenceofabsolutespace,butinthesenseofbeinginvariantorframeindependent.³
AllofthissuggeststhataGalileanspatiotemporalstructureisthe right structureforNewton’sphysics.Thisisthestructurethat’srequiredfor,or presupposedby,thedynamicallaws;thestructurethatrecognizesthespatiotemporalfactsthatthelawsdo.⁴ Newtonwaswrongtothinkthataclassical worldmustcontainabsolutespaceandaconcomitantquantityofabsolute velocity:thephysicsdoesn’trequireit.(Ifthelawswerenotinvariantunder changesininertialframe,thenwewouldinferthatextrastructure.Suchlaws wouldimplicitlyrefertoapreferredframe.)Noticethatwereachedthis conclusionaboutthestructureneededforthelawsindependentlyofthe relational–substantivaldebate,anideathatIwillreturntosoon.⁵
Firstletmesayabitabout “ structure. ” Onmyunderstanding(andasitis oftenusedinphysicsandmathematicalphysics),⁶ structurehastodowith theinvariantfeaturesorquantities,whicharethesameinallallowable referenceframesorcoordinatesystems.Inertialstructure,forexample,is partofaclassicalspatiotemporalstructure:thereisanabsolute,frameindependentnotionofacceleratedversusunacceleratedmotion.Butthere isno “absolute-velocitystructure.” Anobject’svelocitydependsonthe inertialframeweusetodescribeit.SinceNewton’slawsareinvariant underchangesininertialframe,weinferthatthechoiceofframeisan arbitrarychoiceindescription,andthatanyquantitydependingonthat choice,likevelocity,ismerelyframe-dependent,notoutthereintheworld apartfromthatchoice.
Similarly,wethinkthatachoiceoforiginisjustanarbitrarychoicein description,notcorrespondingtogenuinestructureintheworld.Choosea coordinatesystemwithadifferentorigin,andthelawsalwaysremainthe same.Sincethelawsareinvariantunderchangesinorigin they “saythe
³IbelievethatthissenseevadesRynasiewicz’s(2000)argumentsagainsttheclarityof anyabsolute/relativedistinction.
⁴ AlthoughtheinferencetoaGalileanstructureisnowrelativelystandard(Earman (1970);Stein(1970);Huggett(1999,194–5);Maudlin(2012,ch.3)),thereisroomfor debate.Saunders(2013)andKnox(2014),indifferentways,arguethatNewtonian physicsrequiresadifferentstructure.Icontinueasthoughtheaboveinferenceiscorrect.Itis inanycaseagreedthatabsolutespaceisnotneeded,andwhateverstructureisrequired,the exampleillustratesourrelianceontheupcomingprinciple.
⁵ AsimilarpointismadebyStein(1970,271–2),althoughhegoesontosaythat, “the questionwhether...thisstructureofspace-timealso ‘reallyexists’,surely seems tobesupererogatory ” (277).InawayIagree,butIalsothinkthatthereremainsasubstantivedispute.
⁶ MoreisinNorth(2009).
samething”⁷ regardless weinferthatthischoiceismerelyaconventional orarbitrarychoiceindescription.Thereisnopreferred-locationstructure intheworld,nocoordinate-independentfactaboutwhetheragivenpoint is “really” theorigin.Bycontrast,thelawsofAristotle’sphysicsarenot invariantinthisway.Accordingtothem,thereisapreferred-locationstructureintheworld alocationtowardwhichcertainelementsnaturallyfall andawayfromwhichothersnaturallyrise andpreferredcoordinatesystems fordescribingthisstructure,namelythosewithanoriginatthatlocation.
Welikewisethinkthatdifferentchoicesofunitofmeasureareconventionalorarbitrarychoicesindescription.Changefromfeettometersor someotherunitformeasuringdistances,forinstance,andthephysicsalways remainsthesame.Sincethephysicssaysthesamethingregardless,weinfer thatthereisno “preferred-unit-of-measurestructure ” intheworld.
AsIseeit,structurecorrespondstotheintrinsic,genuine,objective featuresorquantities,whichdon’tdependonarbitraryorconventional choicesindescription.Bycontrast,frame-,coordinate-,orunit-dependent quantitiesdependtosomeextentonourarbitraryorconventionalchoicesin description arbitrary,sinceaccordingtothephysicsanychoiceisequally legitimate.Suchquantitiesaren’twhollyabouttheworldasitisinitself,but areinpartaboutourdescriptionsoftheworld,whereasstructuralfeatures areagreeduponbyalltheallowabledescriptions,andsocorrespondto genuinefeaturesoftheworldapartfromanyofthosedescriptions.No matterwhichdescriptionyouuse,afterall,yougetthesameresult.
Spatiotemporalstructureinparticularconcernstheintrinsic,genuine, objectivespatiotemporalfeaturesofaworld,whichdon’tdependonarbitraryorconventionalchoices thattwoobjectsareseparatedbysome amountunderaEuclideanmetric,say,orthataparticle’strajectoryis straightaccordingtoagiveninertialstructure.Noticethatthisideaof structureisneutralbetweensubstantivalismandrelationalism.Bothof theseviewscanrecognizethatthereisadistinctionbetweenspatiotemporal factsthataremoreobjective,andthosethatareframe-,observer-,unit-,or coordinate-relative.
Wearestillworkinguptothegeneralprinciple.Here’sanideathatwe havereachedsofar,whichwillmotivatetheprinciple.Aswecanseefrom theinferencetoaGalileanstructureforNewton’slaws,anyphysicaltheory willconstrain,orhelpdictate,aworld ’sspatiotemporalstructure.Weinfer thestructurefromthephysicsinthisway.Thisisbecauseanytheorywill requireorpresupposeacertainspatiotemporalstructure.Inparticular,it willrequirethestructureneededtosupportthelaws,inthatthelawscannot
⁷ BradingandCastellani(2007)discussdifferentwaysofspellingoutthisidea.
bestatedorformulatedwithoutassumingit theywouldn’tmakesense withoutit. ⁸
Twoexamplesillustratethis.RecallNewton’ s firstlaw,whichtellsobjects tobehavedifferentlydependingonwhethertheyaretravelinginertially, withuniformvelocity,ornot.Thislawwouldnotmakesenseifthere weren ’tadistinctionbetweenuniformandacceleratedmotion:itpresupposesit.Sotheworldmustbesuchthatthereisthisdistinction.Theworld’ s spatiotemporalstructureshoulddistinguishbetweeninertialandnoninertialtrajectories.Assumingthatthelawsareabouttheobjectivenature oftheworld,theremustbeobjectivefactsaboutwhetherobjectsare travelinginertiallyornot.⁹
ConsideradifferentexamplethatI’llreturntolater.Ifthelawsarenot timereversalinvariant ifthey “lookdifferent” whenwe flipthedirection oftime,swappingpastandfuture thenthissuggestsastructural,physical distinctionintheworldbetweenthetwotemporaldirections.Newton’ s lawsaresymmetricinthissense:anybehaviorallowedbythetheorycanalso happenbackwardintime.The filmofanyNewtonianprocess(aball thrownintheair,billiardballscolliding)runbackwardalsodepictsa processthatevolveswiththelaws.Theselawsdon’tdistinguishpastversus future:theysaythesamethingregardlessofthedirectionoftime.By contrast,thesecondlawofthermodynamicssaysthatentropyincreasesto thefuture,notthepast:gasesexpand,icemelts,notthereverse.Areverserunning filmshowssomethingdisallowedbythelaw.Non-timereversal invariantlawslikethismentionorpresupposethedistinctionbetweenpast andfuture,tellingthingstobehavedifferentlydependingonthedirectionof time.Suchlawswouldnotmakesenseifthereweren’ tapast–future distinctionintheworld,correspondingtoanasymmetrictemporalstructure,orobjectivefactsaboutpastversusfuture:theypresupposeit.(Ifyou areworriedaboutthisconclusioninthecaseofthesecondlaw,staytuned: Ireturntoitlaterinthischapter.)
Finally,theprinciple.Theaboveexamplesarefamiliarinstancesofhow wedrawcertainconclusionsaboutthephysicalworldfromthelawsthat governit.Theseexamplesallsuggestthatwerelyonacertainmethodologicalprinciple,whichsaystopositintheworldthestructurethat’ s presupposedbythelaws.Wegenerallypositphysicalstructureinthe worldcorrespondingtothemathematicalstructureneededtoformulate thelaws suchasaGalileanspatiotemporalstructureforNewton’slaws,an asymmetrictemporalstructurefornon-timereversalinvariantlaws,ora
⁸ ConsiderEarman’sstatementthat “lawsofmotioncannotbewrittenonthinair alonebutrequirethesupportofvariousspace-timestructures” (1989,46).
⁹ CompareMaudlin(2012,9–12);Pooley(2013,sec.3).
preferred-locationstructureforAristotle’slaws.Weinfertotheworld whateverthelawspresuppose,whatevertheremustbeintheworldforthe lawstomakesenseandbetrueofit.Thereshouldbea match instructure betweenthelawsandtheworld.TheoriesobeyingwhatIwillcallthe matchingprinciple are “well-tuned,” toborrowaphrasethatJohnEarman (1989,ch.3)usesforasomewhatdifferentidea.¹⁰ (Itakeitthisismotivated byakindofrealism.Iwon’targueforrealismhere.)
Aswithanyguidingmethodologicalprinciple,thisprinciplewon’tyield conclusiveinferences,yetitisstillareasonableguide.Wecannotbecertain thatthereisnoabsolutespaceinaNewtonianworld,butitisreasonableto inferthatthereisn’t.Ortakespecialrelativity.Thematchingprinciplelies behindthethoughtthatthereisnopreferredsimultaneityframe.Sincethe lawsareinvariantunderchangesinLorentzframe,weinferthatthereis noabsolute,frame-independentsimultaneityrelation.Wecan’tbecertain aboutthis,andsomepeoplearguethatwehaveotherreasonstopositthis structure(forpresentismorforcertaintheoriesofquantummechanics,for example).Still,wedogenerally,andreasonably,relyonthisprinciple.We takeittobesuccessful.Asthecaseofspecialrelativityshows,weneedan extrareasontodisobeyit.Toputitanotherway:allotherthingsbeing equal,weshouldinferamatchinstructurebetweenlawsandworld.Those whobelieveinamismatcharesayingthatotherthingsarenotequal,and mustargueasmuch.¹¹
ItissometimessaidthatthereasontopositaGalileanratherthan AristotelianstructureinaNewtonianworldisthatthelatterwouldyield in-principleundetectablephysicalfacts.¹²SinceNewton’slawsareinvariant underchangesininertialframe,noexperimentcouldeverdetectwhichis thepreferredframe.Chooseanyframeinwhichtorunyourexperiment, andthelawsalwayspredictthesameresults.That’sright.ButIthinkthat thereisadeeperreasonfortheinferencetoaGalileanstructure,whichisthe matchbetweenthemathematicalstructureofthetheoryandthephysical structureoftheworld.Thismatchispartofour evidence thatwehave inferredthecorrectstructureoftheworld.Thisisamorefundamental reasonfortheinferencethantheverificationist-soundingprincipletoavoid undetectablephysicalfacts.
¹⁰ Earmansuggeststhatthereshouldbeamatchbetweenthesymmetriesofthelaws andofthespacetime,asaconditionofadequacyontheories.
¹¹Thosewhoarguefromquantummechanicsaren’tproposingamismatch,butthat thelawsofquantummechanicstrumpspecialrelativitywhenitcomestoinferringthis structure.
¹²Mentioned,withvaryingsupport,inEarman(1989,ch.3);IsmaelandvanFraassen (2003);Roberts(2008);Dasgupta(2009);Maudlin(2012,ch.3);Pooley(2013,secs.3–4).
Ihavearguedthatthematchingprincipleisacoremethodological principleweusetoguideourinferencesfromaphysicaltheorytothenature oftheworldaccordingtothattheory.Nowwecanseethatthisprinciple tellsustoposit,orcountenance,orsomehowbeabletotalkabout, spatiotemporalstructure.Forthelawsgenerallytalkabout,theymention orpresuppose,aparticularspatiotemporalstructure.Weshouldcountenancetheparticularspatiotemporalstructureorfactsrequiredforthelaws; ipsofacto,weshouldcountenancespatiotemporalstructureorfactsin general.Inotherwords,thematchingprinciplesaysthatweshouldbe realistsaboutspatiotemporalstructure,sincethelawspresupposesucha thing,andweshouldgenerallypositintheworldthestructurethat’ s presupposedbythelaws.
Importantly,thisconclusionisindependentoftherelational–substantival debate.Regardlessofyourpositiononthatdebate,thematchingprinciple tellsyoutobelievethatthereareobjectivefactsaboutthespatiotemporal structureofaworld;torecognizethespatiotemporalfactsthatarerecognizedbythelaws.Youshouldbeli evethataNewtonianworldhasa Galileanspatiotemporalstructure,forexample(althoughthisclaimmay beunderstooddifferentlybytherelationalistandsubstantivalist,asIdiscuss below).Whowouldrejecttheprinciple?Theconventionalist,forone,like ReichenbachorPoincaré,whodeniesthatthereisanobjectivefactabout the “right” spatiotemporalstructureofaworld:therearenoobjective spatiotemporalfacts.Againstsuchaview,thematchingprinciplesuggests thatspatiotemporalstructureisoutthereintheworld.Itisnotconventional orarbitrarilychosen,asisaninertialframeororiginorunitofmeasure.¹³ Thisstructureexists;itispartofreality.Thereisanobjective,determinate factaboutwhatspatiotemporalstructureaworldhas,evidencedbyitslaws. ThematchingprincipleisnotQuine’scriterionforontologicalcommitment.Quinesaysthatweareontologicallycommittedtowhatthevariables ofourtheoriesmustrangeoverinorderforthosetheoriestobetrue.Thishas todowithontology,withwhatentitiesexist.Thematchingprincipleisabout whatstructureweshouldposit.Itsaystoalignphysicalstructureintheworld withthemathematicalstructurerequiredtoformulatethelaws.Thishastodo withwhatspatiotemporalfactsweshouldrecognize,whichisnotsimplya matterofontology.Toseethatthesecomeapart,notice firstthatagiven spatiotemporalstructure,sayaGalileanone,canbeunderstoodbydifferent
¹³WecanagreewithReichenbachandPoincaréthatthosethingsarearbitrary,since thelawsindicatethatdifferentchoicesareequallylegitimate.Spatiotemporalstructureis different.Wecannotarbitrarilyalterthemetric,forinstance,andkeepthelawsthesame, notwithoutmajorcompensatingchangeselsewhere.
peopleasinvolvingdifferententities:byacertainsubstantivalist¹⁴ asinvolving pointsofspacetimeandarelationalistasinvolvingmaterialbodies.(AsTim Maudlin(2015)putsit,toattribute “amathematicalstructuretophysical items” istosaythatthoseitems “havesomephysicalfeaturesthatmakethem amenabletoprecisemathematicaldescriptioninsomerespects”.Inparticular, itisnotyettosaywhattheitemsmustbe.)Second,twopeoplemightagreeon whatentitiesexist say,pointsofspacetime butdisagreeonthespatiotemporalstructure,forinstanceonwhetherthepointsarearrangedinaGalilean orAristotelianway.Thiswillbecomeclearerasweproceed.
Question:Howshouldweformulatethelaws?Itseemsasthough differentformulationscanpresupposedifferentstructures.Ifso,thenin ordertoadheretothematchingprinciple,wewill firstneedtoknowhowto formulatethelaws,whichisabigquestion.Trustmefornowthatwecan makeprogressinadvanceofansweringthisquestion.Iwillreturntoitatthe endofthischapter.
Somehavearguedforathirdview,neithersubstantivalistnorrelationalist,called ‘structuralspacetimerealism.’¹⁵ Sincethatviewemphasizesrealismaboutspacetimestructure,youmightthinkthatitiswhatIam advocating.Idon’thavespacetoaddressthealternativeindetail,¹ ⁶ but Iwillnotethat,despitesuperficialsimilarities,itisimportantlydifferent frommyoverallapproach.First,Iclaimthatboththerelationalistandthe substantivalistshould(andcan:below)berealistsaboutspatiotemporal structure,whereasspacetimestructuralrealismaimstobedistinctfrom eitherofthoseviews.Second,Iunderstandtheideaofspatiotemporal structuredifferently,toencompassanyobjective,intrinsicspatiotemporal factaboutaworld.Inparticular,countenancingspatiotemporalstructurein mysensedoesnotmeaneschewingfundamentalphysicalobjects(alternatively,intrinsicproperties)altogether,northepossibilityofourknowing aboutsuchthings,asthestructuralspacetimerealistoftenseemstodo.That said,belowwewillseeonewayinwhichmyaccountmirrorscertainclaims ofthespacetimestructuralrealist.
3.ADISAGREEMENTABOUTGROUND
Inordertosaythattherelationalistandsubstantivalistbothshouldcountenancespatiotemporalstructure,Imustbeabletosaythattheybothcandothis.
¹⁴ SeeSection3.3.
¹⁵ DifferentversionsareinDorato(2000;2008);Slowik(2005);Bain(2006);Esfeld andLam(2008);LadymanandRoss(2009).
¹⁶ SeeGreaves(2011).
Youmightwonder:Howcantherelationalistbelieveinspatiotemporal structure?Isn’tthistheverysortofthingtherelationalistrejects?Onthe otherhand,iftherelationalistcanbelieveinspatiotemporalstructure,you mightthenwonderwhatcouldbeleftforthetwoviewstodisagreeabout.
I’llnowsuggestthatthenotionofgroundgivesthesenseinwhichthe relationalistaswellasthesubstantivalistcancountenancespatiotemporal structure,andthatthisyieldsarealdisagreementthat’srelevanttophysics. Thebasicideawillbethis.Bothviewscancountenance,orbelieveinthe existenceof,spatiotemporalstructure.(WhethereachoneisabletorecognizetheparticularstructureneededforthelawsisaquestionthatIwillbe sidesteppinghere,forreasonstocome.)Theviewsdifferonwhatunderlies thisstructure.Essentially,thesubstantivalistsaysthatspatiotemporalstructureisfundamentaltothephysicalworld,whereastherelationalistsaysthat itarisesfromtherelationsbetweenandpropertiesofmaterialbodies.
Puttingthisintermsofground.Agroundingrelationisanexplanatory relationthatcapturesthewayinwhichonethingdependsonorholdsin virtueofanother,withoutimplyingthatthedependentthingdoesn’texist. Groundcapturesa “metaphysical because” inanswertoquestionsabout whysomethingexistsorsomefactholds.(Iusethegeneralidea,without enteringintodebatesoveritsmetaphysics.Iwon’ttakeastandonwhether groundisproperlyarelationbetweenfactsorobjects,butdeliberatelyuse bothwaysoftalking.Itisgenerallythoughtthatthegroundingrelationis transitiveandirre flexive,andthatthegroundsmetaphysicallynecessitate thegrounded.Noneoftheseassumptionshavegoneuncontested,but Iassumethemhere.¹⁷)
Usingthenotionofground,therelationalistandsubstantivalistcan eachsaythatspatiotemporalstructureexists,thatthereareobjectivespatiotemporalfactsaboutaworld.Theydisagreeonwhatthespatiotemporal structureholdsinvirtueof;whatmetaphysicallyexplainsthespatiotemporal facts.Therelationalistsaysthataworld’sspatiotemporalstructureis groundedinthefeaturesandbehaviorsofmaterialbodies.Allthespatiotemporalfactsaregroundedinthefactsaboutmaterialbodies.Thesubstantivalistsaysthatspatiotemporalstructureisn’tgroundedinanythingelse morefundamentaltothephysicalworld;inparticular,itisnotgrounded inmaterialbodies.Therearefundamentalspatiotemporalfactsthatarenot groundedinfactsaboutmaterialbodies.Bothviewscancountenancespatiotemporalstructureorfacts;theydisagreeonwhat,ifanything,groundsthis structureorthosefacts.
¹⁷ DifferentaccountsareinFine(2001);Schaffer(2009).Rosen(2010)defends theidea.
Ispelloutthetwoviewsmoreinamoment.First,afewnotesontheuse ofgroundinthiscontext.JonathanSchaffer(2009,363)andShamik Dasgupta(2011)alsosuggestthatwecanunderstandthisdebateinterms ofground,buttheyputthingsalittledifferently.Theysaythatthe relationalistandsubstantivalistbothbelievethatspacetimeexists,while differingonwhatgroundstheexistenceofspacetime.Isaythatboth(can andshould)believethatspatiotemporalstructureexists,whiledifferingon whatgroundstheexistenceofthatstructure.Ipreferthiswayofputting thingsbecause,we’llsee,itallowsusto fleshoutthecompetingviewsin differentways,allthewhilemaintainingagenuinedisputethatthephysics willweighinon.
Itmayseemunexcitingtoexchangeadebateabouttheexistenceof spacetimeforoneaboutthefundamentalityofspatiotemporalstructure. Therehasbeenmuchdiscussioninmetaphysicsoflateaboutdoingasimilar kindofexchangewithotherexistencedebates(asinSchaffer(2009)),so thatthisinstancemayfeellikeoldhat.Therehavebeensomerelated thoughtsaboutthespacetimedebateinrecentphilosophyofphysicsas well.ThusCarlHoefer(1998)framesthequestionintermsoffundamentality,asthatofhow “tounderstandthebasicontologyofthephysical world,” althoughheformulatesaspectsofthedisputemoretraditionally, sayingforinstancethatsubstantivalismiscommittedtotheexistenceof “asubstantial,quasi-absoluteentity.”¹⁸ GordonBelot(1999;2000;2011) saysthattherelationalist,likethesubstantivalist,canbearealistinthesense of “attribut[ing]torealityadeterminatespatialstructure,” whiledisagreeing on “thenatureoftheexistenceofspace” (2011,1).¹⁹ Thisisclosetomyown wayofputtingthings,althoughhisaccountisnotspelledoutinthesame way(itdoesnotusenotionslikegroundormyconceptionofspatiotemporalstructure,anditfocusesoncertaintraditionalexamples),nordoes hedrawthesameconclusions.Themoreprevalentattitudeinphilosophy ofphysics,especiallyamongthosewhocomplainaboutthesubstantivity ofthedispute,isthatthedebateconcernstheexistencequestion.Soalthough myproposedwayofunderstandingofthedisputeisnotwithoutprecedent,eventhentherearedifferences,anditisanywaynottheprevalent viewpoint.Ifyoudisagreewiththatassessment,though,itwillsoonbe clearthatnovelavenuesofargumentopenuponcewearecompletely explicitaboutthisshift.
¹⁸ Hoefersimilarlyarguesthatthisisasubstantivedispute,whichislikelytoremainso withfuturephysics,andthatgeneralrelativitysupportssubstantivalism.Yetheputs variousthingsdifferentlyfromhowIdo,drawingtheseconclusionsfordifferentreasons. ¹⁹ Belotalsosaysthathisformulation,whileunorthodox,yieldsadebatethatis substantive,relevanttophysics,andreminiscentofthetraditionaldispute.
3.1.Relationalismintermsofground
Therelationalistsaysthatcertainmaterialbodies,andvariousoftheir propertiesandrelations,arefundamental,andaworld’sspatiotemporal structureholdsinvirtueofthem.Allspatiotemporalstructureorfactsare groundedin(factsabout)materialbodies.Insayingthat “certainmaterial bodiesarefundamental,” thismeanswhichevermaterialobjectsturnoutto bemostfundamental:certainparticles,say.(Iassumethefundamental relationscanincludespatiotemporalones,²⁰ althoughtherelationalist mightwantadifferentkindofrelationtobefundamental,causalones beingafamiliarcandidate.Ileavethisopenhere.Theupcomingargument takesaimatalltheseversionsofrelationalismequally.²¹)
So,forexample,thefactthataworldhasaEuclideanspatialstructureis groundedin,holdsinvirtueof,thefactthatitsparticlesare,andcanbe, arrangedinvariousways,withvariousdistancerelationsbetweenthem. (Ireturntothis “canbe” phrasesoon.)TheworldhasaEuclideanstructure because (inthemetaphysicalsense)itsparticlesare,andcanbe,arrangedin thoseways;thisiswhatthespatialstructureconsistsin.Similarly,thefact thataNewtonianworldhasaGalileanspatiotemporalstructureisgrounded inthefactthatitsparticlesdo,andcan,behaveinvariousways,withvarious spatiotemporalrelationsbetweenthem.Thefactthataworldhasaparticularspatiotemporalstructureismadetruebythefactsaboutmaterialbodies. Aworldhasthespatiotemporalstructureitdoesbecausematerialbodies (can)behaveincertainways.
Threenotesonthisuseofground.First,agroundingexplanationis importantlydifferentfromacausalexplanation.InKitFine’swords,ground yields “adistinctivekindofmetaphysicalexplanation,” inwhichtheobjects orfactsareconnectedby “someconstitutiveformofdetermination” (2012,37). Particlebehaviorsdon’tcauseaEuclideanspatialstructure.Thisisrather whatthespatialstructureconsistsinordependson,inametaphysical sense.Comparethistomorefamilia rcases,suchasthegroundingof factsaboutthemacroscopicworldinfactsaboutsubatomicparticles,or thegroundingofmentalfactsinnon-mentalfacts,ormoralfactsinnonmoralfacts.Groundcapturesthismetaphysical “invirtueof ” explanation.²² AsIunderstandit,whenwesaythat “thefactthat x groundsthefactthat y, ”
²⁰ ContraNerlich(1994a,ch.1).
²¹Ialsoassumethattheobjectsandrelationsareequallyfundamental,thoughtheremay beaviewwithonlyonefundamental “ontologicalcategory” inthesenseofPaul(2013).
²²Loewer(2001)discussestherelevantsenseof “invirtueof.”
