Neo-Aristotelian Plenitude Ross Inman University of Notre Dame Center for Philosophy of Religion Philosophical Studies 168 (3):583-597 Abstract Plenitude,roughly,thethesisthatforanynon-emptyregionofspace- time there is a material object that is exactly located at that region, is often thought to be part and parcel of the standard Lewisian pack- ageinthemetaphysicsofpersistence. Whiletheweddingofplentitude and Lewisian four-dimensionalism is a natural one indeed, there are a hand-fullofdissenterswhoargueagainstthenotionthatLewisianfour- dimensionalismhasexclusiverightstoplentitude. These‘promiscuous’ three-dimensionalists argue that a temporalized version of plenitude is entirelycompatiblewithathree-dimensionalontologyofenduringenti- ties. Whilefewwoulddenythecoherenceofsuchaposition,andmuch workhasbeendonebyitsproponentstoappeasecritics,therehasbeen surprisinglylittlebywayofexploringthevariousformssuchanontol- ogymighttakeaswellasthepotentialadvantagesofoneplenitudinous three-dimensional ontology over another. Here I develop a novel form of plenitudinous three-dimensionalism, what John Hawthorne (2006) has called “Neo-Aristotelian Plenitude,” and argue that if one is in- clinedtoendorseanabundantthree-dimensionalontology,oneiswise to opt for a plenitude of accidental unities. 1 Diachronic Plenitude Let’sbeginbydefiningamodaloccupationprofileasafunctionfromworlds to sets of non-empty regions of spacetime in those worlds: each world w is assigned a set of filled regions of spacetime in w. The modal occupation profileofw, then, isthesetoffilledspacetimeregionsinw, callitP .1 With w this in mind, we can then define the thesis of plenitude as follows: 1SeeHawthorne(2006a: 53). 1 N-A P 2 P: for any subset, s, of P , there is at least one object, w o, that exactly occupies s. Asapieceofmetaphysicalmachinery,plentitudeisoftenthoughttogohand in hand with four-dimensionalism of a Lewisian stripe, the view that objects persist by being temporally extended and are mereological fusions of their temporal parts or stages.2 That is, a plenitudinous ontology just is one con- sisting of a plenitude of temporal stages.3 Let’s unpack this a bit. Moving from the occupation profile of worlds to worms, the four-dimensionalist holds that the occupation profile for each persistingobjectisthesetofnon-emptyregionsofspacetimeforthatobject’s spatiotemporal career (for each worm there is assigned a set of non-empty regions of spacetime), call it P . With this in place, the four-dimensionalist o goesontostatethatforanysubinterval,s,ofapersistingobject’soccupation profile, P , together with a function f assigning a non-empty class of objects o f(s) to each s, there is an object o that exactly occupies that interval and is composed of exactly the objects in f(s).4 This rather liberal cross-temporal principle is known as diachronic plenitude and can be stated as follows: (DP) D P: for any subinterval s of P , and o anyfunctionf assigninganon-empty classofobjectsf(s)toeach s in P , there is at least one object o that exactly occupies s and o is composed of all and only the objects in f(s). Let us call the objects specified by DP “plenitudinous objects.”5 As is famil- iar, thefour-dimensionalistconstruestheplenitudinousobjectsgeneratedby DP as temporal parts of either zero or non-zero temporal extant (both of which are themselves fusions of the temporal parts of the objects in f(s)).6 2Here I limit my discussion to standard four-dimensionalism and thus ignore various non-standard varieties such as stage theory (Sider 2001) and 4D-Partism (Hudson 2001). Henceforth,“four-dimensionalism.” 3Sider(2001: 134-149)arguesfromunrestrictedcompositiontoaplenitudeoftemporal parts. 4Hawthorne(2006b: 116). 5Formypurposesinthispaper,IrelyontheparticularformulationofDPasitpertains tothefilledregionsofspacetimewithintheboundariesofpersistingobjectsrecognizedby commonsense. Thefullapplicationoftheprinciple,ofcourse,admitsmuchmorebesides. 6The notion of a fusion here is that of which satisfies the fusion axiom of classical ex- tensionalmereology. SeeSider(2001: 8). N-A P 3 2 Plenitudinous Three-Dimensionalism While the wedding of DP and four-dimensionalism is a natural one indeed, there are a hand-full of dissenters who argue against four-dimensionalism having exclusive rights to DP.7 The view that a superabundance of pleni- tudinous objects as prescribed by DP is entirely compatible with a three- dimensional ontology has come to be known as “promiscuous” or “pleni- tudinous”three-dimensionalism. Asaresult,plenitudinousthree-dimensionalists contend that an influential argument from diachronic vagueness in favor of four-dimensionalism is either blocked or severely crooked indeed.8 The argument, in brief, is as follows. Pace mereological essentialism, ordinary objects undergo mereological alteration over time without thereby ceasing to exist. The question of how much mereological alteration over time an ordinary object (Socrates, say) can undergo without ceasing to exist raisesthequestionofwhetheranobjectcanhavevaguetemporalboundaries. WhilewemaycertainlyadmitthatSocratesmaysurvivethelossofahandful of cells or even an entire limb, there appear to be borderline cases where it is indeterminate as to whether or not Socrates, upon undergoing certain changes, continues to exist at that particular time. As a result, there appear to be cases where Socrates is diachronically vague in so far as he exists at t and it is vague whether he exists at t . Di- 1 2 achronic vagueness is easily accommodated on a four-dimensional ontology equipped with a plenitude of temporal parts. If one takes the plenitudinous objects generated by DP to be a superabundance of temporal parts of ex- tendedspacetimeworms,thenonecanhelponeselftoamultitudeofdistinct, albeitoverlapping,temporalpartsofSocrates(Socrates-at-t andSocrates-at- 1 t -and-t , etc.). Given a plenitude of temporal parts, the four-dimensionalist 1 2 canavoidcountenancingonticvaguenessregardingtheexistenceofSocrates and chalk up diachronic vagueness to the semantic imprecision of our lan- guage, that is, it being semantically vague as to which of the plenitude of temporal parts ‘Socrates’ refers to. The problem is not so easily resolved using the resources of a standard three-dimensional ontology. If objects fail to be temporally extended and thus are wholly present at each moment of their existence as per three- dimensionalism, anditisdiachronicallyvaguewhetherornotsomeparticu- lar collection of cells suffices to compose Socrates over time, then it is some- timesvaguewhetherornotSocratesexists. Andinsofarasexistenceclaims 7Hawthorne (2006), Koslicki (2003), Lowe (2005), Miller (2005, 2008), and Steen (2010). 8SeeKoslicki(2003)andMiller(2005,2008)inparticular. N-A P 4 of this sort can be formulated using a logical vocabulary that is entirely devoid of semantic vagueness, the three-dimensionalist is saddled with the claimthatthevaguenessatworkiseitherepistemicorontic. Withoutaplen- itude of candidates on which to pin vague terms, the three-dimensionalist is unable to avail themselves of a semantic solution to the problem of di- achronic vagueness. Notso,arguesthecohortofplenitudinousthree-dimensionalists. Iffour- dimensionalism does not have exclusive rights to DP and the abundant on- tologythatfollowssuit,thenneitherdotheyhaveamonopolyonasemantic solutiontotheproblemofdiachronicvagueness. Infact,theyargue,withDP in hand they have at their disposal a semantic solution to diachronic vague- ness that is structurally similar to four-dimensionalism yet one that retains a robust ontology of enduring entities. Asarepresentativeofplenitudinousthree-dimensionalism,letusconsider the account put forward by Kristie Miller.9 Miller (2005: 323-4) defines a synchronic fusion as simply “the fusion of the members of a set at a time” and a diachronic fusion as “the fusion of two or more synchronic fusions.” She then goes on to state the following: Forthereisnothinginthreedimensionalismpersethatprohibits thethreedimensionalistfromholdingthatthereexistsanyendur- ingobjectcomposedofarbitrarycombinationsofthingsattimes. Even if the three-dimensionalist accepts that there exist instanta- neous objects (fusions-at-times), she need not concede that per- sisting objects are the fusions of these objects. She could instead holdthatforeverysynchronicfusion,thereissomeenduringob- ject x that is constituted by those fusions at those times. Call such an object a diachronic object. (2005: 324) By Miller’s lights, the three-dimensionalist is entirely within her rights to adopttheviewthatforanyfusionthatexactlyoccupiessomearbitrarysubin- terval of a persisting object’s occupation profile, there is a diachronic (en- during)objectthatisconstitutedbythatfusionandiswhollypresentatthat subinterval. In contrast to the four-dimensionalist’s equating a plenitudinous ontol- ogy with a plenitude of temporal parts, Miller points out that DP is entirely neutral as to the type of entity that is taken to exactly occupy the relevant subinterval as well as the relation between plenitudinous objects and ordi- nary persisting objects. Plenitudinous objects, claims Miller, need not be 9SeeMiller(2005, 2008). Seefootnote7forotheradvocatesofthislineofthinkingor somethingverysimilar. N-A P 5 identified with the temporal parts (nor fusions thereof) of perduring space- timewormsbut,rather,maybefusionswhicharesaidtoconstituteenduring entities. Equippedwithanabundanceofcontinuant-constitutingfusions,the three-dimensionalist has equal access to the requisite pincushions for vague terms: it is semantically vague as to which continuant-constituting fusion (Socrates-at-t Socrates-at-t -and-t , etc.) ‘Socrates’ refers to. 1 1 2 Not all are congenial to the prospects of a three-dimensional appropri- ation of DP. Achille Varzi (2007) contends that while DP is entirely com- patible with a three-dimensional ontology, there is little reason to endorse the view and a compelling reason to reject it. He takes the wedding of DP with three-dimensionalism to generate a diachronic variant of the problem of the many. His concern trades on what he takes to be a crucial asymmetry between three and four-dimensionalism regarding the relationship between the many plenitudinous objects generated by DP. To help get clear on Varzi’s worry, let us introduce ‘is located at’ as a primitive relation that obtains between an object and a region of spacetime, and proceed to define the following location relations:10 x is entirely located at r = x is located at r, and there is no def region of spacetime disjoint from r at which x is located. x is wholly located at r = x is located at r, and there is no def proper part of x not located at r. xispartlylocated atr= xhasaproperpartentirelylocatedat def r. Varzi asks us to consider the following: how many wholly located objects occupyaparticularregionatatime? Thefour-dimensionalisthasastraight- forward answer: one. Given DP, for any arbitrarily chosen subinterval, s, of a persisting object’s occupation profile, there is at least one plenitudinous object that exactly occupies s and is composed of all and only the objects assigned to s by f(s). Call the object that exactly occupies this subinterval O. Now, consider the following three subintervals of a persisting object’s occupation profile: s, s , and s . Exactly occupying s, s , and s will be at 2 4 2 4 least one plenitudinous object composed of all and only the objects assigned to these subintervals by f(s) as prescribed by DP. Call this object O . In 1 addition to O there will be other numerically distinct plenitudinous objects 1 such as the fusions of the occupants of s and s as well as the fusion of the 2 occupantsofsands , callthemO andO , respectively. Invirtueofsharing 4 2 3 O asacommontemporalpart, O (cid:0)O areeachpartlylocatedatsandhave 1 3 10Parsons(2007). N-A P 6 the same synchronic compositional base at s. Thus, O (cid:0)O are not wholly 1 3 located at s, only their common temporal part, O, enjoys this elite privilege. Despite the many overlapping plenitudinous objects at s, only one of these objects is wholly located at s on four-dimensionalism. On Miller’s three-dimensionalism, by contrast, we have wholly located objects in spades in so far as O (cid:0)O each individually constitute a numer- 1 3 ically distinct enduring entity (diachronic object) at s. Each enduring entity that is constituted by O (cid:0) O has precisely the same synchronic composi- 1 3 tional base at s, thereby generating a multitude of distinct mereologically coincident continuants; where we thought there was a single enduring en- tity, there are very many indeed. As a result, Varzi contends that the three- dimensionalistwhoendorsesDPissaddledwithahostofdistinctcoincident entities each of which are wholly located at the interval in question, a di- achronic variation of the problem of the many. Now, Miller and company have replied to the charge of the problem of the many non-identical overlapping continuants raised by Varzi.11 My aim here is neither to evaluate these responses nor examine the overall grounds foraffirmingaplenitudinousoveranon-plenitudinousthree-dimensionalism. Instead, I want to spend the rest of the paper trying to persuade those three- dimensionalists who are inclined to adopt DP that a particular brand of three-dimensionalplenitude,onethatcountenancesaplenitudeofaccidental unities qua hylomorphic compounds, is worthy of their consideration. 3 Neo-Aristotelian Plenitude InthissectionIdevelopanovelbrandofplenitudinousthree-dimensionalism, whatJohnHawthorne(2006)hascalled“Neo-AristotelianPlenitude”(NAP). In the sections to follow, I offer independent motivating factors in support of the wedding of a plenitudinous three-dimensional ontology to hylomor- phism in general, and conclude by showing how NAP is well-suited to deal with some of the difficulties surrounding a three-dimensional appropriation of DP. We have seen thus far that the two main contenders for the role of plen- itudinous objects are the four-dimesnionalist’s temporal parts and Miller’s synchronic and diachronic fusions which constitute enduring entities. Here, I want to offer a third alternative for the status of plenitudinous objects– accidental unities–that takes its cue from the longstanding hylomorphic on- tology of the Aristotelian tradition. While Hawthorne (2006b: 116) relies 11SeeMiller(2008)andSteen(2010). N-A P 7 explicitly on Kit Fine’s (1981) the notion of a “qua-object” (which is in turn inspiredbyAristotle)inhisthree-dimensionalappropriationofDP,Itakeas myguideageneralmedievalAristotelianontologyofmaterialobjectsasput forward by Thomas Aquinas.12 3.1 A Plenitude of Accidental Unities On Aquinas’ hylomorphic ontology, material objects are best construed as compounds of matter (hyle) and form (morphe). As Jeffrey Brower (2012) has aptly pointed out, Aquinas construes matter and form in functional terms. What Aquinas calls ‘matter’ refers to that which plays the role of the enduring subject of change, ‘form’ being that with respect to which the enduring subject changes.13 For my purposes here, we can follow the inter- pretation of Aquinas that construes forms (the substantial form of human persons being a notable exception here) in trope-theoretic terms as non- transferrableindividualizedproperties.14 Ahylomorphiccompound,then,is simply that which exists in virtue of matter possessing a form. For Aquinas, the combining of matter and form results in a hylomorphic compound that is numerically distinct from its matter and configuring form. ForAquinas,therearetwodifferentkindsofhylomorphiccompounds— substancesandaccidentalunities—eachdistinguishedbythesortsofentities thataresaidtoplaytheroleofmatterandformintheirconstituentmakeup. MorerelevantforourpurposeshereisAquinas’notionofanaccidentalunity as a form-matter compound whose immediate proper parts are a substance (or substances) and an accidental form.15 In contrast to substantial forms, accidental forms are said to modify previously existing substances and thus do not confer on matter their modal profiles.16 What plays the matter role for accidental unities is not a non-individualized portion of stuff as with substances, but a full-fledged individual substance in its own right. Consideraratherwell-wornexampleofanaccidentalunity,seated-Socrates. For Aquinas, seated-Socrates is a genuine hylomorphic compound whose immediate proper parts consist of Socrates and the inhering mode of seat- edness.17 The modal profile of seated-Socrates–its existence and identity–is 12In relying on Aquinas’ general hylomorphic framework to unpack NAP, I in no way wanttosuggestthatAquinashimselfwouldhaveendorsedaviewalongthelinesofDP. 13Aquinas(1993: 67-68). 14SeeBrower(2012),BrowerandBrower-Toland(2008)andLeftow(2003: 2). 15See Aquinas (1964) 5.7.842ff. Where x is an immediate proper part of y = x is a def properpartofy andthereisnootherproperpartofy,z,suchthatxisaproperpartofz. 16SeeAquinas(1965: ch. 7). 17ForatreatmentofaccidentalunitiesinAristotleseeMatthews(1982). N-A P 8 grounded in Socrates’ being modified by the accidental form of seatedness. Consequently, seated-Socrates exists at every moment at which Socrates is seated,thatis,itisessentialtoseated-SocratesthatithaveSocratesandseat- edness as its immediate proper parts. How might Aquinas’ accidental unities be put to use in constructing a novelplenitudinousthree-dimensionalontology? Tostart, NAPwillinclude both synchronic and diachronic accidental unties, roughly tracking Miller’s distinction between synchronic and diachronic fusions mentioned above. Synchronicaccidentalunitiesarecompoundswhoseimmediateproperparts are a substance and an accidental form (trope) at a time (seated-Socrates-at- t). Diachronic accidental unities, on the other hand, are accidental unities whose immediate proper parts are other synchronic accidental unities.18 To illustrate, take the arbitrarily chosen subinterval of Socrates’ occupa- tionprofileconsistingofthetwointervalss ands ,whereSocratesissitting 1 5 ats andSocratesisteachingats ,callits. AsperNAP,thereisadiachronic 1 5 accidental unity that exactly occupies s and is composed of all and only the objects assigned to both s and s by f(s). This diachronic accidental unity, 1 5 call it seated-teaching-Socrates, will have two synchronic accidental unities as (immediate) proper parts, seated-Socrates-at-s and teaching-Socrates-s 1 5 and whose (remote) compositional base will include all and only those ob- jects that compose its constituent synchronic accidental unities at their re- spective subintervals. The proponent of NAP will contend that instead of taking s to be exactly occupied by either one of the many temporal parts of a perduring entity or a fusion which constitutes an enduring entity, it is exactly occupied instead by a diachronic accidental unity with a substantial enduring entity as a proper part at a level of decomposition. DP, of course, gives rise to more bizarre and gerrymandered diachronic accidental unities than seated-teaching-Socrates. In this way, DP is indis- criminating in its admittance of plenitudinous objects both within Socrates’ spatiotemporalboundaryaswellasthosethathavenorelationtohimwhat- soever. Takethefilledregionsofspacetimethatareoccupiedbymyclenched righthandatt andTomCruises’sunglassesatt ,callitr. DPdemandsthat 1 4 thereisadiachronicaccidentalunity, clenchedhand-sunglasses, thatexactly occupiesrandhasthesynchronicaccidentalunitiesclenchedhand-at-t and 1 TomCruises’-sunglasses-at t asimmediateproperparts andiscomposedof 4 all and only the objects assigned to t and t by f(s). 1 4 Here it is vital to point out that the synchronic accidental unity seated- Socrates-at-s and the diachronic accidental unity seated-teaching-Socrates 1 18SeeRea(1998: 356,n. 15)fordiscussiononhowDP,beingacross-temporalvariation ofmereologicaluniversalism,mightbedeemed‘Aristotelian.’ N-A P 9 mereologicallyoverlapats . Whilethesetwodistinctaccidentalunitiesshare 1 the same synchronic compositional base at s , they nevertheless differ in the 1 manner by which they are located at the relevant subinterval in question. According to NAP, synchronic accidental unities are wholly located at their respectivesubintervals: thereisnoproperpartofseated-Socrates-at-s thatis 1 notlocatedats . Diachronicaccidentalunities,ontheotherhand,arepartly 1 locatedatthesubintervalsoccupiedbyeachoftheirsynchronicconstituents. Thus, while seated-Socrates-at-s and seated-teaching-Socrates coincide at 1 s , only the former is wholly located at that subinterval. 1 NAP, however, does not identify ordinary persisting objects with syn- chronicaccidentalunties. Attheheartoftheviewisasubstanceontologyin which an enduring particular, e.g. Socrates, is wholly located at the distinct subintervals of its spatiotemporal career. Socrates qua one and the same enduring entity enjoys the privileged status of being wholly located at more than one time. While synchronic accidental unities are wholly located at their momentary instants, they do not persist such that they are wholly lo- cated at more than one such instant. Hence, in our example above, Socrates is a substantial enduring entity that is wholly located at s as a proper part 1 of seated-Socrates-at-s and is wholly located at s as a proper part of the 1 5 distinct synchronic accidental unity teaching-Socrates-at-s . 5 4 Putting Neo-Aristotelian Plenitude to Work Here I want to offer several considerations to help independently motivate theweddingofplenitudinousthree-dimensionalismtoahylomorphicontol- ogyingeneral. Whollyapartfromitsabilitytosolvethediachronicproblem ofthemanyaswellasofferanovelsolutiontotheprobleminitstraditional guise,theneo-AristotelianontologyofmaterialobjectsthatundergirdsNAP is remarkably fruitful in its wider application to debates in metaphysics.19 Here I put on display some of the virtues of a hylomorphic ontology as it pertains to two issues in particular: the problem of temporary intrinsics and truthmaking. 4.1 A Plenitude of Bearers of Temporary Intrinsics To begin, accidental unities prove fruitful in grounding a novel response to the problem of temporary intrinsics. As Jeffrey Brower (2010) has sug- gested,ahylomorphicontologyprovidestheresourcesforaneglectedfourth 19For more on the fruitfulness of a hylomorphic ontology in contemporary metaphysics seeBrower(2010),Johnston(2006),Koslicki(2008),Oderberg(2007),andRea(1998b). N-A P 10 solution—what he calls the constituent solution—that is both robustly en- durantist and structurally similar to an appeal to an ontology of temporal parts.20 On this line of thinking, enduring entities undergo intrinsic change in virtue of successively entering into numerically distinct accidental unities at different times. Socrates qua enduring entity changes from being pale at t to being swarthy at t by being a proper part of the synchronic accidental 1 2 unities pale-Socrates-at-t and swarthy-Socrates-at-t which essentially pos- 1 2 sess the intrinsic features being pale and being swarthy as immediate proper parts. This hylomorphic variant of endurantism is structurally similar to an appeal to an ontology of temporal parts as a solution to the problem of temporary intrinsics. Like temporal parts, accidental unities are essentially defined by their intrinsic features, where both temporal parts (Socrates-at-t) andaccidentalunities(seated-Socrates-at-t)aretheprimarybearersofintrin- sic properties. In addition, both accounts are of the opinion that persisting objectsexemplify(albeitderivatively)therelevantintrinsicpropertyinvirtue of standing in a relation to the primary property bearer, whether a temporal part or an accidental unity. Unliketheplenitudinousobjectsoffour-dimensionalism(temporalstages) andMiller’sthree-dimensionalism(synchronicanddiachronicfusions),Aquinas’ accidental unities are neither proper parts of persisting objects nor do they constitute such objects. Rather, they are complex objects of which persist- ing enduring objects are immediate proper parts. As a result, NAP offers the three-dimensional proponent of DP an abundance of accidental unities as the bearers of temporary intrinsics. 4.2 A Plenitude of Things Qua Truthmakers Let us turn now to the bearing accidental unities have on the issue of truth- making. Thefundamentalinsightdrivingthecommitmenttotruthmakersis that truth is determined by reality. To say that something determines some particular truth is to say that it is the metaphysical ground of that truth, its existenceexplainswhythattruthistrue. Fewwoulddenythatforthesingu- larexistentialproposition<eexists>itiseitselfthatservesasthetruthmaker for such a predication; e determines the truth of <e exists>. The story is a familiar one. Ilimitmydiscussionheretotherelevantmodalimportthatcharacterizes 20Thestandardsolutionsbeing(i)presentismand(ii)propertyrelativizationand(iii)the doctrineoftemporalparts. HereIassumeageneralunderstandingoftheproblemoftem- poraryintrinstics.