metaphysical naturalness and degrees of reality - kris mcdaniel

volume13,no.19 october2013

Degrees of Being

Kris McDanielSyracuse University

© 2013 KrisMcDanielThis work is licensed under a Creative Commons

Attribution-NonCommercial-NoDerivatives 3.0 License. <www.philosophersimprint.org/013019/>

1. Introduction1

Letusagreethateverythingthatthereisexists,andthattobe,tobereal,andtoexistareoneandthesame.Doeseverythingthatthereisexisttothesamedegree?Ordosomethingsexistmore than others?Aretheregradationsofbeing?

Perhapsnoviewismoredespisedbyanalyticmetaphysiciansthanthattherearegradationsofbeing.Butwhatif,unbeknownsttothem,they have helped themselves to the doctrine that being comes indegreeswhenformulatingvariousmetaphysicaltheoriesorconductingmetaphysicaldisputes?What ifgradation of being is alreadyplayingasignificantroleintheirtheorizing,albeitunderadifferentguise?

Consider the following technical terms employed in manycontemporarymetaphysical debates: ‘naturalness’ as usedbyDavidLewis(1986),‘fundamentality’or‘structure’asusedbyTedSider(2009,2012), ‘grounding’ as used by Jonathan Schaffer (2009) and others,andtheubiquitous‘invirtueof’.Ihavearguedelsewherethat,givencertainplausibleassumptions,thenotionofdegreeofbeingorgradeofbeingcanbeanalyzedintermsofthesenotions.2HereIwillarguethat,givencertainplausibleassumptions,eachofthesenotionscanbeanalyzedintermsofthenotionthatbeingcomesindegreesorgrades.

Thereareseveral reasonswhy this result is interesting.First, thenotionsofnaturalness,fundamentality,orstructureareonesthatmostcontemporarymetaphysiciansgrantareintelligible,whereastheclaimthat existence, being, or realitymight come in degrees is regardedbymanymetaphysicians as being unintelligible. Oneway to assistaphilosopheringraspinganotionthatsheregardsasunintelligible

1. Versionsof thispaperwerepresented toaudiencesatSUNYFredonia, theMellonMetaphysicsWorkshopatCornellUniversity,MetaphysicalMayhemat Rutgers University, theMetaphysical FundamentalityWorkshop at Aus-tralianNationalUniversity,theUniversityofBirmingham,TheUniversityofNottingham,theUniversityofToronto,NewYorkUniversity,andtheUniver-sityofAlberta;Ithanktheseaudiencesfortheirhelpfulfeedback.IalsothankMark Barber, Elizabeth Barnes, Karen Bennett,Mike Caie, Ross Cameron,AndyCullison,Neil Feit,DanielFogal,TedSider,BradSkow, JasonTurner,andRobbieWilliamsforhelpfulcommentsonearlierdraftsofthepaper.

2. SeeMcDaniel(2010b).

ImprintPhilosophers’

krismcdaniel Degrees of Being

philosophers’imprint –2– vol.13,no.19(october2013)

on the notion of naturalness or structure and then recapitulate thedefinitionofdegreesofbeingintermsof it.SinceIhavearguedforthisdefinitioninanotherpaper(McDaniel2010b),Iwillbesomewhatbrief. Insection4,Iprovideandmotivateadefinitionofnaturalnessintermsofdegreesofbeing.Insection5,Idiscussseveralquestionsthatonemight have about naturalness and show that there are parallelquestionsonemighthaveaboutdegreesofbeing. In thecontextofthisdiscussion, Iadvancewhat I call the notational variant hypothesis, accordingtowhichtheoriesthatdifferonlyinwhethertheyemploythenotionofnaturalness/structureorthenotionofdegreesofbeingarereallythesametheory,albeitunderdifferentguises.Onewaytoresistthenotationalvarianthypothesiswouldbetopromoteanargumentthat, despite their mutual inter-definability, one of the notions ofstructureordegreeofbeingisinsomewayprior,andhencetherearetwodistinctphenomena inplayrather than twodifferentguises forthesameunderlyingphenomenon. Insection6, Idevelopandthencritically evaluate two plausible arguments for taking the notion ofnaturalnessastheprimarynotion.Althoughtheseargumentsmightseeminitiallycompelling,ultimatelyIdonotthinkthattheysucceed.Insection7,Iinvestigatewhetherthereissomereasontoprefertakingdegree of being as theprimitivenotion.There, Idiscussan intriguingargument based on the idea that theories making use of degree of being aremore ideologically parsimonious. Although this argumentis inconclusive, I view it as in better shape than the arguments fortaking naturalness/structure as the prior notion. I thereby endorsea disjunctive conclusion: either the notional variant hypothesisis true—in which case contemporary metaphysicians have beenemployingdegreesofbeingintheirtheorizing,albeitnotunderthatguise—or the notion that contemporarymetaphysicians have beenemployingought to be further analyzed in terms of degree of being.Ifeitherdisjunct is true, then contemporarymetaphysicians need to rethinkwhat they’ve been up towhen theorizing inmetaphysics and howtheir theorizing isoriented towards those longdeadwho theorizedbefore them. Section 8 briefly discusses an epistemic advantage to

is toshowherhowonecanusethatnotiontodefineonesthatsheantecedentlyacceptsasintelligible.

Second,itiswidelybelievedbymetaphysiciansthatatleastoneofthenotionsofnaturalness,fundamentality,structure,orgroundingistheoreticallyfruitful,whereasmostcontemporarymetaphysiciansseelittleuseforthethoughtthatexistencecomesindegrees.Forexample,metaphysicians such asDavid Lewis arewilling to take the notionof naturalness as a primitive because they recognize that it can beusedtodefineorpartiallycharacterizethefollowingphilosophicallyimportant concepts: objective similarity, intrinsic properties, laws of nature, materialism, meaning and reference, and so forth.3 If we candefine thenotionof naturalness in termsof degrees of being, thenmetaphysicianswillhaveanequallystrongreasontotakethenotionofdegreesofbeingasprimitive,sinceitcandoalloftheworkthatthenotionofnaturalnesscando.

Third,whenevertwonotionsareshowntobeinsomesenseinter-definable (givencertainassumptions), interestingquestionsarise. If,forexample,degreesofbeingandnaturalnessare,insomesense,inter-definable,havemetaphysiciansbeen,insomesense,reallycommittedtotherebeingdegreesofbeingallalong?Canargumentsbegiventhatoneought totakethenotionofadegreeofbeingasaprimitiveratherthannaturalnessorviceversa?

Finally, there are somephilosopherswho remaindubious aboutmetaphysicalprimitivessuchasnaturalness,grounding,orstructure.Isuspectthatthesephilosopherswouldbeoverjoyedtodiscoverthatthenotionofnaturalnessandthenotionofdegreeofbeingareinter-definable,forthen(bytheirlights)thenotionofnaturalnesswouldbedemonstrablydisreputable.Andperhaps somephilosopherson thefencewillbemovedonewayortheother.

Here is the plan for the rest of the paper. The next sectionwillbedevotedtoarticulatingtheviewthatbeingcomesindegreesandbriefly discussing several variants of this view. In section 3, I focus

3. SeeDavidLewis(1983,1984,and1986)forexamples.



relationsuchasx is at least as real as yandholdthatsomethingexistsiff it bears that relation to something, including it to itself. Iwon’tsettle between these, or any other, views on the metaphysics ofquantitynow.4 For themostpart, Iwill use the locution ‘degreeofbeing’moreoutofstylisticconveniencethanoutofaconvictionthatbeingisadeterminablesuchthatitmakessensetoassignnumberstoitsdeterminates.

However,onnooptiondoessomethinghoverbetweenbeingandnon-being:everythingthatthereisexistssimpliciter,althoughofsomethingsexistmorethanothers.PerhapsPlatothoughtthatparticularsare as much as they are not.5 This is not my view. Even thoughsomethingenjoying 1gramofmass is lessmassive than somethingenjoying1kilogramofmass,itwouldnotbesensibletodescribeanobjectenjoying1gramofmassasbeingasnon-massiveasitismassive(or,worse,morenon-massivethanitismassive).Everythingwithmassismoremassivethannon-massive.Similarly,eventhethingswiththesmallestamountsofbeinghavemorebeingthannon-being.

OnthemetaphysicsIamattractedto,somethingsdoexisttothehighest degree,whereas other beings exist to a lesser degree. I amconfident in the maximal existence of myself and other consciousbeingsaswellasmaterialobjectswithoutparts,butIamlessconfidentthat non-sentient composite material objects enjoy full reality.Perhaps the most compelling examples of real but less than fullyreal entities arenegative entities such as shadows, holes, cracks, andfissures.RoySorenson(2008,p.189)claimsthat“holesdonotsitanymorecomfortablyonthesideofbeingthanofnonbeing”.Itwouldbebettertosaythat,althoughholessitonthesideofbeing,theyoccupyalowerpositionthanotherbeingsonthisside.Isuspectthattheview

4. Some interesting papers on the metaphysics of quantity include Eddon(forthcoming),Hawthorne(2006),andMundy(1987).Forthesakeofconve-nience,Iwilloccasionallytalkasifthebasicnotionis‘xhasn-unitsofbeing’,althoughthisisnottheviewIwouldultimatelyendorse.

5. SeePlato’sRepublic 479c–eforadiscussionofthingsthat“millaroundsome-wherebetweenunrealityandperfectreality”.

takingdegreesofbeingasthepriornotionandindicatessomelinesoffurtherresearchworthpursuing.Finally,inanappendix,Idiscusswhetherthenotionofmetaphysical grounding canalsobeaccountedforintermsofdegreesofbeing.

2. Degrees of Being

TheviewImeantodefendistheviewrejectedinthefollowingpassage:

Athingcannotbemoreorlessrealthananotherwhichis also real. It has been said that reality does admitof degrees. But this can … be traced to one of twoconfusions….Sometimesrealityhasbeenconfusedwithpower…[but]athingwhichassertsmorepowerisnotmore real than one that asserts less. Sometimes… thepossibilityofdegreesofrealityisbasedonthepossibilityofdegreesoftruth.…If,forexample,itshouldbetruertosaythattheuniversewasanorganismthanthatitwasanaggregate,thenitissupposedthatwemaysaythatanorganicuniverseismorerealthananaggregate-universe.Butthisisamistake.[McTaggart1927:4–5]

Igrantthatitwouldbeamistaketoconfusepowerwithrealityandamistaketoacceptdegreesoftruth.Solet’snotmakethesemistakes.OntheviewthatIamconsidering,beingisnottobeconflatedwithsomeotherfeaturethatcomesindegrees.Beingitselfcomesindegrees:tobesimpliciteristobetosomedegreeorother,justastohavemasssimpliciteristohavesomedeterminateamountofmass.Andjustasnoteverythinghasthesameamountofmass,noteverythingthat isexiststothesamedegree.

Thereareanumberofwaystofleshoutthisview,anddependingonwhatthecorrectmetaphysicsofquantitiesis,differentwayswillbemoreattractive.Onepossibility is that existence is aquantitativedeterminableakintomassandthatdegreesofbeingaredeterminatesof this determinable. Another possibility is to take as basic some



speakerofa language inwhich ‘isgrue’and ‘isbleen’areprimitivepredicatesand‘isgreen’and‘isblue’areintroducedviaa“disjunctive”definition in the following way: something is green just in caseeitheritisgrueandexaminedbefore2200A.D.oritisbleenandnotexaminedbefore2200A.D.;somethingisbluejustincaseeitheritisbleenandexaminedbefore2200A.D.oritisgrueandnotexaminedbefore2200A.D.Greenandbluewouldseemlikestrangepropertiestothisspeaker.

Nonetheless,greenandbluearemetaphysicallybetterpropertiesthan bleen and grue: although they are, in some sense, inter-definable,grueandbleenought tobedefinedintermsofgreenandblueratherthantheotherwayaround.Grueandbleenaredisjunctive properties,whereasitseemsthatgreenandbluearenot.Thenotionof a disjunctive property is intimately connected with the notionof naturalness, as the following condition for being a disjunctivepropertymakesclear:P isameredisjunctionofQandRonlyif(i)necessarily,somethinghasPifandonlyifithaseitherQorR,and(ii)PislessnaturalthanbothQandR.

Letusturntotwomorecontroversialclaimsaboutthenotionofnaturalness,bothrecentlydefendedbyTedSider(2009).First,Siderarguesthateveryone,evennominalists,shouldholdthat‘isgreen’isametaphysically better predicate than‘isgrue’.Siderpointsoutthatthereareseveralstrategiesavailabletothenominalistformakingsenseofthedistinction.Oneofthemconsistsoftakingatwo-placedoperator‘N’, whichoperatesonopensentencesandyieldsaclosedsentence.Asentenceoftheform‘N(Fx,Gx)’ statesfactsofcomparativenaturalnessand,inthiscase,statesthattobeFismorenaturalthantobeG.7

Second,Siderargues thatweought tomakesenseof judgmentsof comparative naturalness in which the things compared arenot predicates but rather entities from other linguistic categories.

7. InSider(2012),Siderabandonsthetwo-place‘N’operatorandembracesaone-place‘S’operator.AsfarasIcansee,nothinginwhatfollowshereturnsonwhichlocutionthenominalistoughttofavorwhenstatingfactsaboutnaturalness.

thatholesandshadowsexistbutarenotfullyrealistheviewofthecommonpersonnotyetexposedtoacademicmetaphysics.6

3. Naturalness and the Definition of Degrees of Being

Theworld has a privileged structure. Someways of carving up theworld are better than others: they are more natural. The naturalpropertiesare thoseproperties thatpartition theentitieswithin theworldinthebestway.Thenotionofanaturalpropertyinplayhereisnot thenotionofphysical property, i. e.,apropertythatcanbe(orperhaps can only be) instantiated by physical objects. Rather, thenotionofanaturalpropertyisthatofafundamental orbasic property,anditisasubstantivehypothesisthatthefundamentalpropertiesareallandonlythephysicalproperties.

Oneofthecharacteristicsofanaturalpropertyisthatitsinstancesareobjectivelysimilartoeachotherinvirtueofexemplifyingit.Notallpropertiesaccountforobjectivesimilarity:atoasterandaleopardareveryunlikeeachother.Thisistruedespitethefactthattheyarebothnotviolins,arebotheitheraleopardoratoaster,andshareinfinitelymanyotherproperties.Thepropertyofnotbeingaviolinisamerelynegative property.Arguably,whatmakesonepropertyanegationoftheotheristhefactthatalthough,necessarily,everyobjecthasoneofthepairofpropertiesandnothingcanhaveboth,oneofthepairisfarmorenaturalthantheother.

Nelson Goodman (1965) introduced the so-called new riddle of induction bycallingourattentiontothefollowingpredicates:‘isgrue’and‘isgreen’.Saythatsomethingisgruejustincaseeitheritisgreenandexaminedbefore2200A.D.oritisblueandnotexaminedbefore2200A.D.Saythatsomethingisbleen justincaseeitheritisblueandexaminedbefore2200A.D.or it isgreenandnotexaminedbefore2200A.D.

Grueandbleenseemlikestrangepropertiestous,especiallysincethey were introduced via a “disjunctive” definition. But consider a

6. SeeMcDaniel(2010b)forafurtherexplorationofthemodeofbeingenjoyedbyholes,shadows,andother“negative”entities.



thantobewantedorbelievedbysomebachelor,andsentence3tellsusthattobeismorenaturalthantobiz.9

Let’sreturntothetaskofdefiningthenotionofdegreesofbeing.Say that a quantifier is a semantically primitive restricted quantifier just in case it fails to rangeover everything that there is but is notasemanticallycomplexunitconsistingoftheunrestrictedquantifierandarestrictingpredicateoroperator.InMcDaniel(2009,2010a),Iofferthefollowingaccountofmodes of being:therearemodesofbeingjustincasetherearesomepossiblesemanticallyprimitiverestrictedquantifiersthatareatleastasnaturalastheunrestrictedquantifier.InMcDaniel(2010b),Idefendthefollowingdefinitionofdegree of being:x existstodegreen justincasethemostnaturalpossiblequantifierthatrangesoverx isnaturaltodegreen.Insloganform:An object’s degree of being is proportionate to the naturalness of its mode of existence.

Both the notion of amode of being and the notion of a degreeof being can be straightforwardly accounted for in terms of thenaturalnessofcertainquantifiersandcanbeusedbyfriendandfoealike.Thefoeofmodesofbeingcouldclaimthatnootherquantifiercould be as natural as the unrestricted quantifier, thereby ensuring(giventhedefinitionsabove) thateverythinghas thesamemodeofbeingandexiststothesamedegree.

NotethatSider(2009,2012)ishimselfopentotheviewthatthequantifier employed inordinarydiscourse isnot aperfectlynaturalexpression. If this view is correct, it might be that some thingsthat exist are not in the domain of any possible perfectly naturalquantifier.10 If something exists and is in the domain of a perfectly

9. There is some reason tobea littlenervousaboutSider’sN operator.Notethattheboundvariable inthefirstsentencetakestermsas itssubstitutioninstances,theboundvariableinthesecondsentencetakessentencesasitssubstitution instances, and thebound variable in the third sentence takespredicatesasitssubstitutioninstances.Howcanoneoperatorbindvariablesofthesethreedifferenttypes?IthankRobbieWilliamsfordiscussionhere.

10. Thisclaim,ofcourse,doesnotfollowfromtheclaimthattheordinaryEng-lishquantifierisnotperfectlynatural.Butitmightnonethelessbeareason-able conjecture. See alsoMcDaniel (2010b) for further exploration of thisconjecture.

Regardless of your views on modality, the sentence operator ‘it isnecessarily thecase that’ seems tobemuchmorenatural than ‘it iswantedorbelievedbyatleasttwopeoplethat’.Sider’smainconcernistoarguethatsomequantifierexpressionsaremorenaturalthanothers.

Consider a language L that is much like English. L contains aphrasewhichsoundsliketheEnglishphrase‘thereis’.Itiswrittenlikeittoo,butwewilluse ‘therebiz’ insteadinordertoavoidpotentialambiguity. ‘There biz’ functions syntactically and inferentially like‘there is’.Forexample, if ‘Fa’ isa truesentenceofL, then ‘therebizanFa’isatruesentenceofL.Since‘therebiz’hasthesamesyntacticproperties and inferential role as ‘there is’, I will call ‘there biz’ aquantifier-expression. ‘There biz’ is not synonymouswith ‘there is’,andinfactnoexistingexpressioninL currentlyissynonymouswith‘there is’. Moreover, there is someΦ such that ‘there isΦ’ is falsewhereas ‘therebizΦ’ is true.OnSider’sview,wecancompare thenaturalnessof‘thereis’withthatof‘therebiz’.Perhapswearelucky,and the English quantifier ‘there is’ is the most natural quantifierthereis.8

Sider (2009) regiments these claimsvia ‘N’. Inwhat follows, thevariablesthatwouldbefree variableswerethe‘N’operatortobeabsentareitalicized.(RecallthatSider’s‘N’operatortakesasargumentsopensentencesandyieldsclosedsentences.)

1.N(Fx,Gx)

2.N(□P,KP)

3.N($xFx,$*xFx)

Informally,sentence1tellsusthattobeF ismorenaturalthantobeG, sentence2tellsusthattobemetaphysicallynecessaryismorenatural

8. Thereissomecontroversyaboutwhetherthe“thereis”ofordinaryEnglishisproperlythoughtofascorrespondingtotheexistentialquantifierofformallogic;seeSzabo(2011)fordiscussion.Fortunately,allofthemainmovesofthispapercanbemade,albeit inaslightlymorecomplicatedway,withoutmakingthisassumption.IthankDanielFogalforhelpfuldiscussionhere.



D.M.Armstrong(1997)isafull-bloodedrealistaboutnaturalprop-erties,whichheidentifieswithuniversals.Buthisattitudetowardstheless-than-perfectly-natural properties is harder to discern. Considerthefollowingtroublingremarks:

Thefirst-classpropertiesofparticularsaretheuniversalstheyinstantiate.Thesecond-classpropertiesofparticularshave the following necessary and sufficient condition.Theyarenotuniversals,butwhen trulypredicatedofaparticular,theresultanttruthisacontingentone.…Whatistheirstatus?Willitbesaidthattheydonotexist?Thatwillbeadifficultsaying,sinceitcanhardlybedeniedthatinnumerable statements in which these property- andrelation-wordsappeararetrue.[Armstrong1997,p.44]

Tothis isaddedthethesisof theontological free lunch.What supervenes in the strong sense is not somethingthat is ontologically anything more than what itsupervenes upon.… [T]he second-class properties arenot ontologically additional to the first-class properties.… [T]he second-class properties are not propertiesadditional to the first-class properties. But it is to beemphasized that this does not make the second-classproperties unreal. They are real and cannot be talkedaway.[Armstrong1997,p.45]

Armstrong correctly notes that we cannot deny that there aresecond-class properties, because there are true propositions aboutthem.Inthisrespect,heisprecededbyAquinasandothermedievalphilosophers,whosaidsomethingsimilaraboutadifferentgroupofsecond-classontologicalentities:

Weshouldnotice,therefore,thattheword‘being’,takenwithoutqualifiers,hastwouses,asthePhilosophersays

naturalquantifier,ithasthehighestdegreeofbeing:itfundamentally exists.Ifsomethingexistsbutisnotwithinthedomainofaperfectlynaturalquantifier,itexistsdegenerately.Toexistdegeneratelyistoexisttoaless-than-maximaldegree.

4. Defining Naturalness in Terms of Degrees of Being

Iwillnow turn to thequestionofwhetherone canunderstand thenotionofnaturalnessintermsofthenotionofdegreesofbeing.

GivenSider’snominalism,nothingintheworld“backsup”claimsabout naturalness. Note that, although Sider regiments talk ofnaturalnessinaputativelynominalisticwayviahis ‘N’operator,therealist about properties could agree that other expressions besidespredicatescanberankedonthenaturalnessscale.Infact,therealistviewisarguablythemoreintuitiveview:whatmakesentencesusing‘N’truearefactsaboutthecomparativenaturalnessoftheentitiesthatcorrespond to the constituents of these sentences. The propertiesthatcorrespondtosententialoperatorsarepropertiesofpropositions,whereasthepropertiesthatcorrespondtoquantifiersarepropertiesofproperties.Ontherealistconstrual,somehigher-orderpropertiesaremorenaturalthanothers.

Let’s provisionally be realists about properties;we’ll examinelater how much rides on this provisional move. Here is aninteresting question: To what extent do non-natural propertiesexist? Here are two plausible but competing answers. Answerone:Allproperties,naturalorunnatural,existtothesamedegree.Answertwo:More-naturalpropertiesexisttoahigherdegreethanless-naturalproperties.

It seems to me that the second answer is better than the first.One slogan championedbynominalists is that properties aremereshadows cast by predicates. I disagree: perfectly natural propertieshaveaglowof theirown.But less-than-naturalpropertiesaremereshadows, although they are cast by the perfectly natural propertiesratherthanbylinguisticentities.Shadowsarereal,buttheyarelessrealthanthatwhichistheirsource.



Howcouldoneexistentontologically countforlessthananotherunless the former is less real than the latter?

Somephilosophersclaimthatthereisacloseconnectionbetweennumberandexistence.11Thereissomeconnection,asshownbythefactthatonecanrepresentclaimsaboutthenumberofthingsviatheapparatusofquantification,identity,andnegation.Forexample,onecansaythatthereareexactlytwoFsbyassertingthat$x$y(Fx&Fy&~x=y&(∀zFz->z=xorz=y)).

On theviewunderconsideration, thereareat least twopossiblequantifiers in play: a perfectly natural one, ‘$n’, that includes allnaturalpropertiesbutnoless-than-naturalonesinitsdomain,andaless-than-perfectly-naturalone,‘$i’,thatincludesallthepropertiesinitsdomain.Onecandidateforbeing‘$i’istheunrestrictedquantifierofordinaryEnglish.For thesakeofasimpleexample, suppose thatthereareexactlytwonaturalproperties,P1andP2,andoneless-than-naturalproperty,namelythedisjunctionofthem,P1vP2.Accordingly,thefollowingsentencesaretrue:

1.∀nz[zisaproperty->(z=P1orz=P2)]

2.Viz[zisaproperty->(z=P1orz=P2orz=P1vP2)]

WerespecttheintuitionthatP1vP2isnoadditionofbeingbyendorsing1. Given 1, there is a straightforward andmetaphysically importantsenseof ‘being’accordingtowhichthereareexactlytwoproperties.Thatwhich is anontological addition tobeing is thatwhich is tobefoundinthedomainof$n.WerespecttheintuitionthatP1vP2existsbyendorsing2aswell.P1vP2mustbecountedamongwhatthereis,butitcountsforlessinvirtueofbeinglessthanfullyreal.Thedenialof2isthedifficultsayingthatArmstrongwarnsusnottoutter,butthedenialof2mustnotbeconfusedwithaffirmationof1.Byacceptingboth1and2,weaccommodatebothintuitionsinacleanway.

BothArmstrongandAquinasfeelsimilarpressuretorecognizeinsomewaytherealityofsecond-classentitieswhilestillholdingthat

11. See,forexample,vanInwagen(2001).

inthefifthbookoftheMetaphysics.Inoneway,itisusedaproposofwhatisdividedintothetengenera;inanotherway, it is used to signify the truth of propositions. Thedifference between the two is that in the second wayeverything about which we can form an affirmativepropositioncanbecalledabeing,eventhoughitpositsnothing in reality. It is in this way that privations andnegationsarecalledbeings; forwesay thataffirmationisopposedtonegation,andthatblindnessisintheeye.Inthefirstway,however,onlywhatpositssomethinginreality canbe calledabeing. In thefirstway, therefore,blindnessandthelikearenotbeings.[Aquinas, Being and Essence,section4,p.21ofBobik1965].

AccordingtoAquinas,therearetwoproperusesoftheword‘being’:thefirstuseistosignifythingsthatbelongtothecategories—thatis,theentitiesthatenjoynon-degenerateexistence.Buttheremustalsobeasenseof‘being’inwhichentitiessuchasblindnessintheeyearebeings, sincewecan formtrueaffirmativepropositionsabout them.Butthissenseneedn’tbetakentobemetaphysicallyfundamental,forotherwise negations, privations, and the sort would be full-fledgedentities in their own right. Things that are said tobebeings in thesecondsenseposit nothing in reality.Theyare“anontologicalfreelunch”.

Let’sreturntoourdiscussionofArmstrong.Considertheclaimthattheless-than-naturalproperties(andthestatesofaffairsinwhichtheyfigure)are“noadditionstobeing”(Armstrong1997,p.12).Takenatfacevalue,theclaimthatsomethingisnoadditiontobeingistantamounttotheclaimthatitdoesnotexist,forifitweretoexist,itwouldhavetobecountedamongthatwhichexistsandhencewouldbeanadditiontobeing.Soless-than-perfectly-realpropertiesmustbecountedamongtheexistents—Armstrongsaysthattheyarereal—buthowcanthisfactbereconciledwiththeintuitionthattheydon’tcountformuch?



somekindofreality.(Similarfactsaboutshadowsorholescouldbeadducedtoshowthatshadowsorholesenjoysomekindofreality.)Evenifthesenseof ‘thereis’ intheabovesentenceisnotthesamesenseasin‘Thereisadonutinthenextroom’,itsufficesthatthereissome senseof‘thereis’inwhichtheabovesentenceistrue.13Forthissenseof‘thereis’iseitheramaximallynaturalsenseof‘thereis’oritisnot.Ifitisamaximallynaturalsense,thenpropertiesexisttothemaximaldegree.Ifitisnot,thenpropertiesexisttoatleasttheextentthatthatsenseof ‘thereis’ isnatural.Eitherway,propertiesexisttosomedegreeorother.

Coulditbethatthequantifieremployedinthesentence‘thereareproperties’ ismaximally unnatural? Let’s provisionally identify beingmaximallyunnaturalwithbeingnaturaltodegreezero.Anentitythatfallsonlywithin the rangeof amaximally unnatural quantifier is anentitythatexiststo0degrees.Perhapstheclaimthatpropertiesexisttodegreezeroisaversionofextremenominalismworthconsidering.

Unfortunatelyfortheextremenominalist,evenifthequantifierinquestionishighlyunnatural,itisnotmaximallyunnatural.Withrespectto the naturalness scale, there are possible semantically primitivequantifiersthatscorefarworse.Consider,forexample,asemanticallyprimitivequantifier that rangesovereverything rangedoverby theordinaryEnglishquantifierexceptforpinkyfingers,thingswithexactlysevenproperparts,andthepropertyofbeingabachelor.TheordinaryEnglishquantifier,whichrangesoverproperties,isdoingbetteronthenaturalnessscalethanthatone!Sothereisatleastonequantifierthatrangesoverproperties that isnotmaximallyunnatural—i. e., that is

here.Onparaphrasestrategies,theclassicpieceisQuine’s“OnWhatThereIs”,reprintedinQuine(1963),alongwithAlston’s(1958)importantrejoinder.CarraraandVarzi(2001)provideausefuldiscussiontothepossibilityofpara-phrasestrategiesofvarioussorts.

13. Forexample,CianDorr(2008)distinguishesbetweenwhathecallsasuper-ficial senseof ‘there is’anda fundamental sense of ‘there is’.That there isasuperficialsenseof ‘there is’ suffices tomakemypoint,but it isnotneces-sary:allthatisnecessaryisthatsomepossible meaningforthequantifierthatrangesoverpropertiesisnotmaximallyunnatural.

theseentitiesaresecond-classqua entity.Isuggestthatinresponsetosimilarpressures,similartacticsshouldbeemployed.

Suppose I am right that unnatural properties are less real thannaturalproperties,andthattheirdegreeofbeingisproportionatetotheirdegreeofnaturalness. If this is correct, thena straightforwardaccountofnaturalnessin terms of degrees of being isapparent:PropertyPismore natural thanpropertyQ=df.PismorerealthanQ;propertyPisnaturaltodegreen =df.thedegreetowhichPexistsisn.Inshort,wecandefinewhatitisforapropertytobenaturalin terms of the notion of degree of being.Themostnaturalpropertiesarethemostrealproperties.

Twooftheprovisionalassumptionsemployedherearethatthereareproperties,andthattalkofnaturalnessshouldberegimentedbyappealing to a naturalness-ordering on properties. Although thereare ways to regiment talk about comparative naturalness withoutpresupposing that thereareproperties, and thedoctrine that somethings exist more than others does not presuppose that there areproperties,theanalysisofnatural offeredhereintermsofdegreesofbeingseemstomakeineliminableuseoftheassumptionthatthereareproperties.Forthisreason,itwillbeworthwhiletodeterminetheextent towhich theview that therearenoproperties isdefensibleandtheextenttowhichthepresuppositionthattherearepropertiesisineliminable.

Let us distinguish extreme nominalism from moderate nominalism.Extreme nominalism is the view that properties in no way exist.Moderatenominalismistheviewthatpropertiesdonotfundamentallyexistbutdodegeneratelyexist.

Extreme nominalism is not a sustainable doctrine. Considerthe sentence ‘There is an anatomical property hadbybothwhalesand wolves’. This sentence is literally true; it explicitly quantifiesoverproperties;itisnotamendabletoparaphraseintermsofsomesentence that does not.12 These facts ensure that properties enjoy

12. PaceYablo(1998)andelsewhere, Icandetectnowhiffofmake-believeas-sociatedwithsuchsentences.Butperhapshereisaplacewhereonemightattempt toresist theargument; there’sobviouslya lot tobe thoughtabout



5. Theoretical Claims and Questions

Let the notational variants hypothesis (‘the NVH’) be the hypothesisthattwotheoriesthatdifferonlywithrespecttowhethertheyemploythenotionofnaturalnessorthenotionofadegreeofbeingaremerenotationalvariantsofeachother.

It sometimes happens that what we take to be two differentphenomena really are the samephenomenon appearingunder twodifferent guises. And it sometimes happens that a phenomenonappearing in one theory under a particular guise is the samephenomenonplayingthesameroleinanapparentlydifferenttheoryunder a different guise. In either case,we have two differentwaysof talkingabout thesameunderlyingreality.According to theNVH,degrees of naturalness anddegrees of being are,atrock-bottom,thesamephenomenonshowingupunderdifferentguises.

TheNVH is supported bymore than the fact that these notionscanbedefinedintermsofeachother(givenplausibleassumptions).Let’sfirstnotethatthetwoprimitivenotionscanbeusedtopartitionclassesofentitiesinexactlythesameways.Onemightwishtoapplythenotionofnaturalnesstosubstancesaswellasproperties.Justasitisintuitivethatsomewaysofpartitioningclassesofentitiesaremorenaturalthanothers,itisintuitivethatsomedecompositionsofanentityaremorenaturalthanothers.ConsideranarbitraryundetachedpartofTheodoreSider.Whydoesthepartdeservetobecalledarbitrary?Itjustisn’tasnaturalasSiderhimself,or,e. g.,hisbrainoroneofhiscells. The friend of degrees of beingmightwish to grant that bothSiderandthisarbitraryundetachedpartexist,butholdthatSiderismorerealthanhisarbitraryparts.Friendsofnaturalnessemploythephrase‘carvingnatureatitsjoints’—anditis,ofcourse,objectsthatcanhavejointstobecarved.

Just as there is arbitrary decomposition, there is arbitrarycomposition: one might hold that arbitrary fusions of individualsare less natural than the individuals they fuse. The arbitrary sumscountenancedbyunrestrictedmereologyhaveanairofunreality to

naturaltoadegreegreaterthan0.Sincethereisatleastonepossiblequantifierrangingoverpropertieswhosenaturalnessisgreaterthan0,propertiesexisttoagreater-than-0degree.

Extreme nominalism cannot be sustained. If the analysis ofnaturalness in terms of degrees of being ineliminably presupposesthat extreme nominalism is false, then so be it. Good analyses areallowedtoassumethatfalsetheoriesarefalse.

Moderate nominalism, on the other hand, is neither absurd norobviouslyunsustainable.However,theanalysisofferedheredoesnot presupposethefalsityofmoderatenominalism.Recalltheanalysisofnaturalness in termsof degreesof being:PropertyP ismore natural thanpropertyQ=df.P ismorereal thanQ;propertyP isnatural todegreen =df. the degree towhichP exists isn.Neither part of theanalysis ineliminably presupposes that any property exists to amaximaldegree.Aperfectlynaturalpropertyisapropertysuchthatnootherproperty ismore real than it. Itmightwellbe, though, thatthereareotherentitiesthanpropertiesthataremorerealthaneventheperfectlynaturalproperties.

Let Platonism be the view that some properties are more realthanany individuals; letnon-reductive realism be theview that someindividuals and someproperties are such thatnothing else ismorerealthanthem.Letotherism betheviewthattherearesomeentitiesthat aremore real than any property or individual. Platonism, non-reductiverealism,andotherismarethemaincompetitorstomoderatenominalism.Theanalysisofnaturalnessintermsofdegreesofbeingdoesnotpresupposeanyoftheseviewsoranyoftheirdenials.

Givenplausibleassumptions,wecandefinethenotionofdegreeof being in terms of the notion of naturalness. Given plausibleassumptions, we can define the notion of naturalness in terms ofdegreeofbeing.Wenow face somepuzzlingquestions. Isa theorythatmakesuseofthenotionofnaturalnessmerely a notational variant ofatheorythatmakesuseofthenotionofadegreeofbeing?Ifoneofthesenotionsisinsomewayprior,whichnotionshould be definedintermsoftheother?



Ifwe take naturalness as primitive,we can define the notion ofadegreeofbeing.But there arehardquestions facinganyonewhotakesthenotionofnaturalnessasprimitive.Forexample,considerthefollowingquestions:

1. Is being natural natural? How natural is being natural todegreen?

2.Isx is more natural than ymorebasicthanx is natural to degree n?

3.Canthingsotherthanpropertieshavedegreesofnaturalness?

Ifwetakedegreesofbeingasprimitive,wecandefinethenotionofnaturalness.Butthereareequallyhardquestionsfacinganyonewhotakesthenotionofdegreesofbeingasprimitive,suchasthefollowing:

4.Doesthepropertyofmaximallyexistingmaximallyexist?Towhatextentdoesthepropertyofexistingtodegreenexist?

5.Isx exists more than y morebasicthanx exists to degree n?

6.Canthingsotherthanpropertieshavedegreesofbeing?

Thatparallelquestionsariseinthisfashionispredicted bytheNVH.OntheNVH,questions1–3aremerelynotionalvariantsofquestions4–6,andso,giventheNVH,itisunsurprisingthatparallelquestionsariseaboutoneandsameprimitivenotion.

6. Is Naturalness the Prior Notion?

I’vesketchedacasefortheNVH.Butweshouldn’timmediatelyembracetheNVH,fortheremightemergereasonstothinkthatonenotionisin somewayprior to theother.We candefine ‘grue’ and ‘bleen’ intermsof‘blue’and‘green’(plussomeothermachinery),but‘blue’and‘green’canalsobedefinedintermsof‘grue’and‘bleen’(plusthesamemachinery).But it doesn’t follow from this fact that a theory statedusing‘green’and‘blue’isjustanotationalvariantofatheorystatedintermsof‘grue’and‘bleen’.‘Green’and‘blue’aremetaphysically priorto

them—considerthethingmadeoutofSider,themoon,andapieceofcheese—andthefriendofdegreesofbeingmightgrantthatarbitraryfusionsarereal,albeitlessrealthanthatwhichtheyfuse.

Justasnegative “substances”—shadowsandholes—are less realthan “positiveentities”, so tooarenegativeproperties less real thanpositive ones. Recall that one can use the notion of naturalness toaccountforthedifferencebetweenpositiveandnegativeproperties:P1 isthenegationofP2 justincase,necessarily,everythinghasexactlyoneofthemandP1 islessnaturalthanP2.Andjustasarbitrarysumsofsubstancesarelessrealthanwhattheysum,arbitrarydisjunctionsofpropertiesarelessrealthanthatwhichtheydisjoin.(Fromalogicalperspective, the summing function and the disjunction functionbehaveverysimilarly.)RecallthatP isadisjunctionofQ andR onlyif(i)necessarily,ifsomethinghasQ orRithasP and(ii)P islessnaturalthanQ andlessnaturalthanR.AfriendofdegreesofbeingwillholdthatP isadisjunctionofQ andR onlyif(i)necessarily,ifsomethinghasQ orRithasP andP islessrealthanQ andlessnaturalthanR.14

It is true that some philosophers use ‘is natural’ primarily topredicatesomethingofanattribute,butastheexamplesaboveshow,there is insufficient reason to claim that ‘is natural’ cannot also beappliedtoobjects.15AsfarasIcansee,eachoftheaboveclaimsthatemploysthenotionofnaturalnessanditsanaloguethatemploysthenotionofdegreeofbeingareequallydefensible.

ThattheyareequallydefensibleispredictedbytheNVH,sinceontheNVH,eachsuchclaimisamerenotationalvariantofitsanalogue.

Furtherevidence for theNVHstems from the fact that therearemany important questions about naturalness for which there areparallelquestionsaboutdegreeofbeing.

14. SeeMcDaniel(2010a)forantecedentstotheseclaims.

15. Ifitweretoturnoutthat‘isnatural’couldonlybepredicatedofproperties,wecouldalwaysaddaclausetothedefinitionof‘isnatural’requiringthis.Themoreinterestingupshotwouldbethatdegreesofbeingwouldemergeasthemoregeneralnotion,whichwouldsuggest that it isalsothenotionthat isprior.Ithankananonymousrefereeforhelpfuldiscussionhere.



3.Oneofnaturalness anddegrees of being ismorenatural thantheother.

Butwhich ismorenatural? I don’t havemuch to say in favorofpremise4,butisn’tnaturalnessjustintuitivelymorelikelytobenaturalthananycompetitortoit?Thatis:

4.Ifoneofnaturalness anddegrees of being ismorenaturalthantheother,thennaturalness ismorenaturalthandegrees of being.

:.Sonaturalness ismorenaturalthandegrees of being.

Thisargumentisinteresting.However,itcanberesisted.Note that the champion of degrees of being needn’t accept IV1.

Instead,sheshouldaccept:

(IV2):PropertyPobtainsinvirtueofpropertyQobtaining=df.PsupervenesonQ;QismorerealthanP.

IV2hasasatleastasmuchgoingforitasIV1.IV2belongsasapartofanicepictureaccordingtowhichthemaximallyrealserveasthecompletesuperveniencebasefortheless-than-maximallyreal.

Aparallelmeta-Euthyphroargumentusing IV2asabasis canbeconstructedasfollows:

1*. If two properties p1 and p2 are necessarily co-extensionalandp2 obtainsinvirtueofp1 obtaining,thenp1 ismorerealthanp2.

2*.Naturalness anddegrees of being arenecessarilyco-extensional,butoneofthemobtainsinvirtueoftheotherobtaining.

3*.So:oneofnaturalness anddegrees of being ismorerealthantheother.

4*.Ifoneofnaturalness anddegrees of being ismorerealthantheother,thendegrees of being ismorerealthannaturalness.

‘grue’and‘bleen’,soought to be priorindefinitionaswell.Atheorythattakesthenotionof‘grue’asundefinedismakingametaphysicalmistake.

Let’sexaminetwoargumentsfortakingthenotionofnaturalnessratherthandegreesofbeingasthemetaphysically priornotion.

Thefirstargumentisthemeta-Euthyphro argument.Twopropertiesare not metaphysically on a par simply because they mutuallysupervene on each other. Euthyphro puzzles arise whenever wesuspectthatoneofthepropertiesismorefundamentalthattheother.IsthefactitismorallyobligatorywhyGodcommandsthatitbedone,ordoesGod’s commanding that it bedonemake it the case that itis morally obligatory? The question ‘Which property, being morally obligatory orbeing commanded by God isprior?’isintelligible,andtoughto answer even if we grant that both properties are necessarily co-extensive.(Theatheisthasaneasiertimewiththispuzzle.)

Aplausibleaccountofthenotionofpriorityexplicatesitintermsofsupervenience andnaturalness:

(IV1):PropertyPobtainsin virtue ofpropertyQobtaining=df.PsupervenesonQ;QismorenaturalthanP.

The tricky cases are ones in which the relevant properties arenecessarilyco-extensionalandthereforesuperveneoneachother.Insuchcases,IV1saysthesolefactorthatdetermineswhichpropertyisprioriswhichismorenatural.Moreformally:

1.Iftwopropertiesp1 andp2 arenecessarilyco-extensionalandp2 obtainsinvirtueofp1 obtaining,thenp1 ismorenaturalthanp2.

Thepropertiesthatconcernusherearenaturalness anddegrees of being, andweareconsideringthehypothesisthat:

2. Naturalness anddegrees of being arenecessarilyco-extensional,butoneofthemobtainsinvirtueoftheotherobtaining.

Itfollowsfrompremise1and2that:



McDaniel(2009),Iofferedthefollowingaccountofwaysofbeingintermsofnaturalness:therearewaysofbeingjustincasethereismorethanoneperfectlynaturalquantifierexpression.

Buthowcouldwedefinethenotionofaway ofbeingintermsofthenotionofadegree ofbeing?Itseemsthatiftheproposedprimitivenotion isx has n-units of being, thenwecannotusethatprimitivetodefinethenotionofawayofbeing.Ifthereareunitsofbeing,thenthereisafunctionfromthethingsthathavebeingtothepositiverealnumberswithin(0,1].Andifthisisthecase,thentherelationx has at least as much being as y willbecomparable —i. e.,forallxandy,either:x≥ yor y≥ x. If this relation is comparable, theneverythingmustbe real in the sameway, even though thingsmight enjoydifferentamountsofthesamekindofreality.Compare:everythingismassiveinthesameway,althoughsomethingsaremoremassivethanothers.InnonebutthethinnestsenseisanelephantmassiveinadifferentwaythanaLego.

Thisargumentistempting,butnotgood.Thereisawaytoformulatethe doctrine that there aremodes of being even if x has at least as much being as y iscomparable.18Thiswaymimicstheformulationthatemploysthenotionofnaturalness.Westartwiththeideathattherearepossible alternativemeanings for the unrestricted quantifier. Thesemeanings are entities. (Perhaps they are higher-order properties.)Some of these entities aremore real than others. There aremodesofbeingjustincasethereareatleasttwopossiblemeaningsfortheunrestrictedquantifierthataremaximallyreal.

Thisresponserequiresthatsomeabstractentitiesbefullyreal.Amorecautiousformulationisonethatrequiresthatthemodesofbeingbesuchthatnootherentityoftheirtypeismorerealthanthem.(Soifmodesofbeingarehigher-orderproperties,therewillbenootherpropertiesthataremorerealthanthem.)

Furthermore, note that the friend ofways and degrees of beingneedn’ttakex has n-units of being asthebasicnotion.Shemightopt

18. ThiswaywassuggestedtomebyMarkBarber.

:.Sodegrees of being ismorerealthannaturalness.

Premise 1* relies on IV2. Premise 2* is numerically identical withpremise 2. Premise 3* is a logical consequence of premises 1* and2*.Premise4*isasatleastasplausibleaspremise4.Inmyopinion,neitherversionofthemeta-Euthyphroargumentismoreconvincingthantheother.

Infact,theNVHprovidesanexplanationwhyneitherargumentismoreconvincingthantheother.First,thefriendoftheNVHwillholdthatIV1andIV2arenotationalequivalentsofeachother.Moreover,ontheNVH,theparallelargumentsarenotationalvariantsofeachother,and so both have faulty second premises. Finally, it is well knownthathumanbeingsaresubject to framingeffects:oneandthesamephenomenawhenpresentedunderdifferentguisescanelicitdifferentpsychological reactions. When presenting this paper in variousvenues,Iwouldoccasionallyswitchtheorderinwhichtheargumentsappeared.Accordingtothereportsofsomeofmyaudiencemembers,thefirstargumentwasalwayssomewhattempting,regardlessofwhichargumentitwas.IftheNVHistrue,itisunsurprisingthatwemightbesusceptibletothiskindofframingeffect.

Let’sconsiderasecondargument.Thisistheargumentfromways of being.Apresuppositionofthisargumentisthatnotonlydosomethings havemore reality than others, but additionally some thingshaveadifferentkind ofrealitythanothers.Itakethisclaimseriouslyandhavepresentedarguments for itelsewhere.16Oneargument forcaringaboutaccountingformodes aswellasdegrees ofbeinginone’smetaphysicisthatthebestaccountofwhatitistobeanontologicalcategoryisonethatidentifiesthemwithmodesofbeing.Onthisview,thingsbelongtothesameontologicalcategoryifandonlyiftheyenjoythesamemodeofbeing.17

If we take naturalness as primitive, we can use it to define thenotionofaway of being inadditiontothenotionofadegree of being.In

16. SeeMcDaniel(2009,2010a).

17. SeeMcDaniel(ms)foranextensiveargumentforthisclaim.



quantifier, which informally we can take to be a single expressioncapableofbindingmultiplefreevariableswithinanopensentencesoastoyieldasentencewithnofreevariables,hasbeenwellstudied.19Ontheviewunderconsideration,thefundamentalexistentialexpressionwouldbeakindofpolyadicquantifier.Althoughthisisnottheplaceto develop a formal semantics for such an expression, it might beuseful tobrieflyseehowsuchadevicecouldfunction.Let’shave ‘$’ bethepolyadicquantifierthathasasitssemanticvaluex has at least as much being as y.Informally,asentencesuchas‘$x,y(Fx,Gy)’couldbeusedtosaythatsomeFhasatleastasmuchbeingassomeG,whileasentencelike‘$x,y(x=a,y=b)’couldbeusedtosaythatxhasatleastasmuchbeingasy.Andofcourseeitherofx ory mightbeindividuals,orproperties,orobjectsofanyontologicaltype.

Iknowofnootherarguments for takingnaturalness tobemorebasicthanthenotionofadegreeofbeing.Thisdoesn’tshowthattheNVHistrue.Butitisdisquieting.

7. Is Degree of Being the Prior Notion?

WehaveexploredargumentsagainsttheNVHthattriedtoestablishthat naturalness is the prior notion. A secondway of undercuttingtheNVH is to argue that degree of being is themore basic notion.HereIwilldiscussoneplausibleargumentforthisclaim,whichisanargumentfromideological parsimony.

Theideologyofatheoryconsistsinthenotionstakenasprimitiveorundefinedby the theory.Consider two theories.Thefirst theoryappealstothenotionofexistence,butclaimsthatexistencecomesinamounts.Thesecondtheoryappealstoboththenotionofexistence and thenotionofnaturalness,andclaims thatnaturalnesscomes inamounts.Every interestingphilosophicalnotiondefinedorpartiallycharacterized in termsof the ideologyof the second theory canbedefinedorpartiallycharacterizedintermsoftheideologyofthefirsttheory.Fromtheperspectiveofideologicalparsimony,thefirsttheory

19. See,forexample,StanleyandWesterstahl(2006).

instead to take the comparative relationx has at least as much being as y asbasic.Sheshouldsaysomethingaboutthelogicalpropertiesof thisrelation: it is intuitivethat it isreflexive, transitive,andnon-symmetric.Butsheneedn’tholdthattherelationiscomparableinthesensejustelucidated.

Arguably,somerelationsarecomparativewithoutbeingcomparable,although examples are controversial. Consider the relation x has at least as much intrinsic value as y.Ithinkthatmanystatesofaffairshaveintrinsicvalue,includingthoseinwhichsomeoneexperiencessomepleasureandthoseinwhichsomeoneknowssomething.Thereisatleastlimitedcomparability:it isintrinsicallybettertoknowwhetherGodexiststhanitistoexperienceaveryminorpleasure.Butitisnotatallobviousthateverypossibleepisodeofpleasureislessthan,greaterthan,orequalinvaluetoeverypossibleepisodeofknowledge.

Andinthiscontext,itisworthnotingthatitisnotobviousthatx is more natural than yiscomparable.

Asecondwayofcapturingtheideathattherearemodesofbeingisbyclaimingthatx has at least as much being as y failstobecomparable.Saythatsomethingx hasamaximum degree of beingjustincasethereis no y such that y has as least asmuch being as x but x does nothave at least asmuchbeing asy.On thispicture, if there arewaysofbeing—differentwaystobereal—thentherearesomethingsthathaveamaximumdegreeofbeingbutaresuchthatnoneofthemhasatleastasmuchbeingastheothers.Letussupposethatobjectsandpropertiesenjoydifferentwaysofbeing.Bothyouandyourshadowareobjects,butyouaremorerealthanyourshadow.Having -1 chargeismorerealthanbeing grue.Butsinceyouenjoyadifferentkindofrealitythanhaving -1 charge,itisnotthecasethateitheroneofyouhasatleastasmuchrealityastheother.

Thereisaninterestingquestionofwhatistheproperlinguisticguiseforx has at least as much being as y, ifwewishtopreserveaconnectionbetweenbeingandquantification.(Ihavebeenassumingthroughoutthispaperthatwedo;ifwedon’t,thingschangeininterestingwaysthatIlackthespacetoaddresshere.)Fortunately,theideaofapolyadic



Thequestionnowiswhetheratheorythatmakesuseonlyofthenotionofnaturalnessor structurebutdoesnothavequantificationin its fundamental ideology cannonetheless defineup a notion ofquantification. To ensure parallel treatment, we focus on the viewaccording to which the fundamental naturalness notion is alsocomparative: x is at least as natural as y. But from this notion it isnot at all clear howone can defineup eithermonadic or polyadicquantification in terms of it. Of course, if we help ourselves toquantification,wecanuseitplusnaturalnesstodefineacomparativenotion of being, aswas discussed earlier. But in order to establishideological parity, we need to be able to define either absolute orpolyadicquantificationintermsofnaturalness alone — thatis,without the aid of any other quantificational notions.

Thedifficultyofthistaskshouldnotbeobscuredbythefactthatbeing andnaturalness areboth,inasense,“propertiesofproperties”.Butperhaps this factprovidesa clue tohowwecandefineupbeing intermsofnaturalness.Ifweembracethepurportedconnectionbetweenbeingandquantification, then, to say that there is anFamounts toattributingtoFthepropertyof“havinganinstance”.Withthisinmind,letusconsideronewayofattemptingtoaccountforquantificationintermsofnaturalness.SupposewesaythatthereisaPjustincasePisatleastasnaturalasP—thatis,Ex (xhasP) ifandonlyifN(P,P),where‘N’ isthepredicateforcomparativenaturalness.(Ingeneral,saythatanopenformulaissatisfiedbysomethingjustincasethepropertyorrelationthatcorrespondstoitstandsinthecomparativenaturalnessrelation to itself.) If this is a successfulwayofdefiningupbeing intermsofnaturalness,ideologicalparitywillberestored.

Itisobviousthatthiswayofdefiningupbeingintermsofnaturalnesspresupposes that every property and relation is instantiated. Manyembracethispresupposition,butitismetaphysicallycontentious,andIam inclined to think it is false.Whenwe frame theassumption intermsofdegreesofbeing,itisthis:apropertyexiststosomeextent

toprovingthisisthecase,althoughIhavenoconclusiveproofthatthisisnotthecase.AndIunfortunatelylackthespacetoexplorethisquestionfurther.

issimpler.Boththeoriespostulateaprimitivethatcomesinamounts,butthesecondtheoryemploysanadditionalprimitivenotion.

Theprospectsfordefiningthenotionofexistencearenotclear,andso,bymy lights, everymetaphysical theorywill probablyhave thatnotionaspartofitsideology.NotethatSider(2012)commitshimselfto both the structuralness of quantification and the structuralnessof structure itself, which suggests that Sider is also dubious aboutdefining up a notion of quantification in terms of structure. In thisrespect,bothbeingandstructurearepartsofSider’sideology.20Butletusexplorewhethersuchadefinitionispossible.

For the sake of clarity, let’s first consider the view that thefundamentalexistentialnotion is comparative:x has at least as much being as y.21 Recall that in the previous sectionwe briefly discussedhow theproper linguisticvehicle foracomparativenotionofbeingisapolyadicquantifier,which,forsimplicity’ssake,wewillassumeiscapableofbindingtwovariablesatonce.Withthecomparativenotion,wecaneasilydefineupthe“absolute”notionofbeing:tobeistohaveat least asmuchbeing asoneself.We capture this ideabydefining“absolute” or “monadic” existential quantification in terms of thepolyadicquantifierasfollows:foranyformulainwhich‘x’istheonlyfreevariable,‘ExѰ’ifandonlyif‘$x,x(Ѱ)’.AndtosaythatapropertyFisatleastasnaturalaspropertyGistosay,‘$x,y(x=F&y=G)’.Wehave an existential notion, expressed by a polyadic quantifier, andboth“absolute”existentialquantificationandnaturalnessaredefinedintermsofitandthenotionofidentity.22

20.SimilarremarksapplytothesystemofJonathanSchaffer(2009:374),whomakesuseofaprimitivenotionofgrounding ratherthanstructurebutwhoalsoexplicitlydeniesthatexistence canbedefinedintermsofgrounding.

21. Iamconfidentthatasimilarstorycanbetoldforotherviewsaboutthenatureofquantities,butIfocusonthisoneinordertoclearlyexpressthemoralofthestory.

22. Iaminclinedtobelievethatidentityisanothernotionthatwillbepartoftheideologyofanyviablemetaphysicaltheory.Ifthefriendofnaturalnesscandefineawayidentityin a way not available tothefriendofdegreesofbeing,wewouldhavetoreassessthequestionofideologicalparsimony.Iseenoroute



Whentheyheartermslike ‘grounding’,or ‘structure’,or ‘naturalness’,they leap up with excitement and emphatically deny their veryintelligibility. They claim to have no idea what could possibly bemeantbysuchexpressions.Butnophilosophercansincerelydenythat they understand ‘being’, which is not to say that there aren’tinterestingphilosophicalpuzzlesaboutbeing.Everyone has sufficient grasp of the notion of being to entertain interesting philosophical claims about it. Thosewhoclaimtodenythisaremerelyfrothingwithwords.Tothesephilosophers, Isay thatyouunderstandmyprimitiveandyouunderstandthethesisthatthisprimitivestandsforaquantitativeaspect.Investigatetheargumentsforthisthesis!Andtothefriendsofnaturalnesswhohavebeenfrothedupon,notethatifmyargumentsare sound, you have the same response available to you. This ismorethansufficientcompensation,ifanyisneeded,forembracingdegreesofbeing.

Appendix: Degrees of Being and Grounding

Wenowturntothenotionofgrounding.Iwillargueherethatthereisnoneedtopostulateaprimitiverelationofmetaphysicalgrounding,sincetalkofgroundingcanbereplacedwithtalkofdegreesofbeingplusotherinterestingmetaphysicalrelations.

According to Jonathan Schaffer (2009), the fundamental taskof metaphysics is not to determine what kinds of things exist butrathertodeterminewhichkindsofthingsarefundamental.Anentityis fundamental just in casenothinggrounds it; anentity isderivative just in case somethinggrounds it.23OnSchaffer’s view, the relationof grounding is an asymmetric and transitive relation. According toSchaffer,groundingisaprimitiverelation.

On Schaffer’s view, the questions of whether, e. g., numbers,meanings, wholes or holes exist, are uninteresting: they obviouslydo.(Schaffernotesthattherearemanytrue,affirmativepropositions

23. Schaffer(2009:373).

orotheronlyifsomeinstanceofitexiststosomeextentorother.Thefriendwhotakesacomparativenotionofbeingasherprimitivenotionneedn’tacceptthisclaim,thoughsheneedn’trejectiteither.Butitisnotcleartomethatonecandefineupbeingwithoutthisassumption,although,asthekidssay,itishardtoproveanegative.Insofaraswearecautiousabouttheexistenceofuninstantiatedproperties,weshouldbecautiousaboutthiswaytoestablishideologicalparsimony.

But let us provisionally grant this assumption. Then ideologicalparitywillhavebeen restored. Inbothcases, there isoneprimitivecomparative notion. On this view, the notion of naturalness hasstraightforwardexistentialimplications,andnotonlyinthetrivialwayinwhichifsomethinghasaproperty,thenitissomething.(Ofcourse,ifapropertyisnatural,itfollowsthatthepropertyissomething,justas it follows from the claim thatmy dog is hungry, thatmy dog issomething.)An assertion of the naturalness of a property straightforwardly implies the existence of a thing beyond the property itself. In short, thefundamental notion of naturalness is an existentially loaded notion.Oneoughttoconcludethatthosewhospeakofnaturalnessspeakofgradations of being,albeitunderadifferentguise.

EithertheNVHistrueoritisfalsebecausenaturalness oughttobeunderstoodintermsofdegrees of being.

8. Concluding Remarks

Ifmyargumentsaresound,thencontemporarymetaphysicianshavemuchmore incommonwith theirhistoricalpredecessors than theyinitiallythought,andaccordinglyoughttotreatthehistoricaldoctrinethattherearegradationsofbeingwiththerespectitisdueratherthanwiththederisionitiscommonlymetwith.Forthosewhotruckwithnaturalness either truck with gradations of being under a differentguise, or are taking as primitive a notion that demands analysis intermsofgradationsofbeing.Eitherway,theself-conceptionofthesemetaphysiciansmustchange.

There are philosophers who elevate failing to understand theprimitivenotionsoftheirinterlocutorsintoaformofperformanceart.



notethateachofthesefiguresalsobelievedthatsomethingsweremorerealthanothers.Thatwhichisprioristhatwhichismorereal.Theappeal to traditionalmetaphysicalpractice tells against takinggroundingasaprimitive.

In this vein, note also that the semi-mereological notions of anintegrated whole andamere aggregate canbedefinedintermsofdegreesofbeing:anintegratedwholeismorerealthanitsproperparts,whereasa mere aggregate is less real than its proper parts. (Intermediatecasesarepossible:perhapsartifactsaremorerealthantheirarbitraryundetachedpartsbutlessrealthantheirconstituentparticles.)

Onemightworrythatthenotionofgroundingcannotbeanalyzedin terms of the notion of being more real than, since theremight bemetaphysicsinwhichthegroundingrelationimposesmorestructurethan the being more real than relation. A specific examplemight behelpful.Considerametaphysicaccordingtowhichthereareconcreteparticularsandtheirmodes,whichareparticularizedanddependentattributes.Supposethereare twoconcreteparticulars,oneofwhichenjoysamodeofbluenesswhilsttheotherenjoysamodeofredness.Intuitively,themodeofrednessisgroundedsolelybytheredsubstance,whereasthemodeofbluenessisgroundedsolelybythebluesubstance.Intuitively,bothsubstancesareequallyreal,whereasbothmodesareequallyreal,andbothsubstancesaremorerealthanbothmodes.Andso information about the particular connection between the modeofrednessandtheredsubstanceislostifweidentifythegroundingrelationwiththebeing more real thanrelation.

Thereareacoupleofwaystorespondtothisworry.Oneobviousresponse is toaccount for theparticular connection in termsof theinstantiationrelationitself.Theappearancethatthereismoretothegrounding-structurearisesbecausethereisafurtherrelationinplay.

Asecondresponseissimilartothefirst:Insteadofdirectlydefiningx grounds y in terms of x is more real than y, identify the groundingrelationwiththedisjunctionofconjunctionsconsistingofx is more real than y andsomeotherconnectiverelation.Forexample,inanontologythatconsistsofmodes,events,andsubstances,onemightacceptthe

thatimplytherealityofsuchentities.)Theinterestingquestionsarewhethertheseentitiesarefundamentalentitiesorderivativeentities.One of the metaphysical questions currently driving Schaffer iswhetherwholesarepriortotheirparts.OnSchaffer’s(2010)monistic view, the universe is an integrated whole, where the notion of anintegratedwholeisdefinedbyhimasfollows:

x isanintegratedwhole=df.x groundseachofx’s properparts.

(Wecancontrastthenotionofanintegratedwholewiththatofamereaggregate,whichisawholethatisgroundedbyitsproperparts.)

The notion of grounding and the notion of naturalness performsimilar jobs intherespectivemetaphysicsofSchafferandSider.Forthatreason,itwillbeworthwhiletodeterminewhetherwecandefine up thenotionofgroundingfromthenotionofadegreeofbeing.

Thegroundingrelationisnotidenticalwiththerelationx is at least as real as y,asthelatterrelationisreflexiveandhencenotasymmetric.Abetter candidate for thegrounding relation isx is more real than y, whichisasymmetric.24Thislatternotioncanplaymanyofthesamerolesasgrounding.Considerthefollowingdefinitions:

x isfundamental =df.nothingismorerealthanx.

x isderivative =df.somethingismorerealthanx.

As I mentioned, Schaffer argues that the fundamental task ofmetaphysics is to determine which things are fundamental andwhichthingsarederivative.Iagree.Schaffer(2009)alsoarguesthatthiswasunderstoodtobethefundamentaltaskofmetaphysiciansbymanyofthegreatfiguresinthehistoryofmetaphysics,suchasPlato,Aristotle, Spinoza, Leibniz, and Kant. Perhaps he is correct—but

24.Wecaneasilydefinethisnotionintermsofx is at least as real as yasfollows:x is more real than y =df.x isatleastasrealasy anditisnotthecasethaty isatleastasrealasx.



Eddon,Maya.Forthcoming.‘FundamentalPropertiesofFundamentalProperties’,Oxford Studies in Metaphysics.

Goodman, Nelson. 1965. Fact, Fiction, and Forecast, Bobbs-MerrillCompany.

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Lewis,David.1983.‘NewWorkforaTheoryofUniversals’,Australasian Journal of Philosophy 61:343–377.

Lewis,David.1986.On the Plurality of Worlds,BlackwellPublishing.McDaniel,Kris.(ms).‘OntologicalCategories’.McDaniel, Kris. 2010b. ‘Being and Almost Nothingness’, Noûs 44.4:

628–649.McDaniel,Kris.2010a.‘AReturntotheAnalogyofBeing’,Philosophy

and Phenomenological Research81.3:688–717.McDaniel,Kris.2009.‘WaysofBeing’,in Metametaphysics: New Essays

on the Foundations of Ontology,editedbyDavidJ.Chalmers,DavidManley,andRyanWasserman,OxfordUniversityPress.

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Plato.1971.The Republic,inPlato:the Collected Dialogues,editedbyEdithHamiltonandHuntingtonCairns,PrincetonUniversityPress.

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Schaffer, Jonathan. 2010. ‘Monism: The Priority of the Whole’,Philosophical Review119.1:31–76.

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following:x grounds y ifandonlyifx ismorerealthany andeither(i)x instantiatesy or(ii)y isaneventinvolvingx.

A third response is (?) to deny that x is at least as real as y iscomparableinthesensedefinedinsection6.Ifx is at least as real as y isnotcomparable,andwewanttocapturetheconnectionbetweenathinganditsmodeswhollyintermsofthegroundingrelation,wecan do so. In the casementioned earlier, one need only deny thatthemodeofrednessisasrealasthemodeofblueness.(Additionally,neithermodeismorerealthantheother.)

Isuggestthatwhateverworkthenotionofgroundingiscalledtodo,thenotionofdegreeofbeingcandojustaswell.Wethereforehaveachoicebetweentwosystems,oneofwhichtakesthenotionx is at least as real as y asbasicanddefinesexistencesimpliciterandgroundingintermsofit,andanothersystemthattakesboththenotionofexistenceandthenotionofgroundingasbasic.25Isuggestthatthefirstsystemscoresbetterwithrespecttoideologicalparsimony,andsinceitcandothesameworkasthesecond,itistobepreferred.

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25. AsInotedearlier,Schaffer(2009:374)explicitlydeniesthatexistence canbedefinedintermsofgrounding.



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metaphysical naturalness and degrees of reality - kris mcdaniel

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