volume14,no.20 june2014

On the Plurality of

Grounds

Shamik DasguptaPrinceton University

© 2014 ShamikDasguptaThis work is licensed under a Creative Commons

Attribution-NonCommercial-NoDerivatives 3.0 License. <www.philosophersimprint.org/014020/>

R ecentmetaphysicshascontainedagooddealofdiscussion aboutthenotionofground.Thenotionisintuitiveenough.Forinstance,supposethereisaconferenceoccurring.Onemight

saythatthisisgroundedinhowitsparticipantsareacting,meaning(roughly) that theconference “consists in”or is “explainedby”or is“nothingoverandabove”thoseactions,orthatthereisaconference“invirtueof”thoseactions.Theideaisthatonceyouhaveparticipantsactinginacertainway,this“makesitthecase”thatthereisaconfer-ence.Regardlessofwhetherthisclaimabouttheconference’sgroundistrue,weunderstanditreasonablywell.

Onereasonwhythenotionofgroundhassparkedsuchinterestistheideathatitisneededtoformulatemanycorephilosophicalissues.Consider for example theses like materialism about consciousness,normative naturalism, and phenomenalism. These claim thatcertain facts—about conscious states, norms, and external objects(respectively)—“arise out of” or are “determined by” or “fixed by”various underlying facts—aboutmy brain, or natural properties, orsensedata(respectively).Buthowshouldthistalkof“determination”or “fixing”beunderstood?Onemightsuggest that itbeunderstoodin termsof supervenience,or analysis, or identity.But anumberofphilosophers have argued that it is best understood in terms ofground.1Ontheirview,theabovethesesstate(respectively)thatthematerialstateofmybraingroundsmyconsciousstates,thatthenatu­ralfactsgroundthenormative,andthatpatternsofsensedatagroundtheexistenceofexternalobjects.Iftheyareright,thenotionofgrounditselfbecomesanobvioustopicofinterestinitsownright.

In this spirit, one aim of this paper is to argue that ground isirreducibly plural. It iswell known that something’sgroundcanbeaplurality—theoccurrenceofaconferenceisanexampleofsomethingthat ispresumablygrounded inamultitudeof facts concerning theactionsofitsmanyparticipants.Those factstogetherare whatexplainswhy there is a conference occurring, even though none of them isa sufficient explanation individually. But the literature uniformly

1. See forexampleFine (2001),Rosen (2010),andSchaffer (2009). Iwillnotrehearsetheirargumentshere.

ImprintPhilosophers’

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This very book (pointing at the book on my table) is interesting.

I believe that these facts together are (plurally) grounded inpurelyqualitativefacts,eventhoughnoneofthemhasaqualitativegroundwhentakenonitsown.Orconsiderfactsaboutthemass­in­kilograms,suchas:

Obama is 75 kgs.

My laptop is 2 kgs.

The book is 1/2 kg.

I believe that these facts are (plurally) grounded in the massrelationships between things, even though none of them has sucha ground when taken alone. Indeed the same goes (I claim) fordistance­in­meters, time­in­seconds, preferences­in­utils, and othercasesinwhichtherearemathematicalvaluesofagivenquantityinagivenscale.Ineachcasemyviewisthatfactsaboutthemathematicalvaluesinagivenscaleareplu rally groundedintheunderlying,scale­independentfacts(aboutgeometry,time,orpreferencesrespectively).

ButIwillfocusonthecaseofindividualsandmass­in­kilogramsinwhatfollows.Theresultisastructuralist viewofindividualsandkilo­gramsrespectively,sinceanaccountofanyonememberofthegroupisinevitablyanaccountofthemall.2

Now,eachstructuralistviewimpliesastrongclaimthatthereisnoroomtomotivateordefendhere,namelythattheworldisfundamentallyqualitative(inthefirstcase)andthatmassisfundamentallyrelational(inthesecond).SoIcannotverywellarguethatgroundispluraljustbypointingattheseexamples!AndIdonotknowofuncontroversialexamplestoappealtoinstead.

Sotheargumentwillhavetobeindirect.Iwillstartbyarguingforthe conditional claim that if theworld is fundamentally qualitative,

2. ‘Structuralism’isatermthatisalreadyappliedtoowidely,soIapologizeforthe further abuse. Iwill discuss the relationbetweenmy views andotherviewsthatgobythenameaswegoalong.

assumesthatwhatisgroundedmustbeasinglefact.HereIdisagreeandarguethatwhatisgroundedcanbeapluralitytoo:therecanbecasesinwhichthey,themembersofaplurality,are explainedinmorefundamentalterms,eventhoughnoneofthemadmitsofexplanationonitsown.

Ifgroundisirreduciblyplural,thisisimportanttoknow.For(asIsaid)fansofgroundaretemptedtoseemuchcontemporaryphilosophyasattemptingtoestablishwhetherfactsofonetype(say,thenatural)aresufficienttogroundfactsofanother(say,thenormative).Andanobviousstrategyofarguinginthenegativeistoarguethatagivenfactofthelattertypecannotbegroundedinfactsoftheformertype.Butifgroundisirreduciblypluralthenthisformofargumentisinvalid.ForevenifoneweretosuccessfullyarguethatthereisnonaturalgroundofthefactthatIoughtnoteatmeat, itwouldremainopenthatthenormativefactstakentogetherhaveanaturalgroundinwhichcasenormativenaturalismwouldbe vindicated after all.Aswewill see,thisinvalidformofargumentmayberesponsibleforcertainpopularviewsinmetaphysics,inwhichcaseitisimportantthatthemistakebeexposed.

My claim that ground is irreducibly plural is a claim about thelogical form of ground. It is the claim (to be clarified below) that,logicallyspeaking,groundisabinaryrelationpluralinbothpositions:they aregroundedinthem.Ofcoursethelimitcaseisapluralityofone,soitmayturnout(asithappens)thatineachactualcaseofgroundasinglefactisgroundedonitsown.Still,onmyviewtheclaimineachcasewouldstrictlyspeakingremainplural:thatthey (alloneofthem!)aregroundedinthem.

However,Ibelievethatthereareactualexamplesinwhichmanyfacts aregrounded together.Consider the individualistic facts, factsthatconcernparticularindividuals,suchas:

Socrates was wise.

Obama is president.

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rather than (say) a footballmatch. Presumably it has something todowithhow theparticipantsareacting, forexample that somearegivingpapers,othersarecommenting,andsoon.Ananswerofthissecondkindisastatementofwhatgrounds thefactthataconferenceisoccurring.

We should distinguish between full and partial explanations. Asingleconversationmightpartlyexplainwhyaconferenceisoccurring,butdoesnotfullyexplainit.By‘ground’Imeanafullexplanation.4

What is the logical formofaclaimaboutgrounds?Explanationsaretypicallyexpressedwiththesententialoperator‘because’:itwasaconferencebecause itsparticipantswereactingincertainways.Soonestandardviewisthatthelogicalformofaclaimaboutgroundis:

SbecauseΓ

whereSisasentence,Γisalistofsentences,and‘because’isreadinthemetaphysicalratherthancausalsense.5Informally,thesentencesinΓdescribethoseaspectsoftheworldthattogetherexplainitsbeingthecasethatS.ItisimportantthatΓisalistandnotaconjunction:wewouldliketomakesenseoftheplausibleviewthatconjunctionsaregrounded in theirconjuncts,but ifΓwereaconjunction thiswouldcollapseintotheviewthataconjunctionisgroundedinitself.

Now, this logical formpresupposeswhat I call a singularist viewof ground, according towhich any aspect of theworld that admitsof explanation can be explained on its own. I will be arguing thatsingularismiswrongandthatsometimesapluralityofaspectstakentogethercanbeexplainedeventhoughnoneofthemcanbeexplainedwhen takenalone.But thispluralist viewof ground isunintelligiblegiven the above logical form, so the pluralist will instead take thelogicalformtobe:

ΔbecauseΓ

4. Tobeclear,afactmayhavemorethanonefullground.IfPandQbothobtain,thenP∨Qis(fully)groundedinP,andalsoinQ.

5. ThislogicalformissuggestedbyFineinhis(2001)and(2012).

then the individualistic factsareplurallygrounded in thequalitative(sections2–5).ThenIwillargue(onthebasisoftheverysamekindsof considerations) that if mass if fundamentally relational then thekilogram facts are plurally grounded in those mass relationships(sections6–8).Sections9–10thendevelopeachstructuralistviewandrespondtoobjections.Thiswillnotestablishthateitherstructuralistthesisistrue(sinceIwillhaveonlymotivatedtheconditionalclaims),but it will suggest that these structuralist hypotheses are coherentand intelligible andworth taking seriously. And so our view aboutthelogicalstructureofgroundshouldallowforthesehypotheses:weshouldthinkthatgroundisirreduciblyplural.

ThoughIonlyarguefortheconditionalclaimshere,Ihavearguedfor theantecedentofeachconditional inotherwork.3 Sothispapercompletes the argument for structuralism in each case. The paperthereforehasthreedistincttopics—thenatureofground,thenatureofindividuals,andthenatureofquantitieslikemass—buteachtopicwillinformtheothers.

1 More on Ground

Itisimportanttoclarifythenotionofgroundatissue.AsIusetheterm,‘ground’isanexplanatory notion:tosaythatXgroundsYjustistosaythatXexplainsY,inaparticularsenseof‘explains’.Theearlierexampleillustratestheparticularsense.Imagineyouareataconference,andimagineaskingwhyaconferenceisoccurring.Acausalexplanationmight describe events during thepreceding year that ledup to theconference: someone thought that a meeting of minds would bevaluable, sent invitations,etc.Butadifferentexplanationwouldsaywhat goings­on make the event count as a conference in the firstplace.Someoneinsearchofthissecondexplanationrecognizesthatconferencesarenotsui generis,sothattheremustbesomeunderlyingfacts about event in virtue of which it counts as being a conference,

3. IarguethattheworldisfundamentallyqualitativeinDasgupta(2009)and(forthcoming), and thatmass and other quantities are fundamentally rela-tionalinDasgupta(2013).

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oftherecentliteratureonground.9Andithassomeplausibility:iftheeventwasaconferencebecauseofhowtheparticipantswereacting,then thoseactionsarewhat made it the case that itwasaconference,and are that in virtue of which it was at conference. But then (theideais)thoseactionsmustbesufficientfortheeventtohavebeenaconference.Tobesure,theprincipleiscontroversialandsomehavearguedthat it is false.10ButhereIwillassumetheprinciplewithoutfurtherdiscussion.

HoweverIdonotassumethereversescheme,sincetherecanbenecessaryconnectionswithoutgrounds:itismetaphysicallynecessarythat if Obama exists then 2+2=4, but Obama’s existence does notexplainwhy2+2=4.NordoIassumethatthegroundednecessitatesitsground,sinceadisjunctionmaybegroundedinoneofitsdisjunctswithoutnecessitatingit.

Mysecondassumptionisthatallpartsofanexplanationmustbeexplanatorilyrelevant:iftheXsgroundtheYsandx isoneoftheXs,thenx isexplanatorily relevant totheYsinthesensethatx playsatleastsomeroleinmakingitthecasethattheYsobtain.11Thisassumptionis natural in the case of causal explanation: even if the conferenceis causally explained by someone’s desire to orchestrate ameetingofminds,itisnotcausallyexplainedbythatdesireand the number of electrons in Alpha Centauri,forthelatterisirrelevanttothematterinthesensethatitplayednoroleinbringingabouttheconference.Iassumethesameforground:eveniftheevent’sbeingaconferenceisgroundedinvarious facts abouthow itsparticipantsacted, it isnotgroundedin those actionsand the number of electrons in Alpha Centauri, for the

9. SeeforexampleFine(2012)andRosen(2010).ForanextendedargumentinitsfavorseeTrogdon(2013).

10. SeeforexampleLeuenberger(2013)andSchaffer(2010).

11. WhenIsaythatx mustberelevanttotheYs,Imeanthisinthenon­distribu-tivesense:Idonotassumethatx mustberelevanttoeachoftheYsindividu-allyoreventojustoneoftheYs.Fortherootideaisthatexplanansmustberelevanttotheexplanandum—sothenaturalextensionofthatroot ideaifground is irreduciblyplural is thatexplanansmustbe relevant to the (per-hapsmany)explanandainthisnon­distributivesense.

wherebothΓandΔarelistsofsentences.6Informally,theaspectsoftheworlddescribedbythesentencesinΔare explained,whentakentogether,bytheaspectsdescribedbythesentencesinΓ,eventhoughthereisnopresumptionthateachsentenceinΔdescribessomethingthat can be explained on its own. According to the pluralist, thesingularist mischaracterized the logical form by generalizing fromspecialcasesinwhichthenumberofsentencesinΔisone.

Myofficialapproachistotreatgroundasasententialconnective,butitstreamlinesprosetotreatitasarelationalpredicatethatappliestofacts.Sincemytalkoffactsisjustaconvenientshorthand,thereisnoneedtosaymuchaboutwhatfactsare;however,Iwillassumethattheyarereasonablyfine­grainedandthatlogicallyequivalentfactscanbedistinct.7Onthiswayoftalking,asingularistwilltakethelogicalformofagroundingclaimtobe:

YisgroundedintheXs

where‘Y’isasingularvariableand‘theXs’isapluralvariable,bothranging over facts.8 But the pluralist will instead let Y be a pluralvariableandreplace‘is’with‘are’:shesays,ofthemanyYs,thatthey are groundedintheXs,withnopresumptionthateachYhasagroundonitsown.

Imaketwoassumptionsaboutground.Thefirstisthatthegroundedismetaphysicallynecessitatedbyitsgrounds.Moreformally:

IfΔbecauseΓ,thenitismetaphysicallynecessarythatif∧Γthen∧Δ

where∧XistheconjunctionofthesentencesinthelistX.Thisprinciple(or,moreprecisely,thesingularistrestrictionofit)isendorsedinmuch

6. Boththesingularistandthepluralistwilllikelyallowtheliststobeinfinite.

7. Correia(2011)discusseshowfine­grainedthenotionoffactmustbeinthecontextofquestionsofground.

8. ThislogicalformofgroundisendorsedbyRosen(2010).

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Thencallthetransitiveclosureofground(inthissenseof‘transitive’)thenotionofderivative ground.

2 Individualism and Qualitativism

Inowturntomyfirstconditionalclaim:thatif theworldisfundamen­tallyqualitativethen theindividualisticfactsareplurallygroundedinthequalitativefacts(sections2–5).Whatismeantby‘individualistic’and ‘qualitative’? I will not try to define these terms, but roughlyspeaking a fact is individualistic iff whether it obtains depends onhow things stand with a particular individual (or individuals) andqualitative otherwise.16 By ‘individuals’ I mean what in ordinaryEnglish we call ‘things’—apples, alligators, atoms, and so on. Weexpressindividualisticfactswithdirectlyreferringexpressions,e. g.

That (pointing at a particular apple) is juicy.

Obama is the president.

TheseareindividualisticbecausewhethertheyobtaindependsonhowthingsstandwiththatappleandObama,respectively.Andinfirst­orderlogic,weregimentourtalkofindividualistfactswithconstants,e. g.

a is F

a bears R to b

a=b

wherea andb areindividuals.Incontrast,examplesofqualitativefactsinclude

Someone is the president.

16. More precisely: a fact F is individualistic iff there are some Xs such thatwhetherFobtainsdependsonhowthingsstandwiththeXs.ButIwillcon-tinuetousethemorereadableexpressioninthetext.Acompletedefinitionwouldneedtorefinethenotionofdependence,amongotherthings,buttheideaisclearenoughforourpurposes.

latterplayednoroleinmakingtheeventcountasaconferenceandsoisirrelevanttothematter.Thisrequirementofrelevanceiswidelyendorsed;indeeditisoneofthecentralfeaturesusedtodistinguishgroundfrommetaphysicalnecessitationandlogicalconsequence.12

It is important thatwedonotdefine a factx to be explanatorilyrelevanttotheYsiffx isoneofsomeXsthatgroundtheYs,forthenmy assumptionwould become a tautology and lose its teeth. Thisis not theplace to discusswhether thenotionof relevance canbedefinedotherwise: here I take it to be another primitive alongsideground.13Myassumptionisthereforeasubstantiveprinciplelinkingtwodistinctnotions.Theassumptionisnotbeyonddoubt,butIwillnotdefendithere.

Itissometimesassumedthatgroundistransitive.14Whatdoesthismean?Weknowwhatitisforabinarysingular relationtobetransitive,butwhataboutabinaryplural relation?Onecanformulateanumberoftransitivity­likeprinciples,butIwillnotassumeanyofthemhere.Still,itwillbeusefultospeakofthetransitiveclosureofgroundonone sense of the term. To this end, let us stipulate that ground istransitive iff:

(i)IftheXsgroundtheYs,andtheYsalongwiththeY*sgroundtheZs,thentheXsalongwiththeY*sgroundtheZs,and

(ii)IftheXsgroundtheYsalongwiththeY*s,andtheYsgroundtheZs,thentheXsgroundtheY*salongwiththeZs.15

12. Thisassumption isexplicit inFine(2012)andRosen(2010),and iscentralto their respectiveconceptionsofground.Tobeclear, ifX isexplanatorilyrelevanttoY,thisdoesnotimplythateveryexplanationofYappealstoX.Forexample,ifPandQbothobtainthenP∨QisfullygroundedinP,andalsofullygroundedinQ.SonoteveryexplanationofP∨QappealstoP,butPisexplanatorilyrelevanttoP∨Q.

13. Fine(2012)arguesthatgroundandrelevancecannotbedefinedintermsofeachother.

14. Thoughnotalways.Rosen(2010)remainsagnostic,andSchaffer(2012)andTahko(2013)havebotharguedagainsttransitivity.Litland(2013)offersare-sponsetoSchaffer’sarguments.

15. ThankstoDanielBerntsonforhelpinformulatingthisprinciple.

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sufficienttoground(oratleastderivativelyground)theindividualisticfacts.Qualitativistsmaydisagreeonwhatkindofqualitativefactsonefindsatthebottomlevel:thetraditionalbundletheoristsaysthattheyconcernwhichmonadic,qualitativepropertiesarecompresent;otherqualitativists think that they are the facts that can be expressed inpredicatelogicwithidentity(butnoconstants);andotherqualitativistviewsarepossibletoo.18

Individualismisperhapsthemorenaturalposition.Supposethatanindividualx isbothredandround.Itfollowsthatsomethingisredandround.Butitisnaturaltothinkthatsomethingisredandroundbecause x is redandround, justas the individualistsays.However, Ifavorqualitativism.Verybriefly,myreasonisthatifindividualismweretruethentheindividualisticfactsofourworldwouldliebeyondourepistemicken.Theideaisthatourknowledgeoftheworldislimitedtoknowledgeof itsqualitativenature andwhatever is grounded inthatqualitativenature,andsinceindividualismimpliesthattherearefurtherfactsofthematterastowhichparticularindividualsliebehindthose qualities it follows that those facts would be unknowable. Areasonable Occamist principle then recommends that we dispensewithsuchepistemicallyinaccessiblefacts.19

18. ImotivateadifferentqualitativistviewinDasgupta(2009)and(forthcoming),whichusestheresourcesofalgebraiclogictodescribehowqualitativeprop-ertiesare“stitchedtogether”toconstructqualitativefacts.L.A.Paul(2002)and(2012)developsyetanotherversion,basedontheideathatqualitativepropertiesarepartsofindividuals.Hawthorne&Sider(2002)exploreanum-berofdifferentqualitativistviewswithoutendorsingthem.Ihavenotmen-tionedviewsthateliminateindividualisticorqualitativefactsaltogether.Thisisbecausetherecentinterestingroundislargelydrivenbytheideathatthebenefitsofeliminativistviewscanbeenjoyedbymoreplausibleviewsaboutwhatgroundswhat.

19. RoughlythislineofargumentcanbetracedbacktoLeibniz.Idevelopitinsomedetail inDasgupta (2009) and (forthcoming).Note that there is noepistemicproblemforthequalitativistpreciselybecauseshethinksthatin-dividualistic factsaregrounded inqualitative factsandsoshedenies thattheyare(in therelevantsense) “further facts”about theworldbeyond itsqualitativenature.

Theepistemicpremise—thatknowledgeislimitedtothequalitativeandwhatisgroundedinthequalitative—iscontroversial(tosaytheleast!)and

Orange is more similar to red than to blue.

Redness and roundness are co-instantiated.

sincewhethereachoftheseobtaindoesnotdependonhowthingsstandwith any particular individual. Perhaps the first depends onthere being some individual or other who is the president, but it isqualitativebecauseitdoesnotdependonanyparticularpersonbeingthe president.We can express some qualitative facts in first­orderlogic,e. g.

(∃x)Fx

(∃x)(∃y)(Fx&Gy&~x=y)

(∀x)(Fx⊃Gx)

solongasthepredicatesFandGexpressqualitativeproperties.17Butitmaybethatnotallqualitativefactscanbesoexpressed.

One might of course try to define the distinction betweenindividualistic and qualitative facts inmore detail, but the intuitiveideaglossedhereissufficientforourpurposes.

Now,ofthequalitativeandtheindividualistic,whicharethemorefundamental?Anaturalview is that themost fundamental factsareindividualisticfactsabouthowadomainofindividualsarepropertiedand related to one another, and that they are sufficient to ground(orat leastderivativelyground) thequalitative facts.Letuscall thisindividualism. In contrast, let qualitativism be the opposite view thatthe most fundamental facts are qualitative facts and that they are

17. Andwhatisaqualitativeproperty?Roughly,onethatdoesnotconcernanyparticularindividual.Forexample,beingseated,havingasister,andhavingtwosistersareallqualitative:evenifone’shavingtheseproperties impliestheexistenceofother individuals, theydonotconcernanyparticular indi-vidual.Thesecontrastwithnon­qualitativepropertiessuchasbeingKripkeandbeingObama’ssister,whichconcerntheindividualsKripkeandObamarespectively.Obviouslythisraisesthequestionofwhatitisforapropertyto“concern”agivenindividual,butIwillnotanswerthishere(Iamnottryingtogiveareductivedefinition).

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misconceptiontowardoffistheideathatqualitativismper se rulesoutsuchsituations—itdoesnot,evenifsomeversionsofitdo.20

The second potentialmisconception toward off is the idea thatqualitativismisjustanti­haecceitism(andlikewisethatindividualismjust is haecceitism).This is amistake. For anti­haecceitism (at leastas characterized in the recent literature) is amodal thesis, a thesisto theeffect that therecanbenodifference in thewaytheworld isindividualisticallywithoutaqualitativedifference.Admittedly,theterm‘anti­haecceitism’hasbeenusedforanumberofrelatedmodalclaims,someexpressedwithmodaloperatorsandotherswithquantificationoverworlds.21Buttheyareallmodalclaims,notgroundingclaims,andsononeof themimplyqualitativismfor thereasonthatanecessaryconnectiondoesnotimplyaconnectionofground:asIsaidinsection1,iftheXsnecessitateY,thisdoesnotimplythattheXsgroundY.Ofcourseitfollowsfrommyassumptionthatthegroundedisnecessitatedbyitsgroundsthatqualitativismimpliesanti­haecceitism(inatleast

20.Thusqualitativismper se doesnot imply thePrincipleof the Identityof In-discernibles (PII), theprinciple that indiscernible thingsare identical.Thisprinciplecomesinavarietyofdifferentflavorsdependingonwhichnotionof‘discernibility’isinuse.Objectsx andy areabsolutely discernible (roughlyspeaking) iff there isamonadicqualitativeproperty thatx hasandy doesnot.Andobjectsx andy areweakly discernible (again,roughlyspeaking)iffx andy standinanirreflexiverelationtooneanother.(Thesenotionsofdis-cernibilitywereclarifiedandbroughttobearonissuesinthephilosophyofphysics by Saunders [2003].)The two spheres in theMaxBlackworld areabsolutelyindiscerniblesincetheysharealltheirmonadicqualitativeproper-ties,bothintrinsic(e. g.beingbrown)andrelational(e. g.being2milesfromanironsphere).Buttheyareweaklydiscerniblesincetheyeachstandintheirreflexivequalitativerelationofbeing 2 miles from withsomething.Thepointinthetext(then)isthatqualitativismdoesnotimplythePIIstatedwiththenotionofabsolutediscernibility.Nor,wecannowadd,doesitimplythePIIstatedwiththenotionofweakdiscernibility.Forevenifeveryqualitativerela-tionthatthetwospheresstandinisonethateachspherestandsintoitself,itremainsthecasethatsuchasituationcouldbeexpressedinpredicatelogicwithidentity(butnoconstants).

21. Lewis(1986,chapter4)characterizedanti­haecceitismastheviewthatanytwopossibleworldsthatagreequalitativelyagreeaboutwhattheyrepresentde re ofanygivenindividual.Others(forexample,Pooley[2005])character-izeitastheviewthatpossibleworldsthatagreequalitativelyareidentical.Yetothers(includingSkow[2008])characterizeitwithmodaloperators.

However,myaimhereisnottoargueforqualitativismbutinsteadtoarguethatif qualitativismistruethen individualisticfactsareplurally groundedinthequalitative,notonebyone.

Before arguing for this, it is important toward off twopotentialmisconceptions as to what qualitativism is. The first potentialmisconception is thatqualitativismcannotmakesenseof situationsinwhich distinct individuals are qualitatively alike. An example ofsuchasituationistheinfamous“MaxBlack”world,aworldinwhichthere are just two spheres of iron 2miles apart that share all theirintrinsicqualitativeproperties(theyareexactlythesamesize,shape,color,etc).Now, it is true that some qualitativistviewscannotmakesenseofthissituation.Ifthetraditionalbundletheoryistheviewthateach sphere is identical to the collection of its qualitative properties,then—since(byhypothesis)bothsphereshaveexactlythesamesuchproperties—itfollowsthattheyareidentical,andsotherearenottwodistinctspheresafterall.

But as emphasized earlier, there are other qualitativist views.One is that the underlying qualitative facts are those expressed bypredicate logicwith identity(butnoconstants), inwhichcasethereis no difficulty describing such a situationwith something like thefollowing:

(∃x)(∃y)(Fx&Fy&xis2milesfromy&~x=y)

where F expresses the complete intrinsic qualitative nature of eachsphere. And the qualitativist view I develop in Dasgupta (2009)can alsomake sense of such situations. In any event, the potential

deservesmorediscussionthanIcangiveithere.But,justtobeclear,itdoesnot (withoutotherassumptions) ruleoutde re orfirst­personalknowledge,anditdoesnotsaythatweacquiresuchknowledgebyderivingitfromquali-tativeknowledge.It“just”saysthatwhateverisknowninthosecasesmustultimatelyhaveaqualitativeground.

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3 Finding Obama in a Qualitative World

Toseewhy,recall that thequalitativistsays that individualistic factsarederivatively grounded in the qualitative nature of theworld. Thisimpliesthatthereisanon­emptysetSofindividualisticfactsthataregrounded, and not just derivatively grounded, in the qualitative.22 Itwill help toworkwith an example, so let us suppose (without lossofgenerality) thatScontains the fact thatBarackObamaexists.MyopponentthinksthatthisfactwhentakenaloneisgroundedinsomesetQofqualitativefacts.ButwhatcouldQpossiblybe?IwillarguethatanycandidatesetQthatneces sitates Obama’sexistencecontainsirrelevant facts;or,contrapositively,thatifQisrestrictedtofactsthatarerelevant tohisexistencethenitwillnot ne cessitate hisexistence.Somy two assumptions—that a groundmust both necessitate and berelevanttowhat itgrounds—pull inoppositedirectionsandcannotbejointlysatisfied.ThenIwillshowthattheseproblemsdissolveifweplurallygroundallthefactsinStogether.

LetusstartbytryingtoconstructacandidatesetQ.Wemightstartwith facts concerning theexistenceof somethingwith justa fewofObama’squalitativeproperties,suchasbeingbornonasmallislandandbeingwelleducated.But thiswouldclearlynotbe sufficient togroundObama’s existence since it is possible for someone to havethosequalitiesandyetforObamanottoexist.

So let us try adding to Qmore facts about Obama’s qualitativenature.Tothisend,letRbeaboundedregionofspace­timecontainingObama, perhaps the region filled by the entire history of our solarsystem.AndletQR bethesetoffactscharacterizingtheentireintrinsicnature of R in its most fundamental qualitative respects. Does QR groundObama’s existence?No, because it does not necessitate hisexistence. For it is possible for there to be a region of space­timeR* disjoint fromRwhich agrees intrinsicallywithR in all itsmostfundamental qualitative respects—i. e. in which all the facts in QR

22. IfgroundistransitivethenSisthesetofallindividualisticfacts,whileifitisnotthenitmaybeapropersubset;butforourpurposesallthatmattersisthatSisnotempty.

oneofitscharacterizations).Soifyouareananti­haecceitistthismightbebecauseyouareaqualitativist.Butitmightinsteadbebecauseyouareanindividualistwhoholdsindependentviewsabouttheworkingsofde re modalitythatimplyanti­haecceitism.

IbelievethislatterpositionwasLewis’.Hewasananti­haecceitist(inatleastoneofitsguises),butwasheaqualitativist?Isuspectnot.This isnot altogether clear sinceheneverwrote explicitly in termsofground.Butsomeonewithqualitativistinclinations(regardlessofwhethertheyspeakintermsofground)wouldbelikelytoendorsethetraditionalbundletheoryordevelopsomeothertheoryofwhat theunderlyingqualitativefactsarelike,andLewisneverdidthis.IndeedhehadtheperfectopportunitytooffersuchatheorywhentellinguswhatapossibleworldisinChapter1ofOn the Plurality of Worlds,wherehecouldhavesaidthatapossibleworldissomekindofcollectionofqualitativeuniversals.Butinsteadhetellsusthatitisamereologicalsum of individuals. So while Lewis is an anti­haecceitist, I see noevidencethathewasaqualitativist.Inmyviewhisanti­haecceitismisbestunderstoodasfollowingfromhisviewsaboutthenatureofde re modality,nothisviewsaboutnatureofindividuals.

Soqualitativismisanexplanatory(andnotameremodal)claim.Andlikeanyexplanatoryclaim,itfacesthechallengeofshowingthatthe explanantia really are sufficient to explain the explananda—inthis case that the fundamental qualitative facts really are sufficientto explain the individualistic facts. The anti­haecceitist faces nosuch challenge since she only asserts a modal connection and notan explanatory connection. But for the qualitativist, meeting thechallengeiscrucial:ifshecannotmeetit,shewouldhavetoendorseaneliminativismaboutindividualisticfactsandclaimthattherearenosuchthings!Insofarasthisisanintolerableconsequence,meetingthechallengeiscrucialforthesuccessofqualitativism.

ItisthischallengethatItakeuphere.Mythesisisthatthequali­tativist does indeed face significant difficulties in meeting thischallenge if she tries togroundeach individualistic factonebyone,butthattheseproblemsdissolveifshegroundsthemplurally.

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natureofthecosmosoutsideoursolarsystem.Wemightforexampleadd facts concerning thequalitativenatureof some region inAlphaCentauri.ButtheproblemisthateveniftheresultingsetnecessitatesObama’sexistence,thosegoings­oninAlphaCentauriseemirrelevant when it comes to explaining his existence. Surely what happens inAlphaCentauriplaysnoroleinmakingitthecasethatObama exists.Toseethis,supposeyousucceededinexplainingwhysomeone withacertainqualitativeprofileexists,andIthenasked,‘Yes,butinvirtueofwhatisheObama?’IfyouthenstartedtalkingaboutAlphaCentauri,Iwould likelyassumethatyouhadmisunderstoodthequestionsinceyour answerwouldbe toobizarre to take seriously!Remember, thekind of explanation at issue here is metaphysical, not causal. Factsaboutthegoingsonindistantregionsofspacetimemightberelevanttoacausal explanationofhowheavyelementscameintoexistenceandthereforewhatcausedObamatoexist.Butweareaskingforagrounding explanationofObama’sexistenceandit isalmost inconceivablethatthecorrectanswercouldincludethegoingsonoutsideoursolarsystem.

My premise is that these facts about the universe outsideR areirrelevanttothematter.24Iwillsupportthepremiseinsection4below,butitisveryplausible.ForrecallhownaturalitwouldbetoexplainObama’sexistenceintermsoffactsabouttheparticularfundamentalparticlesthatcomposehim,orthefactthataparticularspermfertilizedaparticularegg.Thisexplanationisnotavailabletothequalitativist,butthefactthatitissonaturalshowsthatwetakefactsaboutgoings­onoutsideoursolarsystemtohavenothingtodowiththematter.Ifoneresistsmypremise,oneresistsaveryplausiblestartingpoint.25

24. Byfacts“about”theuniverseoutsideRIincludespecificfactsaboutparticularregions,forexampleaboutparticularelectronsinAlphaCentauri.ButIalsoincludegeneralfactssuchasthateveryregionoutsideRhascertaincharac-teristics.Theinclusionofthelattermakessensebecausetheywill(plausibly)begroundedintheformer,sothatifObama’sexistenceisgroundedinthelatteritwillbederivativelygroundedintheformer.So,iftheformerareob-jectionableinanexplanationofObama’sexistence,thensotooarethelatter.

25. Tobeclear,onemightasktwoquestionshere.First,if qualitativism is true,arefactsaboutAlphaCentauri relevant toexplainingObama’sexistence?And

obtain—but which contains different individuals. It might help toimagine(thoughthisisnotcrucialtotheargument)thatR*isspatio­temporally far removed fromR.Moreover it ispossible for there tobesucharegionR*andyetforRtodifferinsuchawaythatObamaneverexisted:perhapsallweneedtosupposeisthathisparentsnevermet.SinceallthefactsinQR wouldobtaininthispossibility,itfollowsthatQR doesnotnecessitateObama’sexistenceandhencedoesnotgroundhisexistenceeither.

The possibility I describe here is not controversial. It isuncontroversialthatinMoscowtherecouldbeanintrinsicduplicateof my laptop—call it l. And it is uncontroversial that l could existunchanged even if my laptop differed in some intrinsic respect(perhaps it lost akey). I am justmakingananalogousmodal claimaboutthespatio­temporalregionR.

ThisisnottodenythattherearefactsaboutthenatureofRthatcouldexplainhisexistence.EssentialistsaboutoriginsmightexplainhisexistencebythefactthataparticularspermfertilizedaparticulareggwithinR.Othersmight explain his existence in terms of someparticular fundamental particles in R that compose him. I have noobjection to these explanations, but they are not available to thequalitativistsincetheybothappealtoindividualisticfacts.Whattheaboveargumentshowsisthatnothingaboutthequalitative natureofRcouldgroundObama’sexistence.23

WhatthenmustbeaddedtoQR?ItisnouseaddingafactthatisnecessitatedbyQR itself,suchasgeneralizationsthataregroundedinQR,fortheresultingsetwouldstillnotnecessitateObama’sexistence(ifitdid,thenQR wouldnecessitatehisexistenceonitsown).ButQR wasa complete characterizationof the intrinsicnatureof our entiresolar system in its most fundamental qualitative respects. So tonecessitateObama’sexistencewemustaddfactsaboutthequalitative

23.Onemightthinkthatthesolutionistoqualitativelygroundthoseindividu-alistic factsabouttheparticlesortheeggandsperm.Butexactlythesameproblemswill recur.This is just tosay that thecurrentargumentdoesnotdependonmydecisiontodiscussthefactthatObamaexistsandwillapplytootherindividualstoo.

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TheargumenthasnothingtodowithwhetherObamais“discernible”fromotherthingsinthecontemporarymeaningsofthatterm.Forex­ample,ithasnothingtodowithwhetherthereisa(perhapscomplex,highly relational) qualitative property that only he instantiates. Foreven if there is such a property the question remains whether itsinstantiation explains Obama’s existence, and the argument is thatthere are constraints on explanation (necessitation and relevance)thatsuggestnot.26

I said that these problems dissolve if we plurally groundindividualistic facts in qualitative facts. How so? One simpleproposal is to let IT be the set of all individualistic facts and let(as before)QT be the set of all qualitative facts, and say that themembersof IT are(plurally)grounded in themembersofQT eventhough nomember of IT is grounded in any subset ofQT. This astructuralist viewof individuals,since it impliesthatanaccountofanyoneindividualisinevitablyanaccountofthemall.Butthatisjustoneproposalandtherearemanydetailstoargueabout.Somemightarguethatthequalitativegroundshouldincludeonlycertainkindsofqualitativefactssuchasexistentialgeneralizationsorfactsabout how properties are bundled together. Others might insistthatonlyapropersubsetSofindividualisticfacts(e. g. factsaboutthefundamentalparticles)areplurallygroundedinthequalitativeandthatotherindividualisticfactsaregroundedsingularlyinsomemembers of S. Still othersmightwant to say that structuralism isnotjusttruebutnecessarilytrue.Butthesearein­houseargumentsbetween theorists all of whom deserve to be called structuralists.Sincethedifferencesbetweentheirviewswillnotmatterhere,Iwillfocusonthesimpleproposaldescribedabove.

26.There is anextensive recent literatureon thequestionofwhethervariousindividualsarediscerniblefromoneanotherintheabsoluteorweaksensedefinedinfootnote20.ForexampleseeLadyman&Ross(2007)andrefer-encestherein.Thesequestionsaboutdiscernibilityareinteresting,but(asIsaidinsection2)theyarenotours.Idiscusstherelationbetweenqualitativ-ismandtheseotherviewsaboutdiscernibilityinDasgupta(2011).

IgrantedforthesakeofargumentthataddingfactsaboutAlphaCentauri to QR would result in a set that necessitates Obama’sexistence, but thiswas too concessive.Ourprevious argument thatQR does not necessitate his existence made very few assumptionsaboutR,soincrementallyenlargingRdoesnotaddresstheunderlyingproblem.So is thereany setofqualitative facts thatnecessitateshisexistence? Themost plausible suggestion is a complete qualitativespecificationof the entire cosmos, plus a “totality fact” to the effectthattheyareallthequalitativefactsthereare.CallthissetQT.DoesQT necessitateObama’sexistence?IdonothaveafirmintuitioneitherwaysoIamhappytoconcedethatitdoes.IndeedsinceQT containsthe totality factouraboveargumentcannotbeused toshowthat itdoesnot.Moreover,wearearguing that if qualitativism is true then theindividualisticfactsareplurallygroundedinthequalitative,anditfollowsfromqualitativism(andourassumptionthatthegroundedisnecessitatedbyitsgrounds)thatthequalitativefactsnecessitateanygiven individualistic fact. So denying that QT necessitates Obama’sexistence isnotdialecticallyavailablehere.SoQT appears tobethebestcandidateforasetofqualitativefactsthatnecessitatesObama’sexistence.ButofcourseQT containsfactsaboutthequalitativegoings­oninallcornersoftheentirecosmos,andmostofthosegoings­onareirrelevanttoanexplanationofwhyObama exists.

That is thebasic idea: inattemptingtofindaqualitativegroundthatplausiblynecessitates Obama’sexistence,weareforcedtoincludefactsthatareirrelevant tothematter.Orputtheotherway:inzeroingin on the facts that are relevant to an explanation of his existence,we find that they no longer necessitate his existence. The above isan argument­scheme that canbefilled in for different values ofR:if you think (as I do) that the qualitative goings­on in Jupiter areexplanatorilyirrelevanttoObama’sexistence,youcouldtakeRtobearegionthatincludesourplanetandnotmuchelseandtheargumentwouldgothroughjustthesame.

second, regardless of whether qualitativism is true, are facts aboutAlphaCen-taurirelevant?Ithinktheanswertobothquestionsisclearly‘No.’

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producingthisorthataspectoftheworldisarguablytheraison d’etre ofthenotionofground.

Can the virtues of structuralismmentioned above be replicatedwithouttakinggroundtobeplural?Onemighttryusingconjunctionsin place of plurals. For the conjunction of all members of IT—callthis conjunction ∧IT—is (like any conjunction) grounded in itsconjuncts. The structuralist then says that those conjuncts of ∧IT are (plurally) grounded in themembers ofQT. It follows that∧IT isderivatively grounded in QT. One might then try replicating thevirtuesofstructuralismwithouttakinggroundtobeirreduciblypluralbyproposing that∧IT isgroundeddirectly inQT without thedetourthroughitsconjuncts.Thisviewsharesthevirtuesmentionedabove,butitisuntenable.Forevenif∧IT isgroundeddirectlyinQT,itmustalsobegroundedinitsconjuncts(onpainofdenyingtheevidenttruththatconjunctionsaregroundedintheirconjuncts).Andwhatthenofthoseconjuncts?Wecannotsayofanyconjunct that it isgroundedqualitatively(onpainoffallingfouloftheargumentsjustgiven).Andwecannotsaythattheyareeachgroundedintheconjunction(onpainofmovingintootightacircle).Soitlooksliketheymust(onthisview)begroundless.Theresultisthat∧IT isradicallyoverdetermined:itisgroundedinitsconjuncts,anditisalsogroundedinQT,eventhoughthe conjuncts are not grounded in themembers ofQT orvice versa.Thisisnotanexplanatorythesisthatshouldbetakenatallseriously.

4 Cosmic Explanations

Above, I appealed to thepremise thatqualitativegoings­onoutsideoursolarsystemareirrelevanttoanexplanationofObama’sexistence.IsaidearlierwhyIfindthepremiseplausible,butitmightberesisted.IndeedaqualitativistweddedtosingularismaboutgroundmighttakethemoraloftheargumenttobethatthosequalitativefactsaboutfarflungareasofthecosmosarerelevanttoObama’sexistenceafterall.Soletmesupportthepremisewithsomeargument.

Well,thereisofcoursenoknock-down argumenttobehad.Weareengagedinaninferencetothebestexplanation,sotheaimistoshow

AchiefadvantageofstructuralismisthatitavoidsthedifficultieswefacedwhentryingtogroundObama’sexistenceonitsown.Foronething,QT containsno irrelevancieswhen itcomes toexplaining themembersofIT together.Tobesure,QT doescontainirrelevancieswhenexplaining Obama’s existence on its own, such as qualitative factsaboutelectronsinAlphaCentauri.ButsinceIT containsindividualisticfacts about those very electrons the qualitative facts about themwouldappeartobeperfectlyrelevantwhenexplainingIT’smembers!And as we saw earlier (when discussing the idea that QT groundsObama’s existence) it isnot implausible thatQT necessitates all theindividualisticfactsIT.(Moreover,aswealsosaw,ifonedeniesthatQT necessitatesIT thenonedeniesqualitativisim,andhereIamattemptingtoestablishthatif qualitativismistruethen theindividualisticfactsareplurallygrounded in thequalitative.)Theproblemswe facedwhentrying to ground Obama’s existence on its own therefore dissolvewhenweinsteadgroundindividualisticfactsplurally.

None of this implies that structuralism is the best form ofqualitativism,sincestructuralismmaysufferfromproblemsofitsown.Still,itisevidenceinitsfavor.

Ofcourseifstructuralismistruethenthereisa sense inwhichthemembersofQT “giveriseto”Obama’sexistence,evenif theydonotgroundit.Moreprecisely,letussaythatsomefactsΓaccount for afactY iff therearesome factsΔsuch thatΔare (plurally)grounded inΓandYisalogicalconsequenceofΔ.ThenstructuralismimpliesthatQT accountsforObama’sexistence.But ‘accountsfor’ isnotapurelyexplanatorynotion—at least,not if (as Iamassuming) relevance isrequired for explanation—since relevance is not preserved underlogicalconsequence.IfthequestioniswhatthemembersofQ T explain, the structuralist says that they explain themembers IT togetherbutnot individually. Distinguishing between ground and accounting isnotsplittinghairs:asIsaidinsection1,therequirementofrelevanceisoneofthecentralfeaturesusedtodistinguishgroundfromrelatednotionssuchasmetaphysicalnecessitationandlogicalconsequence.Indeed identifying the explanatorily relevant facts responsible for

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farflungcornersof theuniverse that ispartially responsible forhisexistencebutnotRomney’s.Asanexplanatoryhypothesis,theideais(frankly)hardtotakeseriously.

So the differentia must be found within R. This is perhaps themostplausibleoptionavailabletothesingularist,butitisnonethelessodd.FortheintrinsicqualitativenatureofRisnotsufficient(onthisproposal) to groundObama’s existence, facts outsideR are neededtoo.Sotheviewisthatvariousqualitativegoings­onoutsideRplayaroleinmakingitthecasethatObamaexists(andthatRomneyexists),butthatvariousqualitativegoings­onwithinRplayno role whatsoever inmakingitthecasethatObamaexists.Onthefaceofit,thislooksratherbizarre—Ifindithardtoseewhatkindofseriousexplanatorytheorywouldgrantanexplanatoryroletothosefar­flunggoings­onbutnottomorenearbygoings­on.

Moreover it is far from clear that the proposed ground (on thisproposal)wouldnecessitateObama’sexistence.Forsupposethatthequalitativegoings­onwithinRthataresaidtoberelevanttoexplainingObama’sexistencearefactsabouttheexistenceofsomethingwithjustafewofObama’squalitativeproperties,suchasbeingbornonasmallislandandbeingwelleducated.Suppose(thatis)thatitisjustthosefactswithinRplusthevariousqualitativegoings­onoutsideRthataresaidtogroundObama’sexistence.ThentheproposedgroundwouldclearlyfailtonecessitateObama’sexistenceforthesamereasonthattheproposalsdiscussed in section3 failed: itwouldbepossible forsomethingelsewithinRtohavethosequalitativepropertiesandyetforObamanottoexist.

IndeedthisworryaboutnecessitationarisesassoonasweretreatfromQT.Sothegeneralproblemmightbeputlikethis.WecannotsaythatObama’sexistenceisgroundedinQT,else(byparityofreasoning)wewouldhavetosaythatRomney’sexistenceisgroundedinQT too,inwhich casebothhave exactly the sameground,which is absurd.SowehavetoparedownQT tofindsomecoresetoffactsthatisthegroundofObama’sexistencebutnotRomney’s.Butwhenwedosoitisfarfromclearwhethertheproposedgroundnecessitateshisexistence

thatthestructuralist’sexplanationisbetterthanthesingularist’s.Soletmepointoutvariousunattractiveaspectsofthesingularist’sexplanation(Iwillpointoutsomemorevirtuesofthestructuralist’sexplanationinsection9whenIdiscusspluralexplanationsinmoredetail).

StartwiththeideathatObama’sexistenceisgroundedinQT.Thisis (as I saidearlier)perhaps themostplausibleexampleof a setoffacts that necessitatesObama’s existence. Butwhat aboutRomney?Whatgroundshis existence?SupposewesaythatitisalsogroundedinQT.Thenwehave theabsurd conclusion thatObama’s existenceandRomney’sexistencehaveexactly thesameground!HereIdonotassumethatdistinctfactsalwayshaveadistinctground:thefactsPvQandPvRmighthaveacommonground,P.Butitisunsurprisingthatthedisjunctionshaveacommongroundsincetheyhaveacommonconstituent.MypointisjustthatinthecaseofObamaandRomney,itisalmostunbelievablethattheexplanationofwhytheoneexistsisexactly thesameastheexplanationofwhytheotherexists.Surely(thisisanunarguedpremise)ifObama’sandRomney’sexistenceeachhaveanexplanation,theremustbesomedifferentia:somefactsthatplayaroleinmakingitthecasethatObama existsbutnoroleinmakingitthecasethatRomney exists(andvice versa).27

Wheremightthisdifferentiabefound?Therearetwooptions:withinRoroutsideofR.Supposethelatter.Thentherearecertainqualitativegoings­on in far flung corners of the universe that are relevant toexplainingObama’sexistencebut not Romney’s.Andthis isabsurdasanexplanatoryhypothesis(this isanotherunarguedpremise).It isonethingtobitethebulletandsaythatvariousqualitativegoings­oninAlphaCentauriarerelevanttoexplainingObama’sexistence.Icouldperhaps bepersuadedofthat.Butitisanotherthingtosaythatsuchgoings­onplayaroleinmakingitthecasethatObamaexistsbut not that Romney exists,asifObamahashisveryownplotofspace­timein

27. Ofcoursethestructuralistwilladmitthatthesamefactsaccount for Obama’sexistenceandRomney’sexistence,inthesensedefinedinthelastsection.But(asemphasizedthere)thenotionof“accountingfor”isnotapurelyexplana-torynotion.ThepointhereisthatObama’sexistencemusthaveadifferentexplanation fromRomney’s.

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more thann electrons, and then enrolled in astronomy class… ). ItseemsjustasobviousthatfactsaboutAlphaCentauriareirrelevanttoametaphysical explanationofObama’sexistence;butifIhadgoodtheoreticalreasonstobeaqualitativistandgoodreasonstothinkthattheonly way to thenmakesenseofObama’sexistence is togroundit in facts about the entire cosmos, Iwould consider accepting thesurprising result that those facts about Alpha Centauri play a roleinexplainingObama’sexistenceafterall.Butthiswouldbearadicalrevisionofpre­theoreticbelief.

And the point is that this radical revision is not required. Thestructuralist has noneed to revise her pre­theoretic conviction thatfacts about Alpha Centauri are explanatorily irrelevant to Obama’sexistence,preciselybecauseshedeniesthathisexistence(takenalone)hasaqualitativegroundinthefirstplace.Nowonemightsaythatthiscomesat thecostofrejectingsingularismaboutground,whichwasalsoapre­theoreticbelief.Butevenif thiswasapre­theoreticbelief(whichIdoubt),thisobservationcarriesverylittleweight.Forclaimsaboutthelogicalformofground(likesingularism)arehighlyabstractclaimsaboutthenatureofexplanation,anditisnotatallclearwhywe should take our pre­theoretic opinions about that sort of thingseriously.Sostructuralismsavesthepre­theoreticbeliefsthatmatter.

5 The Inter-Dependence of All Things

Itisworthcomparingstructuralismwithotherrelatedviews.Wealreadyknowthatstructuralismisnotjustanti­haecceitism.For

(asemphasizedinsection2)thelatterisjustamodal claimwhiletheformerisanexplanatory claim.

Structuralism is a version of qualitativism, since it says that thequalitative is sufficient to ground the individualistic (so long asweare careful to hear this plurally!). But it has an important point ofagreement with individualism: namely, that a given individualisticfact like Obama’s existence has (when considered on its own) noqualitative ground. Admittedly, it is tempting to infer from thispoint of agreement that individualism is true: we have (after all)

(andinsomecasestheproposedexplanationishardtotakeseriouslyinthefirstplace).

None of this is conclusive: I have just tried to indicate somedifficulties one encounterswhen searching for a qualitative groundofObama’sexistenceonitsown.Insofarasstructuralismavoidsthesedifficulties,thatisapointinfavorofstructuralism.SoI leaveitasachallengetothequalitativistwhowishestogroundObama’sexistenceonitsowntodevelopanaccountthatavoidsthesedifficulties.

At this point one might reject my methodology. I appealed topremisesaboutrelevanceandground(e. g.myoriginalpremisethatfactsaboutAlphaCentauriare irrelevant toObama’sexistence,andmy premise in this section that Obama’a and Romney’s existencehavedifferentgrounds).Butitmightbeobjectedthatthesepremisescannotbeusedasevidencebecause Ihavegivenno theoryofhowjustifiedbelief or knowledgeabout relevanceor ground ispossible.ItistruethatIhaveofferednosuchtheory,buttoconcludethatourbeliefsaboutrelevanceandgroundareofnoevidentialsignificanceisagrossover­reaction.IfsomeoneproposedthattheoccurrenceofaconferenceispartlygroundedinthenumberofelectronsinAlphaCentuari onewould reasonably reject the proposal since the latterobviouslyplaysno role inmaking it the case that theevent countsasaconference.Somehow—evenifweknownothow—ourgraspofthe fact that there isa conference (perhapsalongwith rudimentaryempiricalknowledge)isenoughtoinformusthathowitsparticipantsare acting is relevant to explaining it and the number of electronsinAlphaCentauriisnot.Onecanreasonablypointthisoutwithouthavingadeveloped theoryabouthowthis ispossible. IammakingsimilarpointsaboutObama’sexistence.

Moreover I do not claim that our beliefs about irrelevance andgroundareindefeasible.ItseemsobviousthatthenumberofelectronsinAlphaCentauriisirrelevanttoacausal explanationofwhythereisaconference,butthereareempiricaldiscoveriesthatcouldleadmetothinkotherwise(wemightdiscoverthatsomeoneformulatedaplantoholdaconferenceon thecondition thatAlphaCentauricontains

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eachindividualisticfact.Thisispreciselywhatthestructuralist(inmysenseoftheterm)denies.

WhatIcallstructuralismperhapsresemblesaviewofSpinoza’sinPart IofThe Ethics, at leastonGarrett’s reading.29Spinoza famouslyclaimsthatthefinitemodes—rocks,chairs, tables—followfromtheessenceofGod.ButaccordingtoGarrett, thecorrectreadingis thattheyonlyfollowfromGod’sessencewhentakentogether:itisfalseofanysinglefinitemodethatitfollowsfromGod’sessence,butitistrueofthemalltogetherthatthey followfromGod’sessence.SubstitutethequalitativenatureoftheworldforGod’sessenceandunderstandthenotionof“following”intermsofground,andyouhavethestructuralistviewdescribedabove.

Structuralism is a claim of grounds, not of semantics. So it isconsistentwithacompositionalsemantictheorythatassignsatruth­condition to each individualistic sentence on its own. For example,structuralism isconsistentwithacompositional semantic theoryonwhich ‘Obamaissitting’ is trueinEnglishiffObamaissitting,or iffObamainstantiatesthepropertyreferredtoby‘sitting’orwhathaveyou. So the mere fact (if it is one) that there are correct semantictheoriesofthistypeisnothreattostructuralism.

Whatstructuralismmay implyisthattherearenotruth­conditionsfor a single individualistic sentence in fundamental (i. e. qualitative)terms.Whetherstructuralismimpliesthisdependsonwhatismeantbyatruth­condition(equivalently:whatismeantbytheconnective‘iff’inastatementoftruth­conditions).Butevenifitimpliesthis,thereisnoconflictwiththeprojectofsemantics,foritisnopartofthatprojecttostatetruth­conditionsinfundamentalterms(ifyoudoubtthis,goand count howmany semantic theories are stated in the languageofquantummechanics).30Moreover itmaynonethelessbepossible

29.SeeGarrett(1991).

30.ThepointhereamountstoSider’sdistinctionbetweena“linguisticsemantics”anda“metaphysicalsemantics”(seehisSider[2011]).Theformeriswhatgetsdonebylinguistsandcontemporaryphilosophersoflanguage,inwhichase-manticsfor(say)theterm‘footballmatch’wouldnotbeexpectedtobegivenintermsoftheunderlyingquantummechanicalstatesthatmakeitupsuch

an individualistic fact that cannot be qualitatively explained,whichappears to be a counterexample to qualitativism! And indeed theinference would be valid if singularism about ground were true.Insofaraswehavebeen in thegripofsingularism, then, thismightexplainwhy individualismhas traditionally been themore populardoctrine.Buttheinferenceisinvalid,forevenifasingleindividualisticfacthasnoqualitativeground,theindividualisticfactstogethermay(plurally)haveaqualitativeground,justasthestructuralistthinks.

Onemightobjectthatifstructuralismsaysthatthereareungroundedfactsaboutindividualsthenitisnotaversionqualitativismafterall.Butthisismistaken.Fortheideabehindqualitativismisthateverythingarisesoutofpurelyqualitativefacts,that(tousethepopularmetaphor)allGodhadtodowhenmakingtheworldwasfixthequalitativefacts.Andthisisindeedthecaseaccordingtothestructuralist.Itisjustthatthosequalitativefactsexplaintheindividualisticfactsallatonce,notonebyone.

Perhaps themost familiar versionof qualitativism is the famousbundle theory, on which each individual is identified with a setof compresent qualitative properties. This is rather different fromstructuralism. For while the bundle theorist sees a certain set ofcompresentpropertiesandsays‘HereisObama!’,thestructuralistseesnosuchthing.Forthestructuralist,nopartofthequalitativenatureoftheworldcanbesaidtoberesponsibleforObama’s existence.

Isstructuralism(asdefinedhere)what“onticstructuralrealists”likeLadymanandRosshaveinmindwhentheytalkofindividuals‘whoseidentityandindividualityaresecondarytotherelationalstructureinwhichtheyareembedded’?28Itishardtosay,inpartbecausethistalkofidentityandindividualityareobscureintheextreme.Butsupposetheyhadinmindtheideathateachindividualisticfactisgroundedinfactsaboutrelational,qualitativestructures.Then,likethebundle­theorist,theirviewisthatthereissomequalitativebodyoffactresponsiblefor

28.Ladyman&Ross(2007),p.144.

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intrinsicmassthattheyeachpossess.31 Incontrast,comparativism istheviewthatallfactsaboutthemassesofmaterialbodiesarederivativelygroundedinfactsabouthowtheyarerelatedinmasstooneanother.Somecomparativistswillsaythatthemostfundamentalmassrelationsareratiorelationswhileotherswillinsistthattheyaremerelyordinal,butthisin­housedisputewillnotconcernushere.32

I favor comparativism.My reason is analogous tomy reason forfavoringqualitativism.Theroughideaisthatallwecaneverobserveare the mass relationships between things, for example that onebodyismoremassivethananother.If,astheabsolutistclaims,thereare further facts of thematter concerningwhichparticular intrinsicmass each body has—facts that are not grounded in those massrelationships—then those facts lie beyond our epistemic ken. Areasonable Occamist principle then recommends that we dispensewithsuchepistemicallyinaccessiblefacts.33

However,myaimhereisnottoargueforcomparativismbuttoar­guethatif comparativismistrue,thencertainfactsaboutmassmustbegroundedplurallyinmassrelationshipsratherthanonebyone.Ihaveinmindfactsaboutmassinagivenscale,suchasthatmylaptopis2kilograms,thatBeckhamis75kgs,andsoon.Thecomparativistfacesthechallengeofshowingthatmassrelationshipsreallyaresufficienttoexplainthesekilogramfacts.Ifshecannotmeetthischallenge,thenshewouldhavetobeaneliminativistaboutkilogramfactsandclaimthattherearenosuchfacts.Insofarasthisisintolerable,meetingthechallengeiscrucialtothesuccessofcomparativism.Iwillarguethatthecomparativistfacessignificantdifficultiesifsheattemptstoground

31. And,perhaps, factsabouthow the intrinsicmasses themselvesare relatedtooneanother.Thedetailsoftheviewcanbecashedoutinmanydifferentways, but thesedifferenceswill notmatter inwhat follows.Absolutists in-cludeArmstrong(1988),Eddon(2013),andMundy(1987).

32. Foramorepreciseaccountofthedistinctionbetweenabsolutismandcom-parativism,seeDasgupta(2013).

33. LiketheOccamistargumentagainstindividualismthereismuchmoretosayhere.IsaysomeofitinDasgupta(2013).

totakeasetofindividualisticsentencestogetherandstatethetruth­conditions for them in fundamental (i. e. qualitative) terms (again, Ihedgebecausethisalldependsonwhatismeantbyatruth­condition).Theresultingsemanticswouldbeholistic,deliveringatruth­conditionforthem withoutdeliveringoneforanymemberofthesettakenalone.Whichispreciselythekindofsemanticsinfundamentaltermsthatastructuralistwouldexpect.

6 Absolutism and Comparativism

So much for individuals. Perhaps surprisingly, an analogousstructuralistviewcanbemotivatedwithsimilarargumentsaboutwhatisonthefaceofitaverydifferentcase,namelythatofquantitieslikemass,charge,energy,temperature,length,andsoon.Iwillfocusonthecaseofmass,butthediscussiongeneralizestootherquantities.

Letusstartbydistinguishingtwoviewsaboutmass.Thepropertyofhavingmass isadeterminable thatappears tohave twokindsofdeterminates. It is natural to think that somethingwithmass has adeterminate intrinsic property,aproperty ithas independentlyof itsrelationstoothermaterialbodies.But it isalsonaturaltothinkthatthingswithmassstandinvariousdeterminatemass relationships withoneanother,suchasx beingmoremassivethany orx beingtwiceasmassiveasy.

Now,oftheintrinsicmassesandthemassrelationships,whicharefundamental?AccordingtoaviewIwillcallabsolutism, theintrinsicmasses are prior to themass relationships. The absolutist does notdeny that things stand in determinate mass relationships, she justsaysthatthoserelationships—andindeedallfactsaboutthemassesof material bodies—are derivatively grounded in facts about theparticular intrinsic mass had by each body. If my laptop is moremassivethanmycup,theabsolutistwillsaythatthisisbecauseofthe

matches.Incontrast,acompositionalsemanticsstatedinthosefundamentaltermsiswhatSidercallsa“metaphysicalsemantics”.Inthetext,Iamusing‘semantics’torefertowhatSidercallslinguisticsemantics.

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howmy laptop is related in mass to all other bodies in the entirecosmos:wouldR thennecessitatemy laptop’sbeing2kgs? It isnotclear.Rwouldfixthemassrelationshipbetweenany twobodies,sothequestioniswhethertheentirecosmoscouldbeexactlyasitisinallmass­relationalrespectsandyetdifferinthemassofmylaptop,andIdonothaveaclearintuitioneitherway.

However,wearearguingthatif comparativismistruethenthekilo­gramfactsareplurallygrounded,anditfollowsfromcomparativism(andourassumptionthatgroundedisnecessitatedbyitsgrounds)thatthemass relationships necessitate any fact aboutmass. So denyingthatRnecessitatesmylaptop’sbeing2kgsisnotdialecticallyavailable.So assume that R would necessitate my laptop’s being 2 kgs. Thetrouble is thatRwouldcontainexplanatorily irrelevant information.ItwouldcontainfactsaboutthemassrelationshipbetweenmylaptopandelectronsinAlphaCentauri,and(premise)theseareirrelevanttoexplainingmylaptop’smassinkilograms.SurelyitsmassrelationshipstoelectronsinAlphaCentauriplaynoroleinmakingitthecasethatitis2kgs.

Thispremisemightberesisted,butitisveryplausible.Itcanalsobe supported with argument. For recall how natural it was for theabsolutist togroundmylaptop’sbeing2kgs intermsof its intrinsicmass:thatintrinsicproperty(ifithadsuchathing)wouldexplainitsbeing2kgs.Thisexplanationisnotavailabletothecomparativist,butthefact that it issonaturalsuggeststhatwe(pre­theoretically) takefactsaboutelectronsinAlphaCentauritobeirrelevanttothematter.

Indeed this last pointmight be turned into an objection to any appeal to mass relationships, even mass relationships to IPK. Theargumentwouldstartwiththeobservationthatwefindtheabsolutist’sintrinsic explanation so satisfying. And it would argue that this isevidence that we (pre­theoretically) takemy laptop’smass relationto any other body (including IPK) to be explanatorily irrelevant towhyitis2kgs.PerhapsitsrelationtoIPKisrelevanttoexplainingthesemantic fact that ‘2kgs’picksoutthe intrinsicmass itdoes,butnot(accordingtothisargument)thenon-semantic factofmylaptop’sbeing

eachkilogram fact in turn, but that thesedifficultiesdissolve if shegroundsthemplurally.

Before we start, note that the absolutist can very easily explaineachkilogramfactonitsown.Forifmaterialbodieshavetheintrinsicmasses posited by the absolutist, it is plausible that terms of theform ‘r kilograms’ would refer to those properties. If so, then it isalmostirresistibletosay(forexample)thatmylaptop’sbeing2kgsisgroundedin(orperhapsevenidenticalto)itshavingacertainintrinsicmass;namely,thatintrinsicmassthatisthereferentof‘2kilograms’.

7 Finding Kilograms in a Comparative World

Sotheabsolutisthaswhatappearstobeanattractiveexplanationofeachkilogramfactonitsown.Notthecomparativist,though.Toseethis,considerthefactthatmylaptopis2kgs.Ifthecomparativisttriestogroundthisfactinmassrelationships,shemustfindsomesetRoffactsaboutmassrelationshipsthatexplainsitsbeing2kgs.ButwhatcouldRbe?Iwillargue(asbefore)thatanycandidatesetRthatmightnecessitate mylaptop’sbeing2kgscontainsirrelevant information.Onceagainwehaveacaseinwhichmytwoassumptions—thatagroundmustbothnecessitateandberelevanttowhatitgrounds—cannotbejointlysatisfied.

LetusstartbyconstructingacandidatesetR.Themostobvioussug­gestionistoletRbethesinglefactthatmylaptopistwiceasmassiveasthestandardkilograminParis,oftenknownastheInternationalProto­typeKilogram(IPK).Butthetroubleisthatthisdoesnotnecessitatethe fact thatmy laptop is2kgs.For it ispossible formy laptopandIPKtobothbetwiceasmassiveastheyactuallyare,inwhichcasemylaptopwouldstillbetwiceasmassiveasIPKandyetwouldbe4kgs,not2kgs.

Whatothermassrelationshipsmightnecessitatemylaptop’sbeing2kgs?ItwouldnothelptoaddtoRfactsaboutthemassratiobetweenmy laptopand(say) twentyotherbenchmark items,since thesamekindof argument shows that those relationshipsdonotnecessitatemylaptop’sbeing2kgseither.ButwhatifweletRcontainfactsabout

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Asbefore,thisbeliefthatrelationstootherthingsareirrelevant—bethey relations to IPK, or to electrons in Alpha Centauria—is notsacrosanct.IfIhadgoodtheoreticalreasonstobeacomparativistandif theonly way to thenmakesenseofmy laptop’sbeing2kgsweretogrounditinitsrelationshipstoIPK,forexample,Iwouldconsiderrevising that belief. But the virtue of plural grounding is that norevisionisrequired.

8 Structuralism Redux

Howso?OnesimpleproposalistoletKbethesetofallkilogramfactsandletRbethesetofallfundamentalfactsaboutmassrelations,andthensaythatthemembersofKareplurallygroundedinthemembersofR even thoughnomember ofK is grounded in any subset ofR.Callthisastructuralist viewofkilograms,sinceanexplanationofanykilogramfact is(onthisview) inevitablyanexplanationof themall.As in the caseof individuals therearemanydetails toargueabout:whetherRshouldincludeonlycertainkindsofmassrelationssuchasratiorelations,whetherKshouldincludeonlythosefactsconcerningthemassinkilogramsofthefundamentalparticles,andsoon.Buttheseareallin­houseargumentsbetweentheoristsallofwhomdeservetobecalledstructuralists.Since theirdifferenceswillnotmatterhere Iwillfocusonthesimpleproposaldescribedabove.

An advantageof structuralism (asbefore) is that it dissolves theproblemswe facedwhen trying to groundmy laptop’s being 2 kgsonitsown.Foronething,RcontainsnoirrelevancieswhenitcomestoexplainingthemembersofK.Sure,Rcontainsirrelevancieswhenexplaining my laptop’s being 2 kgs, such as mass relationshipsbetweenelectronsinAlphaCentauri.ButsinceKcontainskilogramfactsaboutthoseveryelectrons,therelationshipsbetweenthemarecertainlyrelevantwhenexplainingK’smembers!Andaswejustsaw(whendiscussing the idea thatR groundsmy laptop’smass in kgs)it isnot implausible thatRnecessitatesK. (Moreover, ifonedeniesthatRnecessitatesKthenonedeniescomparativism,andhereIamtryingtoestablishthatif comparativismistrue,then thekilogramfacts

2kgs.Theargumenthassomeappeal.Afterall,theabsolutistcould in principle appeal tomy laptop’s relation to IPKwhenexplainingwhyit is2kgs,but if shedid thenher resultingexplanationwould lookdecidedlyodd.OnewouldaskwhyshebroughtIPKintothepicturewhenall thatappearsrelevant is its intrinsicmass. Ifweacceptthisargument,thenany comparativistexplanationofitsbeing2kgs—eventheinitialsuggestionintermsofitsbeingtwiceasmassiveasIPK—isobjectionableonthebasisthatitappealstowhatwepre­theoreticallytaketobeirrelevantinformation.34

This is important. For onemight have tried to refine that initialsuggestioninlightofthemodalobjectiontoitdiscussedearlier.Onemighthavesaidthatmylaptop’sbeing2kgsisgroundedinitsbeingtwiceasmassiveas IPKactually is.Oronemighthavedevelopedaviewaccording towhich it is impossible for IPK tohavediffered inmassatall:while the lumpofmetal inPariscouldhavebeenmoremassive (the ideawouldbe) IPKshouldnotbe identifiedwith thatlumpandisinsteadaco­locatedyetdistinctobjectthathasitsmassessentially.35Themodalobjectionwouldhavenoforceagainsteitheroftheseviews,butaccordingtotheaboveargumentbothviewsareobjectionable since they appeal to what we take to be irrelevantinformation,namelymylaptop’smassrelationshiptoIPK.36

34.Onemightrespondtothisargumentbysayingthatifcomparativismistrue,thenthemassrelationsmust berelevant,sincetheyareall thecomparativ-isthastoworkwith.Butthisignoresthepossibilityoferrortheory.Forthecomparativistmightconcedetheargumentinthisparagraphandconcludethatsince there isnogroundingmy laptop’sbeing2kgs in terms thatsherecognizes,thereisnosuchfact.Tosaythatthecomparativistmust grounditsbeing2kgsinmassrelationshipsisakintoclaimingthatbeingawitchmust beexplicableinnaturalterms,sincenaturalfactsareallwehavetoworkwith.

35. ThankstoJackSpencerforbringingthisviewtomyattention.

36.Tobeclear,both the refinedviews in the lastparagrapharevulnerable toanother(perhapsmoredecisive)objection.Theobjectionisthattheybothappeal to the intelligibility of mass comparisons across different possiblescenarios,andyetit isdoubtfulthatthisis intelligibletothecomparativist.But the issueofcross­worldmasscomparisons isdelicateand itwouldbedistractingtodiscussithere(Idiscussitatsomelengthinsection10).SofornowIrestmyobjectiontotheseviewsonthechargeofirrelevance.

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plurality of kilogram facts in K, and that the underlying qualitativefactsinQT arereallysufficienttoexplaintheindividualisticfactsinIT.

Focuson the caseof kilograms,where I think theworry ismostpressing.Thestructuralist says that the totalbodyofmass relationsexplainswhymylaptopis2kgs,mytableis10kgs,mybedis100kgs,etc.But it is consistentwith those relations thatmy laptop is 4 kgs,mytable20kgs,mybed200kgs,etc.Theworryisthenthatameredescriptionofthemassrelationshasmissedsomethingoutandhasnotexplainedwhythekilogramfactsareastheyareratherthan(say)doublewhattheyare.37

Onemightrespondwithabstractargument.Forexample,onemightargueforthegeneralprinciplethatifsomeXsarerelevanttosomeYsandnecessitatethoseYsthentheXsgroundthoseYs.ForitisalmostundeniablethattherelationsinRarerelevanttothekilogramfactsinK.And(asIsaidinsection8)weareassumingthatRnecessitatesK.

But even if this abstract argument has some merits, somethingmoreilluminatingcanbesaidtomakethestructuralist’sexplanationcompelling. The key is to recognize that the basic role of kilogrampredicates in our language is to conveniently store informationaboutmassratios.Oncethatroleisclearlyinview,thestructuralist’sexplanation becomes compelling and the idea that something hasbeenmissedoutevaporates.

37. Care isneeded in formulating theworry.Oneway toput it is thatRdoesnotsingleoutaparticularmaterialbodyasprivilegedandsodoesnot“fixaunitkilogram”.Butthiswayofputtingtheworryisconfused.Forconsiderthestandardabsolutistviewaccordingtowhichagivenmaterialbody’sbe-ingrkgsisgroundedinitshavingacertainintrinsicmass.Onthisviewtheproposedgrounds—i. e.factsaboutwhichintrinsicmasseachmaterialbodyhas—donotsingleoutanyparticularmaterialbodyasprivilegedandsointhat sensedonotfixaunitkilogrameither.Whatthendoesitmean tofixaunit?Presumablytheideaisthattheexpression‘1kg’isstipulatedtorefertothatintrinsicmasshadbytheIPK,andsotheIPKisthensaidtobeofunitmassonthekilogramscale.Butifthat isthequestionofhowaunitisfixedthenitisameta­semanticalquestionaboutwhatdeterminesthemeaningsofourwords,notaquestionaboutwhatgroundsthekilogramfacts.Soneitherabsolutismnorstructuralismshouldbeexpectedtoanswerit.

aregroundedplurallyinthemassrelations.)Soourproblemsdissolvewhenweinsteadgroundkilogramfactsplurally.

Thisdoesnotimplythatstructuralismisthebestformofcompara­tivism,butitisevidenceinitsfavor.

Thoughstructuralismisaversionofcomparativism,ithasanimpor­tantpointofagreementwithabsolutism:namely,thatagivenkilogramfacthas(whenconsideredonitsown)norelationalground.Itmaybetemptingtoinferfromthispointofagreementthatabsolutismistrue,andindeedtheinferencewouldbevalidifsingularismaboutgroundweretrue.Insofaraswehavebeeninthegripofsingularism,then,thismightexplainwhyabsolutismhastraditionallybeenthemorepopulardoctrine.Buttheinferenceisinvalid:evenifthekilogramfacthasnorelationalgroundonitsown,itmaybethatthekilogramfactstogetherhavearelationalground(justasthestructuralistsays).

Ihave focusedon thecaseofmassbut I expect that the lessonshere generalize to other cases in which we have a mathematicalrepresentationofworldlyphenomena, forexamplearepresentationof distance in meters, time in seconds, acceleration in meters­per­seconds­squared,rationalpreferencesinutils,andsoon.InallthesecasesIbelievethatthefactsaboutthemathematicalvaluesinagivenscalewillbeplurally grounded in theunderlying facts thatgive riseto thenumerical representations. If that is right thenwehaveherea general method of approaching the metaphysics of numericalrepresentation,notjustmass.ButI leavethegeneralizationtoothercasesforanothertime.

9 Structural Explanations

SofarIhavearguedthateachstructuralistviewdissolvesproblemsthatwefacedwhenattemptingtogroundeachindividualisticfactoreachkilogramfactalone.Butitisonethingtosaythattheviewsdissolvecertain problems, it is another thing to show that the structuralist’sproposedexplanationineachcasereally isexplanatory, i. e. thattheunderlying mass relations in R really are sufficient to explain the

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Hisideaisthemembersofhiscommunityshouldgoforthandapplythesepredicatestomaterialbodiesinsuchawaythateachapplication“coheres”withotherapplicationsmadeintheircommunity—coheres,inthesensethatinferringbytheaboveruleyieldstruthsaboutmass­ratio.Soaspeaker’sprimaryaiminapplyingoneofthepredicatesisjustthatherapplicationcohereswitha(perhapsweighted)majorityoftheotherapplicationsinhercommunity.

It does not matter how the practice gets going: the very firstspeaker has free rein to apply any of the predicates to any object!Butoncethisfirstapplicationismadetheaboveinferenceconstrainssubsequent applications by other speakers. So the community isnowfacedwithacoordinationproblem.ButthisiseasilysolvedbydistributingDravid­measuringinstrumentstothepopulationthatareallcalibratedwithoneanother—calibrated,inthesensethattheyarealldesignedtoassignnumberstothingsinsuchawayastocohereintheabovesense.38

38.Theirpracticewillonlywork,note,ifitispossibletoassignnumberstoma-terialthingsinacoordinatedmanner.Thisisconfirmedbyaso­calledrepre-sentation theorem ofmeasurementtheory.Saythatafunctionf frommaterialthingstorealnumbersrepresents mass-ratio iffthefollowingistrue:x isr timesmoremassive thany iff f(x) = r.f(y).Thena representation theorem statesthatifthemass­ratiosbetweenthingsobeyvariousconstraintsthenthereisatleastonefunctionthatrepresentsmassratio.Itfollowsthatthereexistap-plicationsofDravidpredicatestothingsthatcohereinthesensementionedinthetext.

Theso­calleduniqueness theorem thenstatesthatgivenanyfunctionf thatrepresentsmassratio,(i)r.f alsorepresentsmassratio,foranypositiverealr,and(ii)everyfunctionthatrepresentsmassratiocanbewrittenasr.f,forsomepositiverealr.Therepresentationanduniquenesstheoremstogetherimply that givenany material body andany real number, there is a unique functionthatmapsthatbodytothatnumberandthatrepresentsmass­ratio.Whichmeansthatthefirstspeakerdoesindeedhavefreereigntoapplyanyofthepredicatestoanyobject,sureintheknowledgethatitispossibleforthecommunity’sotherapplicationsofDravidpredicatestocoherewiththatfirstapplication.

NowIjustslurredovermanydetailsoftherepresentationanduniquenesstheorems.Foronething,thesetheoremsareusuallystatedwithrespecttoanunderlyingrelationallanguagethatcontainsjusttwopredicates:‘x isgreaterorequal inmassthany’andapredicateformaterialcomposition.Butthissimplificationisharmlessforcurrentpurposes.FormorerealistictheoremsandproofsseeKrantzet al. (1971).

Toshowthis,letmefirstdescribeafictionalcommunityinwhichtheirpredicatesarestipulatedtoplayexactlythatroleandthenshowthat the structuralist’s proposed explanation is compelling when itcomestoexplainingthefactsthatthey expresswiththeirpredicates.Then I will argue that our own community is just like theirs in allrelevantrespects.

Considerthenacommunitythatinitiallylackskilogrampredicates.Letusimaginethattheonlyexpressionstheyhavewithwhichtotalkaboutmassarepredicatesoftheform‘x isr timesmoremassivethany’,oneforeachpositiverealr.Ifcomparativismistruethentheirlan­guageiscompleteinthesensethattheycanstateallthefundamentalfactsaboutmass.Nonetheless,theirlanguageissomewhatimpractical:ifoneoftheircitizensRahul ishostingapot­luckdinnerandwantseveryone tocontributehalf theamountof rice inhis cupboard, theonlywayhecanissuetherequestistosaysomethinglike‘Pleasecouldeveryonebringhalf theamountof rice inmycupboard’.EachguestwouldthenneedtovisitRahul’shousebeforethepartytomeasureouttherightamount.

Soitbehoovesthemtofindsomewayofattributingmasstothingsonebyone,asitwere,sothattheycouldallhavedeterminedtherightquantityofriceathome.Theimportantthingisthattheseattributionsshould be coordinated so that they imply themass­ratios that theyare interested in.To this end,Rahul introduces a slewofone­placepredicatesoftheform‘x isr Dravids’intothelanguage,oneforeachpositive real r.His idea is that the ratiosbetweenrealnumberscanthenbeusedtorepresentthemass­ratiosbetweenthematerialbodies.Since this is theprimary functionof thesepredicates theonly thingthatRahulsayswhenintroducingthemisthattheyaregovernedbythefollowinginferencerule:

x isr Dravids

y iss Dravids

Therefore,x isr/s timesasmassiveasy

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there isnoprivileged“standardobject”,suchthatsomethingcanbesaidtobe2Dravidsinvirtueofbeingtwiceasmassiveasit.GiventheroleofDravidpredicatesintheirlanguage,itseemsthatif thereisanexplanationofwhythebrickis2Dravids,itisthatthebrick’sbeing2Dravidscohereswiththemass­in­Dravidsofotherthings—butsincethisanswerappealstothemass­in­Dravidsofotherthingsitisnotananswerthatisacceptabletothecomparativist.Sothebrick’sbeing2Dravidsappearstohavenopurelymass­relationalgroundonitsown.

Butnowtakethecoherentcoresetofapplicationsandaddtheas­yetunacceptedsentencesoftheform‘x isr Dravids’thatcoherewiththatcore,onesentenceforeachmaterialbodyx.TheresultingsetofsentencesD isacomplete representationofmass, in thesense thatonecouldrecovertheentiremassrelationalnatureoftheworldfromitsmembersbywayoftheaboveinferencescheme.AndnowsupposeRahulassertseachmemberofDinturn—‘Thisbrickis2Dravids,mytable is 10Dravids,DavidBeckhamis75Dravids… ’—andsupposethatwhenheisdone(!)weaskhimtoexplainwhatmakesallthatthecase.Well,sincehisprimaryaiminapplyingthepredicatesisjustthathisapplicationscohereinsuchawayastorepresentthemassratiosbetweenthings,itisalmostirresistibletosaythatwhathesaid(whenheassertedthemembersofD) is thecasebecause oftheunderlyingmassrelationshipsbetweenthematerialbodies.Indeed,iftheroleofDravidpredicatesisjusttostoreandcommunicateinformationaboutmass­ratio, it is hard to seewhat else could possibly be needed toexplainthemass­in­Dravidsofthings!

Thisisstructuralismthroughandthrough:theDravidfactstakentogetherareexplainedintermsoftheunderlyingmassrelationships,butnoDravidfactonitsownhasamassrelationalground.Tobeclear,thisstructuralistviewofDravidsisnotlogically implied bythewayRahuluseshispredicates,butitdoesstrikemeasalmostirresistible—oratanyratethebestexplanationgoing.

I believe that the community I just described is in all importantrespectsours:weusekilogrampredicates justasRahulusesDravidpredicates. The primary role of our kilogram predicates is just to

Havingintroducedthesepredicates,Rahul’slifeismucheasier.IfhisownDravid­measuring instrumentsays thathehas2Dravidsofriceinhiscupboard,hecansimplyaskeachofhisgueststobring1Dravidofriceanditwillthenfollow(solongastheinstrumentsarecalibrated) that eachguestwill bringhalf the amountof rice inhiscupboard,asdesired.

Importantly, note that in introducing his predicates Rahul saidnothing abouta“standardobject”intermsofwhichtheterm‘1Dravid’isdefinedorhasitsreferencefixed.Allthatmatters(givenwhatRahulsaid)isthattheirDravid­measuringinstrumentsarecalibratedintheabovesense—itdoesnot matterwhethertheyareallcalibratedwithaspecial“standardobject”.Ofcourse,ifthecommunityallagreesthataparticularbagof rice is 1Dravid, then theymightput thatbag ina(protected)publicspaceanduse itasapracticalaid incalibratingtheirDravid­measuringinstruments.Butthereisnorequirementthattheydefineorfixthereferenceof‘1Dravid’intermsofthatbag.So,iftheydiscoveredthatthebagisactuallyhalfasmassiveastheythoughtit was, theywould not be required by the semantics of ‘Dravid’ tocontinuetothinkthatitis1Dravidcomewhatmay.Rather—aslongastheywerestillconfidentthattheirDravid­measuringinstrumentswerecalibrated—theywouldsaythatthebagisactually0.5Dravids(and theymight then use some other object to help calibrate theirdevicesinstead).Thepointisthatthebagwouldjustbea(dispensable)practicalaidusedtofurthertheprimarygoalofcoordination.

NowsupposethattheDravidpredicatesbecomedeeplyentrenchedinRahul’scommunity, in thesense that thecommunityhasappliedthepredicateswidelyandthereisa(perhapsweighted)coremajorityofthoseapplicationsthatcoherewithoneanother.ThenIclaimthatastructuralistexplanationofDravidfacts—i. e.ofwhat isexpressedby applications of Dravid predicates—is almost irresistible. To seethis,supposeRahulassertsoneofthoseapplicationsinthecoherentcore,say,‘Thisbrickis2Dravids.’AndsupposeascomparativistswethenaskRahulwhatitisabout the underlying mass-ratios thatmakethebrick2Dravids.Thentherewouldappeartobenoanswer.Remember,

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IPKtocalibratevariousmeasuringinstrumentswithoneanotherthecalibrationsucceededeventhoughweweremisledabouttheexistenceof the lump.Howwouldwe report the discovery? Presumably justbysayingthatIPK(surprisingly)doesnotexist,andnotmuchmore.Importantly,ifIhadpreviouslybelievedthatmylaptopis2kgs,thenIwouldnotrevisethatbeliefinlightofthediscovery:Iwouldcontinuetobelieveandassertthatmylaptopis2kgseventhoughthereisnospeciallumpinParis.ButtheKripkeanviewhasdifficultyexplainingthisdatum.FortheviewimpliesthatifitturnsoutthatthereisnosuchthingasIPKthentermsoftheform‘r kilograms’failtorefer,anditisthendifficulttoseewhyIwouldbeinclinedtocontinuetosaythatmylaptopis2kilograms.

Asecondcaseisperhapsmoretelling.Thistime,imaginereadingintheTimesthatwhilethereissuchathingasIPK,itturnsoutthattheFrenchhavebeencreatinganelaborateillusiondesignedtomakeusthinkthatitistwiceasmassiveasitactuallyis.Again,thearticletellsusthattheillusionwassystematic,sothatthemeasuringinstrumentsaroundtheworldthatwerecalibratedwiththehelpofIPKareindeedallcalibratedwithoneother.TheonlysurpriseisthatifweweretoputIPKonanyoneofthemwewouldgetareadingof‘500grams’,not‘1kg’asexpected.Howwouldwereportthisdiscovery?Presumablybysayingsomething like ‘Wow, it turnsout that thestandardkilograminParisisactually500grams!’Inparticular,ifaskedhowmassivemylaptopwas Iwouldbe inclinedtosay ‘It is2kgs, thisarticlehasnobearingonthatquestion.’ButtheKripkeantheorypredictsotherwise.Forthattheorysaysthat‘1kilogram’isstipulatedtorefertothemassofIPKwhatever that mass is,soitimpliesthatthearticleshouldinsteadbereportedastellingusthatwhilethestandardobjectis(ofcourse)still1kg,itturnsoutthatmylaptopis(surprisingly!)4kgsafterall.Andthisisnothowwewouldreportit.

I just discussed two views that give standard objects like IPK acentral role in the semantics ormeta­semantics of ‘kilograms’. Eachviewencouragestheimpressionthateachkilogramfacthasaground

conveniently store information about mass­ratio, so our primaryaiminapplyingthemisthatourapplicationscoherewitha(perhapsweighted) majority of the other applications in our linguisticcommunity.“Standardobjects”liketheIPKinParisarenothingotherthan practical aids at achieving global coordination. Once we seethis, thestructuralistexplanationofwhatweexpresswithkilogrampredicates—i. e. the kilogram facts—is just as compelling andirresistibleasthestructuralistexplanationoftheDravidfacts.

What can prevent us from seeing this, though, are misguidedtheories about the role of “standardobjects” like IPK,which inviteus to think that each kilogram fact ought to have a ground on itsown.Forexample,consider theviewthat ‘x is r kilogram’ isdefined tobetrueofanobjectx just incasex isr timesmoremassivethanIPK.Thisviewencouragestheideathatagivenobject’sbeingr kgshasagroundonitsown,namelyintermsof itsbeingr timesmoremassive than IPK. But as Kripke famously argued, this view aboutkilogrampredicatesisfalse:ithastheincorrectconsequencethatIPKisnecessarily1kilogram.39

OrconsidertheKripkeanviewthatweuseeachtermoftheform‘r kilograms’withthereference­fixingstipulationthatifitistorefertoanything,itistorefertothemassthatisr timesthatmasshadbyIPK.40 OnthisviewIPKisnotpartofthesemanticsof‘kilograms’,butitispartofthemeta­semantictheoryabouthowthereferentof‘r kilograms’isfixed.Still,thisviewalsoencouragestheideathateachkilogramfacthasitsownground,thistimeintermsoftheintrinsicmassesreferredtobytermsoftheform‘r kilograms’.

ButthisKripkeanviewisfalse.Toseethis,imaginereadingintheTimesthatthereisinfactnospeciallumpofmetalinParisknownasIPKandthat theFrenchcreatedthe illusionofsucha lumpwithanelaboratesystemoflightsandholograms.Thearticleexplainsthattheillusionwassystematic,sothatwheneverwethoughtwewereusing

39.SeeKripke(1972).

40.Again,seeKripke(1972).

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quantifier,ruleswhichallowthemtofulfill theirroleofallowingustoconvenientlyreasonaboutwhat isultimatelyapurelyqualitativeworld.IdevelopthisviewofsingulartermsinDasgupta(2009),butthereisnospacetodiscussithere.Still,ifitisright,thenithelpsusseethatthestructuralist’sexplanationofindividualisticfactsintermsofqualitativefactsisextremelyplausible.

10 Modal Problems?

The lastsectionarguedthat thestructuralist’sproposedexplanationof kilogram facts (and individualistic facts) is compelling. Still, onemightthinkthatitcannotbecorrectsinceitissubjecttodevastatingproblems. There is of course no space to consider every potentialproblem,but letmediscuss two that concern structuralism’smodalimplications.41

Thefirst objectionnotices that ifmy laptop is in fact 2 kgs, it isnonethelesspossibleforittohavebeen4kgsandyetforeverythingelse’smass inkilogramstohaveremainedthesame.Thepossibilityof this“independentvariation” isevidence(theobjectiongoes)thatmylaptop’smassinkilogramshasagroundallonitsownwhichcanvaryindependentlyofthegroundsofthemassinkilogramsofotherobjects,contra structuralism.42

The second objection accuses the structuralist of not being abletomake sense of anypossibilities concerningmass in kilograms inthefirstplace.Toseethis,considerthepossibilityjustmentionedofmy laptopbeing4kgs insteadof2.Why think that thestructuralistcanmakenosenseofthis?ShecanmakesenseofaworldWthatisjustlikeourswiththeoneexceptionthatthemass­ratiobetweenmylaptopandallotherthingsisdoublewhatitactuallyis.Buttheworryisthatonthestructuralist’sownlightsthereisnofactofthematterastowhetherWisaworldinwhichmylaptopis4kgs,oroneinwhich

41. I focuson these justbecause theyare theobjections Ihavemostoftenen-counteredwhentalkingaboutstructuralism.

42. ThankstoRichardChappellandBradWeslakeforhelpingmeappreciatetheforceofthisobjection.

ofitsown.Buteachviewisfalse.Seeingthattheyarefalsethereforeremovesobstaclestoseeingthevirtueofstructuralistexplanations.

Thecorrectview,Isaid,isthatweuseofkilogrampredicatesjustlikeRahuluseshisDravidpredicates.ThisviewpredictsourreactionstothetwostoriesintheTimesjustdiscussed,whichisevidencethatitistrue.Andonceweseethatitistrue,thestructuralistexplanationofkilogramfacts—i. e.thefactsweexpresswithkilogrampredicates—isjustascompellingasthestructuralistexplanationoftheDravidfacts.

Tobeclear,youdonotneedtoendorsethisviewofkilogrampred­icatestoendorsestructuralism.ButIhavetriedtomotivateitbecauseitremovesobstaclesfromappreciatingthestructuralist’sexplanation(i. e.byminimizingtheroleofIPKinkilogramtalk)andsomakesitplausible that the underlyingmass relations really are sufficient toexplainthekilogramfacts.

Ishouldemphasizethatthisviewabouthowweusekilogrampredi­cates is consistentwithcompositional semantic theories thatassigntruth­conditionstoeachkilogramsentenceonitsown.WithregardstoRahul’s language,wemightsay that ‘x is2Dravids’ is true in thelanguageofRahul’scommunityiffx is1kilogram,oriffx is2.2pounds,orwhathaveyou.IndeedoncetheiruseofDravidpredicatesbecamedeeplyenoughentrenched,truth­conditionsofthiskindwouldappeartobehighlyplausible.Andtheexistenceoftruth­conditionslikethisis consistentwith the structuralist’s claim that no kilogram fact hasagroundinpurelymass­relationalterms(thisistheanalogueofthepointImadeinsection5regardingstructuralismaboutindividuals).

Ihavediscussedthecaseofkilograms,butIbelievethatroughlythe same goes for individuals. Just as kilogram predicates aredevicesofmeasurementwhoseprimaryroleistoconvenientlystoreinformationaboutunderlyingmass­ratios, so tooaresingular terms“devices of measurement” whose primary role is to convenientlystore information about the underlying qualitative world. And justaskilogrampredicatesfulfilltheirfunctionbybeinggovernedbythecanonical inference described above, so too our singular terms aregovernedbytheintroductionandeliminationrulesfortheexistential

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Now,isthereanythingaboutWinvirtueofwhichitcanbesaidtorepresentmylaptop’sbeing4kgs?Well,noticethatthemassratiosthat my laptop enters into differ systematically from those that itscounterpartinWentersinto,byafactorof2.Thatis,ifmylaptopisr timesmoremassivethananotherobjectx,thenmylaptop’scounterpartinWis2r timesmoremassivethanx’scounterpartinW.Incontrast,consideranyobjectotherthanmylaptop,likemyprinter.ThemassratiositentersintoarealmostexactlythesameasitscounterpartinW.Theonly difference concerns its relation tomy laptop:whilemyprinteris(say)twiceasmassiveasmylaptop,myprinter’scounterpartinWisthesamemassasmylaptop’scounterpartinW.Somylaptopandmy printer differ in this respect:my printer’smass role is verysimilartothemassroleofitscounterpartinW,butmylaptop’smassroleissystematicallydifferentfromthatofitscounterpartinW,byafactorof2.SowemightsaythatitisinvirtueofthisdifferencethatWrepresentsmy laptopasbeing twiceasmassiveas itactually isandeverythingelseashavingthesamemassthattheyactuallyhave.Thestructuralistcanthenpiggy­backonthis,forifWrepresentsmylaptopasbeingtwiceasmassiveasitactuallyisandifmylaptopisactually2kgs,thenwecantakeWtorepresentmylaptoptobe4kgs.

In effect, we just introduced a “mass­counterpart” relation inaddition to the ordinary, Lewisian counterpart relation. Since myprinterand itscounterpart inWresembleoneanotherwithrespectto their mass role, let us call them mass­counterparts. And (theidea is)becausemyprinter’s counterpart inW isalso itsownmass­counterpart,Wrepresentsmyprinterashavingthesamemassas itactually is. Here the mass­counterpart relation is doing analogouswork toLewis’ counterpart relation: justas the latter isnot identitybutinsteadstandsinforitwhendeterminingwhataworldrepresentsde re, themass­counterpartrelationisnotthesame­mass­asrelationbutinsteadstandsinforitwhendeterminingwhataworldrepresentsabout mass. And like Lewis’ counterpart relation, those aspects ofan item’smass­relational profile important to determining itsmass­counterpartswillpresumablydependontheconversationalcontext.

itis2kgsandeverythingelseishalfthemassinkgsthattheyactuallyare. For the structuralist is a comparativistwho thinks that all factsaboutmassaregrounded inmass relationships,and theproblem isthatthosemassrelationshipsdonotfixhowthebodiesintheactualworldarerelatedinmasstothoseinW.AndifthereisnofactofthematterastowhethermylaptopinWismoremassivethanmylaptopactuallyis,theworryis,therecanbenofactofthematterastowhatitsmassinkilogramsisinW.

Ibelievethatbothobjectionscanbeanswered:wecanmakesenseofpossibilitiesconcerningmassinkilograms(answeringthesecond)andthewaywedothiswillimplythatmylaptopcouldhavebeen4kgsevenifeverythingelse’smassremainedthesame(answeringthefirst).

Soletusstartwiththesecondobjection.Oneresponseistoendorsemodalrealismandsaythatthefundamentalfactsabouttheworldarereally facts concerningapluralityofworlds.The comparativistmaythenthinkthatthefundamentalfactsconcerningmassrelationshipsincludehowobjectsindifferentworldsrelatetooneanotherinmass.

Butonemightfindtheideaofinter­worldmassrelationsrepugnantsoletmeoutlineanotherresponsethatdoesnotappealtothem.43Thisresponseaccusestheargumentofusinganincorrectmodelofhowapossibleworld representsmy laptop’smass and introduces abettermodelthatallowshertomakesenseofthepossibilityinquestion.First,howdoesapossibleworldrepresentsomethingde re ofmylaptopinthefirstplace?Lewisfamouslysaidthatitdoessonotbycontainingmylaptop itselfbut insteadbycontainingoneof itscounterparts. Itdoesnotmatterforourpurposeswhetherhewasrightaboutthis,butletusassumethathewassothatwehaveaworkingmodelofde re representationinplay.Giventhisassumption,theworldWintroducedabovecanbe redescribedasaworldcontainingcounterpartsofmylaptopandeveryothermaterialbodyx suchthatifmylaptopisr timesasmassiveasx,mylaptop’scounterpartinWis2r timesasmassiveasx’scounterpartinW.

43. ThepresentationhereoverlapswithDasgupta(2013).

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11 Pluralism and Symmetry

Ihavearguedthatif theworldisfundamentallyqualitativethen thein­dividualisticfactsareplurallygroundedinthequalitative.Ialsoarguedthatif massiffundamentallyrelationalthen thekilogramfactsareplu­rally grounded in thosemass relations. Both claims are conditionalsotheargumentsdidnotpurporttoshowthatthereareactualcasesofpluralgrounding.Buttheydosuggestthattheconsequentsoftheconditionalsarecoherentandintelligiblehypothesesthatareworthtaking seriously. So our view about the logical structure of groundshould allow for them: we should be pluralists and think that thelogicalformofaclaimaboutgroundisirreduciblyplural,i. e.thatthey aregroundedinthem.

Oneconsequenceisthatweneedtotakecarewhenlinkinggroundwith fundamentality.Schaffer(2009)says thata fact is fundamentaliff it has no ground. But this is problematic if one also thinks thatthe fundamental factsare (pictorially speaking) those that lieat thebottomofthe“greatchainofbeing”,thosethat(asthemetaphorgoes)Godhadtodeterminewhenmakingtheworld.Forifpluralismaboutground is correct, thena factmayhavenogroundbutbepartof apluralityoffactswithaground.Inthiscase,thefactwouldcountasfundamental inSchaffer’s sense,but isnot something thatGodhadtodeterminewhenmakingtheworldandso(intherelevantsense)doesnotlieatthebottomofthe“greatchainofbeing”.Ifonewantstousetheword‘fundamental’totrackfactsatthebottomofthegreatchain,one should say instead that a fact is fundamental iff it isnotoneofapluralitywithaground.Soweshoulddistinguishtwosensesoffundamentality:one(Schaffer’s)tracksthosefactswithoutgrounds,whiletheothertracksthosefactsatthebottomofthegreatchain.Ifpluralismaboutgroundiscorrect,thesetwosensescomeapart.

beingtwiceasmassiveasIPKdoesnotnecessitateitsbeing2kgs,theclaimwasthattheydonotnecessitateinthat sense(whateveritis)—whichseemstrue.Asithappens,IbelievethatthenotionofnecessityinquestionmaywellbeFine’snotionofnecessitythatappliestothosetruthsthatfollowfromtheessencesofthings,butIleavefurtherdiscussionofthispointforanothertime.ThankstoJuhaniYli­Vakkuriforahelpfulconversationonthispoint.

Withabitofconversationalcoaxingwemightengineeralaxenoughcontext inwhichmy laptop’scounterpart inWisalso itsownmass­counterpart; and relative to this mass­counterpart relation W willrepresentmylaptopasbeing2kgsandeverythingelseashavinghalfthemassinkilogramsthattheyactuallyhave!44

Lewis’ counterpart theory is often seen as a reduction of de re modality in terms of de dicto modality.We can similarly see themass­counterpart theory just described as a reduction ofmodalityconcerning mass in kilograms in terms of modality concerningmass ratios. We can therefore distinguish between two senses ofpossibility: a fundamental sense that just concerns variations inmass ratios, and a looser sense that (also) concerns variations inmass in kilograms. So the structuralist should concede that in thefundamentalsenseofpossibility,theobjectionsunderdiscussionarewelltaken.Butshecansaythatthereisaloosersenseofpossibilitywherebypossibilitiesconcerningmassinkilogramsareexplainedintermsofpossibleworlds concerningmass ratios in theaboveway.And so she canagree that (inmanycontexts) it ispossible in thisloosesense formy laptop tohavebeen4kgsevenwhileallotherthings have the same mass in kilograms that they actually have,therebyansweringthetwoobjections.45

44. Idevelopthismass­counterparttheoryinmoredetailinDasgupta(2013).

45. EarlierIassumedthatgroundsnecessitatewhattheyground.Havingdistin-guishedthesesensesofpossibilitythequestionarisesastowhichnotionofpossibilitymakes this assumption true. Is it the fundamental sense or thereducedsense?Andifthelatter(contextsensitive)notion,whataretherel-evantcontexts?Thisisadeepquestion,butitisbeyondthescopeofthecur-rentpapersoIwillnottrytosettleithere.Itsufficesforcurrentpurposestodescribethesenseof‘necessary’relevanttothatassumptionbypointingtoparadigmexamplesofground:thattheoccurrenceofaconferenceisground-edintheactionsofitsparticipants,thattheexistenceofatableisgrounded(say)intheexistenceandarrangementofvariousparticles,andsoon.Therelevantsenseofnecessity is then thesense inwhich thosegrounds intui-tivelynecessitatewhattheyground.Soitisthesenseinwhichitisimpossiblefortheparticipantstoactlikethatandnotbeparticipatinginaconference,and inwhich it is impossible for theparticles tobearranged like thatandtherenotbeatable,andsoon.SowhenIsaidthatthequalitativegoings­oninoursolarsystemdonotnecessitateObama’sexistenceorthatmylaptop’s

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exampleifthetraditionalbundletheorist’sviewisthattheunderlyingqualitativefactsjust concernwhichintrinsic,qualitativepropertiesarecompresent, it isdifficult toseehowshecandescribeasituation inwhich there are two individualswith the same suchproperties. But(againaswesaw in section2)otherqualitativistshavenoproblemwiththis.Forexample,aqualitativistmightthinkthatthefundamentalqualitativefactsareexistentiallygeneralfactsthatcanbeexpressedinpredicatelogicwithidentitybutwithoutconstants,inwhichcasetheMaxBlackworldcanbedescribedasfollows:

(∃x)(∃y)(Fx&Fy&~x=y)

where‘F’expressesthequalitiesofeachsphere.47

Butstill,evenifthequalitativistcandescribethefundamentalfactsofaMaxBlackworld,onemightjustifythesecondpremisebyarguingthatthereisnowaytogroundtheindividualisticfactsaboutthetwospheresinthoseunderlyingqualitativefacts.ThisisclosewhatAdamshadinmindwhenhewrotethat

… the clearest way of proving the distinctness of twoproperties is usually to find a possible case in whichonewouldbeexemplifiedwithouttheother.Inordertoestablishthedistinctnessofthisnesses[i. e.individualisticproperties]fromallsuchnesses[i. e.qualitativeproperties],therefore,onemighttrytoexhibitpossiblecasesinwhichtwo thingswouldpossess all the same suchnesses, butwithdifferentthisnesses.48

LabeloneofthespheresAandtheotherB.Putintermsofproperties,Adams’observationisthatAandBsharetheirqualitativeproperties

47. Eventhosequalitativistssuchasmyself,whodonotwishtotreatexistentiallygeneralfactsasfundamental,canfindotherqualitativefactssufficienttode-scribethefundamentalnatureofaMaxBlackworld.IsaymoreaboutthisinDasgupta(2009).

48.Adams(1979),p.12.

Conflatingthesetwosensescanleadtomistakes.IndeedIsuspectthattheconflationliesbehindmuchoftheattractionofindividualism.Suppose you think that the existence of a given individual is notgrounded in further individualistic facts. And suppose you think(correctly,inmyview)thatithasnoqualitativegroundeither.Itfollowsthat its existence is fundamental in Schaffer’s sense. If you conflatethe senses of fundamentality, youwill then think that its existenceliesatthebottomofthegreatchainofbeing,thatitissomethingthatGodhadtodeterminewhenmakingtheworld.Soyouwillthinkthatindividualismistrue.Butthisreasoningequivocatedonthesesensesoffundamentality.ForevenifitsexistenceisfundamentalinSchaffer’ssenseandlacksaqualitativeground,itmaynonethelessbeoneofapluralityofindividualisticfactsthattogetherhaveaqualitativeground.Ifso,thenitsexistencedoesnotlieatthebottomofthegreatchainafterall;contra individualism.(Ialsosuspectthatasimilarmistakeliesbehindtheattractionofabsolutism.)

Soanimportantproject,Ithink,istoidentifyoccurrencesofthiskindofmistake,asItriedtodoearlierinthecaseofindividualsandkilograms. Other mistakes can stem from failing to recognize thatground is irreducibly plural too. I will finish by identifying one. Itinvolvesafamousargumentagainstqualitativismthatturnsouttobeunsound if pluralismabout ground is true.Thefirst premiseof theargumentstatesthatthe“MaxBlack”worlddiscussedinsection2ispossible,i. e.thatitispossiblefortheretobejusttwospheresofironlocated2milesapartwhichsharealltheirqualitativeproperties(theyareofexactlythesamemass,color,shape,etc).Thesecondpremiseisthatthequalitativistcannotmakesenseofthispossibility.Iwillarguethatthesecondpremiseisfalseifpluralismaboutgroundistrue.46

Toseethis,startbyaskinghowthesecondpremiseistobejustified.Onequestioniswhetherthequalitativisthastheresourcestodescribethe fundamental, qualitative facts of aMax Blackworld. Aswe sawin section2, somequalitativists appear tobeunable todo this. For

46. Thisisnottheonlyavailableresponsetotheargument.SeeHawley(2009)foradiscussionofothers.

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grantthesecondpremiseandinsteaddenythefirst.Thus,theliteratureisfullofqualitativistsbendingoverbackwardstoshowthatwemayplausibly deny the possibility of a Max Black world. For example,Hacking(1975)arguesthataMaxBlackworldcanbere­describedasaworldinwhichthereisjustonespheresituatedinanon­Euclideanspacesotightlycurvedthatit is2milesfromitself.AndHawthorne(published as [O’Leary­Hawthorne, 1995]) argues that individualscanbemultiplylocatedinspace,sothattheMaxBlackworldcanbere­describedas aEuclideanworld inwhicha single individualA islocated2milesfromitself.Thereappearstobeanimplicitassumption,then,thattoblocktheargumentthequalitativistmustdenythatMaxBlackworldsarepossible.

Butifpluralismaboutgroundistruethenthisassumptionisfalse.EvenifweconcedethepossibilityofMaxBlackworlds,theabovear­gumentforthesecondpremiseatbestshowsthatneitherA’sexistencenorB’sexistencehasaqualitativegroundonitsown.Butifpluralismistruethenitremainsopenthattheindividualistic facts intheMaxBlackworld—includingA’sexistenceandB’sexistence—areplurallygrounded in the world’s qualitative nature even though none ofthemhaveaqualitativegroundontheirown,justasthestructuraliststates.Asaresult,thequalitativistmayconcedethepossibilityofMaxBlack worlds and yet deny that they are problematic for her view.Qualitativists should welcome this result, for there are compellingargumentsbasedonplausibleassumptionsthatMaxBlackworldsareindeedpossible(forexample,Adams’argumentfromthepossibilityof twospheresthatarealmost qualitatively identical).AqualitativistwhodeniesthepossibilityofMaxBlackworldsmustthereforedenythoseplausibleassumptions,butifpluralismistruethereisnoneedforhertodoso.

Ofcourse,thisisbynomeansafulldefenseofqualitativismsincethereareotherarguments tocontendwith.Still, it isanexampleofacaseinwhichrecognizingthepossibilityofpluralgroundinghasasignificant,andperhapssurprising,impactonanissueinmetaphysics.

andyet sphereAhas the individualisticpropertyofbeing identicaltoAwhileBdoesnot.This suffices toshowthat the individualisticproperty is distinct from any ofA’s qualitative properties,whichwasAdams’aim.Toarguethattheindividualisticpropertyis not grounded in anyofA’squalitativeproperties,wejustaddtheassumptionthatifapropertyPisgroundedinpropertyQ,thennecessarilyanythingwithQalsohasP.

That is the argument put in terms of properties, but since wetake ground to be a relation between facts let us reconstruct it inthoseterms.Tothisend,considerthefact thatAexistsandthefactthatBexists. Inwhatmighteachof thesebegrounded?Puttingthepossibilityofpluralgroundingaside, theremustbesomefactaboutthe distribution of qualitative properties that explainsA’s existence,and likewise for B. But, onewould argue, the qualitative facts thatexplain A’s existencemust be different from those that explain B’s.Afterall,ifoneaskedwhatexplainsA’sexistenceandgotananswer,and then askedwhat explains B’s existence and got the very sameanswer,onewouldnaturallywant to reply ‘Waitaminute, thatwaswhatexplainedA’sexistence;whatthenmakesitthecasethatB exists?’Now,sincebothsphereshavemanyqualitativeproperties,onecouldtry saying thatA’s existence is explainedby something’sbeing ironandspherical,andthatB’sexistenceisexplainedbysomething’sbeingblackandhard.Butthiswouldbeimplausible:sinceAandBsharealltheirqualitativeproperties,itwouldbeamysterywhybeingblackandhardexplainsB’sexistencebutnotA’s.Therefore,theargumentgoes,nothingqualitativecanplausiblybesaidtogroundA’sexistenceandnotB’s;andsoA’sexistencehasnoqualitativeground.Theargumentis therefore slightly different than that which was run against thetraditionalBundleTheory.Inthatcase,theBundleTheorylogically im-plied that the sphereswere identical, contrary tohypothesis. In thismoregeneralcasethereisnosuchimplication;instead,thechargeisnowthatthereisnoplausibleexplanationoftheirexistence.

That is, I believe, the best defense of the second premise. Howshould qualitativists respond? Interestingly, they almost uniformly

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Dasgupta,S.(2009).‘Individuals:AnEssayinRevisionaryMetaphysics.’Philosophical Studies, 145(1):35–67.

Dasgupta, S. (2011). ‘The Bare Necessities.’ Philosophical Perspectives, 25:115–60.

Dasgupta, S. (2013). ‘AbsolutismvsComparativismAboutQuantity.’Ox ford Studies in Metaphysics: Volume 8.

Dasgupta,S.(forthcoming).‘QualityandStructure.’InE.Barnes(ed.),Current Controver sies in Metaphysics.Routledge.

Eddon,M.(2013).‘FundamentalPropertiesofFundamentalProperties.’Oxford Studies in Metaphysics: Volume 8,78–104.

Fine,K.(2001).‘TheQuestionofRealism.’Philosophers’ Imprint, 1:1–30.Fine,K.(2012).‘GuidetoGround.’InF.Correia&B.Schnieder(eds.),

Metaphysical Grounding: Understanding the Structure of Reality,37–80.CambridgeUniversityPress.

Garrett,D.(1991). ‘Spinoza’sNecessitarianism.’InY.Yovel(ed.),God and Nature: Spinoza’s Metaphysics,191–218.E.J.Brill.

Hacking, I. (1975). ‘The Identity of Indiscernibles.’ The Journal of Philosophy, 72:249–56.

Hawley,K.(2009).‘IdentityandIndiscernibility.’Mind, 118:101–19.Hawthorne, J.&Sider,T.(2002). ‘Locations.’Philosophical Topics, 30:

53–76.Krantz,D.H.,Luce,R.D.,Suppes,P.&Tversky,A.(1971).Foundations of

Mea surement Volume 1: Additive and Polynomial Representations.SanDiego:AcademicPress.

Kripke,S.(1972).Naming and Necessity.Oxford,UK:Blackwell.Ladyman, J. & Ross, D. (2007). Every Thing Must Go: Metaphysics

Natural ized.Oxford,UK:OxfordUniversityPress.Leuenberger,S.(2013).‘GroundingandNecessity.’Inquiry,151–74.Lewis,D.(1986).On the Plurality of Worlds.Oxford,UK:Blackwell.Litland,J.E.(2013).‘OnSomeCounterexamplestotheTransitivityof

Grounding.’Essays in Philosophy, 14(1):19–32.Mundy,B.(1987).‘TheMetaphysicsofQuantity.’Philosophical Studies,

51:29–54.

Whetherother issues are similarly affected is aquestion I leave foranothertime.

12 Conclusion

TherecentliteratureongroundhasuniformlyassumedwhatIcallsin­gularism,accordingtowhichthelogicalformofaclaimofgroundsisthatthis (asinglefact)isgroundedinthem.Ihavearguedthatifcertainassumptionsaboutthefundamentalnatureoftheworldaregranted,then it is plausible that certain collections of facts are groundedplurally in theworld’s underlyingnature: they (themembers of thecollection)are groundedinthem eventhoughnoneofthemadmitsofagroundof itsown.Ourviewaboutthelogicalstructureofgroundshould therefore allow for these hypotheses: we should think thatgroundisirreduciblyplural.Ifthisisright,thenitisimportantthatweensurethatourmetaphysicaltheorizingaboutisnotimplictlyinfectedwithsingularistassumptions.49

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