1

REALDEFINITION1

G.Rosen

Reviseddraft,February2015

[Thisversionisquitedifferentfromthepreviousdraft,datedSept.2013.]

1. Thetopic

TheoldSocraticquestionsWhatisjustice?Whatiscourage?callfordefinitions,

notofwordsorconcepts,butofthings.Justiceandcourageandthelikeweresupposed

to be aspects of reality. To answer the question What is courage? in the intended

sense is not to say what theword couragemeans or what passes before themind

when we think when we think of courage. It is to saywhat it is for a person to be

courageoustoidentifythat inwhichthecourageofthecourageouspersonconsists

by specifying nontrivial necessary and sufficient conditions for courage somehow

groundedinthenatureofcourageitself.

The case can bemade that contemporary analytic philosophy is up to its ears in

idiomsofdefinition,analysis,reductionandconstitutionthatarebestunderstoodina

similarly metaphysical keyas demands for real definition rather than linguistic or

conceptualanalysis.Onthisview,whenweaskwhatit isforathingtobeapersonor

foracreaturetobeconsciousorforafacttobealawofnatureorfortwoexpressions

tohavethesamemeaningorforanobjecttobecoloredorforanacttobefreeorfor

anartifacttobeanartwork,wearebestunderstoodasseekingrealdefinitionsofthe

properties, kinds, categories or relations that figure in the question, rather than

semanticorconceptualequivalents,evenwhenthenthecorrectnessoftheaccount is

1ThismaterialwaspresentedattheCRNAPWorkshoponMetaphysicalStructureat

PrincetoninApril2013,attheGenevaWorkshoponGroundingandExistencein

September2014,andatMIT.IamgratefultoRalphBader,SelimBerker,FabriceCorreia,

ShamikDasgupta,MarkJohnston,KathrynKoslicki,BarryMaguire,Michaela

McSweeney,KevinMulligan,JanPlateandAlexSkilesforcommentsandquestions.

2

meanttoberecognizableapriori.Themainargumentforthisviewisthatwhenwetry

toanswer thesequestionswearehappy toentertainanalysescast in terms that fully

competentmastersoftheanalysandumneednotgrasp.Wesimplyhavenoconception

of semantic or conceptual analysis onwhich thismakes sense. And yet our analytical

questions and our practice with them do make sense. And this suggests that our

questions are not semantic or conceptual questions after all. They are rather

metaphysicalquestionsthatcallfordefinitions,notofrepresentationalitems(wordsor

concepts)butofpropertiesandotherfeaturesofmindindependentreality.

Inmytravels Ihaveencounteredresistancetothis idea,evenamongphilosophers

who are otherwise sanguine about the recrudescence of premodernmetaphysics in

postmodernphilosophy.Thebestwaytoovercomethisskepticismwouldbetoexplain,

in clear and independently intelligible terms,what it is to define a thing, or in other

words,toprovidea(real)definitionof(real)definition.Theaimofthepresentnoteis

todojustthat.

2. Preliminaries

Intheorywecanaskfordefinitionsofitemsinanycategory:objects,properties,

relations,connectives,quantifiers,etc.,allunderstoodasworldlythingsandnotasbits

of mind or language (special cases aside). But it will simplify discussion to focus on

propertiesandrelations.Wewrite

Def(F,)

forourtarget:tobeFistobe;beingFconsistsin,orreducesto,being,etc.Asthe

notationsuggests,itwillbeusefultothinkofDefasarelationbetweenthepropertyto

be defined and something else, its definiens. More concretely, I think of as a

structuredcomplex,builtfromworldlyitemsinroughlythesenseinwhichasentenceis

builtfromwords.(ThinkofasastructuredRussellianpropositionalfunctionwithfree

variablescorrespondingtotheargumentplacesinF.) Thisrelationalanalysisisstrictly

3

optional.Defcouldbeaconnectiveinstead.Butitwillbeimportanttobeabletospeak

oftheconstituentsof.Thusifwesay(asweshould)thattobeanevennumberisto

bedivisibleby2,weshouldbeabletoaddthatthenumber2figuresinthedefinitionof

evennumber.Itakethistomeanthat2thenumberitselfisaconstituentofthe

complex in terms of which the property is defined. So even if the property is

mereologically simple, as it may be, its definiens is not. On this conception, real

definitionsarenot identities(thoughtheymayentail identities). Rathertheypairone

(possibly simple) thing thedefiniendumwithanother (invariably complex) thing,

itsdefiniens.Thechallengeistosaywhatittakesforapairingofthissorttoconstitute

acorrectdefinition.2

3. Asimplemodalaccount

Beginwithasimpleproposal:

(0) Def(F,)iffx(Fxx)3

2Def(F,)presumablyentails:ThepropertyofbeingF=thepropertyofbeing.ButitdoesnotfollowfromthisthatFandmustbeidentical.Tomakesenseofthis,thinkofthethepropertyofbeingasstandingforafunctionfrompredicableitems

(propertiesandcomplexes)toproperties.ThepropertyofbeingFisnotidenticaltothe

complex.Butitmaybeidenticaltothevalueofthisfunctionwhenistakenasitsargument.See9forfurtherdiscussion.

3ThisandsubsequentanalysesofDefshouldreallybewritten,notassimple

biconditionals,butasclaimsoftheform:

Def(Def(F,),(F,)))

Thatis:ForittobethecasethatdefinesFisforittobethecasethatFandstandinsuchandsucharelation.Butthisbecomesillegibleveryquickly,sowestickwiththe

shorthandiff.

4

This is immediatelyobjectionablebecause itentailsthateveryproperty isdefinable

Def(F,F),whereas in the sense that interestsus, it isalwaysa substantivequestion

whetherFisdefinable.4WemightrespondbyrequiringthatFnotfigurein.Buteven

withthisstipulationtheaccountwillovergenerate for familiar reasons. Necessarily,a

thingisgreenifandonlyifitisgrueandobservedorbleenandunobserved(Goodman

1947).Butnoonewithaninterestinthemetaphysicsofcolorwouldacceptthisasan

accountofwhatitisforanobjecttobegreen.

4. ALudovicianaccount

Themostconservativemodificationofthesimplemodalviewinvolvesonenewbit

of ideology: David Lewiss idea that some properties are more natural than others

(Lewis 1983). The idea can be explained inmanyways, but lets start with following

roughgloss.Someclassesaremorehomogeneous,moreunified, lessgerrymandered,

thanothers.Thegreenthingsdifferinvariousways:insizeandshape,butalsoincolor,

some being emerald green, others chartreuse. But the grue things are even more

heterogeneous,sincetheycandifferinallofthesewaysbutalsomoreradically,some

beinggreenandothersblue.Ononeview,thenaturalnessofapropertyisameasureof

thehomogeneityofitsintension:

F is more natural than G iff (quantifying over all possible objects) the most

dissimilarFsarelessdissimilarthanthemostdissimilarGs.

Thismaynotbealtogetheradequateasadefinition;butitsafairapproximationofone

versionofLewissidea.

4ManywritersnotethattheidiomsweusetoexpressrealdefinitiontobeFistobe

,beingFjustisbeing,etc.canbeheardasreflexive.Itsoundsperfectlytrue,ifuninteresting,tosaythattoberedistobered.Itakethepoint,andsodenythatImin

thebusinessofexplainingthisordinaryidiom.AsIunderstandtheterm,ifthebestwe

candowithredistosaythatbeingredisbeingred,thentheupshotisthatredisnot

definableintheintendedsense.

5

Withthisinhand,wemightconsideranamendedversionofthemodalaccount

ofrealdefinition:

(1) Def(F,)iffx(Fxx),

wheretheconstituentsofareallmorenaturalthanF.

Thisrulesoutcirculardefinitions,andalsothespuriousdefinitionofgreen intermsof

grueandbleen.Butconsider:

Tobeasquareistobeanequilateralrectangle.

Thismightbeacorrectrealdefinitionofsquare.Buttheconstituentsofthedefiniens

rectangle and equilateral are less natural than square, at least according to the

accountsketchedabove:theclassofrectanglesismorediversethantheclassofsquares.

Everycorrectdefinitionbygenusanddifferentiaisacounterexampletothisproposal.

Lewis sometimes hints at an account of relative naturalness that would avoid

thisproblem(Lewis1986:61).Onthisaccount,relativenaturalnessisdefinedinterms

ofthenotionofaperfectlynaturalpropertythesortorpropertythatmightfigureina

fundamental law of nature, the sort of property that might correspond to an

Armstrongian universal (Armstrong 1978), the sort of thoroughly determinate, non

disjunctive property that makes for perfect resemblance in some respect among its

instances.Takingthisnotionasbasic,thealternativeaccountmaintainsthat

F ismorenatural thanG iff theshortestdefinitionofF (i.e., theshortestopen

sentence cointensive with F) in a language whose predicates correspond to

perfectlynaturalpropertiesisshorterthantheshortestsuchdefinitionofG.

6

Thisissharplyatoddswiththepreviousaccount.Afterall,whereFisperfectlynatural,

notFwillbealmostperfectlynaturalbythisaccount;butofcoursetheclassofnonFs

willbealmostmaximallyheterogeneous.5

The second account iswell suited to solve the problemsmentioned above for

modalaccountofdefinition.Eventhoughtheclassofrectanglesismoreheterogeneous

thantheclassofsquares,itisplausiblymorenaturalthantheclassofsquaresaccording

tothesecondconceptionofrelativenaturalness.Afterall,theshortestcharacterization

oftheclassofsquaresinperfectlynaturaltermswillpresumablyconjoinanaccountof

theclassofrectangleswithanaccountofequilaterality,inwhichcasethedefinitionof

squareinperfectlynaturaltermswillbelonger.

Thissolvesoneproblemforthemodalaccountofrealdefinition,buttheaccount

isunacceptableforotherreasons.Considerasupervenientproperty,liketheproperty

ofbeinganuncle.Thisisnotaperfectlynaturalproperty,butthefactsaboutwhoisand

who is not an uncle strongly supervene on the distribution of perfectly natural

properties: foranytwopossibleobjects,xandy, ifxandyarealike ineveryperfectly

natural respect (includingextrinsic respects), thenbothareunclesorneither is. As is

familiar,thissupervenienceclaimguaranteestheexistenceofanecessitateduniversally

quantifiedbiconditionaloftheform:

x(xisanunclex)

constructedas follows: Takeallof theuncles,actualandpossible:u1,u2, LetD1(x),

D2(x) be their complete descriptions in perfectly natural terms. (D1(x)might be a

completedescriptionofu1inthelanguageofquantumfieldtheory.)Thenconsider:

5LewismayhaveinmindaversionofthisideaonwhichthedefinitionsofFmustconsist

inpositiveformulae:conjunctionsofdisjunctionsofatomicformulaeinvolvingperfectly

naturalpredicates,withoutnegationortheequivalent.Butthentheworrywillbethat

mostordinarypropertieswillbedefinedonlybyinfinitaryformulae,inwhichcasethe

differencesbetween(say)greenandgruewillbelost.

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x(xisanuncle(D1(x)D2(x)))

Everyversionofthemodalaccountthatwehaveconsideredentailsthatthisisacorrect

accountofwhatitistobeanuncle.Butitisnt.Mostimportantly,itfailstobringout

whattheuncleshave incommon. It is likeadefinitionofprimenumberaccordingto

which to be a prime is to be either 2 or 3 or 5 or This account is not just less

informative than itmightbe: it iswrong. It isnotso that3 isprime invirtueofbeing

either 2 or 3 or 5 or ; 3 is prime in virtue of having 1 as its only proper factor.6

Similarly,itisjustnotsothatFesterisanuncleinvirtueofbeingconfiguredinthisfully

determinateway,orthatfullydeterminateway,orHeisanuncleinvirtueofbeinga

manwithasiblingorsiblinginlawwhoisaparent.

This points to another defect in the disjunctive account: it isoverly specific.A

correct definition of uncle should notmention quarks, even though some uncles are

madeof quarks, just as a correct definitionofhouse shouldnotmentionbricks. The

propertyofbeinganuncle isafunctionalproperty inthefollowingsense: itsnature

allows for many fully determinate ways in which a thingmight be constituted as an

uncle,butdoesnotspecifythesewaysindetail.Toknowwhatitisforapersontobean

uncle is to know that uncles must be made of something; but it is not to know an

exhaustivelistofthevariouswaysinwhichanunclemightbeconstituted.7

5. Anessentialistaccount

Theoverspecificityobjectiontomodalaccountsofdefinitionsuggestsadifferent

approach.KitFinenotesthatinmanycases,andperhapsinall,whenaproposition

holdsofmetaphysicalnecessitywecanpointtooneofmoreitemswhosenatures

groundthatnecessity(Fine1994).SupposeJackis,ofnecessity,Tarzansson.Thenwe

canbeconfidentthatthisisso,notbecauseitliesinTarzansnaturetobeJacksfather,

6Foranobjectiontolistdefinitionsfromadifferentquarter,seeField1972:362ff.

7Canwesavethemodalaccountsbyrequiringthatrealdefinitionsbefinite?That

wouldbeunmotivated.Whyshouldnttherebeitemsthatcanonlybedefinedin

infinitarytermsarbitraryinfinitesets,forexample?

8

butratherbecauseitliesinJacksnaturetobeTarzansson.Toputthepointin

epistemicterms,youcanknoweverythingthereistoknowaboutTarzansessential

naturewithoutknowingthefirstthingaboutJack;butyoucantknowJacksessential

naturewithoutknowingthatTarzanishisfather.Similarly,itmaylieinthenatureof

tablesalttocontainchlorinewithoutitslyinginthenatureofchlorinethatsaltshould

containit.InFinesnotation:

JackTarzanisJacksfather,butnot:TarzanTarzanisJacksfather

saltSaltcontainschlorine,butnot:chlorineSaltcontainschlorine

Fineshowsconvincinglythatthishyperintensionalidiomcanbemadeclear(in

severalways),andthatitissuitableforuseinsystematicmetaphysicsevenifitcannot

bedefinedinmorebasicterms(Fine1995,2000).Soletshelpourselvestoitand

considertheproposal:

(2) Def(F,)iffFx(Fxx)

Thisavoidsmostofthepitfallswehaveencountered.Itdoesnotlieinthenatureof

greenthatathingisgreeniffgrueandobservedorbleenandunobserved.Acomplete

accountoftheessenceofgreenmightsaysomethingaboutthevariousshadesofgreen,

oraboutwavelengthsoflight;butitwouldnevermentiongrueoranythingofthesort.8

Thenecessarytruthconnectinggreenwithgrueandbleenisrathergroundedinthe

naturesofgrueandbleen;itisbecausethesepropertiesarewhattheyarethatthetruth

inquestionholds.Similarly,itdoesnotlieinthenatureofunclethatonewaytobean

uncleistosatisfysomemaximallydeterminatephysicaldescriptionD1(x),muchlessthat

oneisanuncleiffoneiseitherD1orD2orRatheritliesinthenatureofunclethat

8Exceptperhapsinsometrivialway:Ifessencesareclosedunderlogicalconsequence,

thenitwillinthenatureofgreenthateverythingiseithergrueornotgrue.

9

oneisanuncleiffoneisamalesiblingorsiblinginlawofaparent.Nothingaboutthe

detailedphysicalnaturesoftherelevantitemsentersin.

Nowonemaywonderwhatsortofadvanceitcouldbetoexplainourtarget

idiomrealdefinitionintermsofFinesnotionofessence,sincethetwoare

obviouslyveryclose.9Soitsworthstressingthatthesenotionsarenotsimply

equivalent.OnFinesaccount,absolutelyeverythinghasanessence.Givenanyitemx,

definableornot,therewillbetruthsoftheformxp.EveniftheGettierexamples

showthatknowledgeisunanalyzable(Williamson2000),itstillliesinthenatureof

knowledgethatifSknowsthatpthenpistrue.Similarly,whilenegationisalmost

certainlyindefinable,itnonethelessliesinthenatureof(classical)negationthatp

~~p.TheseexamplessufficetoshowthatFinesconceptofessenceisdifferentfrom,

andmoregeneralthan,theconceptofrealdefinitionwevebeendiscussing.Onemight

acceptFinesideologyandstillwonder:Whatisitfortoconstituteacorrectreal

definitionofF?Theaccount(2)isdesignedtoanswerthatquestion.

Isitagoodanswer?Notobviously.Weobjectedtothesimplemodalproposal

(0)becauseitentailedthateverypropertydefinesitself:Def(F,F).Thepresentaccount

facesasimilarproblem.ItisnaturaltosupposethatforanypropertyF,Fx(Fx

Fx).Butinthatcase(2)entailsthateverypropertydefinesitself.

WemightrespondbyrequiringthatFnotoccurin.Butinfactthisrestriction

followsfromamoredemandingrestrictionthatisneededanyway.Supposewe

discover(bywhateverpowerfulmethodsweemployforthesepurposes),that

causexy(xcausesyiffyisaneffectofx),and

effectxy(xcausesyiffyisaneffectofx).

Proposal(2)thenentailsthatcausecanbedefinedintermofeffectandviceversa,and

theremaybeasenseinwhichthisisso(cf.thesenseinwhichconjunctioncanbe

9Finehimselfsometimesspeaksofessenceanddefinitionasifthenotionswere

interchangeable.Fine1994(REF).

10

definedintermsofdisjunctionandnegation).Butthereisalsoobviouslyasensein

whichifthisisthebestwecando,therightthingtosayisnotthatcauseadmitsofan

easydefinition,butratherthatcausationisprimitiveandindefinable.(Thedefinitionof

causeintermsofeffectisnotacandidateanswertothequestionthatproponentsof

philosophicalanalysesofcausationhavebeenasking.)

Theneededmodificationisstraightforward.FollowingFine(1994b),saythata

dependsonbwhenbfiguresnontriviallyinasessence:

adependsonbiffa[b],butitsnotthatcasethatax(x).

Wecanthensay:

(3) Def(F,)iffFx(Fxx),wheretheconstituentsofdonotdepend

onF.

Thisrulesoutcirculardefinitionsanddefinitionalcircles(likethedefinitionofcausein

termsofeffectandviceversa).Moreovertheaddedclauseisnotadhoc.Itmakes

sensethattheconstituentsofadefinitionshouldbeontologicallypriortothething

defined(SeeKment2014:159foraversionofthisproposal).

Thisaccountmayseemtoovergenerate.Tobeaprimenumberistobea

numberwhoseonlyfactorsare1andn.Butconsiderthespuriousdefinition:

Tobeaprimeistobeanevennumberwhoseonlyfactorsare1andn,oranodd

numberwhoseonlyfactorsare1andn.

Orconsiderthelistdefinitionmentionedabove:

Tobeaprimeistobeeither2or3or5or

11

Thesearebaddefinitionsofprime,buttheymightsatisfy(3),andiftheydo,(3)is

inadequate.

Thisproblemarisesifweassumethatessencesareclosedunder

logical/mathematicalconsequence,soonemightseektoevadeitbyinvokinganotion

ofessenceonwhichthisisnotso.Finehimselfdistinguishestheconstitutiveessenceof

xfromtheconsequentialessenceofx,withtheformerstandingtothelatterroughlyas

theaxiomsofatheorystandtothetheoryitself.Theconsequentialessenceofxisa

classofpropositionsclosedunderlogicalconsequence.Theconstitutiveessenceofxisa

privilegedsubclassthatservestogeneratetheconsequentialessence.Itmaylieinthe

consequentialessenceofSocratesthatSocratesishuman,andalsothatSocratesis

eitherhumanorsimian.Butonlythefirstpropositionisacandidateforinclusionin

Socratesconstitutiveessence.InhisformalworkFinemainlyoperateswiththenotion

ofconsequentialessence,sinceheseesnogoodwaytoisolatetheconstitutiveessence

fromamongthecompetingaxiomatizationsoftheconsequentialessence.Buthowever

difficultitmaybetoapplythenotioninpractice,theunderlyingideaseemsclear

enough.Wemaydefineconstitutiveessenceintermsofconsequentialessenceas

follows.

pbelongstotheconstitutiveessenceofxiff(a)pbelongstotheconsequential

essenceofx,and(b)therearenopropositionssuchthat:pbelongstothe

consequentialessenceofxinvirtueofthefactthatbelongstothe

consequentialessenceofx.

IfitspartoftheconsequentialessenceofSocratesthatSocratesiseitherhumanor

simian,thisissobecause,orinvirtueofthefactthat,itisindependentlypartofthe

consequentialessenceofSocratesthatSocratesishuman.Whateverdifficultywemay

haveinisolatingtheconstitutiveessenceofathinggivenitsconsequentialessence

derivesfromourlimitedcapacitytodeterminewhenoneessentialisttruthisgrounded

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inanother.Thatsarealproblem,butitsanepistemicproblem.Theconceptsareclear

enough,eveniftheyarehardtoapplyinpractice.

Withthenotionofconstitutiveessenceinhand,wecansolvetheovergeneration

problemfor(3).Thespuriousdefinitionsofprimemaybepartsoftheconsequential

essenceofprime.Buttheyarecertainlynotpartsoftheconstitutiveessence.Soifwe

readFin(3)asitliesintheconstitutiveessenceofFthatwesolveourproblem.

Soclarified,(3)ispromising,butithasanumberofunwelcomeconsequences.

Theontologicalindependenceclauseensuresthatrecursivedefinitionsarenever

realdefinitions.Supposewethinkthatnaturalnumberispriortosetoranysimilar

notionintermsofwhichafullyreductivedefinitionmightbegiven.Onemightstillbe

temptedtosay:

Tobeanaturalnumberistobeeitherzeroorthesuccessorofanaturalnumber.

Thiswouldbeuselessiftheaimweretointroduceamathematicalnovicetotheconcept,

butrealdefinitionsarenotconstrainedtobeusefulinthisway.Theclaimwouldrather

bethatasamatterofmetaphysics,whatmakeseachnaturalnumberaninstanceofthe

kindnaturalnumberisthatitiseitherzeroorthesuccessorofanumber,andthatmight

betrue.

Thisproblemcanbesolvedbydeletingtheontologicaldependenceclausein(3).

Theclausewasintroducedtoblocktrivialdefinitionsanddefinitionalcircles.Butnow

thatwehavespecifiedthatwereoperatingwithaconstitutivenotionofessence,this

maynotbenecessary.ItmaybepartoftheconsequentialessenceofFineverycase

thatx(FxFx).Butthiswillnotbepartoftheconstitutiveessence,sincethatwould

beotiose.Itislessclearwhetherthefocusonconstitutiveessenceisenoughtoblock

definitionalcirclesinwhicharelationisdefinedintermsofitsconverseandviceversa,

butsupposeitis.Thepointisthattherevisedaccountmightstilladmitrecursive

13

definitionslikethedefinitionofnumbergivenaboveorthedefinitionofancestorin

termsofparent,sinceitmaywelllieintheconstitutiveessenceofancestorthatxisan

ancestorofyiffxisaparentofyortheparentofanancestorofy.

Stilltheaccountremainsproblematicforatleasttworeasons.Mostimportantly,

itwouldseemtoblockdefinitionalexpansionofacertainfamiliarandstraightforward

sort.Supposethattobeasquareistobeanequilateralrectangle,andthattobea

rectangleistobearightquadrilateral.Itshouldthenfollowthattobeasquareistobe

aright,equilateralquadrilateral.Butitishighlyunlikelythattheconstitutiveessenceof

squarecontainsbothsquaresareequilateralrectanglesandsquaresareequilateralright

quadrilaterals.Thesepropositionsbothbelongtotheconsequentialessenceofsquare.

Butifthefirstpropositionbelongstotheconstitutiveessenceofsquare,thesecond

doesnt,sincethatwouldrendertheconstitutiveessenceneedlesslyredundant.

Asafinalproblem,notethatanaccountframedintermsofconstitutiveessence

willrenderquestionsaboutthedefinablityofFsensitivetoamanifestlyintractable

question.SupposewearetemptedtosaythattobeFistobe,andunderstandthisas

theclaimthat

itliesintheconstitutiveessenceofFthatx(Fxx).

WethennotetheveryrealpossibilitythattheconstitutiveessenceofFdoesnotinclude

thissingle,universallyquantifiedbiconditional,butrathertwoquantifiedconditionals:

ItliesintheconstitutiveessenceofFthatx(Fxx)

ItliesintheconstitutiveessenceofFthatx(xFx)

Itsabsurdtothinkthatthedefinabilityof(say)primenumberturnsonwhetherthe

constitutiveessenceofprimetakesthefirstformorthesecond.Andthatsuggeststhat

theappealtoconstitutiveessencecreatesasmanyproblemsasitsolves.

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6.TheGroundTheoreticAccount

Idontknowhowtotweaktheessentialistproposaltosolvetheseproblems10,

butevenifitcanbetweaked,itwillstillfailtocaptureanimportantfeatureofreal

definition.Thefeaturehassurfacedoccasionallyinourinformalglosses.Thusin

rejectingtheinfinitelistdefinitionofprimenumber,accordingtowhichtobeaprimeis

beeither2or3or5or,wesaid:

Itisnotsothat3isprimeinvirtueofbeingeither2or3or5or;3isprimein

virtueofhaving1asitsonlyproperfactor.

Thisisobviouslyanobjectiontothelistdefinition,butwhy?Becausewetakeitfor

grantedthatrealdefinitionssupplyexplanatoryinformation.Iftobeprimeistobea

numbernwhoseonlyfactorsare1andn,itfollowsimmediatelythatwhenevernis

prime,nisprimebecausei.e.,invirtueofthefactthatitsonlyproperfactorsare1

andn.

ThisisaninstanceoftheGroundingDefinitionLink:

GDL:IfDef(F,)thennecessarily,forallx,ifxisFthenxisFinvirtueofbeing.

Theessentialistaccountsofrealdefinitionareconsistentwiththisprinciple,butthey

dontentailitorexplainit.ThereisastepfromtheclaimthatitliesinFsnaturethatF

andarecoextensivetotheclaimthatwhenathingisF,itsbeingiswhatmakesitF.

Thechallengefortheessentialististomotivatethisstep.

10Theexamplesshowthatanessentialistaccountofrealdefinitionneedsanotionof

essencethatisintermediatebetweenconsequentialessenceandconstitutiveessence.

Thenaturalthoughtistostartwiththeconstitutiveessenceandthentocloseundera

limitedsetofoperations.Thetrickistospecifytheseoperations,andIcantseehowto

dothat.

15

Icantseehowtodothis,soIproposeanothertack.Theideaistotakethe

GroundingDefinitionLinkasthekeytotheanalysisofrealdefinition.Thesimplest

approachwouldbetostrengthenGDLasfollows,writingpqforthefactthatp

obtainsinvirtueofthefactthatq,orqgroundsp:

(4) Def(F,)iffx(Fx(Fxx))

Thisguarantees,asitshould,thatwhendefinesF,theFthingsarealwaysFinvirtue

ofbeing.Butitaddstheconverse:ifasamatterofnecessity,theFthingsarealwaysF

invirtueofbeing,thenthereisnothingmoretobeingFthanbeing.

Butthisisnotquiteright.Anyaccountofrealdefinitionmustensurethat

wheneverdefinesF,Fandarenecessarilycoextensive.(4)obviouslyensuresthat

whendefinesF,everyFis.11Butwithoutfurtherassumptionsitdoesnotensure

thateveryisF.

Thiswouldfollowgivenanattractivebutunderexploredprincipleinthetheory

ofground:

WeakFormality:Ifforsomepossibleobjectx,Fxx,thenforanypossible

objectx,ifxthenFxx.12

AccordingtoWeakFormality,ifsomepossiblethingisgreeninvirtueofhaving(say)

suchandsuchaspectralreflectanceprofile,thenasamatterofnecessity,anythingwith

thatprofileisgreeninvirtueofpossessingit.GivenWeakFormality,wecanreasonas

follows.Supposethatasamatterofnecessity,wheneverathingisF,itisFinvirtueof

being.LeaveasidethevacuouscaseinwhichFisimpossible.Thereisthenapossible

11SupposeDef(F,),andletabeF.Itthenfollowsimmediatelygiven(4)thataisFin

virtueofbeing,andhencegiventhefactivityofgroundthatais.12WeakFormalityisaweakeningoftheprinciplecalledFormalityinRosen(2010,p.

131.)

16

FthatisFinvirtueofbeing.WeakFormalitythenensuresthateverypossiblething

isFinvirtueofbeing,whichinturnentailsgiventhefactivityofgroundthat

everypossiblethingisF.SogivenWeakFormality,(4)guaranteesthatwhen

definesF,andFarenecessarilycoextensive,asanycorrectaccountofdefinitionmust.

WeakFormality,alas,isnotselfevident.Itamountstotheclaimthatwhena

groundsFainsomeparticularcase,thecapacityofthefirstfacttogroundthesecond

derivesentirelyfromthepredicable,andnotfromthecombinationofanda.But

whyshouldnttherebecasesinwhichandatogethermakeitthecasethatFa,inpart

thankstoanditsdistinctivepowers,butalsoinpartthankstoaanditsdistinctive

powers?Idontknowanyplausiblecasesofthissort,soforwhatitsworth,Weak

Formalitystrikesmeasplausible.Butuntilitcanbegivenafirmerrationale,itwouldbe

unwisetorelyonit.

IfwedontassumeWeakFormality,(4)mustbemodifiedasfollows:

(5) Def(F,)iffx((Fxx)(Fxx))

Thisisinelegant,butitdoesthejob.ItisnowatheoremthatDef(F,)entailsx(Fx

x)).13

Irecommend(5)asthecorrectdefinitionofdefinition.14Althoughitiswritten

asabiconditional,theintendedclaimisstronger:FortodefineFjustisforittobethe

13Proof:AssumeDef(F,)andletabeanarbitrarypossibleobject.From(5)wehave

Faa(Faa).Fromthefactivityofgroundwehave(Faa)(Faa).Hence:(Fava)(Faa),whichislogicallyequivalentto(Faa).Butawasarbitrary,so:x(Fxx).14Well,almost.Theaccountbreaksdownwhenappliedtoimpossibleproperties

propertiesnothingcouldpossess.(ThankstoBrianEpsteinforpressingthispoint.)For

letFbesuchapropertye.g.,thepropertyofbeingaroundsquare,andletbeanarbitrarycomplexe.g.,xisamasslessduckwithnopossibleinstances.OuraccountimmediatelyentailsthattobeFistobe.Sincetherecantbearoundsquare

17

oramasslessduck,itsautomaticthatasamatterofnecessity,anythingthingthatisa

roundasquareoramasslessduckisaroundsquareinvirtueofbeingamasslessduck.

Butthisisjusttosay,given(5),thattobearoundsquareistobeamasslessduck.

Thedraconianwaytoabsorbthepointwouldbetoinsistthatthereareno

impossibleproperties,orthatthereisonlyoneandthatitisindefinable.(Seethe

accountofpropertyindividuationin9below.)Butthatseemsadhoc.Iftherecanbe

manypropertiesnecessarilycoextensivewithgreen,whyshouldnttherebemany

propertiesnecessarilycoextensivewithroundsquare?Itwouldbebettertohavean

accountonwhichitisonethingtobearoundsquare,andanotherthingtobea

masslessduck,sinceitisanindisputablefactofmetaphysicsthatthisisso.

Theproblemarisesbecausetherearetwowaysforaclaimoftheform

(*) x((Fxx)(Fxx)

tobetrue.SuchaclaimcanbetrueinvirtueofthefactthatFandstandinsomeinterestingrelation,oritcanbetruesimplybecausenothingcouldbeeitherFor.Intuitively,isacorrectdefinitionofFonlyifthemodalizedconditionalistrueinthefirstway.Thetrickistosaythisclearly.

Hereisonewaytoimplementtheidea.Eachtruepropositioncanbeassociated

withagroundingtree,whichspecifiesthevariousclustersoffactsthatimmediately

groundit,thefactsthatimmediatelygroundthosefacts,andsoon.Apathinthe

groundingtreeforpwillstartwithpandthenproceedtoanimmediatefullgroundforp,

animmediatefullgroundforthatground,andsoon.(Utterlybasicfactswillhavetrivial

groundingtrees.Butmodalfactsoftheform(*)willneverbebasic.)Saythata

groundingtreeforsuchafactisvacuousiffeverypathinitinvolvesthefactthatFsare

impossible,orthefactthatsareimpossible,ortheequivalent.Thenwecansay:

(6)Def(F,)iff

(a)x((Fxx)(Fxx)),and

(b)Thefact(a)hasanonvacuousgroundingtree.

Thisisawayoffilteringoutspuriousdefinitionsforwhich(a)holdsonlybecauseFsare

impossible.

Imgoingtoignorethiscomplicationinwhatfollows,butforthosewhocare,(6)

istheofficialdefinitionofdefinition.

18

casethat,asamatterofnecessity,wheneverathingisFor,itisFinvirtueofbeing.

Thismaysoundlikeanuglymouthful,butitsequivalenttoaformofwordsthatmany

philosophershavecometofindquitenatural.TosaythatdefinesF,onmyaccount,is

simplytosaythatasamatterofnecessityFsareFifandonlyif,andbecause,theyare

.15,

7.Featuresoftheproposal.

Thegroundtheoreticaccountofrealdefinitionhasanumberofappealing

features.

(a) Itexplainswhytrivialdefinitionsareexcluded.Whyaretherenocasesinwhich

Def(F,F)?BecausetherearenocasesinwhichFaFa,i.e.,becausegrounding

isirreflexive.

(b) Itexplainswhydefinitionalcirclesareexcluded.Whyaretherenocasesinwhich

arelationsRisdefinedintermsofitsconverseR*andviceversa?Becausethere

arenocasesinwhichwehavebothRabR*baandR*baRab,i.e.,because

groundingisasymmetric.

(c) Itallowsrecursivedefinitionstocountasrealdefinitions.Therecursive

definitionofancestorhasitthatforxtobeanancestorofyisforxtobeeithera

parentofyortheparentofanancestorofy.Theproposalsaysthatthisis

correctiffasamatterofnecessity,wheneverxisanancestorofythisisinvirtue

ofthefactthatxiseitheraparentofyortheparentofanancestorofy,andthat

15ThankstoSelimBerkerforpointingthisout,andforcommentsthatledtomajor

changesinthissection.

19

mightbetrue.16Thereisnogeneralprincipleinthetheoryofgroundthatrules

itout.

(d) Itallowsthatasingleproperty,F,mayhavetwocorrectrealdefinitions,and,

providedthatwheneverathingisF,itisFbothbecauseitisandbecauseitis.

Thatthisispossibleisshownbycasesofdefinitionalexpansion.Suppose

Tobeasquareistobeanequilateralrectangle,and

Tobearectangleistobearightquadrilateral.

Theaccountentailsthataissquareinvirtueofbeinganequilateralrectangle,

andrectangularinvirtueofbeingarightquadrilateral.Andfromthese

ingredientsitcanbeshownthataisasquareinvirtueofbeinganequilateral

rightquadrilateral,hencethatsquarehasaseconddefinition:

Tobeasquareistobeanequilateralrightquadrilateral.17

Thereisnoobjectionableoverdeterminationherebecausewehaveachain:

aissquareaisanequilateralrectangleaisanequilateralright

quadrilateral,

16ThisiscertainlymoreplausiblethantheFregeandefinition,whichdefinesancestorin

termsofset.Intuitively,thefactthatMurrayRosenismyancestormightobtainandbe

groundedjustasitisevenif(perimpossibile)therewerenosets.

17Theproofinthissimplecaseisstraightforward.(Leftasanexercise.Thekeypremise

isthestrongtransitivityofground:Ifpq,andq,thenp,.(Rosen2010,p.XXX)Itshouldbepossibletoproveaprinciplethatlicensesarbitrarydefinitional

expansion:

IfDef(F,)andDef(G,),thenDef(F,/G),

where/GistheresultofsubstitutingforGin,butIhaventtried.

20

andgroundistransitive.

Buttheremayalsobecasesinwhichtheseveraldefinitionsofasingle

propertyarenotrelatedinthissimpleway.Itissometimessaid,forexample,

thatprimenumberhastwodefinitions:thegradeschooldefinition,accordingto

whichtobeaprimeistobeanumbernwhoseonlyfactorsare1andn,anda

moreadvanceddefinitionaccordingtowhichtobeprimeistobeanumbern

suchthatwheneverndividesaproductpq,ndivideseitherporq(Tappenden

1998).Thepresentaccountallowsthatthesemaybothbecorrectreal

definitionsofasingleproperty,providedwearepreparedtosaythatwhenever

nisprime,itisprimebothbecauseitsatisfiesthefirstcondition,andbecauseit

satisfiesthesecond.

(e) Finally,theproposalshedslightonwhywemightcareaboutrealdefinitionsin

philosophy.WhyshoulditbeusefulorinterestingtoknowwhatitistobeF?

BecausesuchknowledgeputsusinapositiontoexplainwhyanygivenFisF,and

explanatoryinformationisalwaysworthhaving.

9.TheIndividuationofproperties

Theargumentsagainstthesimplemodalaccountofdefinitionsuggestthatwe

areoperatingwithahyperintensionalconceptionofpropertiesonwhichitisonething

tobegreen,andsomethingquitedifferenttobegrueandobservedorbleenand

unobserved.Anditisalwaysafairchallengetoanysuchaccounttoaskforclarification

ofthisconception,arequestthatissometimesputasthedemandfortheidentity

conditionsofpropertiesandrelations.SupposewehavepropertiesFandGpickedout

bydifferentbitsoflanguageorbydifferentconcepts.Theintensionalistsaystheyare

21

thesamepropertyifftheyaretheynecessarilycoextensive.Whatdoesthe

hyperintensionalistsay?

Perhapsjustthis:IfFandGindefinable,theyarethesamepropertyifftheyare

necessarilycoextensive;iftheyredefinable,theyareidenticalifftheyhavethesame

definitions:

PropertyIdentity:FandGarethesamepropertyiff

(a) FandGareindefinableandx(FxGx),or

(b) FandGaredefinableandforall,(Def(F)Def(G,))

(Ihaventdefendedtheaccountforindefinableproperties,butImawareofnoground

fordistinguishingcointensiveindefinablepropertiesthatwouldnotalsobegroundsfor

distinguishingHesperusandPhosphorus.)Giventhegroundtheoreticaccountof

definition,thisamountstosayingthatdefinablepropertiesareindividuatedbythe

groundsforatomicfactsinvolvingthem.WhenFandGaredefinable,F=Giffinevery

possiblecase,thegroundsforFaarealsogroundsforGaandviceversa.

IftherecanbecasesinwhichFandGarenecessarilycoextensiveandyetthe

groundsforFadifferfromthegroundsforGa,thisaccountwillentailahyperintensional

conceptionofproperties.Butthatturnsouttobeasubstantialif.Strictlyspeaking,

myaccountofdefinitionisconsistentwithanorthodoxintensionalviewofproperties.

Thismaynotbeobvious,sothepointisworthexploring.

IhavecertainlyassumedandoccasionallyarguedthatDef(F,)is

hyperintensional.Thecounterexamplestothesimplemodalaccountallgotoshowthis.

ButthecounterexamplesareallcasesinwhichwehaveDef(F,)andx(xx)

butnotDef(F,).Thatis,theywereallcasesinwhichDef(F,)ishyperintensionalon

22

theright.Theaccountexplainsthishyperintensionalitybyreducingittothe

hyperintensionalityofground.Butallofthisisperfectlyconsistentwiththeassumption

thatDef(F,)issimplyintensionalontheleft,orinotherwords,thatDef(F,)and

x(FxGx)entailDef(G,).

Toseewhy,recallasubtlepointstipulatedattheoutset,namely,thatdefinition

istobeunderstoodasarelationbetweenapropertyandacomplex.Propertiesand

complexesarealikeinthisrespect:bothcombinewithanobject(orasequenceobjects)

toyieldaproposition.Thedifferenceisthatcomplexesarepropositionlikeitemswith

internalstructureopensentencesinaworldlylanguagewhereaspropertiesare

(forallwecare)mereologicallysimple.Thereisthusadifferencebetweenthecomplex

xisgrueandobservedorbleenandunobserved,

whichhasgrue,bleen,observedandvariouslogicalparticlesasconstituents,and

thepropertyofbeinggrueandobservedorbleenandunobserved,

whichdoesnot.Inthisframeworkweshouldthinkofthepropertyofbeing

sometimesregimentedasxxasanoperatorthatattachestoacomplexto

yieldatermthatpicksoutaproperty:xx.Theargumentsforthefunctionare

typicallycomplex;thevaluesofthatfunctionthepropertiesarenot.

ToseethattheviewIvebeendevelopingisconsistentwithintensionalismabout

properties,assumeintensionalismandconsiderthefollowingpackageofclaimsabout

green:

(a) Asamatterofnecessity,athingisgreeniffitisgrueandobservedorbleenand

unobserved.

23

(b) Sothepropertyofbeinggreen=thepropertyofbeinggrueandobservedor

bleenandunobserved.

(c) ButitisnotthecasethatDef(green,xisgrueandobservedorbleenand

unobserved).

Givenouraccountofdefinition,thispackageentailstheplausibleclaimthat

(d) Thereisapossiblecaseinwhichathingisgreen,butnotinvirtueofbeinggrue

andobservedorbleenandunobserved.

Butitalsoentailsthesomewhatsurprisingclaimthat

(e) Thereisapossiblecaseinwhichathingpossessesthepropertyofbeinggrue

andobservedorbleenandunobserved,butnotinvirtueofbeinggrueand

observedorbleenandunobserved.

Thisisaclaimoftheform:

Possibly,x(x)a,butnot:x(x)aa

Anditmaybehardtoseehowanysuchclaimcouldbetrue.Butanintensionalistwho

acceptsthegroundingidiomneednotfindthispuzzlingatall.Shecansay:

Thefunctionxtakesfromacomplexxtotheuniquepropertyintensionally

equivalenttox(whenthereisone),muchasthedefinitedescriptionoperator

takesusfromacomplextotheuniquesatisfierofthatcomplex(whenthereis

one).Inthiscase,thepropertyinquestionthepropertyofbeinggrueand

observedorbleenandunobservedjustisthepropertyofbeinggreen.(They

24

mustbethesameproperty,sincetheyreintensionallyequivalent.)Thisproperty

mayormaynothaveadefinition.Butitsdefinitioncantbereadofffromthe

structureofanarbitraryexpressionthatpicksitout,justastheessenceofthe

inventorofbifocalscannotbereadofffromthestructureofanarbitrarydefinite

descriptionthatpickshimout.Ingeneral,from

aisF,and

F=thepropertyofbeing,

itdoesnotfollowthat

aisFinvirtueofbeing.

WhetherthislastclaimistrueistruedependsonthedefinitionofF(aka,the

propertyofbeing),whichisupforgrabs.

Onthisversionofintensionalism,propertiesarelikeobjectsinthisrespect:theycanbe

pickedoutornamedinindefinitelymanyways,mostofwhichwillfailtoencodetheir

definitions.ThisisafamiliarpointifwethinkofdescriptionslikeFredsfavorite

property.Itislessfamiliarwhenthetermsinquestionareoftheformthepropertyof

being.Stillitisacoherentview,andthefactthatitiscoherentservestoshowthat

theconceptionofrealdefinitionthatIvebeenadvancingis,perhapssomewhat

surprisingly,fullyconsistentwithanintensionalistviewofproperties.

Wearepushedtoahyperintensionalviewofpropertiesonlyifwetakeon

additionalcommitments.ConsiderthethesisthatmightbecalledStrongProperty

Abstraction(SPA):

SPA:Foranycomplex,thereisapropertyFsuchthatDef(F,)

Thisismuchstrongerthanordinarypropertyabstraction(whichmaybetoostrong

alreadygiventhethreatofparadox).Ordinarypropertyabstractiontellsusthatforany

complex,thereisapropertyintensionallyequivalentto:xx.Thisnewprinciple

25

tellsusthatforanycomplex,thereisapropertydefinedby,thatis,aproperty

atomicfactsinvolvingwhicharesystematicallygroundedinfactsoftheforma.A

principleofthissortwouldguaranteetheexistenceofapropertyFsuchthattobeFis

tobegrueandobservedorbleenandunobserved.Andifthereissuchaproperty,

intensionalismisfalse,sincethatpropertyisdistinctfromgreenbutnecessarily

coextensivewithit.Butintheabsenceofsomesuchprinciple,itisconsistenttosay

thateverypropertyequivalenttogreenhasthesamedefinitionandisthusidenticalto

green.

WhatisthestatusofSPA?Ifindithardtosay.Iseenoobjectiontothe

hyperintensionalconceptionofproperties,andoftenfinditnatural.Itstrikesmeas

obvious,forexample,thatthepropertyofbeingasquarenumberisdistinctfromthe

propertyofbeingasumofconsecutiveoddnumbersstartingwithone,andthatthisis

shownbythefactthatyoupossessthefirstpropertyinvirtuebeingsomeonessquare,

andthesecondpropertyforanaltogetherdifferentreason.Butanyconsiderationthat

wouldclinchthecaseagainstintensionalisminthisframeworkwouldbehighly

theoreticalandrecherchinsofarasitgoesbeyondthissortofintuition.Theaccount

ofdefinitionIhavegivenisfitsquitenicelywithahyperintensionalviewofproperties,

sinceitgivesthehyperintensionalistsomethingcleartosayinresponsetothedemand

foranaccountofpropertyindividuation.Thepointoftheargumentjustrehearsedisto

showthatevenifwerejecttheintuitionsthatsupportthehyperintensionalview,we

canstillaccepttheaccountofpropertyindividuationsketchedaboveandthe

conceptionofrealdefinitionitpresupposes.

10.Anapplication:Interpretingthedebateovermoralnaturalism.

Toseewhythismightmatter,supposethatafterthedusthassettledinfirst

orderethics,wefindourselveswithacounterexampleproofequivalenceoftheform:

(N) Necessarily,anactismorallypermissibleiffitis,

26

whereisathoroughlynaturalisticcomplexcomposedofindisputablynonnormative

bitsandpieces:cause,pleasure,etc.Fortheorthodoxintensionalistwhoeschewsfine

grainednotionsofgroundinganddefinition,thisamountstonaturalismaboutmoral

permissibilityonanyplausibleunderstandingofthatthesis,sinceitentailsthatmoral

permissibilityisidenticalwiththepropertyofbeing,whichisclearlyanaturalproperty

byconstruction.18

Inmyframework,bycontrast,(N)isconsistentbothwithnaturalismandwith

nonnaturalismaboutpermissibility.Supposewetakenaturalismtobethethesisthat

everymoralpropertyisanaturalproperty,whereapropertycountsasnaturaliffitis

eitheraprimitivenonnormativepropertyorapropertythatcanbedefined,inour

sense,innonnormativeterms.19(N)isthenconsistentwithnaturalismaboutmoral

permissibility(MP)becauseitsconsistentwithDef(MP,).Thatis,(N)isconsistent

withtheclaimthatwhenanactispermissible,itispermissibleifandonlyif,and

because,itis.But(N)isalsoconsistentwiththedenialofthisclaim.Consider,for

example,thenonnaturalistwhosays:

18Indeed,sincethestrongsupervenienceofthenormativeonthenonnormative

guaranteestheexistenceofatruthoftheform(N)foreachnormativeproperty,an

orthodoxintensionalistwhoacceptsstrongsupervenienceasalmosteveryonedoes

mustbeamoralnaturalistacrosstheboard.

19Thisisaplausibleaccountofwhatissometimescalledreductivenaturalismin

metaethics,aviewthatissupposedtocontrastbothwithnonnaturalismandalsowith

somethingcallednonreductivenaturalism.Iconfesstobeingunabletomakesenseof

thelattercontrast.Wecouldidentifynonreductivenaturalismabout(say)moral

permissibilitywiththeviewthatwhilethefactsaboutmoralpermissibilitysuperveneon

thenonnormativefacts,thereisnononnormativeconditionsuchthatDef(MP,).Butifthatstheview,thenmostselfproclaimednonnaturalistsParfit,Enochand

Scanlon,forexampleareinfactnonreductivenaturalists,andtheonlynonnaturalist

onthecontemporarysceneisKitFine(2000),whorejectsthemetaphysical

supervenienceofthenormativeonthenonnormative.Thatsuggeststhatthisaccount

ofnonreductivenaturalismcantberight;butifthatsnottheview,thenIdontknow

whattheviewissupposedtobe.

27

Iagreethatanactismorallypermissibleifandonlyifitis.Butwhenweask

whyanygivenactismorallypermissible,theansweralwayslookslikethis:Ais

permissibleinvirtueofthefactthatAistogetherwithasubstantivemorallaw

accordingtowhichanactispermissibleifandonlyifitis.

Thisviewaccepts(N)butdeniesDef(MP,)andeverysimilarclaim,andsoconstitutes

agenuinealternativetonaturalism.20

Thisframeworkhastheadvantageofsharpeningthedebateovermoral

naturalisminawaythatmakesitclearwhythedebatehasbeensohardtoresolve.

Thequestionisnotwhethermoralpredicates(orproperties)arenecessarilycoextensive

withnonnormativeconditions,astheymustbegivensupervenience,whichnearly

everyoneaccepts.Nororisitwhethermoralpropertiesareidenticalwithnatural

propertiesonthesimpleintensionalistconceptionofproperties,sinceagain,thatsa

trivialconsequenceofsupervenience.Thequestionisratherwhethermoralproperties

admitofnaturalisticdefinition,orequivalently,whethertheatomicmoralfactsare

systematicallygroundedinnonnormativefacts.ThenaturalistsaysthatwhenAis

permissible,itispermissiblesimplyinvirtueofsatisfyingsomenaturalisticcondition.

Thenonnaturalistdeniesthis,maintainingthatwhenAispermissible,thisfactis

20Toillustratethepointmadeinthelastsection,itsworthnotingthatthisnon

naturalistviewcomesintwoflavors.Themoststraightforwardversionofitis

hyperintensionalist.Onthisview,therearetwopropertiesnecessarilycoextensivewith

:moralpermissibility,whichisnonnatural,andthepropertyofbeing,whichadmitsofasimplenaturalisticdefinition:Def(xx,)Butthereisalsoanintensionalistversionofnonnaturalism.Onthisview,weidentifymoralpermissibilitywiththe

propertyofbeing(sincetheyarecointensive),butinsistthatthispropertycannotbedefinedinnaturalisticterms.InparticularwedenyDef(xx,),rejectingStrongPropertyAbstractioninthiscase.Icanthinkofnogoodreasontoacceptthisview,or

totakeitseriouslyasapossibilityinmetaethics.Imentionitonlytoshowthatan

intensionalistwhoacceptsafinegrainednotionofgroundanddefinitioncanbeanon

naturalistinethicsevenifshebelievesthateverymoralpropertyisequivalenttoa

naturalisticcondition.

28

groundedinnaturalfactstogetherwithasubstantive,syntheticmoralprinciple.21This

issueismanifestlyarcane.Somequestionsaboutwhatgroundswhatareeasy,butthis

oneisnt.Ifthisiswhatthedebateovernaturalisminethicsboilsdownto,itshould

comeasnosurprisethatwehavenomanagedtoresolveit.

10.Conclusion

Philosophyisuniqueamongdisciplinesintakingfullresponsibilityforitsjargon.

Itsnotthemathematiciansjobtosaywhatanumberis.Itsnotthephysicistsjobto

saywhattimeis.Butwhenaphilosopheremploysanidiomforaseriouspurpose,itis

automaticallyherjob,atsomepoint,tosaywhatcanbesaidbywayofexplanation.As

wehavenoted,everypartofanalyticphilosophyisinthebusinessofgivingaccounts

ordefinitionsoranalyses.Andsoitfallstoustosaywhatweredoingwhenwedo

this.

Ihavesupposedthattheobjectsofanalysisarepropertiesandrelations,andIve

givena thoroughly metaphysicalaccountofwhatdefinitioncomes to. According to

that account, to define a property is to identify a necessary truth that specifies, in a

uniform way, how atomic facts involving that property are grounded in more

fundamentalfacts.

Myaccount employsonemoderately exotic primitive: anotionof ground that

seems tome to be needed anyway and forwhich detailed theories have been given

elsewhere.22Itwouldbegoodifwecoulddowithoutit,butIdontseehowthiscanbe

done,andsoIofferthefollowingconjecture.Theidiomsofdefinitionandanalysisthat

wetakeforgrantedinphilosophystandorfallwiththegroundingidiom,sincethereis

nowaytoexplainthemwithoutit.Ifyoureallergictoground,youshouldstopasking

what it is foracreaturetobeconsciousor fora fact tobea lawofnatureor fortwo

21Oralternatively,thattheatomicmoralfactshavenofullgrounds,beingatbestpartly

groundedintheparticularnaturalfactsthatunderliethem.Thisisanoptionforradical

particularists,forwhomgeneralmorallawsplaynoexplanatoryrole.22SeeCorreiaandSchnieder(2012)forthestateoftheart(asof2012).

29

expressionstohavethesamemeaningorforanacttobefreeorforanartifacttobean

artwork,sinceyoucantexplainwhatyourquestionsmeanwithoutinvokingaconcept

youreject.Ontheotherhand,ifyouthinkthesequestionsmakegoodsense,thenyou

shouldmakeyourpeacewithgrounding,sinceyouarecommittedtomakingsenseofit

bythequestionsyoumakeityourbusinesstoaskandanswer.