Kinds, Types, and Musical OntologyAuthor(s): Charles NussbaumSource: The Journal of Aesthetics and Art Criticism, Vol. 61, No. 3 (Summer, 2003), pp. 273-291Published by: Blackwell Publishing on behalf of The American Society for AestheticsStable URL: http://www.jstor.org/stable/1559178 .Accessed: 18/06/2011 09:34Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at .http://www.jstor.org/action/showPublisher?publisherCode=black. .Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.Blackwell Publishing and The American Society for Aesthetics are collaborating with JSTOR to digitize,preserve and extend access to The Journal of Aesthetics and Art Criticism.http://www.jstor.orgCHARLESNUSSBAUM Kinds, Types, and Musical Ontology I.INTRODUCTION any two things are similarin some way or other. In this case, the claim is that musical works and In an influential article,e Nicholas Wolterstorffbiologicalspeciesaresimilar withrespect to makesthefollowingthree claimsconcerning norm-kindhood.But as we shall see, the notion musical works: that species are kinds at all is a contested one; if speciesare not kinds, they are alsonot norm- 1.Musical works are norm-kinds(p. 129). kinds. If the claim that species are norm-kinds 2.Musicalworks displaymany close similarities collapses, sowillWolterstorffsbasis ofcom- to naturalkinds (p. 127). parison. And even ifspecies may be construed 3.Biologicaltaxa (e.g.,categories picked out asnaturalkinds, the comparison with musical byfolk-biologicalspecies-terms like"The works as norm-kindsis,as weshall see,more Grizzly") are naturalnorm-kinds(p. 127). problematicthan it might at first appear.There are also, as I hope to show, independentreasons Wolterstorffdoes (in effect) distinguish naturalfor resisting the assimilation ofmusical works from nominal kinds. The Grizzly is an exampleto kinds entirely. Still, Wolterstorffis, I believe, ofthe former and Red Thing isan example of correct that species and musical works may be the latter, though he does not, for all that, wishusefullycompared. Buttomake thecasefor todenythat "Red Thing" namesa "genuinesimilarity,a differentbasis of comparisonmustbe kind."Whilehedoesnotdosoexplicitly, found. I shall offer one in the next section. In the Wolterstorffalso means to distinguishbetween thirdsection I shall introducea notion of norma- naturalkinds that are norm-kindsand those that tivitythat differs sharply from Wolterstorffs, are not. Just as any "properlyformed" grizzlybut that doessomeofthework ofhisnorm- must sharecertainpredicates"analogically"with kinds. In the fourth section ofthe paper I shall The Grizzly, he proposes, so must any properlyputsomeoftheseconclusions towork inan formed instanceof a musical work sharepredi-attemptto determinewhethermusical works are cates analogically withtheworkitself.But discovered,invented, or created. norm-kinds are just those kinds that may have "improperly formed examples" (p.129),and there can be no improperlyformed examples ofII.BIOLOGICALSPECIES,MUSICAL WORKS, AND water orgoldany more than there can beanREPRODUCTIVELYESTABLISHEDFAMILIES improperlyformed electron or quark.Yet these are surely natural kinds if anything is.IshallIt isdifficult these days tofind any reputable assume that it is only to naturalnorm-kindsthat philosopher of biologywillingtocountenance musical works "displaymany close similarities,"species essentialism,the view that species are and that all of Wolterstorffs naturalnorm-kindskinds whose memberships are determined by are biological entities, that is,speciesor theirsatisfactionof some set of necessaryandsufficient traits. conditions,even genotypicalones. Genotype Toevaluateasimilarityclaim,wemustvaries too much between individuals comprising inquire into the basis ofthe comparison, sincea species, and genotypical considerationscan be The Journal ofAestheticsand Art Criticism 61:3Summer 2003 274The Journalof Aesthetics and Art Criticism trumped byhistorical phylogeneticconsider-play scientificexplanatoryroles may (with certain ations, or by considerationsof reproductiveandcaveats) be regardedas naturalkinds, or to deny ecological isolation in determiningspecies iden-that judgments of"properformation"may be tity. Asa matter offact, many philosophers ofmade regarding them. Butitistoassert that biologyareprepared todenythat biologicaljudgments ofproper formation wouldbeof species are naturalkinds at all, holding insteadmore usetoahealth professional (amedical that theyareontologicalindividuals, that is,doctor oraveterinarian)than toabiological mereologicalsumsofdistributed biomass.5taxonomist, sincetheyare easilytrumped by According to this view, species are contingentlyhistorical, reproductive,and ecological consid- arisingandevolvinghistoricallineagesoferations,and thereforerelatively unimportantin organisms. Thefactthat speciesare spatiallydeveloping anadequate species concept or in and temporallyrestrictedindividuals,these phil-the determinationof species identity.10Yet these osophers claim, explains why names ofspeciesarepreciselythemainconcernsofmusical donot appear inany biological laws. Becauseontology: what iswanted isboth an adequate species are individuals, they instantiate variousconceptof the musicalwork and adequatecriteria biological naturalkinds, for example, Predator,of musical work identity. Once we look a little Prey,Lineage,DarwinianClan,Darwinianmorecarefully than doesWolterstorff atthe Subclan,DarwinianSubcland,6which, accordingbiologicalsituation, thecomparison with bio- to some,7arethe subjectsof genuine(i.e.,universal,logicalspeciesasnorm-kinds appears tofall unrestricted)evolutionarylaws. Otherbiologicalwell short of its original promise. naturalkinds,forexample,InteractororStill,theideathatmusicalworksdisplay Replicator,which figure in laws of evolutionarysome importantsimilaritiesto biological species biologyandgenetics,maybeinstantiated,is a valuableone thatcan and shouldbe salvaged. respectively, bythe individual organisms con-Toaccomplish thisweshall needadifferent stitutinga species or by their genomes. Anotherbasis of comparison, a notion that carves out a view of species ontology agrees that species arecategory capable of comprising both biological individuals, butinsiststhattheyarenaturalspecies and musical works. But there issuch a kind-liketo the extentthey groundreliableinduc-notion, namely, that ofa reproductivelyestab- tions: knowing that an organism belongstoalished family(hereafterREF). Ignoring for the biological taxon makes it possible to make reli-moment the importantdistinctionbetween first- able predictionsabout it, say, predictionsaboutandsecond-order REFs,Millikandefinesan its metabolic processes and learningcapacities.8REF as follows: Naturalkinds are those kinds traditionallyheld to groundreliable inductions.Still anotherviewAny set of entitieshavingthe sameor similarrepro- denies that species are individuals and regardsductivelyestablishedcharactersderivedby repetitive them as sets of organismsthat constitutenaturalreproductionsfromthe same characterof the same kinds because they figure in legitimatescientificmodel or modelsform a first-orderreproductively explanations,even if they are not mentionedbyestablishedfamily. name in universallaws.9 A corollary of this last viewisthat not allscientific explanation needThis idea isuseful onanumber offronts. (1) be nomological in character.Both the performancesofamusical work and Noneofthisaffords much comfort tohimthe individualorganismsthat make up a species whowould compare musical works tospeciesconstitute, as I shall argue, REFs. (2) An REF construedas naturalnorm-kinds.Eitherbiologicalmay (though it need not) be regardedas consti- speciesare individuals (mereological sums oftuting a naturalkind. (3) The notion of an REF parts) and therefore not kinds at all, naturalorisneutralbetween the two competing viewsof otherwise;or they are spatiotemporallyrestrictedspecies as mereological sums of biomass and as setsoforganisms whosemembers are histor-sets of historicallyconnectedorganisms.(4) While ically, reproductively,and ecologically related,notallREFsaresubject tonormative con- notnorm-kinds thatmustthemselvessharestraints,many are, including biological species propertieswith their properlyformed instances.and musical works, becauseissuesofproper This isnot to deny that sets oforganisms thatfunction come into play. (The notion of "proper NussbaumKinds, Types,and Musical Ontology275 function" willbe explained presently.) Speciestotokensas"replicas.",15 Regarding setsof (and, asIshallargue, musical performances)tokensasREFsistherefore consistentwith, proliferate differentially becauseofselectionperhaps evenmandated by,Peirce'soriginal pressures,and selection pressuresare normativeusage. Interestingly,the Greekroot (in its verbal constraints.(5) The REF notion makes perspicu-infinitiveform)oftheEnglishword"type" ousconnection withanapproach tomusical("typtein")means "to strike,"and the correspond- ontology that has recentlybecome quite popular,ing substantiveterm ("typos")means "blow that namely, the construalof musical works as typesisstruck." BothPeirce'soriginalusageand and their performances astokens.12Whatevertheseetymologicalconsiderations suggesta elseperformancesas tokens ofa musical typefactor of causal reproduction. maybe,itisdifficulttodenythat theyareSecond, it is sometimes claimed that types, as reproductively established familiesofevents.opposed to kinds and universals,may be created (6) The notion of an REF is ontologically parsi-and destroyed.16Such a claim isvindicated to monious: it remains uncommittedto the exist-the extent the existence of types requiresrepro- ence of abstractentities. An REF of tokens mayduction oftokens: any such reproductivepro- be held to instantiatea type qua abstractobject;cess constitutes a unique, causally linked chain or it may be held merely to exhibit a mode ofthat is initiated at one point in time and comes genidentity,thegenidentityofacausally-toanendatanother. Doesthismandate the historicallyorderedcollection of entities. On thenominalistic interpretationoftypes astokens- second, more nominalistic interpretation,thereof-a-type, rather than asabstract objects that are no abstracttypes, there are only tokens-of-a-may or may not be instanced?We shall address type.13(7) The genidentityconditions that applythis question in Section IV below. Without the toREFsreinforce theconception ofmusicalconditionsof reproductionand historicalunique- works astypes and lend support tothe strongness that the REF notion imposes on classes of intuition that musical works are particularsthattokens, however,the reasonableclaim thattypes, are createdby composers, because types exhibitunlike kinds and universals, "straddlethe onto- characteristicsof particulars.logical divide between particularand general" 17 Types have been considered to be particularsremains unsupported.Wolterstorff,for one, and for at least tworeasons. First, names oftypesKivy,18 for another,do not feel the need to dis- function naturally assingular logicalsubjects:tinguishexplicitlybetween"kind,""type,""sort," wetend tousethe definite article when refer-and "universal"in their discussions. ring to them in ordinarylanguage, for example,As REFs, biological species constitutesecond- "theletter 'a,' " "theviolin,""theModel T Ford."order, and not first-order,REFs, inMillikan's Wedo,itistrue,alsosay"the great whiteterminology. While an organism's genome isa shark";but this, I submit, points to the fact thatdirect copy ofthe genetic material contributed biologicalspeciespossesstypecharacteristicsbyitsimmediate ancestors, whether sexually (astheymustiftheyaretobeconsideredreproducingor not, the organism or phenotype REFs). Weare much lessinclined tosay "theitselfisnotadirect copyofanything. Itis quark"or "the electron," which isnot to claimconstructed according toitsgenotypical plan, we do not say such things at all: witness the rela-and the resulting phenotypicalexpression is the tivefamiliarity oftheexpression "the atom."jointproduct ofitsgenotype and itsenviron- This may tell us something already fairly obvi-ment. Any set of entities so producedaccording ous,namely, that the distinction between kindto plan, but not directly copied from any model and type isnot demarcatedwith perfect clarityor prototype,constitutesa second-orderREF. A in ordinarylanguage. My suggested principleofset of buildings constructedaccording to a sin- demarcationis that types must involve a processglearchitecturalplan, for example, would also ofhistorical reproduction oftokensandtheconstitute a second-orderreproductivelyestab- transmissionof reproductivelyestablishedchar-lishedfamily.Performances ofscored music, acters,14 whilekinds need not. It isfrequentlyinterestingly enough, constitute both first- and acknowledgedthat the contemporarytype/tokensecond-order REFs. Insofar asamusical per- distinction isdue to C. S.Peirce. What islessformance complieswithascore, itwillbea frequently noticed isthat hespecifically refersmember ofasecond-order REF,since(qua 276The Journalof Aesthetics and Art Criticism compliantperformance) itwasnotdirectlyvariations;and those genetic variationsthatcode copiedfromanotherperformance. Butthefor phenotypictraitsof increasedadaptationwill, compliant performancewillalso bea memberleaving aside contingent factors such as genetic of at least one first-order REF, namely, a tokendrift orenvironmental cataclysms, crowd out ofinterpretation.Asan interpretation,the per-the original forms. Millikan terms the capacities formance willbemodeled onother perform-oforganic traits and mechanisms that enable ances,mostlikelythoseemanating fromthetheirpossessorsto proliferatesuccessfully"proper school of interpretationto which the performerfunctions." belongs; or it will be modeled on interpretationsItisimportant tobear inmind that while the performeradmires.This suggests that whileMillikan's theory of REFs and properfunctions Sharpe may overstate the caseinarguing thatisinspired byevolutionary biology,itisnot themusical typesofwhichperformances areintended as a contributionto the philosophy of tokens just are interpretationsand not works atbiology.It isa theory ofsigns, and assuch a all, heisonto something important.Copies ofcontributiontophilosophical semiotics and to scoresthemselvesalsoconstitutefirst-andthe philosophiesof languageandmind.Millikan's second-order REFs.Theyareeithercopiesprincipalconcern is the developmentof a natur- printedfrom a single master templatethat itselfalisticaccountbothofintentionality andof isa copy ofthe original autographscore or ofcontent for mental and linguistic representations earlier master templates, thereby constituting a("intentionalicons," asshecallsthem inthe second-orderREF;19 or they are directcopies ofgeneral case). Of particularconcern to her are the autographscore or of copies of these copies,those public representationsthat carry propos- therebyconstitutinga first-orderREF; or, in theitional content, namely, declarative sentences. absence ofan autographscore, they are copiesTokensofdeclarativesentencesproliferate, ofsomeversion held tobeauthoritative.Per-form continuing REFs, to the extent they serve formancesof musical works that are not scored,"adapted"proper functions: they are produced that belong toaperformancetradition lackingand used by mechanismspresentin the brainsof musicalnotation,on the otherhand,will constitutespeakers and hearers because declarative sen- first-order REFsexclusively.Sincebuildingstenceshavehistorically adapted speakers and andmusicalperformances, givenMillikan'shearersto their environmentsby mappingthose definitions,constituteperfectlyacceptableREFs,environmentsfrequently enough with a degree REFs, itisclear, need not benaturalkinds orofaccuracy sufficient tosatisfythestandard even natural-kindlike.evolutionarytradeoff between cost and benefit. Theintentionality ofrepresentationsdepends upon their derived20properfunctions, what they III. REPRODUCTIVELYESTABLISHEDFAMILIES,PROPER are supposed to bedoing according tonatural FUNCTIONS,AND THE IDENTITYOF THE MUSICAL WORKdesign. If declarative sentences did not realize these functions, then speakers would stop pro- Not every REF is subjectto normativeconstraintsducing them and hearerswould stop responding or selection pressures.An idly bouncing ball ontothem. And ifdeclarative sentences had not awet,sandy surface willproduce a(second-satisfiedthese constraintshistorically,the mech- order) REF of impressions ofits surface in theanisms for producingand using them would not sand, second-orderbecause the impressions arehave proliferated. all copies ofthe surface ofthe ball and not ofIdonotendorsewithoutqualification each other. Biological REFs, however, are sub-Millikan's original and challenging evolution- jecttonormativeconstraintsbecausetheyaryaccountofmentalcontentandsentence proliferateor do not proliferatein a competitivemeaning. But Ishall not stop here toprobe it environment depending ontheadaptations offurther.The point to bear in mind is that in the theirmembers.Thereisalsoanormativecontext ofher theory, familiesofrepresenta- requirementoffidelity ofreplication at work,tions, both public and internal ("in the head"), namely, fidelity to the genotype;but this require-areimportant examplesofREFsthathave ment is,ofcourse, importantlylimited. Everyderived proper functions. Concerning aesthetic biologicalreplicationeventproducessmallsymbolism, Millikan has little to say, and what NussbaumKinds, Types,and Musical Ontology277 she does say, relegating aesthetic objects exclu-placeincontemporaryconceptions ofspecies sivelyto the realm ofnonconventional impro-identity.Noncompliancewith the scorein musical visedsigns,21is,byherownadmission,inperformanceisstrongly discouraged, indeed is some error.A nonconventionalimprovised signconsidered so serious a threatto the identity of (e.g., "one if by land, two if by sea") generallythe work astohave moved sometheorists to willnotbeamember ofanREF,sinceitsdeny that a performancewith even one noncom- production willtendtobeaone-timeaffairpliantnote(orsoundevent)countsasan tailoredtosomeuniquelyoccurringsetofinstance of the work. The concernhere involves circumstances. Itwillnotbecopieddirectlya variety ofsorites paradox:How many wrong from any previous models, nor will it serve as anotes does it take to change the identity ofthe model for any subsequentsigns. To what extentwork? Without a principled answer, the open- music isrepresentationaland bears contents ofingmotiveofBeethoven'sFifthSymphony, somekindare important but vexedquestionsGoodman notoriously warns,25 couldquickly that I shall also not attemptto addresshere. Butmorphinto ThreeBlind Mice. theclaimthatmusic,includingscoresandLevinson has attemptedto finesse this issue performances, issymbolic,that itconsistsofbydistinguishing betweeninstances and per- conventional symbolic entities subject tosyn-formances: an instance ofa work must exhibit tactical or quasi-syntacticalformation rules, isperfect fidelitytothenotational score,buta thesedays hardly acontroversial one.Totheperformanceof it need not. We may, that is, be extent musical symbols are conventional, theyoffered aperformanceofawork, "possibly a form REFs. And to the extent they are producedgreat one," that isnot an instance ofit.26 But andconsumed,theirproliferation(or lack thereof)this just postpones the difficulty, for what work issubject to some set of normativeconstraints,isthispossiblygreat performanceaperform- albeit not the environment-mappingconstraintsance of?For Levinson, itistheonethe per- towhichdeclarative sentencesaresubject.23formerintendedtoperform,butfailedto Performances(now includingrecordedperform-instance (p. 86). In orderto have provideda per- ances) ofcertain musical works have prolifer-formance ofthe work, hesays,the performer ated massively, judging byfrequency oftheirmust succeed "to a reasonable degree": "What appearance onconcert programs andrecord-differentiatespoor or marginalperformancefrom ings,and havecrowded outperformances ofnonperformance,is for many compositions per- otherworks,as have performancesthatexemplifyhaps markedby the ability ofan informed and certain interpretiveapproaches to these works.sensitive listener to grasp, at least roughly, what Considerthe amazing fecundity of the "faithful-S/PM[sound/performance-means]structure is ness to the composer's intentions"traditionofstruggling tobepresented" (p.86,n33).But orchestral performanceinitiated byToscanini.what is it to "grasp"an S/PM structure?Absent Like declarative sentences, ifmusical symbolssome mysterious act ofintuition, surely it is to ceased doing whateverit is they do for producerstake the performanceto instantiatethe abstract and users, ifthey ceased to fulfill their derivedS/PMstructure,which justistotake itasan properfunctions, they would not continue to beinstance ofthe S/PM structure.This, however, producedand would stop proliferating.isparadoxical,for itseems that any informed Although musical REFs are thus normativelyand sensitive listenerwho succeeded in grasping constrained, and tothis extent exhibit similar-the S/PM structure"strugglingto be presented" ities to biological ones, there are importantdif-wouldhavetobeinnocent oftheGoodman- ferencestoo.InthecaseofscoredmusicalLevinsontheory ofmusical-work identity, or works there is also a fidelity requirement,but awould have to disbelieve it to do what Levinson requirementthat is prima faciemore stringentsays she must be able to do, that is, to take what than theoneoperative inthebiological case:thetheory saysmust beanoninstance asan performances, itisthought,ideallyshouldinstance.It might be counteredthatthe informed comply exactly with the notationalaspects24ofandsensitivelistener needonlycompare the thescore.Thisintroduces anapparent strongwould-be performance with a genuine instance essentialist elementintothedetermination ofshecanrealize inher head upon reading the the identityof a scored musical work that has noscore (orcan realize from memory). But this 278The Journalof Aesthetics and Art Criticism response faces two difficulties. First, it seems toI intendto playa famouswaltzby YI havenot heard require that the listener benotonlyinformedandhaveneverseenthe scoreof. Someonedevilishly and sensitive, but also possess the powers ofagives me a scoreof theDadaisticcomposerZ's recent Brahms, who reputedly preferredthe perform-waltz, which strangelyenoughhas the same S/PM ance ofDonGiovanni hecould realize inhisstructureas Y's waltz.I thinkthatthe soundevent head tothe public performancehecould haveI produceis a performanceof Y's waltz,not of Z's attended. This is,tosay the least, implausible.waltz. Yetthere isnocontinuouscausal chain Second, it lands us back in Goodman's soritesrunningfrom Y's creativeact ofindicationto my paradox:How similar to the internallyrealizedperformanceof Y'swaltz...I am inclinedto believe instance must the performance attempt betothatwhereintentionalandcausalcriteriaconflict,the achieveperformanceratherthannonperformance?formerwill generallydeterminethe identityof the The REF notion may be of some help here. Aperformance. scored musical work, Ihavesuggested, isan REF ofscores and performances.ComplianceButwhyshould weaccept this? Suppose the with the score certainly serves as one importantwaltz isscored for piano, four hands. Suppose, epistemological criterionof musical work iden-moreover, that it is none other than Levinson's tity, perhaps even,for scored music, the mostperformingpartner,devil of a fellow that he is, important one: compliance is good, indeed very whohas perpetrated thehoax.Inthiscase, strong, evidence that a given performanceisaLevinson and his mischievous colleague would token ofa certain work. But as a metaphysicalbesimultaneouslyengaged in performancesof identity condition,perfect or even close compli- twodifferent pieces while reading thesame ance with the score is, as I now shall be arguing,printedscore, a result that, while not beyond all neither necessary nor sufficient. The principalconceivability, strainscredulity. Better, I think, determinerof musical identityfor scored music,just to say thatLevinsonthoughthe was perform- I propose, isthe fact that a performancearisesing Y's waltz but was not. If, contraryto hypoth- causally from aperformer's visual interactionesis, Levinsonis alreadyacquaintedwith Y s score with a token of the score, and not from its com-and with earlier performancesof it, his own or pliance with the score. A performanceof a workothers,the identityconditionsof his performance could,ofcourse, alsoderive causally from aare considerably murkier, for nowthere isan performer's aural interaction withanearlieralternativereproductivecausal chain extending performance ofthat work; but this isunusualback toY's score and itsperformances.Asa with scored music. In either case, the questionresult,Levinson'spresenteffortmightbe claimed weshould be asking is not how compliant withbythree different REFs: asecond-order REF the score must a performanceattemptbe to be aofperformances ofZ'swaltz,asecond-order performance ofaparticularwork, but rather,REF ofperformancesofY's waltz, and a first- how noncompliant must it be to trump its causalorder REF of (tokens of)an interpretation of provenance.Yswaltz. Still, unless Levinson has the piece Levinson takes an opposing view:committed tomemory and isusing the substi- tuted score littleornot atall,weshould say Theidentityof a performance,say,is morea matterof(I maintain) that the causal provenance ofthe what work the performerhas in mind,of how thescore read inthepresent performancetrumps performerconceivesof whathe or sheis doingthanofthealternative causalpath and that itisZ's whatworkis thecausalsourceof thescoreor memorywaltz he is performing. whichdirectlyguidesthe performerin producingtheBothintuition andadeterminationtotake appropriatesoundevent.27seriously an informedcomparisonbetween bio- logical species and musical works recommend, This approachwill, however,spike any attemptthen, that we assume as our default option that a to gain leverage from the biological analogy inperformancewith the right causal provenance dealingwith the metaphysicalproblemof musicalqualifies as a token of that particularwork. An work identity. It also generates counterintuitiveimportantcorollaryis thatif a performancelacks consequences. Suppose, says Levinson (p.99,the right causal provenance,no degree of com- n23), thatpliance with the score, even perfect compliance, NussbaumKinds, Types,and Musical Ontology279 willsufficetomake itan instance ofagivenciststoweight allcharactersequally has been work.28This makes causal history a metaphysi-criticized as arbitraryand a priori.As a result of callynecessaryconditionformusicalworkthesedifficulties,thepheneticistaccountof identity. Asweshall see,however, itisnot aspecies identity collapsed into subjectivity.31 sufficient condition, for there are requirementsCladism(called "phylogeneticsystematics"by ofstructuralaffinity that must besatisfied or,its originatorWilli Hennig) began as an attempt perhapsbettersaid,mustnotbeviolated.to provide objective conditions of species iden- Considered inthis way, the musical case doestity. On the strict cladist view,what counts for display some interesting similarities to the bio-species membershipis exclusively phylogenetic logical one, ifwe take, as do many these days,history:speciationoccurs at the branchingpoints either a strict cladist view or an "evolutionary"in the unique phylogenetic treelike patternthat view(whichcombines cladist and pheneticisthas been traced out bylifeon the planet, and elements) of species identity.29only at such points. Only monophyletic groups Pheneticism, which initspure form isnow(lineages with neithergaps nor branchingevents widely discredited,was an attemptto determinethat postdate amost recent common ancestor) taxonomy byapplying mathematicalsimilaritycount as species. Structuralsimilaritiesand dif- metrics toa large number ofequally weightedferencesmaybeindicators ofthesecausal- phenotypical characters of organisms withouthistoricalrelations,but they are not determiners invoking phylogenetic history at all. The organ-ofspeciesidentity.Onlythecausal-historical isms that come out closest in multidimensionalrelations are. Moreover, alineagestructurally similarity space after the calculations are com-similar to an already existing species that came pleted are grouped together into taxa at variousinto existence at a later time, but is not causally levels.The problem isthat equally valid basesconnected totheexistingspecieswouldnot, for clustering insimilarity space yieldincom-accordingto a strictcladist, constitutea continu- patibleresults.Eachdimensionofsimilarityation of the existing species. It would be a new space is correlatedwith a specific character.Asspecies, whateverits structuralor morphological the clusters form in multidimensionalsimilaritysimilarity.32Such considerationscohere nicely space, it can happenthat a given organism30willwithLevinson'sreasonable insistencethata be claimed by two different clusters, dependingmusical work isnot merely an abstractsound/ upon what principlesare employed.For example,performance-meansstructure,but such a structure if an organismis nearerto the nearest organism"indicated"by an individual(the composer) at a ofone cluster but nearer to the farthest organ-definite time and place within a musical context ism of the other cluster, to which group shouldthat has a history. itbelong? Orshould theorganism's distanceLevinson briefly considers theevolutionary from an average ofthe positions ofthe organ-comparison himself.33 But heissuspicious of isms forming the two competing clusters count?Wolterstorff'sassimilation of musical works to There isno way to resolve such ambiguities inbiological norm-kinds,and rightly so.For one an objective, nonarbitraryway. Assuming simi-thing, Wolterstorffsessentialist conception of larity space to be Euclidean, there isalso morespecies membershipis crude and outdated:there than onemathematicalmetrical technique thatjust isno set of"featureswhich a thing cannot can be used to calculate distance, with differentlack if it is to be a properlyformed example"34 techniquesyielding differentresults.For the sakeof a biological species, since the "properform" of simplicity, consider two organismslocated inofaspecies,assuming such anotion iseven atwo-dimensional similarity space.Willtheintelligible from an evolutionarypoint of view, distance between them be the hypotenuseof thevaries historically.35For another,Wolterstorffis right triangle whosesidesaretheir distancesnot sufficiently sensitive to the importantdiffer- from each other along each ofthe two dimen-ences between the biological and musical cases. sions? Or will the distance between them be theLevinson observes36that musical works possess average of the distances along each of the twono causally relevantinnerconstitutionthat plays dimensions?Pheneticists were unable to supplya role analogous to that ofthe genotype ofan a principled defense ofone technique over theorganism; andhedoubtsthatthenotionof other. Even the decision on the part of pheneti-"naturalfunction" hasanyapplication inthe 280The Journalof Aesthetics and Art Criticism musical sphere. Both points are welltaken. Asidentityalso emphasizephylogeneticprovenance, tothefirst, biologicalspeciesmayqualify asbut are willingtoletstructuralconsiderations naturalkinds (or as natural-kindlike)to the extenttrumpcausal provenanceifthey are significant theyground reliable inductions and figure inenough.So,forexample,whileevolutionary scientific explanations.But this depends on thetaxonomists class the crocodilia with lizards as presence of underlying causal mechanisms thatreptiliaonthebasisofrobust phenotypical maintainthe rich clusterof projectablepropertiessimilarities, and donot classifyaveswith the that naturalkinds have and that nominal kindscrocodilia because of rapid and extreme pheno- lack. We can, to be sure, make reliable predic-typicaldivergence,cladistsrefusetodothe tionsabout current performances ofmusicalformer, becausecrocodilesandbirds havea works based on past ones. But insofar as thesemore recent common ancestor than docroco- are causally groundedand explanatory,the rele-diles and lizards, and happily do the latter. For vant causal mechanisms inquestion are tobethe cladists, the reptilia simply do not constitute found in the brains, bodies, and instrumentsofa well-formed monophyletic group. Other bio- the performers,and not in the musical work, iflogists (e.g.,Mayr) regard capacity and oppor- by "causalmechanisms"we mean (as I think wetunityfor interbreedingas primary,which creates shouldmean)"physical causalmechanisms."notorious difficulties regardingthe identities of Yet the musical work issupposedly the norm-nonsexuallyreproducing species;stillothers kind. Astothe second point, whilewemight(e.g.,van Valen) emphasize ecological consid- agree that Levinson's notion of"naturalfunc-erations.The last two views arefor fairlyobvious tion" (were weable to render it precise) mightreasons irrelevantto the musical case. The evo- wellhavenoapplication tomusicalworks,lutionaryview, however,is not: if musicalworks a more careful handlingof the many varieties ofare to be comparedto species, an approachsuch REFsandthevarietiesofproper functionsas the evolutionaryone seems to fit best, since appropriateto their members would, I think, bethere clearly comes a point at which a noncom- capable ofmuting his concerns. Levinson alsopliant performance willnolonger count asa doubts37that S/PMstructures, asopposed toperformance ofawork,whatever itscausal biological species, can have properlyand improp-provenance. erly formed instances: they are either perfectlyUnfortunately,there seems tobelittle con- instancedor not instancedat all. But this, I havesensus, either within biological science or in the argued,is of doubtfultenability.philosophyof biology, concerningwhich account While essentialism may be a discreditedviewof species identity is the right one. (Kitcher,for inbiology,theessentialistelementwehaveexample, isa pluralist whocountenances nine discernedin the determinationof the identity ofdistinct varieties ofapproach, three structural scoredmusicalworksistooobvioustobeand six historical or phylogenetic.) Against the ignored. This, as wesaw, isan importantpointevolutionary view,the pure cladist willargue of disanalogybetween the biological and musicalthat the inclusion of a pheneticistelement (judg- cases. Indeed, on a strictcladist view of species,ment ofmorphological similarity) reintroduces no degree ofdissimilarity,even significantgeneticasubjective factor that isunacceptable ina divergence(shoulditoccur),issufficienttoscience(evolutionary biology)that, according trumpspecies identity. Strict cladists, that is, doto the title of its own founding text, purportsto not recognize speciation byanagenesis, speci-explain the origin of species; but cladists do not ation within a single phylogenetic branchin thealways recognize their own dependenceon con- absence ofanewbranching event. Without asiderations ofgeneflowand ecologicalisola- branchingevent, a historically connected grouption to determinethe genuine branchingevents. of organismsremainsthe species it is regardlessHowever this may be,there isat work inthe ofstructuralor morphological alterations.Norcladistargument anunderlying realistmeta- will a strictcladistcountenanceas a taxonanythingphysical assumption,namely, that there is a fact otherthanamonophyleticgroup,whateverof the matterconcerning the identity of species degree ofsimilarity, genetic or morphological,that itisthe business ofbiological science to happensto obtainbetween organisms.Biologistsferret out. At least one reputablephilosopherof whotakethe"evolutionary"viewofspeciesscience convinced ofthe need for a pluralistic NussbaumKinds, Types,and Musical Ontology281 approach tospeciesidentity hasgrasped theusaleguponsolvingthesorites paradox of nettleandembracedanirrealism regardingmusicalidentity.Similarity judgments,how- species.38 InStanford's estimation, whateverever,playanimportant roleaswell;indeed, species concept furthersthe aims ofbiologicalthey seem to play a more significant role in the science at a particularhistoricaljuncture, be itmusical context than they dointhe biological evolutionarybiology,comparativeanatomy,one. We may not be able tosay in the case of functionalphysiology, or paleontology,is, in themusicalworksexactlyhowmuchstructural context ofthescienceinquestion, legitimate.divergence is enough to trumpcausal-historical Thereneed be no one-size-fits-allspecies concept.provenance;but at least we can deny that com- Sometimeshistoricalconsiderations willbeplete compliance with a score is metaphysically paramount,sometimes structuraloneswillbe;either necessary or sufficient to maintain work sometimeshistoricalcontinuitywillbearidentity. It isnot necessary because giventhe emphasis, sometimes historical discontinuity.Ifright causal provenance, a performancethat is the variousspecies concepts are mutuallyincom-not completely compliantmay still be counted a patible,as Stanfordthinks they are, so much thetoken of a given work. Complete compliance is worse for realism concerning species. Kitcher,not sufficient because even a totally compliant on the otherhand, who stoutly maintainsthathisperformance willnot,absent theright causal ninespeciesconcepts can becoherently com-provenance,count as a token of that very work. bined, is unwilling to forgo realism.If a pluralismthat recognizes the importanceof Is there a metaphysicalfact of the mattercon-structuralsimilarityalong with causal history is cerning the identity of musical works as there isanoption inthecaseofspeciesidentity (the concerning speciesforthebiologicalrealist?evolutionary approach), itisalsoavailable in We need not attemptto answerdefinitively here.the case of the identity of musical works. Again, Whateverwe say, irrealismconcerningmusical-this should not betaken as an endorsementof work identity isat leastnomore problematicmetaphysicalirrealismin eithercase, but merely thanirrealismconcerningbiological-speciesiden-as an attemptto loosen the grip of the Goodman tity, if both are regardedas REFs. Indeed, con-worriesconcerningtheidentityofmusical sidered in a certain way, it seems considerablyworks. less problematic.While species may be naturalThere is, in addition, a furtherconsideration. kinds or natural-kindlike,musical works mostItwillberecalled that compliance withthe assuredly are neither. (The question of whetherscoreisrelevantonlytosecond-order REF musical works are abstractPlatonic entities willmembership. But aperformancealsobelongs, be takenup in Section IV below.) I hold no briefas we saw, to a first-orderREF, namely,an inter- for an unqualifiedirrealismconcerningmusical-pretation.In the case of nonscoredmusic,say folk work identity, much lessfor an irrealism con-traditionsor improvisationaljazz, this distinction cerning species identity, but the claim that thecollapses:various interpretationsjustarethe identity ofthe products ofhuman culture suchwork. Since the work is now a variety of REFs as musical works may be sensitive to our simi-all deriving from a common ancestor, our grip larityjudgmentsand so infectedwith subjectivityon the identity ofnonscored musical works is inawaytheidentity ofnatural products likesignificantly more tenuous than isour grip on biologicalspeciesshould notbehasaprimaworks of scored music. But this is not to say we facieplausibility. Aperformance,provided ithave no grip at all. The effective principleseems has the right causal provenance, isan instanceto be the one I have recommended.What should of a work if performersand listenersare preparedbe fundamentalfor identityis causal provenance to regard it as an instance of that work. Leavingor the replication oftokens; but at some point aside for the presentthe musical Platonismto bethatwecannotspecifyprecisely,structural discussed below, therejust is no reason at all todivergence will trumpcausal provenance. demandthat musical works should be amenableNow if, as I have argued,the performancesof tomore rigid metaphysical identity conditionsamusical work constitute anREF oftokens, than are biological species. Like species, musicaland if an REF of tokens constitutes a type, then works are historical entities, and construing athe performancesof a musical work constitutea musical work as a causal-historicalREF givestype. But if the performancesof a musical work 282The Journalof Aesthetics and Art Criticism constitute a type, then the musical work itself istodifferent types because they donot share a a type. And ifthe musical work isa type, thecommon causal origin? They are alleyes,are claim that the work is a particularis now a well-they not? Reply: This isalso a case ofoverde- groundedone, or at least it is bettergrounded.Aterminationinvolving a functionalessence. But reproductivelyestablished family ofreplicas isbecauseoftheholdofcladistprinciplein an historical,spatiotemporallyrestrictedparticu-biologicaltaxonomy,wemayberather less lar that can come into and goout ofexistence.inclined here toletfunctional essencetrump Onceitdisappears, that veryparticular, thatcausal ancestry. Even the evolutionarytaxono- causally connected family of replicas, cannot bemist,tosaynothing ofthepure cladist, will recreated.Kinds, and naturalkinds in particular,denytrait identity basedonmerefunctional are different. Water exists wherever and when-convergence. Wemight justhavetoadopt a everhydrogen hydroxide showsupinthisorpluralism such asKitcher's orStanford's and any possibleworld.The historyof waterinstancesallow the two identity criteria an uneasy coex- is not importantas regardstheir identities, theiristence.Whenwewishtorefer toallthese microstructureis. No instanceof water,moreover,structuresas"eyes," wewillfavor functional need be a copy or a replica of anythingin orderessence and regardthem as a kind. When we are to be water.engagedinbiologicalclassification,wewill Objection:Surelyan artifactlike the incandes-regard themasanalogues,andtherefore as cent lightbulb isatype,and surely individualdifferent types. Notice,though, that individual lightbulbs are tokens that constitute asecond-speciesdonotpossessfunctional essencesin orderREF. Suppose Earthto be destroyedalongthe way eyes do. Only the naturalkinds instanti- with all existing lightbulbs. Dowe really wantated by species, kinds such as Prey or Predator, tosaythat ifsomefuture raceofintelligentcould be said to possess such essences, and then beings reinventedthe lightbulb and startedpro-only at a high level of functionaldescription.As ducing tokens having nohistorical connectiona result, the same sort of pressuresdo not arise to the prototypeoriginatedin Edison's workshop,with regard tospecies, or at least do not arise thentheseobjectswouldnotbelightbulbs?with the same intensity. Nowone may quibble Reply:No,that wouldbeabsurd. What thisinonewayoranother withthecelebrated showsisacertainoverdeterminationintheKantian dictum that works ofart evince"pur- application ofthe kind/type distinction. Light-posivenesswithout apurpose"; butwhatever bulbs are indeed tokens that form REFs; but themusicalworksare,surelytheypossess,qua incandescent lightbulb also possesses a causal-individual works, no functional essences. They functional essence,an essence that would alsoarethereforemoreunambiguously typelike belong to anythingthatproducedlight by exploit-than arelightbulbs oreyes,and,asIhave ingthesame physical principles, whatever itsargued, in this regard similar to species. But to causalancestry. Inthiscase,wewouldbemake thiscaseconcerning musicalworksas inclined to regard the lightbulb as also a func-types, must we be ontologically parsimonious? tional kind, and, inthe caseofconflict, toletMust we regardthe musical type merely as the functional essencetrump causalprovenance.historically connected setofperformances,or Incandescent lightbulbs are type-identical; buttokens-of-a-type?Or can the musical type be an they are also kind-identical.abstractobject? This will be a topic of the next Objection: What, then, dowesay about thesection. organsystems of living things?Eyes have origin- atedmultipletimesinevolutionaryhistory because of theirfunctionalvirtuesfor locomoting creatures intransparent media,andbecauseIV.DISCOVERY,INVENTION,AND CREATION differing designswereaccessiblegivenlight- sensitive organic structures"on hand." This isLikethe spaceof possiblefive-hundred-pagenovels, whytheeyesofvertebrates, arthropods, andorfifty-minutesymphonies,orfive-thousand-line cephalopodsare analogousbut not homologous:poems, the space ofmegabyte-longprogramswill they do not all derive from one set of primordialonly ever get occupiedby the slenderestthreadsof structures.39Must we regardthem as belongingactuality,no matterhowhardwe work.40 NussbaumKinds, Types,and Musical Ontology283 Are musicalworksdiscoveredby theircomposers?doctrine that only the actual is possible, is false One who adopted the ontologically parsimoni-at some levelofdescriptionf44Establishing the ous interpretationof musical works as REFs offalsity of actualism,or even delimitingthe proper tokens would quickly answer "no,"for the workapplicationof the concept (if it does have appli- does not exist before its first tokening, whethercationatall),wouldbeatask extending far autographscore, first performance,or perhapsbeyond the scope of this paper. first complete mentaltokeningby the composer.Now it might be hastily assumed by one who The more Platonically inclined theorist who istookaconventionalist lineregarding abstract committedto the propositionthat musical worksobjects that the onlyobjects that are properly are (ormaybe)discovered might reasonablydiscoverable areobjectsofempirical know- object that the parsimoniousinterpretationbegsledge. But this once againwould beg the question the question. Such a theorist,moreover,will notagainst the Platonist, for mathematicalobjects restsatisfiedwithLevinson'sasseveration41provide prima faciecompellingexamplesof that the discovery view offends against a deeplydiscovered objects.45Pythagoras(or some other entrenchedintuitionof a creatabilityrequirementpre-Socraticthinker), it isperfectly reasonable for musical works, and rightly so. 2 While suchtoclaim,discovered ageometrical factabout an intuition should not be cavalierly dismissed,Euclidean plane right triangles, justasCantor the fact that itisdeeply entrenched, ifitis,43discovered that the power set of a set (the set of does not make it right. Let us, then, addressandallthesubsets ofaset)always hasagreater not beg the questionof a creatabilityrequirementcardinalitythan the set itself whetherthat set is byassuming the ontologically more profligateinfiniteorfinite,andGbdeldiscoveredthe interpretationof the musical work as a type thatincompletenessof all consistent finite axiomati- is an abstractobject that might be discoverable.zations of arithmetic.If Pythagoras,Cantor,and In this section, I shall attemptto show that theGodelmadethesediscoveries,maynotthe intuitionbehind Levinson's creatabilityrequire-musical Platonistjustifiably claim that Wagner ment is defensible after all.discoveredthe "Tristanchord"as a musicaltype, To proceed, I requirean assumptionthat I doan abstractmusical-combinatorialobject?46And not know how to argue for, but one that mightifhe may say that, may he also not claim with be considereda postulateof realism.The assump-equaljustificationthatWagnerdiscovered tion isthat discovery, as opposed toinventionTristanund Isolde itself? Unfortunately,no, for and creation, affectsonlytheepistemologicaltherearesomeimportant features tonotice modality and not the ontological modality of anabout themathematical casesthat ultimately object already actual. A discovered object, thatwork to the detrimentof the musical Platonist. istosay,isonethat is(or oncewas)alreadyThe featureto notice first is that the discover- there. It either is actual, or it once was actual. ItiesofPythagoras, Cantor, and Gddel allwere isnot actualized by its discovery; rather,whatdemonstratedbywayofchainsofdeductive changes are its epistemic relationsto those whoreasoning;and deductive connections, whatever have come to know it, in some acceptablesenseelsethey may be,are atemporal.Valid deduc- of "know."(Letus ignorehereas irrelevantrevela-tiveinferences are timelesslyvalid.Should a tions from quantummechanics, onsome inter-mathematical intuitionist/constructivistdemur, pretations, concerning theeffectsthat actsofweat least have reason not toexpect such an observationmay have on the states of subatomicobjection from the consistent musical Platonist. particles,giventheinverserelation betweenThis, however, allows ustosay the following degreeofuncertainty regarding positionandaboutthemathematical cases.Ifdeductive degreeofuncertainty regardingmomentumrelations (expressed astruths oflogicand set established by the Heisenberg uncertaintyprim-theory)are timelesslyvalid, then the Pythagorean ciple.)Inventionandcreation,ontheothertheorem always has been true and the abstract hand, actualizepossibilia. I shall assume for themathematicalobjectsofwhichitistrue sake ofpresent discussion that collapsing the(Euclidean plane right triangles) havealways distinction between the actual and the possibleexisted, if they exist at all.Similarly, it always is not an option. I shall proceed, that is,on the,has been the case that the power set of the set of assumption that "actualism,"themetaphysicalnatural numbers isuncountable and that these 284The Journalof Aesthetics and Art Criticism abstract objects (numbers and their sets)haveObjection: "On a modal realist view, possi- always existed, justasitalways has been thebilia exist." Reply: This is just a terminological case that no consistent finite axiomatizationofvariant ofthe viewI am urging, for the modal arithmeticcan be complete. Moreover, Godel'srealist exploits a distinction between the actual incompleteness theorem, as well as the integersand the existent. Allpossible worlds exist; but and theinfinite number offiniteaxiomatiza-actuality isanindexical notion.49Aworld is tions of arithmetic,have always existed. Indeed,actual only from the standpointof beings at that astrong casecan bemade forthe claimthatworld.(Doesthisentailthat possibleworlds suchobjects,asthereferentsofnecessarylacking intentionalbeings exist but remainnon- truths,exist, if they exist at all, necessarily, thatactual?) Wedonotdiscover actuals inother is, in all logically possible worlds, or at least inpossible worlds; our counterpartsdo. Wemay all nonemptylogically possible worlds.47It mayknow that the Pythagoreantheoremis true in all be thatno one before the twentiethcenturycouldpossibleworlds,orthatwaterishydrogen havebeeninapositiontoarrive atGidel'shydroxide inallpossible worlds,50but that is results,just as no one before the nineteenthcen-because we have discovered these things to be tury could have been in a position toarrive atthe case in our world. Cantor's. Indeed, how could anyone have doneObjection:"Modalrealismandissuesof Gddel's work before the appearanceof Principiacross-world discovery aside, can't wediscover Mathematica? Buttheseareepistemologicalpossibilia?" Reply:Thisisjustamisleading pointsthat,onaPlatonicinterpretation ofway ofspeaking. We may discover that some- mathematics, are completely irrelevant tothething is possible. But such a discovery consists ontological statusof its objects.inactualizing someasyetnonexistent object, Tomakethecasethat musicalworksareprocess,or state of affairs,or in determininghow discovered, themusical Platonist must take athese might be actualized. Such cases are more similar lineregarding musical works. But canproperly seenascasesofinvention (compare: he?Ithink not.Sincethere are notimelesslyEliWhitneydiscoveredthepossibilityof valid deductive routes to specific musical worksconstructing interchangeableparts and, conse- in the space of musical possibility, as there arequently,ofmassproduction byactualizing to specific formal results in logical space, therethem). Alternatively, the discovery ofa possi- arenogrounds whatever forregarding thesebility may consist in demonstratingthatthe con- worksasactual beforetheywerecomposed.cept ofsome nonexisting thing isnot logically While musical terms may, of course, be substi-incoherentorinconsistentwithestablished tuted in logically true expressions, they do notphysicallaworother relevant standing prin- appear "essentially"inany ofthe theorems ofciples (compare:physicist X claims to have dis- logicorsettheory asmathematicalterms (orcoveredthepossibilityofatimemachine). theirset-theoretical equivalents) do.MusicalNeither ofthese seems to bewhat the musical works,therefore, arenotactual beforetheirPlatonisthas in mind.A possibilityspaceallowing composition inthe waymathematicalentities,a limited numberofcombinatorialpossibilities quanecessarilyexistingabstractobjects,that could be exhaustively searchedby way of a (arguably) areactualbeforetheirdiscovery;brute procedure, say thespace ofallthe pos- musicalworksnotyetcomposedaremeresible four-note seventh chords in root position, possibilia.Andiftheyare notactual beforemay give rise to an illusion of discovery, since their composition, theycannot bediscoveredthe Tristanchord seems alreadyto be "there"in bytheir composers, ifmy original assumptionthisspace waiting tobefound. But itisonly beagreedto.Thisisanontologicalpoint:"there"as a possible, not an actual. It is, there- paceKivy48 thereason Beethoven'sSeventhfore,notdiscoveredbutactualizedwhen Symphonywasnot"discovered" beforethetokened. This illusion of discovery is aided and seconddecade ofthenineteenth century wasabetted byaconflation ofmusicalsetswith notbecausenoonewasinapositiontoabstract set-theoretical objects.Abstract set- discover itbefore that time. It isbecause, thetheoreticalobjects, along with their subsets,both symphony not being actual, there was nothingordered and nonordered, may,onaPlatonist to discover.telling,besaidtobeactual; but, contrary to NussbaumKinds, Types, and Musical Ontology285 Levinson,51a sequenceof sets of "sonicelements"Gradus ad Parnassum. But this extreme case is isnot itself a "mathematicalobject." Rather,ithardly representativeofwhat generally occurs isan instantiation ofan abstractmathematicalin musical composition. (i.e.,set-theoretical)object. Aterm referringtoInvention, then, differs from discovery pre- aset ofmusical tones may, that is,count as aciselywith regard tochanges wrought inthe substitutioninstance in some (necessarily true)ontological modality of the objects in question: formal expression.possibilia are renderedactual. Invention brings Objection:"Do not composers find solutionssomethinginto existence; discovery does not. If tocompositional problems, and isnot findingthis is right, then creationdiffers a fortiorifrom just discovering?"(Compare Kivy's example5discovery. Like invention, creation also carries of "finding"a third species of counterpointto aimplications concerning achange in the onto- cantusfirmus.)Reply:Aproblemsituationlogical modality of the created object. But cre- requiringa solution may indeed arise duringtheation alsodiffers significantly from invention. composition ofawork. (Compare: BeethovenHere, though, we shall be able to recognize only found a solution to the problemof recapitulatingadifference ofdegree, not an absolute differ- the triumphantopening theme ofthe Finale ofence such as the modal differencedistinguishing his Fifth Symphonyby reintroducingthe pianis-discovery from invention, thus ruling creation simoversionofthesecondmotiffromtheexnihilooutofconsideration and respecting Scherzo.) But since the work did not exist (wasKivy's puckishobservationthat "in one sense of not actual) before its composition, the exigent'creator,'there has never been one at all except problemsituationand its solution also could nottheLordGodJehovah himself."53 Compare have antedatedcomposition of the work. Simi-Archimedes's invention ofthe water screw or larly, Kivy'sthird speciesofcounterpointdidEdison'sinvention oftheincandescent light- not exist before the cantus firmus did. But solu-bulb with Shakespeare'screation of Hamlet or tions do not suddenly pop into existence once aBeethoven'screation ofthe Eroica.Allwere problem situationarises, either, and then wait topossibilia before they were actualized.But there befound. Thefactthat thecomposition ofais a difference: if Archimedes had not invented work will often producea relatively determinatethe water screw, or if Edison had not invented problem situation (determinate, that is,com-thelightbulb,otherswouldhave.Butif pared totheproblem situation ofwriting theShakespeareor Beethoven had never lived, or if work itself) creates the illusion that the solutiontheseindividuals hadbeenbornunderless is "thereto be found,"for once composition hasfortunatecircumstances(less fortunatefor art,that begun, the range of possibilities that a composeris), the chancestheseworkswouldeverhave come willtakeseriouslyissignificantly narrowed.into existence are next tonil.4Isthis because Kivy'scounterpointexample may constitute aShakespeare andBeethoven,asKivywould limiting case because ofthe extremely narrowhave it,55were uniquely qualified to make "dis- range ofpossible solutions in this tightly rule-coveries" that nooneelsecouldhavemade, bound musical context. No doubt this is why hebefore or since? Not if it is correctto deny that chose it. Yet even here, the solutions are possi-such works were actualbefore they were written bilia,and not actuals, because they cannot beor composed, and therefore to deny they could actualizedbeforethecantusfirmusis,andhave been discovered. But did Shakespeareand because they are generally not strictly predeter-Beethoven create?Or did they merely invent? mined even once the cantus firmus isin place.Theinferences ofCantor and Gbdel, how- One can perhapsimagine a situation where theever massive the intelligence requiredto make choice is so narrowthat there is only one thingthem before anyone else did, were what Dennett to be done that remains in accordancewith thehascalled"deep forced moves" because they rulesofcounterpoint. Perhaps wemust grantinstantiatetruthsoflogic,set theory, and arith- that in this extreme case, the problem situationmetic.56Edison'sinventions werenotforced and itssolution comeinto existence together,moves. But they were, again following Dennett, and that in this limited sense, the solution may"GoodTricks,"functionallysuperiorlocationsin be there to be "discovered,"given the actualitya space ofdesign possibilities that was "Vast" of the cantus firmus and the strict rules ofthe(hugealbeit finite),but that werereasonably 286The Journalof Aesthetics and Art Criticism accessible,given the materialsand the technologyofthe work is174 pages long.Score-printing on hand. If one wanted to constructan incandes-conventions,however, are such that when fewer cent lightbulbin late-nineteenth-centuryAmerica,than thefullcomplement ofinstruments are there were only somany ways, perhaps reallyengaged, rests are not printed out. The staves onlyoneway,57toskin that particularcat. Abelonging to the resting instrumentsare simply similarphenomenoncan be observed in the casenotprinted, andthestavesbelongingtothe ofnatural (evolutionary) design.Just aseyesremaininginstrumentalcombinationsare wereinvented (notdiscovered!) byevolutiondoubledor tripledup on the same page. So by all morethanonce,theincandescent lightbulbrights, the score is really quite a bit longer than could also have been and, ifnecessary, would174 pages, sincerests are, ofcourse, possible have been. They are both Good Tricks.notationalitems. But let us ignore this wrinkle, OtherVast design spaces include the space ofsince doing sowillnot work inmyfavor. To possible500-page booksusingRoman letterskeep things manageable,let us take the Scherzo (Dennett's"LibraryofBabel"), thespaceofas our base case, where the meteris three-quarter possiblegenomesof finitelength('The Libraryoftime and the rhythms are relatively simple and Mendel"), and the space ofpossible computeruniform,and let us assume that these conditions programs (relativized toa particularlanguage)applythroughout. Thisassumption alsodoes up to the length of one megabyte that can be runnotworkinmyfavor.Letussimplifyeven onacomputer withatwenty-megabyte hardfurther and pretend that theonlypermissible disk ("The Libraryof Toshiba").The Libraryofnotationalvariantsare quarternotes and quarter Babel contains 100 tothe power of1,000,000rests, and thatthese constraintsapply throughout volumes,58 compared withan estimated 10tothe length of every one of the fifty-minutesym- the power of70atoms in the visible universe.phonies. (This would, of course, requiremaking Consideringa (permutationally)possible genomeappropriateadjustmentsoftempo tomaintain astringofthefournucleotidesadenine,the fifty-minute length.) Let us give each line a cytosine, guanine, and thymine (ACGT) that isconservativetwo-octave(twenty-five-note)chro- approximately3 x10 to the 9th power long (thematic range. (This will grossly overestimatethe length ofthe human genome), it would take apitch range ofthe tympani and willignore the set of 3,000 500-page volumes in the Libraryoflimitationsof Beethoven's naturaltrumpetsand Mendelcontaining onlytheletters ACGT tohorns; but it willalso underestimatethe ranges representit. So the Libraryof Mendel containsof some of the other instruments.)Finally, let us allthe 3,000-volume sets that representall thestipulatethat each line of staff containsten bars, possiblegenomesofthat length.Thedesignaround, butnotwildlyinaccurate estimate. space of fifty-minute symphonies, while a Van-Giventhesehighlyartificial limitations, how ishingly small subspace ofthe design space ofmany fifty-minute symphonies are there in the all musical compositions of finite length is also,Libraryof Acousmata?Well, with 19 lines per I hope to show, Vast.page, 10 bars per line, and 3 "character-spaces" Letus,withacknowledgment dueRogerper bar, this will give us19 times 10 times 3 or Scruton,59callthismusicaldesignspacethe570 character-spacesper page. Each character- LibraryofAcousmata.Aperformanceofspace willcontain aquarterrest oraquarter Beethoven'sEroica will take aboutfifty minutes.note from the two-octaverange.(We are ignoring The natureof musicalnotationand scoringmakesthe fact that giventhe different ranges ofthe it impossible to givea precise specification ofinstruments,thiswillnotalways bethesame numberof lines and character-spacesper page astwooctaves. Butthisisjustanother artificial Dennett doesforthebooksintheLibrary ofsimplificationthat does not work to my advan- Babel.Nevertheless, someuseful,ifartificial,tage.) Multiplying 174 pages times 570 charac- approximationscan be made.The Eroica is scoredtersperpagegives99,180character-spaces for pairs offlutes,oboes,clarinets, bassoons,per score,sothere are 26(25notesplusthe and trumpets;three horns and tympani;and thequarter rest)tothe99,180thpowernumber usualstringcomplementof firstandsecondviolins,offifty-minute symphonies intheLibrary of violas, cellos,and basses. This yields nineteenAcousmata, anumber perhaps not aslarge as potentially independentlines. My pocket scorethe numberof 500-page novels in the Libraryof NussbaumKinds, Types, and Musical Ontology 287 Babel,butstill(evenwiththeconsiderableinthereprise oftheScherzo, comecloseto simplifications wemade) significantly greaterimplementingGood Tricks that someone else is than thenumber ofatomsintheobservablelikelytohavearrived at independently;much universe.Thedesignspaceoffifty-minutelessare theyforced moves,deeporshallow. symphonies is Vast.The Tristan chord, by contrast,may be consid- When the space ofpossibilities isVast, andered aninvention. Ifso,itisa paradigmatic the locations in this space are not accessible asGood Trick, and not a creation,accordingto the Good Tricks orforced moves,then, itwouldproposal of the previous paragraph.Tristanund seem,thelanguage ofcreation asopposed toIsolde itself, on the otherhand, is, as I now shall that ofinvention, isin order. Levinson's creat-argue, mostcertainly acreation and nomere ability intuition,therefore,is vindicated:musicalGood Trick. works are neither the results offorced movesRecallthat between invention and creation nor are they Good Tricks. The foregoing con-wehavebeenabletorecognizenoabsolute siderationsalso suggest that even when consid-difference, just one ofdegree; that isthe price eredasabstract objectsandnotmerelyasof "naturalizingpossibility" using the notion of tokens-of-a-type,types are mere possibilia, notnaturaldesign space in the Dennett way. But by actualslike mathematicalobjects (on the Platonicinvoking just this difference ofdegree wealso interpretationof such objects). But if an abstractblock Kivy'sslippery slope argumentfrom the type ismerely a possible, then its actualizationTristan chord to Tristan und Isolde. We recog- requires the production of tokens of the type. Itnize the slope, all right; but we have principled is, ofcourse, importantnot to confuse Platonicgrounds for denying that it isall that slippery. mathematicalobjects with the symbolic systemsAn item like the Tristanchord seems to lie close that represent them.Thelatter doconsistoftowhereinventiongoesoverintocreation. types and tokens that are historicallyactualized,This, no doubt, iswhat lends Kivy'sargument forexample, Roman and Arabic notations forsome of its plausibility.It would not, indeed, be numbers.It is also importantnot to confuse thesurprisingif anothercomposerhad incorporated, ontological modality ofabstract mathematicalindependently ofWagner,ahalf-diminished objects themselves withthemodality oftheirseventh chord into acomposition somewhere; concrete instances. Aninstance ofan abstractthe chord, after all, does have a generic music- set-theoretical object,sayaparticular setoftheoreticaldesignation.Whatwouldbe surprising, three, forexample the"three B's"ofmusic,though, istheindependent incorporationofa maybe,atsomepoint intime,apossible: ahalf-diminished seventh chord with Wagner's given particularisa contingent thing that maydistinctivevoicing:therootanddiminished or may not be actualized.But the abstractmath-fifth inthe bass and tenor, the seventh inthe ematical objects themselves just are actuals onalto, and the thirdin the soprano,as the chord is a Platonic construal.voiced in the bassoons, English horn, and oboe Now it is certainlyfair to object that no com-in the opening of the Prelude to the opera.More poser enters the LibraryofAcousmata entirelysurprisingstill would beitsappearanceas the unconstrained.(Of course, no writer enters thevery first chord ofan independentlycomposed Library ofBabel entirely unconstrainedeither.piece. Downrightastoundingwould be the inde- Foronething,onlyasmallsubsetofthesependentinventionofWagner'sunexpected bookscan besemantically interpreted.)Whenresolution toadominant seventh chord rooted Beethoven composed the Eroica, only asmallone half-step belowthe initial half-diminished subset ofthe permutationallypossible combin-seventh chord. This begins toappear creative, ations of notes and rests were live options, givenand not merely inventive; and at this point we standingmusic-theoreticalrequirements,the stateare barely into the opera. Incredible would be of symphonic art in his time, and constraintsofthe independentdecision byanother composer musical taste. These points may be granted.Still,tousetheverysame(type-identical) half- noneofthereallydistinctivecompositionaldiminished seventh chord (withafewenhar- decisions that make the Eroica the Eroica, onemonic notationalreplacements)as Wagnerdoes smallbut significant examplebeing thestillat the climax of the Prelude, now fortissimo in shocking introductionof four bars of alla brevefullorchestral voicing.This, likeBeethoven's 288TheJournalof AestheticsandArtCriticism fourbarsofcuttimeintheScherzoofthe Eroica, is the sort of thing we are accustomedto calla"stroke ofgenius," a genuinely creative move that is neitherforced nor a Good Trick. If Wagnerhadn't done it, it is unlikely that anyone else would have. V.CODA: CRANES, SKYHOOKS,AND THE MUSICAL IMAGINATION60 Tiger,tiger,burningbright In theforestsof thenight, Whatimmortalhandor eye Couldframethyfearfulsymmetry?61 Ihaveargued that Wolterstorff's strategy of comparingmusical works with biological species remains a useful one. But its properdeployment yields a numberof conclusions that departfairly radically from his own. These include the fol- lowing.Musicalworksaretypes,notkinds, because they are historicallyproducedfirst- and second-orderREFs of tokens, that is,perform- ances, including realizations"in the head." Qua REFs, musical works and biological spe- ciesdo,as Wolterstorffclaims, display certain "close similarities."Like biological species on theevolutionary interpretation, theprincipal determinerofthe identity ofmusical works is historical provenance;but with musical works, as with biological species (again on the evolu- tionaryinterpretation),historicalprovenancecan be trumpedby structuraldivergence.Construing musical works asREFs supports aprincipled distinction between types and kinds, allowing us to explain, or at least to begin to explain, why types seemtofunction as particularsand why theymight beheldtodiffer from kindsand universalswith respect to the possibility of their creationanddestruction. Theseconclusions yielded some grounds in supportof Levinson's "creatabilityrequirement"formusicalworks. Adducing these groundsrequiredrecognitionof an absolute difference ofontological modality separatingdiscovery from invention, but only a relative one separatinginvention from creation. The distinction between invention and creation turnedout to be a difference in degree but not of kind, and todepend ontheaccessibility ofa designproduct innatural designspace.By invoking this distinctionof degree we were able tohalttheslidedownKivy'sslippery slope from invention to creation;but invoking it also requiredus to place creativity on a continuum thatincludesundirected evolutionary design. Althoughsuchanapproach maydemystify musicalcreativity bybringingitwithinthe ambit ofnaturaldesign, it need not disenchant it. The musical imaginationthat has, over time, established theslender threads ofactuality in musicaldesignspacemaybeacrane(ora cascade ofcranes) and notaskyhook, firmly anchored, likenatural selectionitself,tothe terrestrialsurface whence it arose. But it consti- tutes whatis arguablythe most directlyaccessible andcompellingskyhooksimulacrumencountered in human experience, framing design products sonearlyimmaterial andyetsodensewith intentionality62that they seem to slip the bonds ofnaturalnecessity,63their only constraintthe patternof their own fierce symmetries.64 CHARLESNUSSBAUM University of Texas at Arlington Arlington,Texas76019 INTERNET:Nussbaum@uta.edu 1.Nicholas Wolterstorff, "Toward an Ontology ofArt Works,"Nous 9 (1975): 115-142. 2.Wolterstorff remainsuncommitted concerningthe question of whetherall instances of a musical work must be performances, that is,productsofintentionalaction on the part ofaperformer. RuthLorand (Aesthetic Order: A Philosophy of Order, Beauty, and Art [London:Routledge, 2000], p.139) claims that not all performancesofmusical works are interpretations.One may hum a tune to remind someone of it; a musicianpracticinga piece may play all the way throughthe score in the process of learningit. (But are these performances?)For the sake ofpresent discussion I shall assume that instances are performancesand that per- formancesare (tokens of) interpretations. 3.The Grizzly growls, and so do properly formed griz- zlies,but not in the same sense: The Grizzly produces no longitudinal atmosphericcompression waves(p.128), but properlyformed grizzlies do. Similarly, both the Prelude to Wagner's Tristanund Isolde and properlyformed instances of it begin with the A below middle C in the cellos. But the Ain the work, as opposed to the Aina properly formed performance, isnotawaviformacousticphenomenon exhibiting a periodic frequencyof approximately220Hz. 4.Butcompare Stephen JayGould,The Structure of Evolutionary Theory (Cambridge, MA:Harvard/Belknap Press, 2002), p. 10. 5.DavidHull,"The Ontological Status ofSpeciesas EvolutionaryUnits," reprintedin Hull, The Metaphysics of Evolution (SUNYPress,1989), pp.79-88;Mark Ridley, NussbaumKinds, Types,and Musical Ontology289 "The Cladistic Solution tothe Species Problem," Biology and Philosophy 4(1989):1-16; Alexander Rosenberg, The Structure ofBiologicalScience(Cambridge: Cambridge University Press,1985); ElliotSober, "Sets, Species,and Evolution:CommentsonPhilipKitcher's'Species,"' Philosophy of Science 51 (1984): 334-341. 6.SeeMary B.Williams, "Deducing the Consequences of Evolution:A MathematicalModel,"Journalof Theoretical Biology29(3)(1970):343-385."DarwinianClan," "DarwinianSubclan," "DarwinianSubcland"are technical terms introducedby Williams in her formal axiomatization ofthe theory ofnatural selection. AClan isasetofbio- logical entitiesandall the descendantsof thatset, anda Subclan is one or more branchesof a Clan. Whereas the size of both Clans and Subclans remains relatively constant because of environmentallimitationsofspaceandresources,a Subcland istheSubclan ofaSubclan that mayexpand, because ofthe differential fitness ofits members, soas to take over the entire Subclan ofwhich it isa part (seealso Rosenberg, The Structureof Biological Science, p. 142). 7.See, for example, David Hull, "ConceptualEvolution andtheEyeoftheOctopus," inTheMetaphysics of Evolution, pp. 221-240;see also Rosenberg, The Structure of Biological Science, pp. 213-216. 8.PaulE.Griffiths,What Emotions Really Are:The Problemof Psychological Categories(Universityof Chicago Press, 1997), p. 213. 9.Philip S. Kitcher,"Species,"Philosophy of Science 51 (1984): 308-333. 10.Cf. Rosenberg, The Structureof Biological Science, p. 205: "Because, according to the theory ofnaturalselec- tion, species evolve,they should not be treated asclasses whose members satisfy some fixedset ofconditions-not even a vagueclusterof them-butshouldbe treatedas lineages, lines of descent, strings of imperfectcopies of predecessors, among whom there may not even bethe manifestationof central and distinctive, letalonenecessary and sufficient common properties";Sober, "Sets, Species, and Evolution," p. 339: "it strikes me that there is no characteristicof an off- spring that in itself is necessary or sufficient for its being in the same species asits parents. The reason isthat species determinationis retrospective." I1.Ruth G.Millikan, Language,Thought, andOther BiologicalCategories:NewFoundationsforRealism (Cambridge,MA: Bradford/MITPress, 1984), p. 23, emphasis in original. If Aand Bhave certain propertiesin common and Binherits these properties causally from A,then the propertiesin questionare reproductivelyestablishedcharacters (pp. 19-20). 12.Jay Bachrach,"Typeand Token and the Identification oftheWork ofArt," Philosophy andPhenomenological Research31(1971):415-420;NigelHarrison, "Types, Tokens, and the Identity of the Musical Work," The British Journal of Aesthetics 15 (1975): 336-346;Joseph Margolis, "The Ontological Peculiarityof Works of Art," The Journal of Aesthetics and Art Criticism36 (1977): 45-50;Margolis, Art andPhilosophy (Atlantic Highlands, NJ: Humanities Press,1980);RogerScruton,TheAestheticsofMusic (Oxford: Oxford University Press,1997);R.A.Sharpe, "Type, Token, Interpretation,and Performance,"Mind 88 (1979):437-440;Richard Wollheim, Art and ItsObjects (Cambridge: Cambridge University Press,1970).Sharpe actually identifies interpretationsofworks, not theworks themselves, as musical types, a viewcriticized by Kivy in "Platonism inMusic:AKindofDefense,"reprinted in Kivy, The Fine Art of Repetition: Essays in the Philosophy of Music (Cambridge:CambridgeUniversity Press, 1993), pp.35-58.Asweshall see,construing musical perform- ances as REFs can do justice to both positions. 13.Cf. Margolis, "The Ontological Peculiarityof Works of Art." 14.Peter Simons argues in "TokenResistance,"Analysis 42(1982):195-202,that typesare exemplified patterns ratherthan classes of similar tokens. To the extent patterns are considered to be reproductivelyestablished characters, this viewwould beconsistent with the nominalistic inter- petation of REFs. The REF interpretationof the type/token distinction Irecommend isclosetoHull's"evolutionary sense of'term-type"'(Hull, "ConceptualEvolution and the Eye of the Octopus,"p. 233). 15.Charles S.Peirce,Collected Papers,ed.Charles Hartshorne andPaulWeiss(Cambridge, MA:Harvard University Press, 1932), 2.247. 16.Margolis,Art and Philosophy, p. 75. 17.Scruton,TheAesthetics of Music, p. 104. 18.PeterKivy,"PlatonisminMusic:AKindof Defense"; "Platonismin Music: Another Kind of Defense," reprintedinKivy,The Fine Art ofRepetition, pp. 59-74; "OrchestratingPlatonism,"reprintedin Kivy, The Fine Art of Repetition,pp. 75-94. 19.Theprinted copiesconstitute asecond-order REF because they are copies of the mastertemplate,not of earlier printedcopies. 20.So-called because these properfunctions are derived from the mechanismsthat producethe representations. 21.Millikan, Language, Thought,and Other Biological Categories:New Foundationsfor Realism, p. 123. 22.Personal communication. In recent times, Millikan has modified her position. See her On Clear and Confused Ideas: AnEssayabout Substance Concepts (Cambridge: CambridgeUniversity Press, 2000), chap. 2. 23.What these normative constraints are and what the "properfunctions" ofmusical symbols might be isa large and fascinatingtopic that is beyond the scope of the present discussion. 24.The notationalaspects of the score include the indi- cations of pitches, meter, and rhythms, but exclude verbal indicationsof tempo and dynamics. 25.Nelson Goodman,Languagesof Art (Second Edition) (Indianapolis:HackettPress, 1976), p. 187. 26.JerroldLevinson, "Whata Musical Work Is," p. 87, n34,reprinted inMusic,Art,andMetaphysics (Cornell UniversityPress, 1990), pp. 63-88. 27.Levinson,"AutographicandAllographicArt Revisited,"p. 105, reprintedin Music,Art, and Metaphysics, pp. 89-106. 28.Hullargues foracausal-historical account ofthe identity ofconceptual systems and theories, for example, identity of the theory of evolution itself. For Hull, it would seem, the burdenof argumentis significantly higher than it is for me because of the great significance of the same (or similar) semantic content inthedeterminationoftheory identity, aburden mycognateaccount ofmusicalwork identity doesnot bear, sincemusic, evenifitisinsome sense representational,isnot conceptual. On Hull's view, twotheory tokens, evenifthey carry the samesemantic 290The Journalof Aesthetics and Art Criticism content, are not tokens ofthesame theory iftheylack a common ancestor (Hull, "The Naked Meme," in Learning, Development,and Culture,pp. 290 ff., ed. Henry C. Plotkin [New York: John Wiley and Sons,1982], pp. 273-327;see also"ConceptualEvolution and the Eyeofthe Octopus," pp.233ff.).Here too,onanalogy with the musical case, somedegreeofsemantic divergencesurelywilltrump common ancestry inthe determinationoftheory identity. Against Hull'sstrictly causal-historicalaccount oftheory identity,however, we surely wish to allow for the possibility of convergence,since we recognizethe independentdiscovery ofthesametheory ortheoretical content. Onthisissue compareGould, The Structureof EvolutionaryTheory,p. 8. 29.MarkRidley,EvolutionandClassification:The Reformationof Cladism(London:Longman, 1986), pp. 6 ff. 30.See Ridley, Evolution and Classification. In his dis- cussion ofpheneticist metrics Ridleyspeaks generally of the distance between species, not organisms. But he is clear that these similaritymeasurementsare to apply to biological taxaatanyLinnaean level,aswellastotheindividual organismsthemselves (p. 36). 31.See Ridley, Evolution and Classification, pp. 36-41 for furtherdetails. 32.Hull,"AMatter ofIndividuality," Philosophyof Science 45 (1978): 335-360. 33.Levinson, "Whata Musical Work Is," p. 81. 34.Wolterstorff, "Towardan Ontology ofArt Works," p. 128. 35.Hull, "A Matterof Individuality,"p. 353. 36.Levinson, "Whata Musical Work Is, Again," p. 260, n103, in Music, Art, and Metaphysics,pp. 215-263. 37.Ibid. 38.PrestonKyle Stanford,"ForPluralismandAgainstReal- ism aboutSpecies,"Philosophyof Science62 (1995): 70-91. 39.Cf. Hull, "ConceptualEvolution and the Eye ofthe Octopus." Gould (Structureof Evolutionary Theory) char- acteristicallyinjects a note of complexity into this "poster- boy" example of evolutionaryanalogy: convergence at one level,constraint duetohomologous developmental path- ways at another, or homoplasy. Although the closesimila- rities in adult anatomybetween single-lens cephalopod and vertebrateeyes are primarilydue to convergence (p.1128), there is evidence that all eye developmenteven across phyla maybetriggered byasetof"master controlgenes." Versions ofthese genes in nonvertebratesare homologous tomammalian Paxgenes,"mostnotablythePax-6" (p. 1123). Pax-6genesfrom miceexpressed inflieshave beenshowntobecapable ofinducing theformation of normalarthropodeyes (p. 1124). 40.DanielC.Dennett,Darwin'sDangerousIdea: Evolution and the Meanings of Life (New York: Simon and Schuster, 1995), p. 450. 41.Levinson, "Whata Musical Work Is," pp. 66 ff. 42.Cf.Renee Cox,"Are Musical Works Discovered?" The JournalofAestheticsand ArtCriticism 43(1985): 367-374. 43.Kivy("Platonism inMusic:AKind ofDefense," pp. 41 ff.) doubts that it is all that entrenched,or at least that it has been in all times and places. 44.Cf.Dennett, Darwin'sDangerous Idea:Evolution and the Meanings of Life, p. 106. 45.This should not be taken as an endorsementof math- ematical Platonism. 46.Kivy, "Platonismin Music:A Kind of Defense,"p.46. 47.Cf.SaulKripke, "Identity and Necessity,"p.79, reprinted inNaming, Necessity,andNaturalKinds, ed. StephenSchwartz(CornellUniversityPress,1977), pp.66-101:"Some things, perhaps mathematicalentities such as the positive integers, if they exist at all, necessarily exist." 48.Kivy,"PlatonisminMusic:AnotherKindof Defense," p. 70. 49.SeeDavidLewis,OnthePluralityofWorlds (Oxford:Basil Blackwell, 1986), pp. 92 ff. 50.Unlike mathematicalobjects, water is not a candidate fornecessary existence.Tosaythat water isnecessarily hydrogenhydroxideis to say thatthis claim, if true, is neces- sarily true; and itistosaythat inany possible world in which waterdoes exist, it is necessarilyhydrogenhydroxide. 51.Levinson, "Whata Musical Work Is," p. 66. 52.Kivy,"PlatonisminMusic:AnotherKindof Defense," p. 69. 53.Ibid., p. 40. 54.Cf.Dennett, Darwin'sDangerous Idea:Evolution and the Meanings of Life, pp. 139-140. 55.Kivy, "Platonismin Music:AnotherKindof Defense," pp. 72 ff. 56.Dennett distinguishesbetween "deep"forced moves, thosedictated bythelawsofphysics,mathematics, and logic, and "shallow"ones, those that are forced because, for historical reasons, there happens onlytobeonewayof doingacertain thingataparticular historical juncture (p.129).Ingeneral, whenasituation dictates aforced move, the language of discovery is appropriate. 57.If there had been only one way, then Edison's inven- tion would not be a Good Trick,but a "shallow"forcedmove in design space. 58.Cf.Dennett (Darwin's Dangerous Idea:Evolution and the Meanings of Life, p.108): "Supposethat each book is 500 pages long, and each page consists of 40lines of 50 spaces, so there are two thousandcharacter-spacesper page. Each space is either blank, or has a characterprinted on it, chosen from a set of100 (the upper- and lower-case letters ofEnglish and other European languages, plus the blank and punctuationmarks)...Five hundredpages times 2,000 characters[i.e., character-spaces]per page gives1,000,000 character-spacesper book." Dennett's formula seems coun- terintuitiveuntil you try it with manageablenumberswhose combinatorialpossibilities can be exhaustively checked by hand using a bruteprocedure.How many possible "books" are there consisting of only one page, each page containing only four character-spaces,and using only two characters, say the blank and one other? Two to the fourth power, or exactly sixteen. How many one-page books with five char- acter spaces? Two to the fifth power, or thirty-two. 59.Scruton (The Aesthetics of Music) dubs the experi- ence of musically organizedtones "acousmaticexperience." Scruton seems to have derived the term "acousmatic"from Pierre Schaeffer,theoriginator of"musique concrete." W. L. Windsoralso employs the term,but in a very different way. See his A PerceptualApproachto the Descriptionand Analysis of AcousmaticMusic (City University:Unpublished Doctoral Dissertation, 1995), available onthe webhttp:ll www.personal.leeds.ac.uk/-muswlw/w/w.html. 60.The distinction between "cranes"and "skyhooks"is a central metaphorof Dennett (Darwin's Dangerous Idea). NussbaumKinds, Types,and Musical Ontology291 The idea is that while a range of highly organizedphenom- ena in the naturalworld, including the products oforganic designandofhuman creativity, seemtorequire "sky- hooks," that is,nonnatural"mind-first"productivepowers, Darwin has shown us how some such phenomenahave been in fact how others can be in principlebuilt up incrementally and recursivelyby way of bottom-upundirectedmechanistic processes("cranes" andseriesof"cascading cranes"), whichincludenatural-selectionist processes.Hencethe "dangerousness"ofDarwin's idea ofnatural selection: it worksasauniversal intellectual acidbysystematically renderingskyhooks explanatorilyotiose. 61.William Blake, The Tiger. 62.Thatmusicexhibitshighdegreesofintentional organizationand significance seems scarcely open to doubt; how it doessoraises issues ofmusical representationand understandingthat go beyond the scope of this paper. 63.Cf. Scruton(TheAesthetics of Music): "Thecausality that we hear in the musical foregroundis thereforethe 'caus- ality of reason' which, for Kant, was the ground of human freedom.It is the more easy to hear this 'causalityof reason' in music, in that the world of physical causes-the'causality ofnature'-hasbeen set aside, discounted, hidden behind the acousmaticveil." 64.This essay is dedicatedto the memory of Eli Carmen, greatbassoonist.Thanksto D. E. Bradshawand membersof the University of Texas at Arlington Chapterof Phi Sigma Tau,thephilosophystudent national honorsociety,for thoughtfulquestionsand commentsafteran oral presentation ofsomeofthismaterial. Thanks alsotoananonymous reader for The Journal of Aesthetics and Art Criticism for some useful observations,and to CharlesChiasson for help with Greek etymology. Any remainingerrorsor infelicities are, of course, my own.