ForthcominginPhilosophyandPhenomenologicalResearch;pleaseciteofficialversion.

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GROUNDING,ESSENCE,ANDIDENTITY

FabriceCorreiaUniversityofNeuchâtel

AlexanderSkiles*

NewYorkUniversity

Abstract:Recentmetaphysicshasturneditsfocustotwonotionsthatare—aswellashavingacommonAristotelianpedigree—widelythoughttobeintimatelyrelated:groundingandessence.Yethow,exactly, thetwoarerelatedremainsopaque.Wedevelopaunifiedanduniformaccountofgroundingandessence,onewhichunderstandsthembothintermsofageneralizednotionof identityexaminedinrecentworkbyFabriceCorreia,CianDorr,AgustínRayo,andothers.Wearguethattheaccountcomportswithantecedentlyplausibleprinciplesgov-erninggrounding,essence,andidentitytakenindividually,andilluminateshowthethreeinteract.Wealsoarguethattheaccountcomparesfavorablytoanal-ternativeunificationofgroundingandessencerecentlyproposedbyKitFine.

Recentmetaphysicshasturneditsfocustotwonotionsthatare—aswellashaving

a common Aristotelian pedigree—widely thought to be intimately related:

grounding(whensomephenomenonnon-causally‘derives’fromanother)andes-

sence (when some phenomenon is in the ‘nature’ of another). However, how

they’rerelatedremainsquiteopaque.1Weaimtoclarifytheirlinkbyproposinga

unifiedanduniformaccountofbothnotionsthatanalyzesthemintermsofathird:

whatwecall,followingLinnebo(2014),generalizedidentity.Alongwiththeintrin-

sicdesirabilityofaccountingforeithernotionalone(whichhasprovenelusive),

ourproposalilluminateshowthetwointeractbymeansofasingle,relativelywell-

behavedconceptualtool.

Whatdowemeanby“generalized”identity?Objectualidentities(e.g.“Hesperusis

Phosphorus”) are familiar, anddisplay a canonical form: an identity-indicating

* Thisarticle istheproductof fullandequalcollaborationbetweenitsauthors;theorderof

authorshipisalphabetical.

1 How grounding and essence interact is explicitly taken up in Audi (2012; 2015), Carnino(2014),Correia(2005;2013),Dasgupta(2014;2016),Fine(2012;2015),Guigon(forthcoming),Greenberg(2014),Kment(2014),Koslicki(2012;2015),Rosen(2012;2015),Skiles(2015),Trog-don(2015),andZylstra(forthcoming).

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phraselike“is”getstreatedasarelationalpredicate,flankedbytwodesignators

forentities.Despitetheunfamiliarname,generalizedidentitiesarenolessphilo-

sophicallycommonplace.Consider:

(1) Forathingtobeabachelorisforittobeanunmarriedadultmale.

(2) Forathingtoknowapropositionisforittotruly,justifiablybelievethat

proposition.

(3) FortheAtlanticOceantobefilledwithwaterisforittobefilledwithH2Omolecules.2

Thesestatementsareclearlyanalogoustoobjectualidentities:onecouldreadily

substituteinphraseslike“isthesameas”or“isnodifferentthan”,cancellingany

implicationthatthe“is”atissueisoneofpredicationorexistence.Yettheydeviate

inlogicalform,atleastatthegrammaticalsurface.“FortheAtlanticOceantobe

filledwithwater”in(3),e.g.,doesn’tseemtobeinthedesignatingbusiness,and

thetruthof(3)doesn’tseemtohingeuponitsbeingso.Surelyweshouldbelieve

(3),amundanechemical-geologicaltruth,evenifmetaphysicalinquiryrevealsno

‘fact-shaped’entitieswithjusttherightindividuationconditions(Cameron2014,

p.431;Dorr2016,pp.40-1;Rayo2013,pp.66-8).Andcertainexamplespatently

resistastraightforwardobjectualreading.Consider:

(4) Forathingtobeanon-self-instantiatorisforittobeapropertythat

doesn’tinstantiateitself.

FamiliarRussellianreasoningdemonstratesthatthereisnosuchpropertybeing

anon-self-instantiator,raisingobvioustroublefortheviewthat(4)expressesan

identityinvolvingit(Correia2006,pp.761-2;Dorr2016,p.40).3

2 Foradditionalexamplesoftheidiom,seeCorreia(2010,pp.256-7),Dorr(2016,p.39),King

(1998,p.156),Kment(2014,p.153),Koslicki(2012,pp.197-203),andRayo(2013,p.3).

3 Thosewho, likeus,denythatthatgeneralized identitiesareobjectual identities indisguisemightnonethelessupholdthefollowing,morecautiousprinciples:

(i) IfthepropertyofbeingFandthepropertyofbeingGbothexist,thenforathingtobeFisforittobeGiffthepropertyofbeingF=thepropertyofbeingG.

(ii) Ifthefactthatpandthefactthatqbothexist,thenforittobethecasethatpisforit

tobethecasethatqiffthefactthatp=thefactthatq.

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Althoughnotthemselvesobjectualidentities,recentstudieshaveshedlightonthe

nature,logic,andepistemologyofgeneralizedidentitiesbyextendingprinciples

widelythoughttogovernobjectual identity, tocoverthe“is”ofstatements like

(1)-(4).4Acommonrefrain—acrucialoneforourpurposes—isthatgeneralized

identityneedn’tonlybefull,asin(1)-(4).Itcanalsobepartial,aswhenonesays

thatforapropositiontobeknownisinpartforittobetrue(butnotinfull,since

itmustalsobejustifiablybelieved).Currentworkfocusesonpartialgeneralized

identitiesoftheconjunctivevariety,liketheonementioned.Yetitalsocomesina

disjunctivevariety,andbothareanalyzableintermsofthefull.Distilledtoitscore,

ouraccountunifiesgroundingandessencebyanalyzingessenceintermsofthe

conjunctivevariety,andgroundingintermsofthedisjunctivevariety.

Here’sourplan.Insection1,wefurtherintroducethenotionofgeneralizediden-

tity.Insections2and3,wedevelopaccountsofessenceandgroundinginterms

ofgeneralized identity,respectively. Insection4,wearguethat the framework

comparesfavorablytoaunificationofgroundingandessencerecentlyproposed

by Fine (2015). Finally, in section 5we concludewith several open questions

aboutgeneralizedidentitytoguidefutureresearchongroundingandessence.

1. GeneralizedidentityOurtakeongeneralizedidentitybuildson—yetincertainkeyrespectsdeviates

from—frameworksputforwardbyCorreia(2010;2016),Rayo(2013),andDorr

(2016).Spacelimitationsprecludeafulldevelopmentandcomparison,sowecon-

centrateonlyon thoseelementsof the resulting theorymost relevant for later

purposes.

We(theauthors)disagreeovertheseprinciples,duetocertainbackgrounddisagreementsregard-ingthenatureandexistenceofpropertiesandfacts.Fortunately,forpresentpurposeswecanletthesedisagreementslie:neither(i)nor(ii)isassumedinthecourseofwhatfollows.(Butseetheendofsection3.2forsomeremarksonviewswhichendorse(i)or(ii).)

4 SeeCorreia(2010;2016),Dorr(2016),Linnebo(2014),andRayo(2013).AlsopertinentisthecriticaldiscussionofRayo’sdistinctivetheoryandapplicationsofthenotioninhisTheConstruc-tionofLogicalSpace:seeCameron(2014),Eklund(2014),Greco(2015),Hofweber(2014),Russell(2014),Sider(2014)andTurner(2015),andseeRayo(2014;2015b)forreplies.

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FollowingRayo,weexpressgeneralizedidentitywithanoperator,º,indexedby

zeroormorevariables,whichtakestwoopenorclosedsentencesandyieldsan-

other.Wherepandqareopenorclosedsentences,

(5) p ºq

shouldbereadas“Forittobethecasethatpisforittobethecasethatq”;and

whereFandGaremonadicpredicates,

(6) FxºxGx

shouldbereadas“ForathingtobeFisforittobeG”.5Moregenerally,astatement

oftheform

(7) pºx,y,…q

shouldbereadas“Forsomethingsx,y,…tobesuchthatpisforthemtobesuch

thatq”.6Wereadsuchstatementsasnotrequiringthattheflankingexpressions

betrue/satisfied:forinstance,itisintuitivelynoobjectionto(1)thattherearen’t

anybachelors.Forshort,wereadthemnon-factively.Wecalltype-(5)statements

factualidentities,andcalltype-(7)—andthereforetype-(6)—statementsgeneric

identities.

Althoughit’stemptingtoread“For…isfor___”statementsasindicatingatypeof

priorityofonesidetotheother,ºisinsteadtobereadaswhatRayoevocatively

callsa“no-differenceoperator”(2014,pp.518).Accordingly,wetakeittobehave

5 Hereandelsewhere,wefudgetypicaluse-mentionconventionswhennoconfusionshouldre-

sult,andallowcontexttosortoutwhetherweuse“identities”torefertostatementsaboutwhatisidenticaltowhatvs.theidentitiesoutthereintheworld(sotospeak).

6 Notethatinsuchastatement,thevariablesx,y,…neednotbindallfreevariablesinpandq:touseanexampleofDorr’s(2016,p.48),toassumeotherwiseprecludesquantifiedgeneralizedidentitystatementlike“$y(xisGermanºxxisfromy)”,whicharesurelysensible.Alsonotethatwefocusoncasesinwhichºbindsfirst-orderandsingularvariablestosimplify.Infactthereareexamplesplausiblyregimentedwithºinsteadbindinghigher-ordervariables(asin“Forittobepossiblethatpispfortheretobeaspatiotemporallyisolateduniverseinwhichp”;cf.Lewis1986)orpluralvariables(asin“Forxxtobecountablyinfiniteisxxforxxtoone-onecorrespondtothenaturalnumbers”);cf.Rayo(2013,p.146)andDorr(2016,pp.49ff.).Workingwiththisbroaderclassofgeneralizedidentitieswouldallowustoextendouraccountsofgroundingandessenceincorrespondinglybroaderways,butdoingsowouldcomplicatematterstoomuchhere.

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likethefamiliarno-differencepredicateforwhatwe’vecalledobjectualidentity

(a.k.a.=).Assuch,wetakeºtobereflexive,symmetric,andtransitive,i.e.thatthe

followingholdforanyp,q,andr,andanysequencevofzeroormorevariables:

Reflexivity: pºvp Symmetry: Ifpºvq,thenqºvp Transitivity: Ifpºvqandqºvr,thenpºvr

Thetruthofpºvqalsoallowsforrepresentationaldifferencesbetweenpandq.

Exceptinthetrivialreflexivecases,thereisasyntacticdifferencebetweenthem,

andperhapsfurtherdifferencesintheirsemanticvaluesorcognitiveuptake(e.g.

the‘guise’theircontentsarepresentedunder).Butsuchdifferencesnomoreun-

dermineageneralizedidentitythanthosebetween“Hesperus”and“Phosphorus”

underminethetruthof“Hesperus=Phosphorus”(cf.Dorr2016,pp.42-6;Rayo

2013,pp.52-4).

Wealsotakeitthatsome(interesting)restrictionofLeibniz’sLawforºmustbe

correct:

LL: IfpºvqandF,thenF[q//p]

whereF[q//p]resultsfromsentenceFbyreplacingoneormoreoccur-rencesofpbyq,withtheconditionthatnovariablethatisfreeinpºvqisboundinForF[q//p](seeDorr2016,p.49)

Wesay“somerestriction”,because,justlikeitsobjectualcounterpart,thelawfails

ifunderstoodunrestrictedly.Beliefascriptioncontextsprovideclearcounterex-

amples:grantedthatforathingtobeawatermoleculeisforittobeanH2Omol-

ecule,wecannotinferthatJohnbelievesthathisglassisfilledwithH2Omolecules

fromtheassumptionthathebelievesthathisglassisfilledwithwatermolecules.

Otherclearexamplesof ‘opaque’ linguisticcontextsarequotationcontexts,and

contextslike“thepropositionthat…isdistinctfromthepropositionthat___”and

“theconceptofbeing…isdistinctfromtheconceptofbeing___”onasufficiently

fine-grained conception of propositions and concepts, respectively (see Dorr

2016,pp.43-46and53-54). Determiningexactlywhich linguisticcontextsare

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opaqueforobjectualidentityisnoeasytask,andthesituationisnodifferentinthe

caseofgeneralizedidentity.Fortunately,wewon’tneedtoprovideadetaileddis-

cussionoftheissue,andwetrustthereaderwillagreewithusthatourapplica-

tionsofLLwillalwaysinvolvecontextsthatareclearcandidatestobetransparent

(oratleastnotclearcandidatestobeopaque).7

Aswithobjectual identity,generalizedidentityistightly linkedtometaphysical

necessity.Specifically(andignoringnon-monadiccases):

(8) IfFxºxGxthen£"x£(FxiffGx)(9) Ifp ºq, then£(p iffq)

Weareindeedhappytoholdthatthecontexts“£"x£(Fxiff...)”and“£(p iff...)”

aretransparentforgeneralizedidentity,andhencetoderivetheseprinciplesfrom

LL.Butwerejecttheconversesof(8)and(9):

(10) If£"x£(FxiffGx),thenFxºxGx(11) If £(piffq),thenpºq

Westraintohearanintuitivereadingofº(thattreatsitasano-differenceopera-

torakinto=,anyway)thatverifiesallinstancesof(10)and(11).GivenhowGood-

man(1955)defines“grue”and“bleen”,(10)hastheseeminglyfalseconsequence

thattobegreenistobeeithergrue-if-observed-no-later-than-3000-A.D.orbleen-

if-observed-afterward(seeDorr2016,pp.70-1fordiscussionofthisexampleina

related context). Given the standard assumption thatmathematical and logical

truthsholdnecessarily,(11)hastheseeminglyfalseconsequencethatforto2+2

toequal4isforeverythingtobeself-identical.8

7 Thankstoarefereeforpressingustoclarifyhere.Weshouldaddthatwealsobelievethatthe

context“…ºv___”isanarchetypicalexampleofatransparentcontext(cf.Dorribid.),andhencewearehappytoderivethesymmetryandtransitivityofºfromitsreflexivityusingLL,inthesamewaythatthesymmetryandtransitivityof=isstandardlyderivedfromitsreflexivityusingLeib-niz’sLawfor=.

8 Foranothercounterexample,seeCameron(2014,p.431).ThoughRayo(2013)endorses(10)and(11),welackthespacetoevaluatehismotivationanddefenseoftheseprincipleshere,whichreliesonsomehighlycontentiousstancesthatRayotakesaboute.g.thenatureofmodality,whichthosewhotheorizewithgeneralizedidentityperseneedn’tadopt(cf.Linnebo2014,fn.26).

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Here’soneadvantageoftreating(8)-(11)aslogicallyvalid,though:alogicforº

followsfromone’spreferredmodallogicfor£automatically.Sincewereject(10)

and(11),thingsaren’tsoeasyforus.Luckily,wecanfocusonanarrowerquestion

whereprogresshasbeenmade:whichtruthsoftypepºvqholdasamatterofthe

logicalformofpandq?

Correia(2016)provideswhatwetaketobeacorrectpartialanswerforthecase

of factual identity.9Startwitha standardpropositional languagewithnegation

(¬),conjunction(Ù),anddisjunction(Ú)leftprimitive,anddefinetheformulasas

usual.Correiaarguesfromsemanticconsiderationsthatthelogicaltruthsofthe

formpºq,wherepandqareformulasinthelanguagedefined,arejustthetheo-

remsofthesystemwecall“GI”,definedbythefollowingaxiomsandrules(struc-

turallyanalogousprinciplesarelistedhorizontally):

AxiomsofGI:A1. pº¬¬p

A2. pºpÙp A3. pºpÚp

A4. pÙqºqÙp A5. pÚqºqÚp

A6. pÙ(qÙr)º(pÙq)Ùr A7. pÚ(qÚr)º(pÚq)Úr

A8. ¬(pÙq)º¬pÚ¬q A9. ¬(pÚq)º¬pÙ¬q

A10. pÙ(qÚr)º(pÙq)Ú(pÙr)

RulesofGI:R1. pºq/qºp

R2. pºq,qºr/pºr

R3. pºq/pÙrºqÙr R4. pºq/pÚrºqÚr

9 Weareawarethatthecorrectlogicofgeneralizedidentityremainsamatterofcontroversy;

cf.Dorr’s(2016)detaileddiscussioninsections6,7and8forsomekeypointsofdispute.However,webelievethatouraccountofgroundingandessenceintermsofgeneralizedidentityiscompati-blewitharangeofdifferentviewsaboutthelogicofthenotion.Giventhepopularityofthetheoryofstructuredpropositionsanditsvirtuesforthepurposeofsemantictheorizing,itisbothnaturalandappropriatetowonderwhetherthisrangeofviewsincludestheviewthatfactualidentitiesareequivalenttoobjectualidentitiesbetweensuchpropositions.Inlinewithapreviousremark(see fn.3),wewanttoremainneutralonwhether factual identitiesareequivalent toobjectualidentitiesbetweenstructuredpropositionswhenthelatterareavailable.Butwewanttostressthatforaviewofthatkindtobeviable,itshouldnotinvolveatoofine-grainedconceptionofprop-ositions.Similarconsiderationsapplytotheoriesofstructuredproperties.

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Importantly,thedualofA10,

A11. pÚ(qÙr)º(pÚq)Ù(pÚr),

isn’tatheoremofGI,andarulefornegationcorrespondingtoR3andR4,

R5. pºq/¬pº¬q,

doesn’tpreservetheoremhoodinGI.(GivenA1-10andR1-4,addingA11turnsout

equivalenttoaddingR5:seeFine2016,pp.204.)

GI is neatly related to systems characterizing notions of equivalence more

coarselygrained than factual identity.AddingA11orR5yieldsAngell’s (1989)

first-degree system for analytic equivalence (adding A11 actually yields Fine’s

2016aaxiomatizationofthatsystem).Foranothercomparison,consider:

A12. pºpÙ(pÚq) A13. pºpÚ(pÙq)

AsAngell(1977)stresses,addingeitherA12orA13asaxiomstothe(1989)sys-

tem—whichareprovablyequivalentinGI,whichthissystemcontainsasafrag-

ment—yields the logicofmutual first-degreeentailmentofAnderson&Belnap

(1962;1963).AddingeitherA14orA15toAnderson&Belnap’s logicmakesº

behavelikeclassicallogicalequivalence:

A14. pºpÙ(qÚ¬q) A15. pºpÚ(qÙ¬q)

(A14andA15arealreadyequivalentinAngell’ssystem.)

Sinceourmaininteresthereareapplicationsofgeneralizedidentity—leavingonly

somuchspacetoinvestigateitstheory—we’llmakesome(wethinkreasonable)

assumptions.WeassumethatGIspecifieswhichfactualidentitiesholdasamatter

ofthetruth-functionallogicalformoftheirflankingexpressions,andthatR1-R4

aren’tonlyvalidity-(i.e.logicaltruth-)preserving,butalsotruth-preserving.We

alsoassumethatthegenericoperatorsºx,y,…logicallybehaveinmuchthesame

wayasthefactualoperatorº(whichisnottosaythatextraprinciples,specificto

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theseoperators,arenotrequired;seee.g.Dorr’s(2016,p.49)principleofAlpha-

beticVariation).Finally,wegrantourselvestheresourcestoquantify intonon-

nominalpositionsoccupiedbypredicationalandsententialexpressions,andthat

doingsoneedn’tbereadascovertlyrangingoveradomainofentities.10Yetwe

won’tneedthefullstrengthofalltheseclaimsinwhatfollows.Wewillindicate

exactlywhichpostulatesforgeneralizedidentitywetakeforgrantedandwhy,and

whywerejectcertainprinciplesvalidatedbylogicsforcoarsernotionsofequiva-

lence.

Finally,we adopt theworking hypothesis that generic and factual identity are

piecesofprimitive ideology.Cowling (2013) argues—convincingly,we think—

thatwhendetermininghowideologicallycommittedatheoryis,oneshouldcount

thekindsofprimitiveideologyitemploys,noteachpieceindividually.Thoughwe

finditintuitivelynaturaltogroup=,ºv,andºtogether,andthusthattakingthe

lattertwoasprimitiveisnomoreideologicallyprofligatethantakingthefirstas

primitivealone,weneedn’tpressthecasefurtherhere.11Ourprimarygoalisto

analyzetwoothernotionsthatmanytakeasdistinctkindsofprimitiveideology:

groundingandessence.Giventhatallthesenotionsmustbeaccountedforsome-

how,ouraccountleavesonenomoreideologicallyloadedthanbefore:eitherone

startswithatmostfourkinds(groundingandessence;objectualandnon-objec-

tualidentity)andendswithatmosttwo,oronedecreasesinstancesofprimitive

ideology (groundingandessence;objectual, generic, and factual identity)byat

leasttwo.12

10Fordefenseandapplicationsofthenon-substitutionaltakeonthisapparatusthatweprefer,

seee.g.Dunaway(2013),Prior(1971,ch.3),Rayo&Yablo(2001),Williamson(2003),andWright(2007);alsocf.Dorr(2016,pp.49-50)fordiscussionoftheseresourcesinthecontextofgeneral-izedidentity.

11There’salsoamoretheoreticalcasetobemade(buttoreiterate,itsprospectsdonotaffectourmainaim).Supposethatinteranalyzabilityamongaclusterofprimitivesisstrongevidencetheyfallunderthesamekind(cf.Cowling2013,p.3900forasomewhatsimilarview).Thenonemay reasonably argue the condition ismetby analyzing theobjectual “a =b”with “a” and “b”propernamesasthegeneric“xisaºxxisb”(cf.Rayo2013,p.69),analyzingthegeneric“pºx,y,…q”asthefactual“£"x"y…(pºq)”,andanalyzingthefactual“pºq”asthegeneric“xissuchthatpºxxissuchthatq”.

12Modulotheissueofwhetherthehigher-orderquantificationalresourceswehelpourselvestomustbetreatedasprimitiveideologyaswell.Ourownviewisthatoneoughttodosoregardless,butlackthespacetodefendthatviewhere(butseetheworkcitedinfn.10).

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2. EssenceintermsofgeneralizedidentityPhilosopherstraditionallyspeakofessencewhenspeakingofthevery‘nature’of

somephenomenon(or‘whatitis’)ratherthanhowthatphenomenon'incidental-

ly'happenstobe.LikeFine(1994)andmanyothers,wedenythatwhat'sessential

tophenomenon ismerelywhatholdsof itnecessarily; andmoregenerally,we

denythatthebroadlyAristoteliannotionofessenceatissuehereisanalyzablein

purelymodalterms(seee.g.Robertson&Atkins2016forageneraloverview).Yet

essenceissaidinmanyways;toproperlysetupouraccount,acouplepreliminar-

iesaboutitsvarietiesneedintroduction. Weconcentrateonessentialiststatementsfallingunderthreebroadcategories:

objectual,generic,andfactual(cf.Correia2006;2013,whouses“alethic”instead

of“factual”).Examplesinclude(12),(13),and(14)respectively:

(12) It’sessentialtoSocratestobeahuman.(13) It’sessentialtobeingahumantobearationalanimal.(14) It’sessentialtoSocrates’sbeingahumanthathebearationalanimal.

Tokeepmattersmanageable,amongthegenericstatements,wefocusonmonadic

caseslike(13)(theextensiontorelationalcasesisobvious),andinthissectionwe

leaveasideotheressentialiststatementsthatdon’tfitneatlyintothesethreeclas-

ses.Importantly,insection4wewillbroadentheperspectiveandconsidercollec-

tiveessentialiststatements,whichwillallowustohighlightapleasingsymmetry

betweentheconceptofessenceandtheconceptofgrounding.13

Itwillalsobeimportanttodistinguishbetweendescribingwhatsuch-and-suchis

infullvs.atleastinpart(cf.Dasgupta2015,pp.18-20).Atruthoffullessencemust

at least specify a necessary and sufficient condition for such-and-such. As it is

sometimesput,suchtruths‘individuate’theirtarget,andinthecaseofobjectual

13Weconcentrateonessentialiststatements(inEnglish)forsakeofperspicuityandease,though

strictlyspeakingourconcerniswithwhateveritisoutthereintheworld(sotospeak)thesestate-ments are equipped to report. To avoid distractions regarding how this more metaphysicallyloadedwayofspeakingistobeunderstood(e.g.doesitrequirecommitmenttoentitiesofsomesort,orwouldamoredeflationaryapproachsuffice?),weprefertospeakinthefirstway,butoneisfreetotranslateourdiscussionifonewishes.

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essencemustspecifyan‘individualessence’oftheobjectinquestion.Sounder-

stood,ouruseof“full”istolerantofmultipletruthsoffullessence:(13),forin-

stance,mightstatethefullessenceofbeingahumanevenifit’salsofullyessential

tobeinghumantohaveacertaingeneticmakeup/evolutionarylineage.Truthsof

partial essenceneed only specifywhat’snecessary for such-and-such. Sowhile

everytruthoffullessenceis(trivially)atruthofpartialessence,giventhatthere

canbehumansbesidesSocrates,(12)ischaritablyreadasatruthofthesecond

sortbutnotthefirst.

Preliminariesintow,againconsider(13).Weclaimthat(13)justisastatementof

generalizedidentity:ittrulycharacterizeswhatbeinghumanisinfull(generices-

sence)iffthisis, infact,whatbeinghuman is(genericidentity).Moregenerally

(again,westicktothemonadiccase):

FULL-GENERIC-ESSENCE BeingFiswhatitistobeGinfulliff:forathingto

beGisforittobeF(insymbols:GxºxFx).

WeofferFULL-GENERIC-ESSENCEasitselfageneralizedidentity,anduse“iff:”forthe

sakeofreadability.Wemakenocommitment,however,onwhethertheright-hand

sideofFULL-GENERIC-ESSENCEexpresseswhatphilosophers‘meantallalong’when

speakingoffullessence(recall,generalizedidentitytoleratesrepresentationaldif-

ferencesbetweentheflankingexpressions).Thatsaid,weofferitnotmerelyasa

stipulativedefinitionofsomespecial-purposetechnicalnotion.Afterall,FULL-GE-

NERIC-ESSENCEself-applies:itstruthrequiresthatititselfstatewhatfullessenceis

infull(inthetolerantsenseof“full”).Wetakeitthatphilosophersgraspatleast

someessentialtruthsaboutfullessence,andonthisbasiscangraspcertaincore

applications of the notion about which there’s widespread (albeit imperfect)

agreement.WethusaccepttheburdenofshowingthatFULL-GENERIC-ESSENCEcom-

portswiththesecoreapplicationstoahighdegree(andsimilarlyforfurthercom-

ponentsoftheaccounttocome).

Statementsofpartialessenceare,incontrast,statementsofgeneralizedidentity

thatarepartialinacertainsense:beingananimalispartofwhatbeinghumanis

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(genericessence)iffthisis,infact,whatbeingahumanpartiallyis(genericiden-

tity).Moregenerally:

PARTIAL-GENERIC-ESSENCE BeingF ispartiallywhatit istobeG iff:thereis

someHsuchthatforathingtobeGisforittobebothFandH(insymbols:GxºxFxÙHx).

Therelevantsenseofpartialidentityistiedtoconjunction.Suppose(13)istrue;

thenbeingrational,andbeingananimal,arewhatwe’llcallconjunctivepartsof

beingahuman.(Talkofconjunctiveparthoodshouldn’tbereadasconcerninga

properrelationofparttowhole,thoughwe’llcontinuetotalkloosely.)

WhybelievethatFULL/PARTIAL-GENERIC-ESSENCEaretrue?Inpartbecausetreating

themassuchshedslightonhowgroundingandessencerelateinwaysillustrated

later.Yettherearealsoconsiderationsspeakingfavorofthemintheirownright.

Oneisthatphilosophersroutinelycharacterizeessenceasifit’sintimatelylinked

tonon-objectualidentity,inatleasttwoways.First,“TobeF…”statementsare

oftenintroducedasgenericessencestatements,thenassumedtoatleastentailan

objectualidentityinvolvingthepropertybeingF(seee.g.King1998,p.157andfn.

26;Kment2014,p.153-5;Koslicki2012,pp.197-201;Wedgwood2007,pp.138-

9).Butthisrunsintodifficultieslikethoseweraisedattheonset.Whatisittobe

anon-self-instantiator?It’s,inpart,tobesomethingthatdoesn’tinstantiateitself.

Yetthere’snopropertybeinganon-self-instantiator(cf.Correia2006,pp.760-3

forthisandfurtherarguments).Treatingessenceasalsolinkedtonon-objectual

identityviaPARTIAL-GENERIC-ESSENCEevadestheproblemwhilestilllinking“Tobe

F…”tostatementsofidentity.

Second,whendiscussingobjectualessence,philosophers routinelyusephrases

like“athing’sessence”interchangeablywithphraseslike“theidentityofathing”

(seee.g.Fine1994,p.3;Lowe2008,p.37;Shalkowski2008,p.37).However,an

objectualreadingrendersthislinkmysterious.Tospeakofathing’sidentityinthe

senseofessenceisn’tmerelytoreportthetrivialitythatit’sself-identical(Lowe

ibid.),northattherearenon-trivialnecessaryandsufficientconditionsforbeing

identicaltoit:onlysomesuchconditionsdescribewhat’sessentialtothethingat

13

issue(asstraightforwardmodificationsofFine’sfamousexampleshavetaughtus:

1994,pp.4-5).Essenceandidentitylinktogetherperfectly,though,ifonebrings

innon-objectualnotionsofboth.FollowingCorreia(2006,pp.764-5)weaccount

forobjectualessenceintermsofgenericessence:

FULL-OBJECTUAL-ESSENCE BeingFiswhatxisinfulliff:beingFiswhatitis

tobex.

PARTIAL-OBJECTUAL-ESSENCE BeingF iswhatx is inpart iff:beingF ispartofwhatitistobex.

PARTIAL-OBJECTUAL-ESSENCEandPARTIAL-GENERIC-ESSENCEtogetheryieldanaccount

ofpartialobjectualessenceintermsofgeneralizedidentity:astatementlike(12)

trulydescribespartofwhatSocratesis(objectualessence)justincaseittrulyde-

scribeswhatbeingSocratespartiallyis(genericidentity).AndsimilarlyforFULL-

GENERIC-ESSENCEandFULL-OBJECTUAL-ESSENCE.

Theaccountcanalsobeextendedtofactualessence:

FULL-FACTUAL-ESSENCE Itsbeingthecasethatpiswhatitisforittobethe

casethatqinfulliff:forittobethecasethatqisforittobethecasethatp(insymbols:qºp).

PARTIAL-FACTUAL-ESSENCE Itsbeingthecasethatpisinpartwhatitisforit

tobethecasethatqiff:thereissomersuchthatforathingtobeqisforittobethecasethatbothpandr(insymbols:qºpÙr).

We’venotedafewcoreapplicationsofessenceouraccountaccommodates,but

thecaseforextensionaladequacyextendswellbeyondthese(wecontinuetofo-

cusonmonadicgenericessence,butwhatwesaybelowgeneralizes).

Toillustrate,compareouraccountwithoneproposedbyRayo(2013,pp.122-3),

whichtakesroughlytheformoftheabove,yettakesmutualnecessitationtobe

necessaryandsufficientforgeneralizedidentity.SincebeingFisnecessaryforbe-

ing a particular thing,a, iff being amutually necessitates beinga andbeingF,

Rayo’saccountentailsthatitisessentialtoathatitisFiffbeingFisnecessaryfor

beinga.Rayo’saccountisthusill-suitedtocapturethebroadlyAristoteliannotion

14

ofobjectualessenceweaimtocapture(as,again,Fine’sfamouscaseshavetaught

us).14Moreover,ifmutualnecessitationsufficedforgenericidentity,thefollowing

woulduniversallyhold:

(15) FxºxFxÙ(FxÚGx)

(16) FxºxFxÙ(GxÚ¬Gx)

ThesearegenericversionsofprinciplesA12andA14,respectively,mentionedin

section1.WedeniedA12andA14thestatusoflogicalvalidities,anddothesame

with(15)and(16):clearly,tobeanumberisn’tthesameasbeinganumberand

either-a-number-or-blue,norisitthesameasbeinganumberandeither-blue-or-

not-blue(recallourearlierdiscussionof“grue”and“bleen”).Werejectthatmu-

tual necessitation suffices for generic identity, evading seemingly false conse-

quences that (15)–(16)wouldhave if fed throughPARTIAL-GENERIC-ESSENCE: that

beinganumberisessentiallylinkedtobeingblue.15

PARTIAL-GENERIC-ESSENCEalsolooksextensionallyadequateincaseswherebeingF

isagenus(i.e.beingananimal),withbeingGaspeciesofthatgenus(i.e.being

human).Inthesecases,adifferentiaofthegenus(i.e.beingrational)servesasthe

‘supplementary’HinPARTIAL-GENERIC-ESSENCE,andgenusanddifferentiaturnout

essentialtothespecies,asdesired.Butothercasesmayraisedoubts.Forinstance,

ifhavingamassispartofwhatitistobeanapple,it’shardtoseewhichsupple-

mentaryHcouldbesuchthattobeanappleistohaveamassandtobeH.

Thoughthisobjectionisnatural,wecanofferaremarkablysimpleproofthatthe

biconditionalcorrespondingtoPARTIAL-GENERIC-ESSENCEiscorrect.Let“Fx⊆xGx”

abbreviate“BeingFispartofwhatitistobeG”(topreviewnotationintroduced

later).Theproofreliesonthefollowinggeneralprinciplesaboutgenericidentity,

partialgenericessence,andtheirinteraction:

14Rayoiswellawareofthis(2013,p.122).Butlikewesaidinfn.8,certaincontentiousthesesserveasbackdropforhisdiscussionthatwecannotevaluatehere(butcf.Rayo2016,pp.17-21forfurtherdiscussionofhisviewsonessence,whichdifferssomewhatfromhis2013).

15Theaccountofgroundingthatemergesinsection3providesafurtherwaytoarguethatouraccountevadestheseconsequencesofRayo’saccount:seetheendofsection4.

15

(i) ºxissymmetric

(ii) FxºxFxÙFx idempotenceofÙ

(iii) Fx⊆xGxÙFx Ù-introI

(iv) Fx⊆xFxÙGx Ù-introII

(v) IfFx⊆xGx,thenFxÙHx⊆xGxÙHx Ù-adjunctionfor⊆

(vi) IfFx⊆xGxandGxºxHx,thenFx⊆xHx substitution

(vii) IfFx⊆xGx,andGx⊆xFx,thenFxºxGx antisymmetry

Andhere’stheproof:

Left-to-right.SupposeFx⊆xGx.Thenby(v),FxÙGx⊆xGxÙGx.By(i),

(ii)and(vi),itfollowsthatFxÙGx⊆xGx.Fromthis,plus(iii)and(vii),

inferthatGxºxFxÙGx.Hence,forsomeH,GxºxFxÙHx.

Right-to-left.Suppose foragivenH thatGxºxFxÙHx.Thenby(i), it

followsthatFxÙHxºxGx.By(iv)and(vi),inferFx⊆xGx.

Theproofisremarkableinitssimplicity,butalso(wetakeit)bytheplausibilityof

the principles it assumes. (i) and (ii) are compulsory principles about generic

identity,andcounterpartsofprinciplesaboutfactualidentityadvocatedearlier.

(iii)-(v)areanalytic-soundingprinciplesaboutpartialgenericessence.(vi)isan

instanceofLeibniz’sLawforº(seesection1).Weassumeineffectthatthecontext

“Fx⊆x…”istransparentforgenericidentity(surely,forinstance,ifbeinganani-

malispartofwhatitistobeahumanbeing,thengiventhattobeahumanbeing

istobeaHomosapiens,beingananimalispartofwhatitistobeaHomosapiens).

And(vii) lookscompellingprovidedthat“partial” in“partialessence” isunder-

stoodintheliberalsensediscussedbefore.

Theabovereasoningalsogivesadirectreplytotheobjectionputforwardabove.

TheobjectionwasthatthereappearstobenoHsuchthattobeanappleistohave

amassandtohaveH(althoughofcoursetheworrygeneralizes).Theleft-to-right

directionoftheproofaboveprovidesuswithsuchafeature:beinganapple.The

16

objectioninitiallylookedcompelling,wethink,duetoassumingthatHmustbe

properconjunctivepartofbeinganapple.Asshouldbeplainatthispoint,nosuch

readingofPARTIAL-GENERIC-ESSENCEisintended.16

Butwhatoftheintimatelinkwidelythoughttoholdbetweenessenceand ‘real

definition’?Ouraccountentailsthatpartialgenericessenceisreflexive(sincefor

athingtobeFisforittobeFÙFby(ii)fromtheproofabove),andthatfullgeneric

essenceisreflexiveandsymmetric(sinceºxisreflexiveandsymmetric).Onone

hand,theseconsequencesseemundeniable.Ifanythingisessentialtobeinghu-

man,itisbeinghuman;andwefindithardtofathomwhybeinghumanwouldfail

tobewhatit istobearationalanimal, ifoneacceptsthereverse.Ontheother

hand,onemightcomplainthatessentialiststatementsnolongersupplyrealdefi-

nitions,sincerealdefinitions—atleastgivenatraditionalconceptionthatmodels

themafterreductiveanalyses—cannotbecircularineitherway.

Thereareinfacttwoobjectionstoconsider:oneturnsonamerelyverbalmatter,

whiletheotherissubstantive.Butfirstofall,whatisarealdefinition?Weadopt

themoreor lessstandardviewthat takes it tobeatruthofacertainsort,one

that—inthecaseof(13)—characterizesnotwhattheword“human”happensto

meaninEnglish(whichisthepurviewofanominaldefinition),butratherwhat

beingahumanis ‘initself’(seee.g.Fine1994;Kment2014,pp.158-9;Koslicki

2012,pp.190,197-201;Lowe2012,pp.104-5;Rosen2010,p.122;2015).Onour

view,onlysometrue“TobeFis…”statementsexpressrealdefinitions.Anddis-

tinguishingthosethatdoarguablyonlyrequiresappealingtonotionsthatarean-

alyzableintermsofgeneralizedidentity,orthatareplainlynotessentialist(e.g.

thetruth-functionalconnectives).Sincerealdefinitionsareexpressedbyaproper

subsetoftrueessentialiststatements,wehandlethemoresubstantivechallenge:

tolinkessenceandrealdefinitioninanintimateway.17Butsupposeoneinsistson

16Tobeclear:wearenotdenyingthatconjunctiveparthoodobeyssomethingliketheclassical

mereological principle ofweak supplementation (thanks to a referee for pressing us to clarifyhere).Rather,whatwesayhereisthatit ishardtoseewhatthesupplementalconjunctivepartwouldbeincasesliketheoneathand,whichisofcoursecompatiblewiththereinfactbeingone.Whetherconjunctiveparthoodobeysthis(orsomeother)supplementationprincipleisasubstan-tivequestionthatwehopetoaddressinfuturework.

17We’renotdenyingthatphilosopherscan(anddo)communicaterealdefinitionsusingstate-mentsmakingnoexplicitmentionofessence(e.g.necessitateduniversalbiconditionals),northat

17

amoreintimatelink:i.e.thateverytruthofessencemustexpressarealdefinition,

ifonlyapartialone.Wedemur,butthe‘dispute’herestrikesusasmerelyverbal.

Thosewhoinsistonusing“realdefinition”inthisfashioncouldreadouraccount

asimplicitlydefiningthenotionofproto-essence,andthenletusanalyze(what

theycall)thenotionofessenceinafashionexactlyanalogoustowhatwesuggest

below.

Now,thereisnoconsensus—andconsiderableimprecision—aboutwhatkindof

trutharealdefinitionis,andspecificallyoverwhethera‘reductiveanalysis’type

modelistheonlyviableone(e.g.Rosenarguesthatrecursivedefinitionscanbe

realdefinitions:2015,pp.196-7).Wecertainlydon’twishtotakeastanceonthe

matterhere.Norwillweattempttosurveyhowouraccountstacksuptocertain

morepreciseproposalsintheliterature(thoughwehopetodosointhefuture).

Ourgoalhereismodest:tochallengetheimpressionthatthereissomeobstacle

inprinciple,andontheassumptionthatrealdefinitionsmustbenon-circular.

Startwithmerelypartialrealdefinitionandlet(12)beourstockexample.Ifour

account iscorrect, thetruthof(12)requiresthatbeinghumanisaconjunctive

partofbeingSocrates.Oneobviouswaytogo is to furtherrequireof(12)that

beingSocratesisn’titselfaconjunctivepartofbeinghuman.Sinceconjunctivepar-

thoodisantisymmetric,thisamountstorequiringthatbeingSocratesandbeing

humannotbegenericallyidentical—andtheyclearlyaren’t.Moregenerally,re-

quiringthatconjunctiveparthoodholdasymmetricallyinacaseofmerelypartial

realdefinitiongivessubstancetotheideathatthedefinienscannotitselfbe‘built

up’fromthedefiniendum;andtotheideathatthelattercannotbeapartofthe

essenceoftheformer,giventhatnotbeingaconjunctivepartofsuch-and-such

entailsnotbeingpartofitsessence.(Anevenmoredemandingconditionalong

theselinesusesthenotionofdisjunctiveparthoodthatweanalyzeintermsofgen-

philosophersuse“realdefinition”torefertowhateverthedefiniensphrasecontributestothetruthoftherelevantsortofessentialiststatement,ratherthantothetruthasawhole.Theconditionsweconsiderforanessentialiststatementtoexpress(whatwecall)arealdefinitioncanbetweakedinobviouswaystocomportwiththesebroaderusesofthephrase.

18

eralizedidentityinsection3,andrequiresthatthedefiniendumbeneitheracon-

junctivepart,noradisjunctivepart,noreitheraconjunctiveordisjunctivepartof

anyconjunctiveordisjunctivepart,or…ofthedefiniens).

Fullrealdefinition—let(13)bethestockexample—requiresseparatetreatment.

The firstoptionwillnotdo,ofcourse,since(13) isageneric identity,andthus

beinghumanisaconjunctivepartofbeingarationalanimalandviceversa.Nor

canwesaythat(13)expressesarealdefinitiononlyifbeinghumanisgrounded

inbeingarationalanimal,giventhestandardassumptionthatnothinggrounds

itself.Thisobservationhasledsometodoubtthatgenericidentitycouldbeused

tostatewhatafullrealdefinitionis,giventhatthelatterhasabuilt-inpriority-

indicatingdirectionality(cf.Cameron2014,pp.429;Fine2015,pp.308).Buteven

ifthetwonotionsshouldnotbeidentified(whichwereadilyconcede),itmaywell

bethatthesecondcanbeanalyzedpartiallyintermsofthefirst,perhapswiththe

aidoffurthernon-essentialistnotions.

Oneapproach—afairlytraditionalone—stemsfromthethoughtthata“TobeFis

tobeG”statementexpressesarealdefinitiononly if it takesacertain form.At

minimum,thedefiniendumphrasemustbedifferentfromtheoneexpressingthe

definiens;butsincethiswouldnotruleoutpathologicalcaseslike“TobeFistobe

bothFandF”,moremustbesaid.Often,furtherconstraintsareplacedonthecon-

stituentexpressionsfromwhichthedefiniensexpressionisbuilt.Wecannotap-

praiseeverysuchconstraintthathasbeensuggestedhere(seee.g.King1998and

Koslicki2012forjustacouple).Butonecanimaginevariousconstraintsofthis

sortthatareamenabletoouraccount.Oneistorequirethatwhateverisexpressed

bysomeproperconstituentofthedefiniensphrasenothavewhatisexpressedby

thedefiniendumphraseasaconjunctivepart.Notonlydoes(13)seemtomeet

thistest,butasbeforethisproposalgivessubstancetoideathatthedefinienscan-

notitselfbe‘builtup’fromthedefiniendum,andthatthelattercannotbepartof

theessenceoftheformer.(Althoughagain,perhapsthemoredemandingcondi-

tionwementionedbeforeispreferable.)

Infloatingthesetentativeproposalsabouthowtosiftoutessentialiststatements

thatexpressrealdefinitionsfromthosethatdonot,letusbeclear:wehavenot

19

surveyedwhethertheycomportwithallthenebulousways“realdefinition”gets

usedinphilosophicalparlance,andtherearenodoubtotherviableproposalsto

explorethanthetwooffered.18Whatwehaveshownisthatourcriticmustexplain

whytheseproposals(orsomeextensionthereof)arenotuptothetask.

Ifoneagreesthattheaccountofessencewe’veofferedisextensionallyadequate,

onemightfinallywonderwhetheritissuitably‘reductive’.Thecaseismixed.On

onehand,somewhopartakein“TobeFis…”talkareskepticalofbroadlyAristo-

teliannotionsofessence(cf.Rayo2013,p.5;2015a).Ontheother,othersattempt-

ingtocommunicatetherelevantnotionsofessencetreat“TobeFis…”talkasa

representativeformofexpression.Ourownopinionsdivergeontheissue;butthe

importantpointisthatevenanon-reductiveapproachisfaithfultoouraims.Ide-

ologicaleconomyispreserved,asweultimatelyanalyzegroundingwith“TobeF

is…”talk:ifsuchtalkisessentialist,onestilltradestwoprimitiveideologicalkinds

(groundingandessence)forone.Andeventhen,analyzinggroundingintermsof

suchtalkisanoteworthywaytounifythetwoindeed.Solet’ssetasidewhether

suchtalkisessentialist,andturntothefruitsofunificationwecangainfromit.

3. GroundingintermsofgeneralizedidentityPhilosopherstraditionallyspeakofgroundingwhentheysaythatsuch-and-such

insomesense‘makes’or‘bringsabout’so-and-so,inaconstitutiveratherthana

causalsensethatisunanalyzableinpurelymodalterms(seee.g.Bliss&Trogdon

2014forageneraloverview).Beginwithfactualgrounding,asit’smorefamiliar

(genericgrounding,whichislessfamiliar,isleftforlater).Weexpressthenotion

withstatementslike

Itsbeingthecasethatp1,p2,…makesitthecasethatq;

wewritethemwithFine’s(2012)familiar‘

20

Forsakeofease,wewilloftenspeak in ‘predicationalist’ termsas ifgrounding

werearelationbetween factsreferred toby theseGreek letters,butmerelyas

shorthandforthe‘operationalist’readingabove(cf.Correia2010,pp.253-254).

Weanalyzedpartialessence,recall,intermsofconjunctiveparthood,whichwas

definedintermsofgeneralizedidentity.Wenowproposetoanalyzegroundingin

termsofanotherparthoodrelation—disjunctiveparthood—whichweanalyzein

ananalogousfashion,invokingdisjunctioninsteadofconjunction.Saythatpisa

disjunctivepartofq(insymbols:p⊑∨q)iff:forsomer,forqtoholdisforp Ú rto

hold.(So,forinstance,theball’sbeingredisadisjunctivepartofitsbeingeither-

red-or-round.) Strictly speaking,we analyze grounding in terms of disjunctive

parthood,togetherwitha‘hybrid’notionwhichisitselfdefinedintermsofdis-

junctiveparthood.Saythatpisaconjunctivepartofadisjunctivepartofq(insym-

bols:p⊑∧∨q)iff:there’ssomer suchthat pÙr⊑∨q.(So,forinstance,theball’s

being red stands in this hybrid relation to being either both-red-and-roundor

blue.)

Weclaimthatacollectionoffactsp1,p2,…groundsanotherfactq iffconjoiningp1,

p2,…givesyouadisjunctivepartofq (thuseachofp1,p2,…isaconjunctivepart

ofadisjunctivepartofq),yetthere’snowayofconjoiningfactswithqthatgives

youadisjunctivepartofanyofp1,p2,…(thusq isnotaconjunctivepartofany

disjunctivepartofthefactsinthatcollection).Insymbols:

FACTUAL-GROUNDING p1,p2,…<qiff:(i)p1Ùp2Ù…⊑∨q;and(ii)nei-

therq⊑∧∨p1,norq⊑∧∨p2,nor…

Aconcreteexampletoillustrate:takethehighlyplausibleclaimthata’sbeingred

(p1)anda’sbeinground(p2)jointlygroundtheirconjunction(q).Sinceforqto

holdisforqÚqtohold(byaxiomA3ofthesystemGIfromsection1),thefirst

conditionismet,asdesired.Andsolongasqisnotitselfaconjunctivepartofa

disjunctivepartofeitherp1andp2inturn—anassumptionthat’seminentlyrea-

sonable,butthatweputonfirmerfootingshortly—thesecondconditionismet.

Hence,FACTUAL-GROUNDINGgetstherightresult.

21

It’s not surprising that FACTUAL-GROUNDING handles this ‘tailor-made’ example.

What’ssurprisingisthatthere’sgoodreasontobelieveithandleseventheless

obviouscases.Butfirst,acoupleclarifications.

Firstclarification:notethatFACTUAL-GROUNDINGemploysthenon-factivenotionof

generalizedidentity.Thusitcharacterizesanon-factivenotionofgrounding:it’s

notrequiredthatp1,p2,…,andq allholdforp1,p2,…togroundq (cf.Fine2012,

pp.48-50).Afactiveanaloguecanbewroughtbyaddingafactivitycondition:i.e.,

thatp1,p2,…allhold.(We’llcontinuetoworkwiththesimplernon-factiveaccount

above,althoughthefollowingdiscussionwon’tturnonit.)

Secondclarification:giventhatgeneralizedidentityissymmetricandtransitive,

andthattherulesR3andR4aretruth-preserving,FACTUAL-GROUNDINGentailsthat

ground-theoreticstatusispreservedunderfactualidentity.Moreprecisely:

(17) a. Ifp,p1,p2…groundqandpºp*,thenp*,p1,p2,…groundq. b. Ifp1,p2,…groundqandqºq*,thenp1,p2,…groundq*.

FACTUAL-GROUNDINGthuscapturesaworldlyconceptionofgroundinginthesense

ofCorreia(2010,pp.256-259)—albeitwiththemerelycosmeticdifferencethat

Correiathereusestheterm“factualequivalence”,andthemoresubstantivedif-

ferencethatwehaveadoptedthesuccessorlogicofCorreia(2016),i.e.thesystem

GI. This substantially impacts how FACTUAL-GROUNDING should be understood,

whichisclearlyvisibleinlogicalcases.pisarguablyfactuallyidenticaltopÚp,to

pÙp,andto¬¬p,differingnotinthewaytheworldisrepresentedasbeing,but

ratherhowtheyrepresenttheworldasbeingthatway(asFineputsit:forthcom-

ing, pp. 10-1). Yet if grounding is irreflexive, FACTUAL-GROUNDING entails that p

doesn’tgroundthese ‘other’ facts. Incontrast,aconceptionofgrounding that’s

representational (“conceptual” is the term used in Correia 2010) requires that

ground-theoreticstatusonlybepreservedundersomemorerepresentation-sen-

sitivenotionofequivalence,whichmaydistinguishpfrompÚp,pÙp,and¬¬p.

ThatFACTUAL-GROUNDINGappliesonlytoworldlygroundingdoesn’tdiminishitsin-

terest,wethink,astheprimarymetaphysicalinterestingroundingconcernshow

22

itstructurestheworlditself,independentlyofhowwethinkortalkaboutit(cf.

Correia2010,pp.258-9;Krämer&Roski2015,pp.60-1). Seeninthislight,FACTUAL-GROUNDINGisinasensenotcompletelynew:thesystem

forthelogicofworldlygroundingthatCorreia(2010)developshasatheorem—

hecallsittheReductionTheorem—thatisjustafactivity-requiringanalogueofthe

biconditionalcorrespondingtoFACTUAL-GROUNDING.Yetheisn’thappywiththisre-

sult.Correiaworriesthatthefirstnecessaryconditionimposedongroundingby

FACTUAL-GROUNDING—embodiedinwhathecallstheReductionAxiom—entailsthat

whatever is grounded “has a disjunctive nature”, and that “grounding always

arisesviadisjunction”,whichhetakestobeimplausibleingeneral:“althoughone

canmaintain[…]thatthefactthat{Socrates}existsisgroundedinthefactthat

Socratesexists,theviewthattheformerfactisthedisjunctionofthelatterfact

andanotherfactisimplausible”(ibid.,p.272).

Thereareanumberofworriesthatcouldbelurkinginthebackgroundhere.And

evensettingthoseaside,totheextentonehasintuitionsaboutwhatis(andisn’t)

a ‘disjunctivepart’ or a ‘conjunctivepart of adisjunctivepart’ ofwhat, they’re

weakindeed;thusit’shardtoseehowtomotivateouraccount.Let’schangetack

bytakinganindirectroutefromgroundingtogeneralizedidentity:byanalyzing

thefirstintermsofthesecondbymeansofamoreintuitivenotionwecallsub-

sumption.Bymakinguseofsubsumption—whichmanywillfindeasiertograsp,

andalreadyplaysanotableroleinrecentliteratureongrounding—wecanmore

easilyfendoffworrieswithouraccount,andalsoprovidereasonstoacceptit.

3.1 ThenotionofsubsumptionSubsumptioncomesinagenericaswellasinafactualvariant—thelatterwillbe

usedforfactualgrounding,andtheformerforagenericnotionofgroundingthat

weintroducelater.Althoughgenericgroundingislessfamiliar,genericsubsump-

tionisintuitivelyeasiertograspandsowefocusonitfirst.

Tostartwith,considerabroadernotionthatsubsumes(intheordinarysenseof

theterm)subsumption.Supposethattobeahumanisbearationalanimal.Then

wetakeitthatthere’sanintuitivelynaturalsenseinwhichonecouldtheninfer

23

thatbeinghumanisaway(ormanner)ofbeingananimal—adifferentwaythan,

say,beingacat.Thislinkbetweenconjunctiveparthoodand“isawayof”talkis

notincidental,asitreadilygeneralizesbeyondspecies-genuscases:onecansay,

forinstance,thatbeingSocratesisawayofbeingahuman(ifbeinghumanisa

conjunctivepartofbeingSocrates),thatbeingredandroundisawayofbeingred,

andsoon.

Importantly,thisuseof“isawayof”talkreadilycontrastswithcausalreadingsof

this idiom—expressedwhenonesays, for instance, that travelingwestwardon

theHumeHighwayisawayofgettingtoMelbourne.Travelingwestwardonthe

HumeHighwaycould—inthemetaphysicalsense—havefailedtobeawayofget-

ting toMelbourne,while being red and round could not—in this sense—have

failedtobeawayofbeingred.

Wetakeanycaseofsubsumption,likeanycaseofconjunctiveparthood,tobea

caseofbeing-a-way-ofinthenon-causalsenseintendedhere.Instancesofthede-

terminate-determinablerelationyieldarchetypicalcasesofsubsumption:ifbeing

F(e.g.beingred)isadeterminateofbeingG(e.g.beingcolored),thenwetakeFto

besubsumedbyG,and(thus)takebeingFtobeawayforathingtobeG.None-

theless,whatholdsforthedeterminate-determinablerelationneednotholdfor

subsumptionmore generally. First, a determinable property is always distinct

fromeachdeterminate(by“distinct”,wemeannon-identicalinthesenseofgen-

eralizedidentity):beingcolored,e.g.,isdistinctfrombeingred.Yetoneshouldnot

takethisasevidencethatsubsumptionisirreflexive,sincebeingF(trivially)sub-

sumesbeingF.Second,thedeterminatesofadeterminablepropertyaretypically

manyinnumber,andsomeofthemmaywellbemutuallyincompatible:thusbeing

redandbeingbluearebothsubsumedbybeingcolored,andnosinglethingcould

beboth.Yet,again,oneshouldnottakethisasevidencethattherewillalwaysbe

severalincompatiblewayssubsumedbybeingso-and-so,providedthatthereisat

leastone.Forinstance,wetakeitthatbeingSocratesissubsumedbybeingamem-

berof{Socrates},yetpresumablythereisnofurther,incompatiblewayofbeinga

memberof{Socrates}thanbeingSocrates.

Wealsodon’t identifysubsumptionwithbeing-a-way-of itself, as the former is

24

systematicallyconnectedtogroundinginwaysthatthelatterisn’t.Itisnatural,

andstandard,toassumethatwhatservesasagroundmustbewhollyrelevant(or

containnopartthatisirrelevant)towhatitgrounds(cf.Dasgupta2014,pp.4-5;

Litland2016,p.534).Thisisnotalwaysthecaseforbeing-a-way-of: it isclear

enoughthatbeingredandroundisnotwhollyrelevanttobeingred.Yetdetermi-

nate-determinableconnectionssatisfythisconstraint:athing’sbeingredisnot

onlyawayofbeingcolored,butalsowhollyrelevanttobeingcolored.Asweun-

derstandit,“subsumption”standsforlinksofbeing-a-way-ofthatmeetthisrele-

vanceconstraint.

Whatwesaidaboutgenericsubsumptionwealsowanttosay,mutatismutandis,

aboutthefactualvariety.Examplesoflinkoffactualsubsumptionareeasilyseen

onacase-by-casebasis(e.g.viatheplausiblethoughtthattheball’sbeingeither

redorbluesubsumesitsbeingred),andthankstotheplausibleprinciplethatif

beingGsubsumesbeingF,thenforanyx,x’sbeingGsubsumesx’sbeingF.

Forreasonsthatwillsoonbecomeclear,weregimentstatementsofsubsumption

withFine’s(2012)“≤”notationforweakfullgrounding,andembellishitwitha

subscriptwhenthestatementisgeneric.Thuswewritethegenericsubsumption

statement“Beingredissubsumedbybeingcolored”as“xisred≤xxiscolored”

(andsimilarlyfornon-monadiccases),andwritestatementsoffactualsubsump-

tionoftheform

Itsbeingthecasethatp issubsumedbyitsbeingthecasethatq

as

p≤q.

3.2 GroundingintermsofgeneralizedidentityviasubsumptionSowhat,exactly,issubsumption?Andwhatbearingdoesithaveonouraccount

ofwhatgroundingis?Tothefirstquestion,wewillarguethatsubsumptionisthe

converseofdisjunctiveparthood:such-and-such’sbeingawhollyrelevantwayof

beingthus-and-soisnothingmorethantheformerbeingadisjunctivepartofthe

25

latter.Andtothesecondquestion,wewillarguethatgroundingcanbeanalyzed

intermsofsubsumptioninamannerexactlyanalogoustohowweproposedto

analyzegroundingintermsofdisjunctiveparthood.Let’staketheseclaimsinre-

verseorder,andasbeforefocusonfactualgrounding(wewillintroduceandana-

lyzethegenericnotioninduecourse).

Wespokeearlierof conjunctivepartsofadisjunctivepart of such-and-such. In

analogousway,itisnaturaltospeakofconjunctivepartsofwhat’ssubsumedby

such-and-such.Forexample:giventhatbeingananimalisaconjunctivepartof

beingahuman,whichissubsumedbybeingalivingorganism,beingananimal

bearsthisrelationtobeingalivingorganism.Saythatpisquasi-subsumedbyq(in

symbols:p≲q)iffthereissomersuchthatp∧r≤q.Replacing⊑∨with≤inour

originalaccountofgrounding,and⊑∧∨with≲,deliversthefollowingsubsump-

tion-theoreticanalogue:

(18) p1,p2,…<qiff: (i) p1Ùp2Ù…≤q;and (ii)neitherq≲p1,norq≲p2,nor…

We arenot the first to offer something akin to (i) as a requirement on factual

grounding:Litland (2013,pp.23-25) similarly takesp1,p2,… togroundq only

whenp1,p2,…“collectivelyconstituteaway for [q] tobe thecase”,and in that

sense“[make]adifferencetohow[q]obtains”,andusesthisconditiontoaddress

putativecounterexamplestothetransitivityofgroundingduetoSchaffer(2012).

Theideathat(ii)isafurtherrequirementcanbesupportedasfollows.Suppose

forreductiothatp<q,andyetq≲p(caseswithseveralgroundscanbetreated

inthesameway).Thenq∧r≤pforsomegivenr,andthereforeq∧r<q(wehere

appealtoaplausibleprinciple:ifs1≤s2ands2<s3,thens1<s3).Which—wetake

it—couldneverbe:conjunctionsdon’tgroundanyoftheirconjuncts.

Moreover,therearestrikingsimilaritiesbetween(18)andprinciplesdefendedin

theliteraturethat linkgroundingtonotionsinthevicinityofsubsumption.For

instance,whenFine(2012,pp.51-54)introducestheweakfullgroundsofafact,

hecharacterizesthemwitha“For…isfor__”idiomthatallows“__”tobeplural,

andthatdifferfromthefact’sstrictfullgroundsasthey“mayalsomoveusside-

waysintheexplanatoryhierarchy”.Withthisnotion,Finetentativelyproposesa

26

definitionofstrictfullgroundingthatisanalogoustoour(18):

(19) p1,p2,…

27

worthtakingseriously.Soreturnnowtothefirstquestion:whatissubsumption?

Ourproposal is that it’ssimplytheconverseofdisjunctiveparthood. Ifso, then

(18)deliversexactlytheaccountofgroundingintermsofdisjunctiveparthood

thatwestartedwith.Moreover,onecanmotivateitsextensionaladequacybyre-

flectingonintuitionsaboutwhatsubsumeswhat(andwhatdoesn’t).Recallour

exampleofa’sbeingred(p1)anda’sbeinground(p2),whichgroundtheircon-

junction(q).Earlier,wesimplyassertedthat it is ‘eminentlyreasonable’ tosay

thatqisaconjunctivepartofadisjunctivepartofneitherp1norp2,butnowwe

cangiveitintuitivelyfirmerbacking:forqandsomethingelsetoholdisn’tawholly

relevantwayforp1tohold(sinceapartofq,namelya’sbeinground,isintuitively

irrelevanttoa’sbeingred),andsimilarlyforp2.

Butwhyacceptthatsubsumptionistheconverseofdisjunctiveparthood?Since

disjunctionsplausiblysubsumetheirdisjuncts,itseemssafetosaythatifpisa

disjunctivepartofq,thenqsubsumesp.Butwhyacceptthereverse?Itturnsout

thatacompellingproofforthisbiconditionalcanbegiven—onestrikinglysimilar

totheproofprovidedinsection2thatpartialessenceiscoextensivewithconjunc-

tiveparthood.Itreliesongeneralprinciplesaboutfactualidentity,subsumption,

andtheirinteractionwhicharestructurallyanalogoustothoseusedintheearlier

proofandjustasplausible:

(i) ºissymmetric

(ii) pºp∨p idempotenceof∨

(iii) p≤q∨p ∨-introI

(iv) p≤p∨q ∨-introII

(v) Ifp≤q,thenp∨r≤q∨r ∨-adjunctionfor≤

(vi) Ifp≤qandqºr,thenp≤r substitution

(vii) Ifp≤qandq≤p,thenpºq antisymmetry

Andhere’stheproof:

28

Left-to-right.Supposep≤q.Thenby(v),p∨q≤q∨q.By(i),(ii),and

(vi),itfollowsthatp∨q≤q.Fromthis,plus(iii)and(vii),itfollowsthat

qºp∨q.Hence,thereissomersuchthatqºp∨r.

Right-to-left.Supposethatqºp∨r forsomer.Thenby(i), itfollows

thatp∨rºq.Henceby(iv)and(vi),itfollowsthatp≤q.

Alongwithprovingthatpisadisjunctivepartofqiffqsubsumesp(whichisgood,

albeitdefeasible,reasontobelievetheoneistheother),aswiththeearlierproof,

theleft-to-rightdirectionofthepresentonehelpsdispelworrieswiththeaccount

ofgroundingwegavedirectlyintermsofgeneralizedidentityearlier.

Correia’s(2010)worrythathisReductionAxiom—whichrecordsthefirstneces-

saryconditionimposedupongroundingbyFACTUAL-GROUNDING—entailsthatifa

factpgroundsafactq,thenqisthedisjunctionofpandanotherfactr,while,on

thefaceofit,manygroundedfactsaren’tdisjunctiveinthatway.Yettheleft-to-

rightdirectionoftheproofaboveprovidesuswithsuchafact:theimproperdis-

junctivepartofq,namelyqitself.Thus,theworryturnsouttobeunfounded.

SimilarcommentsapplytoanobjectionabouthowwehandlewhatFine(2015)

callsgenericgrounding.Wehaveinmindthenotionexpressedwhenonesaysthat

somethingsbeingsuch-and-suchawaymakesthembesuch-and-suchotherway,

understoodnon-factively(e.g.whenit’ssaidthatathing’sbeingredmakesitbe

colored,withoutimplyingthatanythingisinfactred).AddingsubscriptstoFine’s

“

29

worrythatitrenderswhat’sgenericallygroundeddisjunctiveinsomeextended,

equallyproblematicsense.Suppose,forinstance,thatathing’sbeinginacertain

neurophysiological statemakes it be conscious.Given GENERIC-GROUNDING, tobe

consciousistobeeitherinthatneurophysiologicalstateorconscious.Sothen,one

mightworry,aswiththenotoriouslydisjunctivepropertybeinggrue, thingsno

longergenuinelyresembleasamatteroftheirbeingconscious—fromwhichone

mightinferthatbeingconsciouscannotbecausallyefficacious,figureintolawful

generalizationsorinductivelyconfirmablehypotheses,andsoon.

Setasidewhetherdisjunctivitydeservesthisbadmetaphysicalreputation,which

somehavechallenged(cf.Antony2003,Clapp2001,andSkiles2016).Evenso,

having adisjunctivepart alone cannot suffice fordisjunctivity of this allegedly

problematicsort.ForanyFyoulike,athing’sbeingeitherForFisnodifferentthan

itsbeingF(whatelsecoulditbe?);thusthecriterionwouldovergeneralize.And

indeed,ifthingsdogenuinelyresembleasamatteroftheirbeingconscious,then

havingaproperdisjunctivepartcannotsufficeforproblematicdisjunctivityeither.

Evenifbeingintherelevantneurophysiologicalstateisadisjunctivepartofbeing

conscious—andevenifbeingintherelevantstateisitselfproblematicallydisjunc-

tive—itremainsthecasethatconsciousthingsinthisstate(trivially)genuinely

resembleconsciousthingsthataren’t:namely,asamatteroftheirallbeingcon-

scious.Theworryinitiallylookscompelling,wethink,duetoassumingthatbeing

consciousmustbe‘builtup’frombeinginthisstateandsomefurtherproperdis-

junctivepartthatbestownogenuineresemblancesbetweenthem.Butnosuch

understandingofdisjunctiveparthoodisintended.20

Nowthereisasenseinwhich,giventheaccountofessencedevelopedinsection

2,whatisgroundedhasa‘disjunctivenature’:ifp1,p2,…groundsq,thenit’ses-

sentialtoq’sholdingthat(p1Ùp2Ù…)Úqholds.Yetmanyfinditobjectionable

fora fact’sgroundsto figure into itsessence ingeneral.AsFineputs it,even if

Socrates’sbeingaphilosophergroundsthattherearephilosophers,thegrounded

20Whatwesayhereiscompatiblewiththeviewthatdisjunctiveparthoodobeysweaksupple-

mentation. The questionwhether the view should be countenanced is, like the correspondingquestion about conjunctiveparthood (see fn. 16), substantive, andwehope to address it else-where.

30

fact’sessencestill“knowsnothingofSocrates”;andiftheball’sbeingredgrounds

itsbeingcolored,thegroundedfact’sessencestill“knowsnothingofthespecific

colors”(2012,pp.74-75;cf.Rosen2010,pp.130-133).Butweseenowaytomake

thisworryprecisethatwefindtroublesome.Onecanrepresentthattherearephi-

losophersinthoughtortalkwithoutreferencetoSocrates,since(aswestressed

before)generalizedidentityiscompatiblewithrepresentationalnon-equivalence.

Andindeed,wefinditatleastasintuitivetosaythatp1,p2,…dofigureintothe

essenceofq,iftheirconjunctionissubsumedbyqaswe’veclaimed.Ifsuch-and-

suchareallwhollyrelevantwaysfortheballtobecolored,thathardlyseemsinci-

dentaltothisparticularfact.

Another,relatedobjectiongoesasfollows.21Call“C”theclaimthatSocrates’sbe-

ingaphilosophergroundsthattherearephilosophers.OuraccountandC,theob-

jectionstarts,togetherentailthatthefactfthattherearephilosophersisidentical

tothefactgthatSocratesisaphilosopherortherearephilosophers.Yetthisis

incompatiblewiththeview—callit“V”—thattheexistenceoffdoesnot,whilethe

existenceofgdoes,necessitatetheexistenceofSocrates.Therefore,ouraccount,

togetherwithC,precludesV.Butsurely,anaccountofgroundingshouldremain

neutralwithrespect toV,even in thepresenceofC. Hence, theobjectioncon-

cludes,ouraccountshouldberejected.WedenythatouraccountandCtogether

entailthattherearefacts,andaccordinglywewouldrejecttheveryfirststepof

theobjection.Butletuscharitablyassumethatfactsfandgdoexist.Thenwefavor

differentresponses.Wehaveallalongremainedneutralonthequestionwhether

generalizedidentitiesyieldobjectualidentitieswhenthecorrespondingentities

(facts,properties)areavailable(seefn.3).Oneofusdeniesthattheydo,andre-

jectsthefirststepoftheobjection.Theotherbelievesthattheydo,andrejectsthe

neutralityrequirement formulatedat theendof theobjection.22Webelievethe

neutralityrequirementisnotatallobviousoncewerememberthattheissuehere

21Thankstoarefereeforraisingthisconcern.

22Notethat,interestingly,rejectingVdoesn’trequireholdingtheviewthateverything(f,gandSocrates,inparticular)existsnecessarily:onemayadopttheviewthat(i)Socratesisacontingentexistent,(ii)thefacththatSocratesisaphilosopherexistsataworldiffSocratesexists(andper-haps:isaphilosopher)atthatworld,and(iii)ghasdisjunctiveexistenceconditions,existingataworldiffeitherforhexistsatthatworld.

31

is the existence conditions of facts conceived of asworldly ‘chunks of reality'

(whateverthosemightbe;we'replayingalongforthesakeofargument),notfacts

conceivedofaspropositions.Nothing(as faraswecansee)preventsone from

saying that thepropositionthat Socrates is aphilosopheror there arephiloso-

phers requires the existence of Socrates, whereas theworldly 'chunk of reali-

ty'thispropositionreportsupondoesn’t.Blurringthetwoissuestogethermight

bewhytheobjectionsoundscompellingatfirst.23

Havingnowmotivatedouraccountsofgroundingandessenceindividually,what

canreasoningwiththeircommonideologicalcore—generalizedidentity—tellus

abouthowtheyinteract?Weconsiderthisquestionintheremainder.

4. FineonunifyinggroundingandessenceFine(2015)intends,likeus,tounifyessencewithgrounding.Ourtwoaccounts

aren’tindirectcompetition,ashistargetnotionsaren’tthesameasours:oursare

worldly,whilehisarerepresentational.24Yetcomparingthetwoallowsustohigh-

lightseveralattractivefeaturesofourownaccountvis-à-visFine’s. Fine’saccountpresentsasignificantdeparturefromhisolderviewsonessence

andgrounding:whileheusedtofocusontheformerintheobjectualsense(asin

e.g.his1994)andonthelatterinthefactualsense(asine.g.his2012),henow

acknowledges—likeCorreia(2006)—thegenericdimensionofessence,and—like

us—thatessenceandgroundingcanbeeithergenericorfactual.Hisgenericno-

tionsoftheseareexpressed,respectively,as:

(21) It’sessentialtox,y,…beingsuchthatq1,q2,…thattheybesuchthatp

(insymbols:p¬x,y,…q1,q2,…)

(22) Somethingsx,y,…beingsuchthatp1,p2,…makesthembesuchthatthatq(insymbols:p1,p2,…®x,y,…q)

Hisfactualnotionscanbeexpressedasfollows:

23SeeMulliganandCorreia(2013,section2)forasurveyofviewsthatdistinguishfactsfrom

truepropositionsandthatallowforfactstohavedisjunctiveexistenceconditions.

24EvidenceisgivenbythefactthatFineholdsthatthenotionofessenceheisconcentratingonisirreflexive(2015,pp.296-297)andthatpisessentialtopÙp(ibid.,p.308).

32

(23) It’sessentialtoitsbeingthecasethatq1,q2,…thatitbethecasethatp(insymbols:p¬q1,q2,…)

(24) Itsbeingthecasethatp1,p2,…makesitbethecasethatq(insymbols:

p1,p2,…®q)

The structureof Fine’s statementsof groundmirrors thatof the statementsof

groundwe’reinterestedin:oneormoreitemsgroundagivenitem.Incontrast,

Fine’sstatementsofessencemayinvolveseveralitemssaidtobe(collectively)es-

sentially such-and-such,whereas the statements of essencewe focused on are

one-one.Fine’sessentialistnotionsarealso‘strict’,i.e.irreflexiveornon-circular:

anitemcannotbeessentialtoitself,ortoapluralityofitemswhichcomprisesit.

Yettheappearanceofaconflicthereisillusory.Forwecanexpressthekindsof

essentialiststatementsFineputsforward,andaccountfortheminawayperfectly

dualtoouraccountofgrounding.Use“p⊂x,y,…q1,q2,…”for“It’sessentialtox,y,

…beingsuchthatq1,q2,…thatp”,anduse“p⊂q1,q2,…”for“It’sessentialtoits

beingthecasethatq1,q2,…thatitbethecasethatp”,bothunderstoodasworldly

and‘strict’.Defineanotionofquasipartialessence⫇asfollows:

(25) p⫇vqiff:pÚr⊆vqforsomer.

Inotherwords,p⫇vqholdsjustwhenpisadisjunctivepartofsomethingthatis

essentialtoq.Thenwecanaccountfor⊂-statementsasfollows:

(26) p⊂vq1,q2,…iff: (i)p⊆vq1Ùq2Ù…,and (ii)neitherq1⫇vp,norq2⫇vp,nor…

(Thisisanon-factivenotion;afactivenotioncanbedefinedintheobviousway.)

Taking⊂-statements onboard significantly improves our ownaccount, forwe

thenseeaperfectparallelismbetweenouraccountsofgroundingandessence,as

illustratedinthefollowingtable(correspondingfactivenotionsareleftaside):

33

Grounding Essence

Weaknotion

SUBSUMPTION(≤)

p≤vqiff:pisadisjunctivepartvofq

PARTIALESSENCE(⊆)

p⊆vqiff:pisaconjunctivepartvofq

Quasiweaknotion

QUASISUBSUMPTION(≲)

p≲vqiff:pÙr≤vqforsomer

QUASIPARTIALESSENCE(⫇)

p⫇vqiff:pÚr⊆vqforsomer

Strictnotion

STRICTGROUNDING(

34

q”as“pisconstitutiveofq,andasufficientconditionforq”.Theproblem,atleast

if“necessarycondition”and“sufficientcondition”areunderstoodinthefamiliar

modalfashion,isthatunacceptableresultsfollow.Forinstance,beinganumber

(F)isessentialtobeinganumberandblue-or-not-blue(G).So,beingFisconstitu-

tiveofbeingG.ButsincebeingFnecessarilyimpliesbeingG,theview,understood

modally,entailsthatbeingFgroundsbeingG(anditdoesn’t).

Now, Fine acknowledges notions of necessary and sufficient conditions which

aren’tmodal,andwhicharenotconversetoeachother(ibid.,pp.306-7),andit

maybethoughtthattheviewinquestionisinsteadtobereadasinvokingthese.

Butnowweareleftwithoneproblem,whichalsoaffectsthemodalview:howis

thisnotionofbeingconstitutiveoftobeunderstood?Absentafullerstory,theac-

countseemsincomplete. Thesecondoptionistoclaimthat“constitutively”inthephrases“constitutively

necessary/sufficientcondition”isintendedtomarktwokindsofnon-modalcon-

dition—the constitutively-necessary kind vs. the constitutively-sufficient kind—

whichdifferintheirmodalimport.Butthisoptionseemsatleastasproblematic

asthepreviousone.Thepreviousoptionsecuredatleastsomeformofunityin

theaccountofessenceandgrounding,asbothareanalyzedintermsofasingle

notion:beingconstitutiveof.Yetwiththepresentoption,itisnotatallclearwhat

unifiesconstitutively-necessaryconditionswithconstitutively-sufficientonesin

morethannameonly,orwhythesenon-modalconditionshavethemodalimport

theyallegedlydo.Perhapspartoftheexplanationisthatbotharedeterminatesof

thesamedeterminable:beingaconstitutiveconditionof.Butagain:howisthisno-

tiontobeunderstood?Absentafullerstory,theaccountseemsincomplete.Our

account,incontrast,analyzesgroundingandessenceintermsofthesamefamily

ofnotions,whichwebackedupwithatheoryaboutthesenotionswetaketobe

independentlymotivatedbyhowweintuitivelyunderstand“For…isfor___”state-

mentsasthey’reusedinphilosophicalsettings.

Fine(ibid,p.308)alsoclaimsthatbothconstitutiverelationsaretobetakenas

primitive.Nowofcourse,wehavenobasisforfaultingFineforthisreasonalone:

we’veassumed(forthepurposesofthispaper,atleast)thatgenericandfactual

35

identityarenotreductivelyanalyzableeither.Evenso,workingwiththis latter

class of primitives has significant advantages overworkingwith Fine’s.We’ve

mentionedanumberofrespectsinwhichouraccountisappealingwhenapplied

toessenceandgroundingindividually.Giventhatthesedependcruciallyonthe

distinctivefeaturesofgeneralizedidentity,itatbestisunclearhowtoreplicate

themwithinFine’saccount—thatis,absentanas-yetuntoldstoryaboutthena-

tureandlogicofconstitutiverelations.(Notthatthenatureandlogicofgeneral-

izedidentityiscompletelytransparent;butatleasttherearetightanalogieswith

another,morefamiliar‘no-difference’notiontoguideus,i.e.objectualidentity.)

Thisbecomesevenmoreapparentwhenweusegeneralizedidentitytoevaluate

principleslinkinggroundingandessence.Forinstance,FineclaimsthatifbeingF

groundsbeingG,thenbeingG“willnotingeneral(andperhapswillneverbe)”

partofwhatitistobeF;forotherwise,beingFwouldbeconstitutiveofbeingG

andviceversa(ibid.,pp.306-7).Butthisexplanationstrikesusasincomplete.If

being constitutively-necessary for andbeing constitutively-sufficient forareboth

primitive,why couldn’t the twohold in oppositedirections? In contrast, Fine’s

claimfollowsimmediatelyfromourframework.ForsupposeFx

36

bepromptedbythisseparatefact.

Second,perhapsagenericessentialistfalsehoodaboutbeingredisbeingconfused

foranobjectualessentialisttruthaboutthepropertybeingred:i.e.,thatbeinga

colorispartofwhatitistobethisveryproperty.Supposethisisso,andthata

thingcannotberedwithouthavingthisproperty.Thenitfollowsthatthething

hasapropertywhichisacolor(or,toputitmorenaturally,thatithasacolor).

Presumably,athing’shavingacolorjustisitsbeingcolored;thusitfollowsthata

thingcannotberedunlessit’salsocolored.Givenhowsubtlethesedistinctions

betweentheobjectualandgenericcanbe,perhapsitshouldn’tsurpriseusthat

oneessentialistclaimisconfusedfortheother.

Herearetwofurtherexamplesofhowgeneralizedidentityilluminatestheunity

ofgroundingandessence.First,considertheclaimthatgroundingholdsonlyif

thereissome‘underlying’truthaboutessence.25Ouraccountpredictsatleastone

sense inwhich this is correct. Specifically, our account predicts that if beingF

groundsbeingG, thefactthatbeingFnecessitatesbeingGcanbederivedfrom

whatitistobeG.ForifbeingFgroundsbeingG,ouraccountimpliesthatbeingG

justisbeingForHforsomegivenH,andwhichonouraccountgivesthe(ora)full

essenceofbeingG.Itthenfollowsthatnecessarily,athingisGiffitisForH,which

entailsbystraightforwardmodalreasoningthatnecessarily,athingisFonlyifit’s

alsoG,asdesired.26

Second,considertheclaimthatnoteverynecessaryentailmentorequivalentof

such-and-suchisalsoessentialtoit.Thisisonlytrueinsomecases—butinwhich

casesisitfalse?Ouraccountallowsappealtoground-theoreticresourceswhen

addressing thequestion.Specifically, since (worldly) ground-theoretic status is

preservedundergeneralizedidentity,ouraccountentailsthatbeingFisatleast

inpartofwhatitistobeG,onlyifFisground-theoreticallyequivalenttobeing

25Fordiscussionofprinciplesofthistype,seethearticlescitedinfn.1.

26Somearguethatwhat’sgroundedneedn’tbenecessitatedbywhatgroundsit,butseeSkiles(2013,ch.4;2015,pp.739-41)foranalternativeidentity-basedproposalofgroundingdesignedtobecompatiblewith‘groundingcontingentism’.WhetherSkiles’sproposalandtheonedefendedinthispapershouldbeviewedascompetitors—orinsteadascharacterizingtwokindsofground-ingunderoneideologicalumbrella—isaninterestingquestion,butforanothertime.

37

bothFandG(inthesensediscussedinsection2).Yetthisneedn’talwaysbethe

caseifbeingFisnecessarilyentailedbyorequivalenttobeingG.Torecalloneof

Fine’s(1994)famousexamples:beingSocratesandsuchthatthereareinfinitely

manyprimenumbersisnecessarilyentailedbyandequivalenttobeingSocrates,

yetpresumablytheformerisground-theoreticallylinkedtothearithmeticrealm

inwaysthatthelatterisn’t.Givenouraccount,thisprovidesreasontobelievethat

theformerisn’tpartoftheessenceofthelattereither,asdesired.

Tobeclear,wedon’tclaimthatFine’saccountcannotbesupplementedwithan

informativestoryofwhatconstitutiverelationsarethatperformsaswell in its

intendeddomain.Wedo,however,thinkthatthesecomparisonsbringsomeofthe

attractivefeaturesofouraccountintostarkrelief.

6. LookingforwardWehavearguedthatgroundingandessencecanbothbeaccountedforintermsof

identity—generalizedidentity—andexplainedwhytheresultingframeworkisat-

tractive.Butthisishardlythelastwordonthematter.Atleasttwoclassesofques-

tionsemergeforfurtherwork.

Oneclassconcernshowgeneralizedidentity—andthus,onourview,grounding

andessence—fitintoourcognitivelives.Suchquestionsinclude:cantheaccount

beextendedtorepresentationalnotionsofgroundingandessence?Howdoesone

come to know which statements of generalized identity hold? And why does

graspingsomeofthembringatleastsomedegreeofexplanatoryunderstanding,

whilegraspingothers(e.g.“Tobehumanistobehuman”)doesn’t?

Anotherclassofquestionsinsteadconcernshowgeneralizedidentity—andthus,

onourview,groundingandessence—fitintofundamentalreality.Theseinclude:

aregenericandfactualidentityprimitivenotions,aswe’veassumed?What(ifan-

ything)groundsfactsaboutwhatisgenerically/factuallyidenticaltowhat?And

dothesenotionsfallunderthesameideologicalkindasobjectualidentity?

We suspect that existingwork on questions such as these, insidemetaphysics

properandout,wouldprovehighlyusefulforansweringrelatedquestionsabout

groundingandessence.Grounding,essence,andidentity individuallyhavebeen

38

topicsatthecenterofmetaphysicalinquiryforquitesometime.Afullerunder-

standingofhowthethreebehavecollectivelyshould,wethink,beatthecenterof

metaphysicalinquiryforsometimetocome.27

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27Fortheircommentsonancestorsofthisarticle,wewishtothankDominikAeschbacher,An-drewBailey,RiccardoBaratella,SamBaron,CorrineBesson,PhilippBlum,MartinaBotti,ClaudioCalosi,PabloCarnino,RebeccaChan,MichaelJ.Clark,ChristinaConroy,PaulDaniels,LouisdeRos-set, Cian Dorr, Jeremy Goodman, Dana Goswick, Vincent Grandjean, Ghislain Guigon, MiguelHoeltje,KathrinKoslicki,OlivierMassin,Anna-SofiaMaurin,KrisMcDaniel,NeilMehta,RobertMi-chels,KevinMulligan,BenjaminNeeser,DonnchadhO’Conaill,BryanPickel,JanPlate,MikeRaven,AgustínRayo,HenrikRydéhn,PierreSaint-Germier,MariaScarpati, JonathanSchaffer, JonathanSimon, Robin Stenwall, Tuomas Tahko, Elanor Taylor, Naomi Thompson, Kelly Trogdon, JanWalker,JenniferWang,NathanWildman,TobiasWilsch,JustinZylstra,severalanonymousrefer-ees,andaudiencesinAscona,Bergamo,Bern,Bucharest,Dresden,Geneva,Gothenburg,Helsinki,Istanbul(Koç),Leeds,London(King’sCollege),Neuchâtel,Oslo,Oxford,andSassari.Thisarticlewas written while F.C. was funded through the Swiss National Science Foundation projects“Grounding–Metaphysics,Science,andLogic”(CRSII1-147685),“TheMetaphysicsofTimeanditsOccupants” (BSCGI0_157792),and“Essences, Identitiesand Individuals” (100012_159472), theUniversityofNeuchâtel’smoduleoftheEuropeanCommission’sHORIZON2020MarieSklodow-ska-CurieEuropeanTrainingNetworkDIAPHORA(H2020-MSCA-ITN-2015-675415),whileA.J.S.receivedfundingasaSwissNSFAdvancedPostdoc.Mobilityresearcherintheproject“MetaphysicsasanExplanatoryDiscipline:Grounding,Essence,andIdentity”(167721),andwhilebothreceivedfundingthroughtheSwissNSFproject“TheNatureofExistence:NeglectedQuestionsattheFoun-dationsofOntology”(10012_150289).Wearegratefulfortheirgeneroussupport.

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