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10 Categories and Normativity MICHAEL GORMAN Anyone฀who฀tries฀to฀understand฀categories฀soon฀runs฀into฀the฀problem ฀of฀giving฀an฀account฀of฀the฀unity฀of฀a฀categor y.฀Call฀this฀the฀“unity problem.”฀In฀this฀essay฀I฀describe฀a฀distinctive฀and฀under -studied฀version ฀of฀the฀unity฀problem฀and฀discuss฀how฀it฀might฀be฀solved. First,฀I฀describe฀various฀versions฀of฀the฀unity฀problem.฀Second,฀I฀focus ฀on฀one฀version฀and฀argue฀that฀it฀is฀best฀dealt฀with฀by฀thinking฀of฀at least฀ some฀categories฀as฀“norm-constituted,”฀in฀a฀sense฀that฀I฀tr y฀ to make฀clear.฀Third,฀I฀discuss฀some฀objections฀to฀my฀proposal.฀Fourth,฀I compare฀norm-constituted฀categories฀to฀categories฀that฀are฀normative in฀a฀different฀sense.฀Fifth,฀I฀briefly฀discuss฀the฀possibility฀of฀groundin the฀ normativity฀of฀norm-constituted฀categories.฀Finally ,฀ I฀raise฀a฀few questions฀for฀further฀research. Let฀me฀make฀two฀preliminar y฀points.฀When฀I฀say฀“categor y”฀in฀this paper฀I฀am฀talking฀very฀generally฀about฀kinds฀or฀classes฀and฀not,฀in฀the specif cally฀Aristotelian฀sense,฀about฀ highest kinds฀or฀classes.฀And฀I฀am restricting฀my฀discussion฀to฀genuine฀categories฀as฀opposed฀to฀spurious ones;฀by฀“spurious”฀I฀mean฀categories฀like฀“games฀played฀in฀ 1997 by red-headed฀boys.”฀The฀restriction฀presupposes฀that฀there฀is฀such฀a฀dis tinction ,฀but฀I฀cannot฀provide฀an฀account฀of฀it฀here. versions of the unity problem To฀think฀in฀terms฀of฀categories฀is฀to฀suppose฀that฀things฀belong฀in groups฀and฀that฀such฀groups฀have฀something฀to฀do฀with฀common฀traits of฀the฀individuals฀so฀grouped.฀What฀I฀am฀calling฀the฀“unity฀problem”฀is the฀problem฀of฀accounting฀for฀the฀unity฀of฀a฀group฀or฀categor y,฀that฀is to฀say,฀the฀problem฀of฀understanding฀what฀sort฀of฀commonality฀gives rise฀to฀a฀category’s฀unity.฀And฀one฀reason฀why฀the฀unity฀problem฀is฀particularly ฀problematic฀is฀that,฀typically,฀members฀of฀a฀categor y฀have฀not only฀commonality฀but฀also฀differences.฀W e฀must฀explain฀how฀the฀com monality ฀ is฀not฀undermined฀by฀the฀differences.฀There฀are฀variations 151 within฀categories,฀and฀we฀need฀to฀understand฀the฀unity฀that฀categories have฀in฀a฀way฀that฀is฀consistent฀with฀those฀variations. There฀is฀no฀good฀reason฀to฀suppose฀ahead฀of฀time฀that฀there฀is฀a฀single ฀unity฀problem฀or฀a฀single฀solution฀to฀it;฀per haps฀there฀are฀several types฀of฀categories,฀each฀of฀which฀has฀a฀different฀type฀of฀unity.฀Hence฀it makes฀sense฀to฀speak฀of฀“versions”฀of฀the฀unity฀problem.฀A฀convenient way฀of฀uncovering฀two฀versions฀of฀the฀unity฀problem฀at฀once฀is฀by฀reflecting on฀a฀famous฀passage฀from฀Wittgenstein’s฀Philosophical฀Investigations : Consider,฀ for฀example,฀the฀proceedings฀that฀we฀call฀“games.”฀I฀mean฀boardgames ,฀card-games,฀ball-games,฀competitive฀games,฀and฀so฀on.฀What฀is฀common to฀all฀of฀them?—Don’t฀say:฀“There฀must฀be฀something฀common฀to฀them,฀or฀else they฀would฀not฀be฀called฀‘games’”—but฀look฀and฀see฀whether฀there฀is฀anything common฀to฀them฀all.฀For฀if฀you฀look฀at฀them฀you฀will฀not฀see฀something฀that฀is common฀to฀them฀all. .l.l.฀Are฀they฀all฀“amusing”?฀.l.l.฀[I]s฀there฀everywhere฀winning ฀ and฀losing,฀or฀competition฀between฀the฀players?฀. l.l.฀ Look฀at฀the฀roles played฀by฀skill฀and฀luck.฀And฀how฀different฀skill฀in฀chess฀and฀skill฀in฀tennis฀are.1 Here฀Wittgenstein฀takes฀aim฀at฀the฀idea฀that฀categories฀have฀to฀have their฀unity฀in฀virtue฀of฀features฀shared฀by฀all฀their฀members.฀This฀suggests ฀a฀distinction฀between฀categories฀that฀do฀have฀their฀unity฀in฀that way฀and฀categories฀that฀do฀not.฀Let฀us฀consider฀them฀in฀turn. First,฀there฀are฀what฀we฀can฀call฀“rigid฀categories.”฀Good฀examples฀of such฀ categories฀come฀from฀geometr y.฀ Consider฀the฀categor y฀ triangle and฀ consider฀three฀figures:฀a฀triangle฀of฀area฀ten,฀a฀triangle฀of฀are twenty,฀and฀a฀square฀(of฀any฀area).฀These฀figures฀have฀various฀features One฀is฀a฀feature฀that฀all฀the฀figures฀share,฀namel ,฀that฀of฀being฀closed; another฀is฀a฀feature฀that฀only฀the฀first฀two฀share,฀namel ,฀that฀of฀being three-sided;฀still฀another฀is฀a฀feature฀that฀the฀first฀has฀but฀that฀the฀sec ond฀does฀not,฀namely,฀that฀of฀being฀of฀area฀ten.฀Now ,฀the฀category฀triangle contains฀only฀figures฀that฀are฀closed฀and฀three-sided.฀Being฀bot closed฀and฀three-sided฀is฀ non-optional for฀being฀a฀triangle.฀This฀means that฀the฀third฀figure,฀the฀square,฀cannot฀be฀a฀triangle,฀whereas...

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