TheGeographyofFundamentality
AnOverview
RickiBlissandGrahamPriest
Realityisaratherlargeplace.Itcontainsprotons,flamingos,economies,headaches, sentences,smiles,asteroids,crimes,andnumbers,amongstverymanyotherthings. Muchofthecontentofourrealityappearstodependonotherofitscontent. Economies,forexample,appeartodependuponpeopleandthewaytheybehave, amongstotherthings.Someofthecontentofourrealityalsoappearstobe,insome significantsense,moreimportantthanotherofitscontent.Whilstnoneofuswould wishtodenytheveryimportantrolethateconomiesplayinourlives,mostofuswould agreethatwithoutmatterarrangedcertainwaysinspace,forexample,therecouldbe noeconomiesinthefirstplace.
Therealitythatwehappentooccupyis,insomeimportantsense,aphysicalone. Accordingly,matterisaffordedaspecialplaceinourstoryaboutit.Indeed,notonlyis matteraccordedaspecialplaceinourontology,butsomefromamongstitselements arealsothoughttobeparticularlyimportant.Chairsandflamingosandpeopleare madefromparts,andthosepartsfromfurtherpartsandsoon—withmostfolksbeing oftheviewthatatsomepointthesedependencechainsmustterminateinabsolutely basic,orsimple,partswhichthemselveshavenofurtherparts.Itisthesebasicparts, sothestorygoes,thatgiverisetoeverythingelse.
Thecontentofrealitytowhichthesepartsgiveriseisarrangedrelativelyneatly intolayers:factsabouteconomiesandcrimesresideatahigherlevelthanfacts aboutbiologicalsystems,whichresideatahigherlevelthanfactsaboutchemical systemsandsoon.Orperhapswemightprefertosaythateconomicsystemsare furtheruptheGreatChainofBeingthanecosystems,whicharefurtherupthe chainthancarboncompounds.1 Thispicture,orsomethingverymuchlikeit,looms largeovercontemporaryanalyticmetaphysics:apictureaccordingtowhichrealityis hierarchicallyarrangedwithchainsofentitiesorderedbyrelationsofgroundand/or ontologicaldependenceterminatinginsomethingfundamental.
1 TheGreatChainisnormallytakenasrunningdownwards,withthegroundatthetop;weupendithere.
thegeographyoffundamentality:anoverview
Thehistoricalliteratureisalsolitteredwithwhatappeartobevariationsonthis kindofview.ConsiderbothPlatoandAristotle,forexample.Theformerbelieved thateverythingwasgroundedintheForms,withalloftheFormsbeingultimately groundedintheFormoftheGood.Thelatterdistinguishedbetweenprimaryand secondarysubstances,withapriorityorderingamongstthem—along,arguably,with makingappealtoprimematter,withoutwhichtherewouldbenothingwhatsoever. JustasverymanyoftheMedievals(Aquinas,forexample)andEarlyModerns (Descartes,Spinoza,Leibniz)thoughtthateverythingdependedonGod,theneed toestablishafundamentalgroundbreaksoutincertainoftheContinentalthinkers, suchasHeidegger,intheformofTheProblemofBeing:theremustbesomething (fundamental),Being,ifwearetoaccountforthefactthatanythinghasbeingatall.
Turningalsotonon-Westerntraditions,weseethattheideathatrealityisstructured bymetaphysicaldependencerelations,wherethereissomethingfundamental,isby nomeansanunfamiliarone.2 VariousoftheIndian,Chinese,andJapanesetraditions relyheavilyonnotionsofmetaphysicaldependenceandfundamentality.Infact, wholeschoolswereformedbasedondisagreementsoverthefundamentalstructureof reality.AccordingtotheIndianAbhidharmikatradition,forexample,theremustbe dharmas—simples—asthereareaggregateswhicharebuiltfromthem.Andaccording toKyotoSchoolthinkerNishida,theultimategroundofeverythingisconsciousness, whichisalsoabsolutenothingness.Theideathatrealityisstructured,andthatthere mustbesomethingfundamental,isbynomeansthemonopolyofcontemporary Westernanalyticthought.
Thekindofview,orclusterofviews,thatappeartodominatethecontemporary analyticdebatecanbethoughtofbroadlyas,orasspeciesof, metaphysicalfoundationalism.Aswillbecomeclearerinduecourse,thereare,infact,avarietyof waysinwhichonecanbeametaphysicalfoundationalist;withdifferentspeciesof foundationalisminvolvingdifferentcorecommitments.Althoughthislistisbyno meansexhaustive,weassumethefollowingtobeamongstthecorecommitmentsof metaphysicalfoundationalism ascommonlyendorsedinthecontemporaryliterature.
1.Thehierarchythesis:Realityishierarchicallystructuredbymetaphysicaldependencerelationsthatareanti-symmetric,transitive,andanti-reflexive.
2.Thefundamentalitythesis:Thereissomething(s)whichisfundamental.
3.Thecontingencythesis:Whateverisfundamentalismerelycontingently existent.
4.Theconsistencythesis:Thedependencestructurehasconsistentstructural properties.
Strictlyspeaking,inordertobeconsideredaspeciesoffoundationalism,aview needsonlycommittothethefundamentalitythesis:2.,then,isbothnecessaryand 2 SeeBlissandPriest2017.
sufficientforaviewtocountasakindoffoundationalism.Forproponentsofwhatwe canthinkofasthe standardview,however,allfourthesesarenecessary,withnoone ofthembeingsufficient.3
Isthistheonlyviewofthefundamental,orbasic,structureofrealitythatisavailable tous,though?Ofcourseitisn’t.Tobesure,deviationsfromthestandardviewexist intheliterature.4 Butthefullspreadofpossibleviewshas,sofaraswecantell,been bothgrosslyunderestimatedandgrosslyunderexplored.
Itisimportantandinterestingtonotethatinfoundationalepistemology—where thestructuringrelationsarestrikinglysimilartothoseinvokedintalkoffoundational metaphysics—onecanbeanepistemicfoundationalist(ofvarioussorts),anepistemic infinitist,oranepistemiccoherentist.Isasimilarspreadofpossibleviewsavailableto usinfoundationalmetaphysics?Weareinclinedtothinkthatitis,asdoMorgantiand Thompson(thisvolume).Justasanepistemicinfinitistthinksthatchainsofbeliefs orderedbyananti-symmetric,anti-reflexive,transitiverelationordersbeliefswithout termination,ametaphysicalinfinitistthinksthatchainsofentitiesorderedbyanantisymmetric,anti-reflexive,transitiverelationordersentitieswithouttermination.So tooforcoherentism.Justasanepistemiccoherentistthinksthatbeliefsareorganized intoahighlyintegratedweb,withjustificationemergingfromit,themetaphysical coherentistthinksthatentitiesareorganizedintoahighlyintegratedwebwith somethinglikebeingorrealityemergingfromit.Asonemightexpect,therewillalso bevariouspossibleshadesbetween.
Thepaperscontainedwithinthisvolumecanbethoughtofascontributingtoa broaderdiscussionofthereasonsforwhichwearesupposedtobelieveaspectsof thestandardview,thereasonswemighthaveforembracingoneorotherofthe alternatives,andwhatthosealternativesmightbelike.Notallofthepapersinthis volumeendorsetypesofanti-foundationalism,buteachofthemspeaksto,andchallenges,insomewayorother,oneorotherofthecorecommitmentsofmetaphysical foundationalismasnotedabove.Insomecases,ourauthorsevensupportoneorother oftheassumptions,withtheaimoftheircontributionbeingtohighlightweaknesses intheargumentscommonlyofferedintheirdefence.Thepapersinthisvolumeare arranged,then,accordingtothecoreassumptionthattheyprimarilyaddress.
3 Theideathattheworldisontologically‘flat’,witheverythingbeingfundamental—arejectionof1— hasbeendescribedbyBennett2011as‘crazypants’,forexample.Justasmanyphilosophersbaulkatthe suggestionthatthefundamentaliaarenecessarybeings.
4 Itisworthnotingthatitdoesnotfollowfromtheappearanceofasmatteringofpaperschallengingthe standardviewthatthestandardviewisnotstilljustthat,thestandardview.Ahandfulofdissentingpapers doesnotaheterodoxymake.Althoughsomeauthorshavechallengedaspectsofthefoundationalistpicture, thedominantparadigmthatdrivesmanycontemporaryanalyticresearchprogrammesisoneaccordingto whichrealityhasalayeredstructureandafundamentallevel.Eventhoughasmallnumberofphilosophers havechallengedaspectsofthestandardview,tothebestofourknowledge,thesechallengeshavenot resultedinresearchprogrammesoftheirown,norhavetheyimpacteduponthewaymuchresearchis conducted.
Inwhatremainsofthisintroduction,wetakeupthemantleofintroducingand engagingwithsomeofthemostimportantissuesthatwebelieveneedtobedealt withiffoundationalismistobeaviewthatweactuallyhavegoodreasonstoendorse; andifthealternativesaretobeconsiderednotjustlogically,butalsometaphysically, possible.
1TheLieoftheLand
Manyphilosophersacceptaviewaccordingtowhichtheworldhasanoverarching causalstructure.Thunderstormscausetreestofalldown,andwateriscausedto boilbytheapplicationofheat.Thisvolumetakesasoneofitsstartingassumptions thattheworld(also)hasanoverarchingmetaphysicalstructure.Ofcourse,causal structureisakindofmetaphysicalstructure;however,whatphilosopherstendto meannowadayswhentheyspeakofmetaphysicalstructureisthatthisstructureis inducedbyrelationsofgroundand/orontologicaldependence.5 Werefertotheseas metaphysicaldependence relations,andtheyaretherelationsaroundwhichtheideas presentedinthefollowingessaysarecentred.
Thereisalotthathasbeen,andcontinuestobe,writtenonmetaphysicaldependencerelations.Andthereisanenormousamountofdisagreementovereventhe mostbasicofconceptsinoperationintherelevantliterature.6 Isgroundingtobe understoodontheoperatorvieworthesententialconnectiveview?Isgroundingjust explanation?Howaregroundingandontologicaldependencerelated?Isgrounding unitary?Theseareamongstsomeofthemanyissuesthatthoseworkingonissues pertainingtothestructureofrealityareconcernedwith.Thisvolumeisnotprimarily concernedwithmostofthosedisagreements,however.Weleaveittoourcontributors toassumewhattheywillregardinghowtheydefinetheirtermsandtheconceptual connectionsthattheytaketobeinoperation;andweleaveittoourreaderstofind appropriatereadingmaterialifwhattheyareinterestedinarethosedebates.Forthe sakeofclarityinthisintroduction,however,wethinkitwisetosaysomethingabout howweshallbeunderstandingthings.
Itisnotuncommontoseeadistinctiondrawnintheliteraturebetweenrelations of ground and ontologicaldependence.Relationsofground,saymany,obtainbetween facts,whererelationsofontologicaldependenceobtainbetweenentitiesofanyand allcategories.7 So,whereonewouldsaythatthefactthattheweatherismiserable todayisgroundedinthefactthatitispouring,onewouldsaythattheshadow ontologicallydependsontheobjectthatcastsit.Andwhereonewouldsaythatthe factthattheskyisblueorweareinAustralia,isgroundedinthefactthatthesky
5 SeeSchaffer2016foradiscussionoftherelationshipbetweengroundingandcausation,andaview accordingtowhichgroundingisakindofcausing.
6 SeeBliss2014foranoverviewofsomeofthemajorsourcesofdisagreement.
7 SeeSchaffer2009forthedevelopmentofaviewaccordingtowhichgroundingobtainsbetweenentities ofanyandallcategoriesandcross-categorically.
isblue,onewouldalsosaythatthefactthattheskyisblueontologicallydepends onitsconstituents—theskyandblueness.Again,whenwetalkaboutrelationsof metaphysicaldependence,wemeanthistermtoactasacoveringtermforboth groundingandontologicaldependence.Where,inthisintroduction,wethinkit necessarytodiscriminatebetweenthetwo,wesayasmuch.Wealsodon’tthinkmuch asregardsthereasonstoendorseonefundamentalviewofrealityoveranotherisgoing toturnonwhethergroundingobtainsbetweenfactsalone,forexample.Whatbears considerationwhensettlingthekindsofmattersthatthisvolumeisconcernedwith willbethesame,webelieve,whetheritturnsoutthatontologicaldependencejustis akindofgroundingornot.
Itisaplankofthegroundingliteraturethatgroundingissomehowinvolvedwith metaphysicalexplanation.Itisanopenquestion,however,whethertherelationsare merelyassociatedwithmetaphysicalexplanationorwhethertheyareidenticalwithit. Thompson(thisvolume)offersussomecompellingreasonstothinkthatgrounding isbetterthoughtof asbeing anexplanatoryrelation.Shearguesthatweregrounding relationstoberelationsthatunderwriteourexplanations,wewouldstillneedto accountforhowtherelationsandtheexplanationstheybackarerelatedtoone another.Ifthewaytheyarerelatedtooneanotherisviagrounding,thenweare reallyintrouble,saysThompson,becausethenotionofametaphysicalexplanation istypicallyinvokedtoshedlightonhowwearesupposedtounderstandgroundingin thefirstplace.Trogdon(thisvolume),ontheotherhand,thinksitnaturaltoassume thatgroundingrelations back metaphysicalexplanations.Sofaraswecantell,not muchturnsonresolvingthisparticularissueforwhatwehavetosayhereinthis introduction.Itisenoughforustopointoutthatweassumethatgroundingismost certainlyinvolvedwithmetaphysicalexplanation,howeverthatturnsouttobe,and moveon.
Ithasbeensuggestedthattheconnectionbetweenontologicaldependenceand explanationisweakerthantheconnectionbetweengroundandexplanation.Tahko andLowesuggest,forexample,thattheexistenceofhydrogenandoxygen—upon whichwaterdepends—donot,alone,explaintheexistenceofwater.8 Whilstweagree thatthemereexistenceofhydrogenandoxygendoesnotfullyexplaintheexistence ofwater,westruggletounderstandhowtheexistenceofthetwocouldfailtobe appealedtoinanexplanationoftheother.PerhapsTahkoandLowearecorrectthat theconnectionis weaker,butweherefeelconfidentproceedingontheassumption thatontologicaldependenceissufficientlystronglytiedtometaphysicalexplanation nonetheless.
Letusturnnowtothenotionoffundamentalityitself.Weassumethatthecategories offundamentalandderivativeareexclusiveandexhaustive.Someentityiseither fundamentalorderivativebutneverboth.9 Thecategoryofderivativethingsisjust
8 SeeTahko2015. 9 SeeBarnes2012forargumentsagainsttheexclusivityassumption.
thegeographyoffundamentality:anoverview
thecategoryofmetaphysicallydependentthings;whichisjusttosayitisthecategory ofgroundedandontologicallydependententities.Itistruebydefinitionthata derivativeentityisdependentand,thus,thatithasametaphysicalexplanation.The fundamentalia,ontheotherhand,bydefinition,dependuponnothingelse(except perhapsthemselves)andare,thus,withoutmetaphysicalexplanation(exceptperhaps intermsofthemselves).Thisisnottosay,however,thatbeingindependentlyexistent isa sufficientcondition forbeingfundamental(onsomeaccounts,it’snoteven necessary).Theremaywellbeaplethoraofindependententitiesthat,nonetheless, donotserveascandidatefundamentalia.10 Althoughtherearealternativewaysof understandingfundamentality,suchasdiscussedbyTakhoandBarnes(thisvolume), Fine,andSider,wearehappytoproceedontheindependenceunderstanding.11
Itisopen,andindeedthecaseonmanyaccounts,thatthefundamentalfactsbe fundamental qua groundingstructureandyetdependent qua ontologicaldependence structure.Thisisbecauseforanyaccountaccordingtowhichafactisdependent uponitsconstituents,afundamentalfactwillbeungroundedandyet,nonetheless, dependent.Theterm‘fundamentalia’canthenbetakentorefertoeitherfundamental factsorfundamentalthingsdependinguponwhichorderingonewishestoforeground.
Werecognizethattherearealsosubtlydifferentwaysinwhichthenotionof beingfundamental canbeformallycashedout.Onedistinctionthatwethinkit particularlyimportanttomentionisthatbetweentherelationbeing well-founded and ithavinga lowerbound. 12 Tosaythatdependencerelationsarewell-foundedistosay that(i)chainsorderedbytherelationdownwardlyterminateinafundamentalium, and(ii)thatthereisafinitenumberofstepsbetweenanymemberofachainand thefundamentaliumthatitterminatesin.Althoughit’snotuncommontohear philosophersspeakinthelanguageofwell-foundedness,whattheyoftenmeanis thatanychainofentitiesorderedbythatrelationhasalowerbound.Importantly, wherearelationisboundedfrombelow,thereneed not beafinitenumberofsteps betweenanymemberofthatsetandthefundamentaliumthatgroundsit.Tobetter understandthis,considertherelationshipbetweenGodandthecontentsofreality; althoughtheremaybeaninfinitenumberofstepsbetween,say,thenumber7and God,thenumber7,alongwitheverythingelse,dependsonhimnonetheless.In ordertoremainneutralonanunderstandingoffundamentalityaswell-foundedness andfundamentalityaslowerboundedness,wechoosetocapturethisaspectof foundationalismformallyintermsofthenotionofextendability(E)anditsnegation; moreofwhichanon.
10 Factsaboutnumbers,forexample,maybeindependent,withoutthatentailingthattheyaretherewith fundamental.
11 Fine2001andSider2011.SeeRaven2016foranotheralternateaccountoffundamentality.
12 SeeDixon2016,andRabinandRabern2016,forformaltreatmentsanddiscussionsofdifferent possiblewaysofunderstandingfundamentality.
2Taxonomy
Thehierarchythesissaysthatthedependencerelationisanti-symmetric,transitive, andanti-reflexive.Thefundamentalitythesissaysthattheremustbesomething fundamental.Althoughitiscommontoassumethattherelevantdependencerelationshavesomecombinationoftheaforementionedproperties,avarietyofdifferent combinationsareatleast logicallypossible.Toseethis,letusfirstintroducesome notation.13
Wewrite‘x dependson y’as x → y. 14 (Wemaywrite x → x as x .)Next,four structuralproperties:
Anti-reflexivity, AR.
• ∀x¬ x → x [Nothingdependsonitself.]
•So ¬AR: ∃xx → x [Somethingdependsonitself.]
Anti-symmetry, AS
• ∀x∀y(x → y ⊃¬ y → x)[Nothingsdependoneachother.]
•So ¬AS: ∃x∃y(x → y ∧ y → x) [Somethingsdependoneachother.]
Transitivity, T .
• ∀x∀y∀z ((x → y ∧ y → z ) ⊃ x → z ) [Everythingdependsonanythinga dependentdependson.]
•So ¬T : ∃x∃y∃z (x → y ∧ y → z ∧¬x → z ) [Somethingdoesnotdependon whatsomedependentdependson.]
Extendability, E
• ∀x∃y(y = x ∧ x → y) [Everythingdependsonsomethingelse.]
•So ¬E: ∃x∀y(x → y ⊃ y = x) [Somethingdoesnotdependonanythingelse.]
Wecannowgiveataxonomy,whichisasfollows.Aftertheenumerationcolumn, thenextfourcolumnslistthe16possibilitiesofourfourconditions.
ARASTE Comments SpecialCases
1 YYYY Infinitepartialorder I
2 YYYN Partialorder A, F , G
3 YYNY Loops I
4 YYNN Loops F , G
13 ThecontentsofthissectionarereproducedfromBlissandPriest2017.
14 Onemaydistinguishbetweenfulldependenceandpartialdependence.(Seee.g.Dixon2016,sec.1.) Justtobeclear:thenotionofdependenceweareconcernedwithhereispartialdependence.
Consider,next,theCommentscolumn.Here’swhatitmeans.
•Thereisnothingincategories5,6,sinceifthereare x, y,suchthat x y,then by T , x y ,contradicting AR.(¬AS and T imply ¬AR.)
•Thereisnothingincategories9–12,sinceifforsome x, x → x,thenforsome x and y, x y,contradicting AS.(¬AR implies ¬AS.)
•Alltheothercategoriesarepossible,assimpleexamples(lefttothereader)will demonstrate.
•Incases13–16,since ¬AR implies ¬AS,thesecondcolumn(AS)isredundant.
•Incategories1and2, → isa(strict)partialorder;andincategory1,theobjects involvedmustbeinfinitebecauseofE.
•Incategories13and14 → isa(strict)preorder,soloopsarepossible.(Aloop isacollectionofelements, x1 , x2 , ... , xn 1 , xn ,forsome n 1,suchthat x1 → x2 → ... → xn 1 → xn → x1 .)
•Incases3,4,7,8,15,16,transitivityfails,andtherecanalsobeloops.Incases7,8, therearenoloopsoflengthzero, x ,since AR holds. Turningtothefinalcolumn,thisrecordssomeimportantspecialcases.
•Thediscretecaseiswhennothingrelatestoanything.Callthis atomism, A.Inthis case,wehave AR, AS, T , ¬E.Soweareincase2(thoughthisisnottheonlything incase2).
•If → isanequivalencerelation(reflexive,symmetric,transitive),wehave ¬AR, ¬AS, T ,soweareincases13or14(thoughthisisnottheonlythinginthese twocases).Incase13,theremustbemorethanonethingineachequivalence class,becauseof E.Alimitcaseofthisiswhenallthingsrelatetoeachother: ∀x∀yx → y.Callthis coherentism, C
•Call x a foundationalelement (FEx)ifthereisno y onwhich x depends,except perhapsitself: ∀y(x → y ⊃ x = y) Foundationalism, F ,istheviewthateverything groundsoutinfoundationalelements.Onewaytocashouttheideaisas
rickiblissandgrahampriest
follows.15 Let X0 ={x : FEx},andforanynaturalnumber, n ∈ ω : x ∈ Xn+1 iff x ∈ Xn or ∀y(x → y ⊃ y ∈ Xn ). X = n∈ω Xn F istheviewthateverything isin X , ∀xx ∈ X . 16 Intuitively,thismeansthateverythingisafoundational element,ordependsonjustthefoundationalelements,ordependsonjustthose andthefoundationalelements,andsoon. E entailsthattherearenofoundational elements.Hence,thisisincompatiblewith F .So,given F ,wemustbeinaneven numberedcase—exceptthosethatarealreadyruledoutbyotherconsiderations. (Allarepossible.Merelyconsider x → y → z . z isfoundational;addinarrows asrequiredtodelivertheotherconditions.)
•Aspecialcaseoffoundationalismiswhenthefoundationalobjects,andonly those,dependonthemselves: ∀x(FEx ≡ x → x).Callthisview F .Since AR mustfailinthiscase,wemustbeincases14or16ofthetaxonomy.
•Anotherspecialcaseoffoundationalismiswhenthereisauniquefoundational objectonwhicheverythingelsedepends: ∃x(FEx ∧∀y(y = x ⊃ y → x) [Somethingisafoundationalelement,andeverythingelsedependsonit.]The x in questiondoesnotdependonanything,exceptperhapsitself,anditmustbe unique,oritwoulddependonsomethingelse.Callthiscase G (sincethe x could beaGodwhichdependsonnothing,oronlyitself).Thisisaspecialcaseof F , andcouldbeinanyofthecasesinwhich F holds.
•Write ∗ x → y tomeanthat y isinthetransitiveclosureof → from x.Thatis,one cangetfrom x to y bygoingdownafinitesequenceofarrows.Anelement, x, is ultimatelyungrounded, UGx,if,goingdownasequenceofarrows,onenever comestoafoundationalelement: ∀y( ∗ x → y ⊃¬FEy).Infinitism, I ,istheview thateveryelementisultimatelyungrounded: ∀xUGx. 17 WenotethatInfinitism allowsforthepossibilityofloops,thatis,repetitionsintheregress.Thus,wehave thefollowingpossibility: x → y → z → x → y → z → However,if → istransitiveandanti-symmetric(T and AS),suchloopsareruledout.Infinitism entailsExtendability, E.Soif I holdswemustbeinanoddnumberedcategory ofourtaxonomy(whichisnotruledoutbyotherconsiderations).Allsuchare possible,assimpleexamplesdemonstrate.(Merelyconsider x0 → x1 → x2 → x3 →...,wherethesearealldistinct.Addinotherarrowsasrequired.)Notethat ifthereareatleasttwoelements,then C isaspecialcaseof I .
15 Wenotethat,how,exactly,tocashouttheideaoffoundationalismiscontentious.Forsomediscussion ofthematter,seeDixon2016.Wesuspectthatthenotionmaybevague,toacertainextent,andso susceptibletodifferentprecisifications.Thedefinitionwegivehereisstrong,simple,andverynatural.
16 Onemay,ifonewishes,iteratetheconstructionintothetransfinite,collectingupatlimitordinalsin theobviousway.
17 WenotethatInfinitism,also,iscertainlysusceptibletovariousprecisifications.Forexample,one mightrequirethatonly some elementisungrounded.Again,thedefinitionwegivehereisstrong,simple, andnatural.
thegeographyoffundamentality:anoverview
•Afinalspecialcase.Let x y iff x → y ∨ y → x.Then x and y areconnected alongthedependencerelation, xCy,iffforsome n 1: x y ∨∃z1 z2 ... zn (
)
[Everythingrelatestoeverythingelsealongsomesequenceofdependencerelations.] → itselfisconnectediff ∀x∀yxCy.Inallofthetenpossiblecases, → maybeconnectedornotconnected. G isaspecialcaseofconnectedness; C is anextremecaseofconnectedness;and A isanextremecaseofdisconnectedness.
Letusfinishthissectionwithaninformalsummary.Thetaxonomyisbuiltonfour conditions.(i) Anti-reflexivity, AR:nothingdependsonitself.(ii) Anti-symmetry, AS: nothingsdependoneachother.(iii) Transitivity, T :everythingdependsonwhatever adependentdependson.(iv) Extendability, E:everythingdependsonsomethingelse. Thisgivesus16(= 24 )possibilities.Sixoftheseareruledoutbylogicalconsiderations, leavingtenlivepossibilities.Withinthese,somespecialcasesmaybenoted.Atomism, A:nothingdependsonanything.Foundationalism, F :everythingisafundamental elementordepends,ultimately,onsuch. F :Foundationalism,wherethefundamental elementsandonlythosedependonthemselves. G:Foundationalismwherethe fundamentalelementisunique.Infinitism, I :therearenofundamentalelements. Coherentism, C:everythingdependsoneverythingelse.
3OntheMetaphysicalPossibilityoftheAlternatives
Sofar,wehaveseenthatalternativestometaphysicalfoundationalismingeneral,and thestandardviewinparticular,arelogicallypossible:lines1–4,7,8,and13–16.One mightwonder,however,iftheyare metaphysically possible.Inthissection,wewill arguethattheyare.Butbeforeturningtoadiscussionoftheviabilityofthealternatives tothestandardview,letusfirstaddressoneparticularissuethatwewillfacetime andagain.
Itisquitecommontohearfriendsofthestandardviewdefendtheircommitments tovariousaspectsoftheviewbyappealtotheirintuitions.Thesephilosopherswill claimtohaveintuitionsthatthereissomethingfundamental,thatnothingcanground itself,andsoon.Moreover,thesephilosophersappeartotaketheirintuitionstoserve assomethinglikeargumentsindefenceoftheview:thesephilosopherswillnotonly claimtohavesaidintuitions,butalsothatnothingmoreneedstobesaidonthe matter.Wesimplydonotsharetheseintuitions.Infact,neitherofushasanyintuitions whatsoeverregardingasubjectmatterasabstractandrecherchéasthefundamental structureofreality.But,moreimportantly,wealsofirmlybelievethatintuitionsare noreplacementforactualarguments.Thatintuitionshavebeenallowedtoplaythe roletheyhaveinthedependence/fundamentalitydebatesthusfaris,inourview,why alternativeviewshavebeensopoorlyexplored,andwhyactualargumentsindefence oftheviewhavebeenallowedtobesobad.
Inwhatfollows,althoughappealtointuitionisoftenmadeindefenceofone commitmentoranother,wewillnotrespondtothemfurther.Ourresponsein eachcaseisasstatedhere.Letuscontinueourinvestigation,then,byturningtoa considerationofactualarguments,beginningwiththehierarchythesis.
3.1TheHierarchyThesis
Accordingtotheproponentofthestandardview,realityishierarchicallyarranged. Thatrealityislikethis,wearetold,isintuitiveandsomehowobvious.18 Ithasbeen suggestedthattochallengetheideathatrealityhassuchashape,byquestioning whetherdependencerelationsaretransitive,irreflexive,andanti-symmetric,ispreposterousforthereasonthatmetaphysicaldependencerelationsareintroducedinto thephilosophicalvernacular exactly tocapturethisaspectofreality.Areasonoften citedinfavourofabandoningtalkofsupervenience—asymmetricandreflexive relation—infavourof,say,groundingtalk,isthatweneedarelationthatcancapture reality’shierarchicalstructure.Weagreethat if metaphysicaldependencerelations areintroducedexactlytoallowustocapturetheideathatrealityhasahierarchical structure,thenitmakeslittlesensetocallintoquestionthepropertiesthataresecuring thatstructure.Buttheimportantquestion,wethink,iswhyweoughttobelievereality hassuchastructureinthefirstplace.Anditiswhenwefocuson this questionthat reasonssooftenofferedtocommittothehierarchythesislooklesscompelling.Letus nowconsiderthem.
..anti-reflexivity
Indefenceoftheclaimthatdependencerelationsarenecessarilyanti-reflexive, philosophershavetendedtoarguethatitwouldbeabsurdtoassumethatsomething cangrounditself,orthat,giventhetightconnectionbetweengroundingandexplanation,asitisaprincipleofexplanationthatnothingexplainsitself,itoughttoalso beafeatureofdependencerelations.19
Letusfirstconsiderwhyonemightthinkitabsurdtoassumethatmetaphysical dependencerelationscanbereflexive.Asdependencetalkis about reality,itis reasonabletowonderifself-dependenceisabsurdbecausethereissomewaythat theworldwouldhavetobe,suchthatthingscandependonthemselves,whichis unacceptable.Butwhatmightthisbe?
Afirstworryaboutself-dependenceisthatanythingthatdependsuponitselfwould haveto bootstrap itselfintobeing.Butwhythinkthisisaproblem?Inthecase ofcausation,theproblemisapparent:somethingthatisself-causedwouldhaveto exist priortoitselfintime inordertobringitselfintoexistence.Butmetaphysical dependencerelationsaretypicallythoughtofasbeingsynchronic,sowhatgoes
18 SeeRaven2013forawell-articulateddefenceofthehierarchythesis.
19 SeeJenkins2011forasomewhatdifferentdiscussionofdependenceandirreflexivity.
thegeographyoffundamentality:anoverview
forcausationheredoesnot(necessarily)goformetaphysicaldependence.20 As metaphysicaldependencerelationsarethoughtofasinducingapriorityordering, perhapstheproblem,then,isthatwheretherelationsarereflexive,theveryideaofa priorityorderinggoesoutthewindow.Thismaywellbethecase,butofcoursethisis no reason tothinkthatdependencerelationscannotbereflexive,foritisjusttoassert thattherelationmustbeanti-reflexiveinthefirstplace.Exactlywhatisrequiredin ordertohaveapriorityorderingisthattheorderingrelationisanti-symmetricand anti-reflexive.
Anyonewithevenapassingfamiliaritywiththehistoricalliteraturewouldbeaware thatthereis,infact,precedentforaviewaccordingtowhichthereisatleastonething thatisself-dependent,namely,Leibniz’saccountofGod.AccordingtoLeibniz,God exists,indeed,existsnecessarily.Hedoessobecauseexistenceispartofhisessence; buttosaythismeans,interalia,thatGodnecessarilyexists.SoGodnecessarilyexists becausehenecessarilyexits.Onemightwonder,then,ifagoodreasontoreject thepossibilityofreflexiveinstancesofgroundisthatanythingthatisself-grounded wouldbeanecessarybeing.Now,ofcoursethisisonlygoingtobeaproblemifthe wrongthings,orkindsofthings,turnouttobeself-grounded;take,forexample, thefundamentalia.Apotentialseriousworry,then,isthatifthefundamentaliaare necessarybeings,andtheygroundthebeingofeverythingelse,thenthereisonlyone waytheworldcanbe,whichisexactlyhowtheworldactuallyis.21
Arewecompelled,though,toacceptthisstory—thestoryaccordingtowhich self-groundedentitiesarenecessarybeings?Bliss(thisvolume)suggeststhatweare not.Butifthisisthecase,weseemnoclosertounderstanding(i)whatreflexive dependenceamountstoand(ii)whyitisunacceptable.Failingallelse,onemight simplyworrythattheideathatanythingcandependuponitselfisabsurdjustbecause itisplainweird.Maybeitisweird(thejudgementofwhichwouldseemtorequire knowingwhatself-dependenceactuallyamountsin),butwestruggletoseehowselfdependenceisanyweirderthanthecommonlyheldbeliefthattherearesomeentities thatpopintobeingfromnowhereandfornoreasonatall—whichisexactlywhatthe fundamentaliaarelikebymostpeople’slights.Metaphysicallyspeaking,itisnotso clearwhatissobadaboutsomething’sbeingself-dependent.
Morecompelling,wethink,areexplanatoryreasonsforthinkingthatreflexive instancesofdependenceareunacceptable.Itisaplankinmuchoftheliteratureon explanationthatreflexiveexplanationsaretrivial,uninformative,andexplanatorily useless.Areflexiveexplanation,sothethoughtgoes,isasgoodasnoexplanation atall.Weareinclinedtothink,though,thatwhilsttheremaybesomethingtothis, mattersherearethornierandmoresubtlethantheyappear.22 Forastart,notall
20 Therearereasonstobelievethattherearecasesofnon-synchronicgrounding,justastherearecases ofsynchroniccausation.Obviouslytheintricaciesoftheseissuescannotbecoveredhere.
21 SeeDasgupta2016foradiscussionofthisviewaccordingtowhichitwouldnotbeaproblem.
22 SeeKeefe2002foramostilluminatingdiscussionofissuesrelevanttothisdebate.
circularexplanationsaretrivial—wehavealreadyseenthisinthecaseofGodand hisexplanatoryrelationshiptohimself—noraretheynecessarilyuninformativeor useless.Afterall,comingtounderstandthatsomethinghasnofurtherexplanation is comingtounderstandsomethingmoreaboutthatthing.Intheworstcase,whatwe maybedealingwithisaproblemwithexplanatorysuperfluity:something’sexplaining itselfisasgoodasithavingnoexplanationwhatsoever,sowhybotherpermittingselfdependenceinthefirstplace.
Asthingsstand,thereasonstodisavowself-dependenceappeartobefairlythinon theground.Metaphysicallyspeaking,it’snotclearhowaworldwouldhavetobesuch thatthingsdependonthemselves,leavinguswithexplanatoryconsiderations.But ifthisistheconclusionitishardlywelcome.Suddenlytheproblemswithreflexivity appeartobe epistemic ratherthanmetaphysicalwhichwouldseemtoflyinthefaceof howthefriendsoffoundationalismunderstandtheoverarchingstructureofreality.
..anti-symmetry
Letusnowturnourattentiontoanti-symmetry.Advocatesofthestandardviewrely on(somecombinationof)argumentsfromintuition,argumentsfromthedata,and argumentsfromstructuralsimilaritieswithexplanation.Appealisalsomadetowhat wemightcallargumentsfromrelativefundamentality.Theargumentfromrelative fundamentalityisjustavariationonthekindofargumentintermsofstructurethat wementionedintheintroductiontothissection.Weconsiderthesefirst.
Accordingtotheargumentfromrelativefundamentality‘dependenceisintimately connectedto(andperhapsevenexplainsorisoneandthesamethingsas)relevant notionsoffundamentality,priority,grounding,etc.Dependenceisthekindofrelationthatexplainstheconnectionbetweenthefundamentalandthederivative(the dependent)tothefundamental(theindependent).Anyrelationthatplaysthisrole mustbeasymmetric’(Barnes,thisvolume).Theideathatrealityisorderedintoa hierarchicalstructureisaveryoldonethatcanbetracedbacktotheAncientGreeks. Indeed,rightthewaythroughthehistoryoftheWesterntradition,manyphilosophers havebeenengagedinsomewayorotherwithfillinginthedetailsofthispicture.23 Thatsomefolksclaimtohaveintuitionsregardingthestructureofrealityishardly surprisinggiventhepervasivenessofthisview(andimagery)inthehistoryofWestern thought.24
AsBarnespointsout,ifmovingusfromthefundamentaltothederivative is therole thatdependenceissupposedtoplay,thenitseemsrighttosupposethatdependence mustbeanti-symmetric.Indeed,asalreadymentioned,itjustfollowsfromtheidea
23 SeeLovejoy1934foraninformativeandcharmingdiscussionofthenotionoftheGreatChainof BeinganditscentralitytothedevelopmentofWesternmetaphysics.
24 Theideathatrealityishierarchicallystructuredhasnotonlybeenthepurviewofthemetaphysician, butwasalsocommonplaceinthesciences,art,andtheologyupuntiltheendofthenineteenthcentury. Thisviewwentoutofvoguewiththemomentouschangestoourunderstandingoftheworldprecipitated byscientificdevelopments.
thegeographyoffundamentality:anoverview
thatrealityishierarchicallystructuredthatthestructuringrelationisanti-symmetric. Butexactlywhattheargumentfromrelativefundamentalitydoesnotprovideuswith isa reason tosupposethattherelationisanti-symmetric—itsimplyassumesit.One waytorespondtotherelativefundamentalityargument,then,istochallengetheidea thatwehavereasonstosupposethatrealityishierarchicallystructuredinthefirst place.Toputthepointmorefinely,wecanchallengetheideathatrealityexhibitsa robusthierarchicalstructurebyarguingthatmetaphysicaldependencerelationsare eithersymmetric(whichmightgenerateaspeciesofmetaphysicalcoherentism)or thattheyarenon-symmetric(aweakerclaimthatmayyetallowforahierarchyto emergenonetheless).
Whilstweagreethattheworldappearstopresentuswithcasesofanti-symmetric dependence,thatdependencerelationsarenecessarilyanti-symmetricisnotobvious tousatall.AsBarnesandThompson(thisvolume)argue,someofourmostbeloved metaphysicaltheoriesappeartopositsymmetricinstancesofdependence;oratleast makemoresenseiftheydo.Consider,forexample,Armstrong’saccountofstates ofaffairs.Armstrong’spictureisoneaccordingtowhichatomicstatesofaffairsare ontologicalrock-bottomwiththeirconstituentsasabstractionsfromthosestatesof affairs.Theproblemwiththispictureisthatthestatesofaffairsreallyseemtodepend ontheirconstituents,withthoseconstituentsexplainingthenatureandexistenceof thosestatesofaffairs.BarnessuggeststhatifArmstrongweretoallowsymmetric instancesofdependence,thenhecouldhavehiscake,asitwere,andeatittoo:atomic statesofaffairsdependingontheirconstituents,buttheconstituentsdependingon theirstateofaffairs.
Theoreticalcasesaside,consideralsotherelationshipbetweenthenorthandsouth polesofamagnet:withoutthenorthpole,thesouthpolewouldnotexistandwithout thesouthpole,thenorthpolewouldnotexist.Thelist,itwouldseem,goeson.We appeartohavecompellingreasonstotemperourcommitmenttoanti-symmetryand endorsethemoremodestsuggestionthattherelation(s)isnon-symmetric.
Whataboutthemuchstrongerclaimthatdependenceis,infact, symmetric? Canthecasebemadeforsuchastrongview?Well,itcanbecauseithasbeen.As Priest(thisvolume)discusses,theChineseHuayanBuddhisttraditionendorsesa speciesoffull-blowncoherentismwitheverythingdependingsymmetricallyupon everythingelse.25
Ithasbeensuggestedthatasmetaphysicaldependenceisintimatelyinvolved withexplanation,wecaninferfromthestructuralpropertiesattributedto(good) explanationsonsomemodelsthatmetaphysicaldependencerelationsalsosharesuch properties.Asexplanationsareanti-symmetric,sotheobjectiongoes,sotooare dependencerelations.ButasbothBarnesandThompson(thisvolume)pointout, therearealternative(verygood)explanatorymodelsonwhichexplanationsarenot
25 SeealsoPriest2014,esp.chapters11–13,foracontemporarypresentationofacoherentistpicture inspired,inpart,byHuayan.
necessarilyanti-symmetric.Indeed,accordingtoBarnesandThompson,explanation asunderstoodwholistically,maywelldoabetterjobofcapturingcertainaspectsof oureverydayandtheoreticalexplanatorypraxis.
Thatmetaphysicaldependencerelationsareintroducedtocapturerealityashierarchicallystructureddoesnotprovideuswithareasontothinkrealityhasthatstructure inthefirstplace.Although‘thedata’suggeststhatsomeinstancesofdependence relationsareanti-symmetric,thisisalsonoreasontosupposethattherelationisin general.Indeed,thecherry-pickingofinstancesofdependencerelationsthatappear tobeanti-symmetrictouseasourparadigmaticcasesofdependenceoughtnotblind ustothepresenceofotherinstantiationsoftherelationthatareplausiblythoughtto besymmetric.Alltold,thereseemstobegoodreasonstosupposethatmetaphysical dependencerelationsareatleastnon-symmetric.
..transitivity
Thereissomethingnatural-seemingabouttheideathatmetaphysicaldependence relationsaretransitive.Whereapersondependsontheirvitalorgans,italsoseems truethattheydependuponthecellsthatcomposethosevitalorgans.However, anumberofauthors,includingNolan(thisvolume),havepointedoutthatatthe veryleast,wecouldwellallowthatsomeinstancesofdependencerelationsfailto betransitive,andholdaviewaccordingtowhichmetaphysicaldependenceisnontransitive.
Whyquestionthetransitivityassumption?Well,onegoodreasonisthatreality appearstopresentwith actual casesoffailuresoftransitivity.Schafferasksusto considerthefollowingpropositions:(1)thefactthat o hasadent, d,groundsthefact that o hasshape S,(2)thefactthat o hasshape S groundsthefactthat o ismoreorless spherical,and(3)therefore,thefactthat o hasadentgroundsthefactthat o ismoreor lessspherical.Ifgroundingweretransitive,thenwewouldexpectthisargumenttogo throughbut,Schafferargues,itdoesnotbecause o ‘ismore-or-lesssphericaldespite thedent,notbecauseofit’.26 AsfarasSchafferisconcerned,thefactthat o hasadent doesnot groundthefactthat o ismoreorlessspherical,inwhichcasegroundingis notnecessarilytransitive.27 Orconsiderotherproblematiccases:singletonObamais dependentuponitsmemberObama,andObamaisdependentuponhisparts,andyet wemightwellnotwanttosaythattheexistenceofObama’sheart(partially)explains theexistenceofsingletonObama.
Onewaytorespondtothesesortsofcasesistopointoutthatdependenceisnot univocal.Whatonemightthinkisgoingoninthesecasesisthechainingtogetherof instancesofdependencerelationsthatdon’t,infact,properlybelongtogether.One mighttryandargue,forexample,thatthewayinwhichasingletondependsupon
26 Schaffer2012,p.127.
27 ThisisnottheonlypurportedfailureoftransitivitythatSchafferpresentsuswith.SeealsoRaven2013 foradefenceofthethoughtthatgroundingistransitive.
thegeographyoffundamentality:anoverview
itsmemberisdifferenttothewayinwhichthememberdependsuponitsparts.28 Wereonetopursuesuchanapproach,however,onemustremainmindfulofthecosts suchanapproachmightincur:dowereallywantorneedaproliferationofspeciesof dependencerelations,forexample?29
Anotherapproachmightbetodistinguishbetweenrelationsof mediate and immediate dependence,wheretheformeristransitiveandthelatterisnot.Indeed,inthe literature,philosophershavesuggestedthatweshouldtakeseriouslyadistinction betweenimmediateandmediatedependence.30 Purportedfailuresoftransitivitycan thenbeunderstoodasinvolvingthetransitiveclosureofanintransitiverelation.So whatappearstobeafailureoftransitivity,infact,involvesacaseofmistakenidentity.
Thereareadvantagestoadmittingadistinctionbetweenatransitiveandanontransitivespeciesoftherelation.Ontheonehand,itallowsustoavoidaproliferation ofrelation-typesinresponsetothepurportedproblem:wherepart/wholerelationsare aspeciesofdependencerelation,truthmakinganotherandsoon.And,ontheother hand,itallowsforcertainpossibilities.Nolan(thisvolume)suggests,forexample, thatsomespeciesofdependence,orinstancesoftherelation,mayfailtobetransitive allowingthepossibilityofgiantcosmologicalloops.Andmoregenerally,wherethere isaspeciesoftherelationthatisintransitive,loopsofvarioussizescouldbeadmitted without beingforcedtosacrificeanti-symmetryandanti-reflexivity.Alltold,there arereasonstodoubtthatmetaphysicaldependencerelationsarenecessarilytransitive. Notonlydoweappeartobeinpossessionofcounterexamplestothetransitivitythesis, butwehavereasonstosupposethatadmittinganintransitivespeciesoftherelation toourrepertoirewouldbetoouradvantage.
Ofcoursethereissomuchmoretobeconsideredregardingthewidespread commitmenttothehierarchythesis,andthepossiblealternativestoit.Rabin(this volume)believesthatunorthodoxaccountsofgroundingallowustobettercapturethe layeredconceptionofreality.Lookingtoothertraditions,asPriest(thisvolume)does, wecanseethatanumberofaccountsfromtheAsianBuddhisttraditions,forexample, rejecttheideathatrealityishierarchicallystructured.Anyoneseriouslyinterestedin non-standardconceptionsofthestructureofrealitywoulddowelltolookbeyondthe Westerncanon.AndLitland(thisvolume)arguesthat,whathecallsabi-collective accountofground,mayhaveinterestingapplicationsforcertaintypesofcoherentist structures.
28 ConsiderwhathappenswhenwesaythatHarrybanksonSallyandSallybanksonTuesday.Noone wouldclaimthat,therefore,HarrybanksonTuesday.Norwouldanyoneclaimthattherelation bankingon, asdemonstratedbythisexample,isnot,therefore,transitive.Whatwewouldbeinclinedtosayisthatthe expression‘bankson’picksoutdifferentrelationsinthetwocases.
29 SeeWilson2014foradefenceoftheclaimthatallweneedarethemanydifferentkindsofsmallggroundingrelationswithwhichwearefamiliar—supervenience,parthood,etc.—ratherthanonebig-G groundingrelation.
30 See,forexample,Fine1994,1995,and2013fordiscussionsofsuchpossibilitiesasregardsboth ontologicaldependenceandgrounding.
3.2TheFundamentalityThesis
Onemightwellhavetheimpressionthatnaryapaperisproducedinanalyticmetaphysicsthesedaysthatdoesnotmakereferencetothenotionoffundamentality.31 Somewhatsurprising,then,isthedearthofgoodargumentsavailableintheliterature indefenceofthefundamentalitythesis.Broadlyconstrued,thereappearstobeat leastthreetypesofargumentonoffer.Thefirstofthese,asmightbeexpected,are argumentsfromintuition;thesecondoftheseareargumentsfromviciousinfinite regress;andthethird,argumentsfromtheoreticalvirtue.Inkeepingwithourpromise above,wedesistfromdiscussingargumentsfromintuitionandturnimmediatelyto regressarguments.
..regressarguments
Whatexplainsthefactthatweexist?Agoodplacetostartwillsurelyinvolveappealto factsabouttheexistenceofourparentsandthegeneticmaterialtheyhavebequeathed tous,ourvitalsorgans,andsoon.Ofcourse,wearecausallydependentupononour parents,butwearealso metaphysically dependentuponthem:it’snotsimplythatour parentscauseustoexist,buttheyalsogroundourexistenceaswell.Althoughthe storyoftheexistenceofanyoneofusismetaphysicallycomplex,mostofuswould feelconfidentinassumingthatwehavesomeroughideaofhowtotellit.Suppose, now,thatwealsowishtoexplaintheexistenceofourparentsandourvitalorgans. Again,acomplexmatter,butsurelyonethatwillinvolveappealtotheirparents—our grandparents—andthecellularstructureoftheorgansandsoon.Ateachstage,it wouldappearasthoughwehaveexplainedsomethingabouttheentitiesforwhich weareseekinganexplanation,andthatthisprocesscouldgoonsuccessfullywithout termination.Butexactlywhatthefundamentalitythesistellsusisthatitdoesn’t(or can’t)goonforever,andajustificationforthispositionisgoingtohavetotelluswhy thisisthecase.32
Oneobviousseemingthoughtisthatwherewehavelimitlessdescendingdependencechains,althoughwehaveexplainedsomething(probablyevenalot),wehaven’t yetexplained everything thatweneedanexplanationfor.33 Oranotherthoughtmight bethatwherewehavelimitlessdescendingdependencechains,althoughwehave explainedsomething,wehaven’tyetarrivedatanexplanationthatiscomplete,or atleast completelysatisfactory.And,ofcourse,thereisawayofunderstandingthese twoexplanatoryconcernsthatisintimatelyrelated,foranexplanationwillsurelybe
31 Oneneedsnotonlybereadingfromthedependence/fundamentalityliteraturetonoticethis.Appeal tofundamentalityismadeintheliteraturerangingfromtopicsasdiverseasthephilosophyofmindto aestheticsandethics,toofferbutafewexamples.
32 SeeBliss(forthcoming),fromwhichmuchofthefollowingdiscussioninthissectionisborrowed,for amoresustainedelaborationofthesethoughts.
33 SeeBliss2013.
