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10. Categories and Normativity
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10 Categories and Normativity MICHAEL GORMAN Anyonewhotriestounderstandcategoriessoonrunsintotheproblem ofgivinganaccountoftheunityofacategor y.Callthisthe“unity problem.”InthisessayIdescribeadistinctiveandunder -studiedversion oftheunityproblemanddiscusshowitmightbesolved. First,Idescribevariousversionsoftheunityproblem.Second,Ifocus ononeversionandarguethatitisbestdealtwithbythinkingofat least somecategoriesas“norm-constituted,”inasensethatItr y to makeclear.Third,Idiscusssomeobjectionstomyproposal.Fourth,I comparenorm-constitutedcategoriestocategoriesthatarenormative inadifferentsense.Fifth,Ibrieflydiscussthepossibilityofgroundin the normativityofnorm-constitutedcategories.Finally , Iraiseafew questionsforfurtherresearch. Letmemaketwopreliminar ypoints.WhenIsay“categor y”inthis paperIamtalkingverygenerallyaboutkindsorclassesandnot,inthe specif callyAristoteliansense,about highest kindsorclasses.AndIam restrictingmydiscussiontogenuinecategoriesasopposedtospurious ones;by“spurious”Imeancategorieslike“gamesplayedin 1997 by red-headedboys.”Therestrictionpresupposesthatthereissuchadis tinction ,butIcannotprovideanaccountofithere. versions of the unity problem Tothinkintermsofcategoriesistosupposethatthingsbelongin groupsandthatsuchgroupshavesomethingtodowithcommontraits oftheindividualssogrouped.WhatIamcallingthe“unityproblem”is theproblemofaccountingfortheunityofagrouporcategor y,thatis tosay,theproblemofunderstandingwhatsortofcommonalitygives risetoacategory’sunity.Andonereasonwhytheunityproblemisparticularly problematicisthat,typically,membersofacategor yhavenot onlycommonalitybutalsodifferences.W emustexplainhowthecom monality isnotunderminedbythedifferences.Therearevariations 151 withincategories,andweneedtounderstandtheunitythatcategories haveinawaythatisconsistentwiththosevariations. Thereisnogoodreasontosupposeaheadoftimethatthereisasingle unityproblemorasinglesolutiontoit;per hapsthereareseveral typesofcategories,eachofwhichhasadifferenttypeofunity.Henceit makessensetospeakof“versions”oftheunityproblem.Aconvenient wayofuncoveringtwoversionsoftheunityproblematonceisbyreflecting onafamouspassagefromWittgenstein’sPhilosophicalInvestigations : Consider, forexample,theproceedingsthatwecall“games.”Imeanboardgames ,card-games,ball-games,competitivegames,andsoon.Whatiscommon toallofthem?—Don’tsay:“Theremustbesomethingcommontothem,orelse theywouldnotbecalled‘games’”—butlookandseewhetherthereisanything commontothemall.Forifyoulookatthemyouwillnotseesomethingthatis commontothemall. .l.l.Aretheyall“amusing”?.l.l.[I]sthereeverywherewinning andlosing,orcompetitionbetweentheplayers?. l.l. Lookattheroles playedbyskillandluck.Andhowdifferentskillinchessandskillintennisare.1 HereWittgensteintakesaimattheideathatcategorieshavetohave theirunityinvirtueoffeaturessharedbyalltheirmembers.Thissuggests adistinctionbetweencategoriesthatdohavetheirunityinthat wayandcategoriesthatdonot.Letusconsidertheminturn. First,therearewhatwecancall“rigidcategories.”Goodexamplesof such categoriescomefromgeometr y. Considerthecategor y triangle and considerthreefigures:atriangleofareaten,atriangleofare twenty,andasquare(ofanyarea).Thesefigureshavevariousfeatures Oneisafeaturethatallthefiguresshare,namel ,thatofbeingclosed; anotherisafeaturethatonlythefirsttwoshare,namel ,thatofbeing three-sided;stillanotherisafeaturethatthefirsthasbutthatthesec onddoesnot,namely,thatofbeingofareaten.Now ,thecategorytriangle containsonlyfiguresthatareclosedandthree-sided.Beingbot closedandthree-sidedis non-optional forbeingatriangle.Thismeans thatthethirdfigure,thesquare,cannotbeatriangle,whereas...