e　purpose　of　measurement；　the　objects　will　be　quantities　only　to　the　extent　of　participating　in　Quantity。　　　　　So　with　the　numbers　themselves：　how　can　they　constitute　the　category　of　Quantity？　They　are　measures；　but　how　do　measures　come　to　be　quantities　or　Quantity？　Doubtless　in　that；　existing　as　they　do　among　the　Existents　and　not　being　adapted　to　any　of　the　other　categories；　they　find　their　place　under　the　influence　of　verbal　suggestion　and　so　are　referred　to　the　so…called　category　of　Quantity。　We　see　the　unit　mark　off　one　measurement　and　then　proceed　to　another；　and　number　thus　reveals　the　amount　of　a　thing；　and　the　mind　measures　by　availing　itself　of　the　total　figure。　　　　　It　follows　that　in　measuring　it　is　not　measuring　essence；　it　pronounces　its　〃one〃　or　〃two；〃　whatever　the　character　of　the　objects；　even　summing　contraries。　It　does　not　take　count　of　condition…　hot；　handsome；　it　simply　notes　how　many。　　　　　Number　then；　whether　regarded　in　itself　or　in　the　participant　objects；　belongs　to　the　category　of　Quantity；　but　the　participant　objects　do　not。　〃Three　yards　long〃　does　not　fall　under　the　category　of　Quantity；　but　only　the　three。　　　　　Why　then　are　magnitudes　classed　as　quantities？　Not　because　they　are　so　in　the　strict　sense；　but　because　they　approximate　to　Quantity；　and　because　objects　in　which　magnitudes　inhere　are　themselves　designated　as　quantities。　We　call　a　thing　great　or　small　from　its　participation　in　a　high　number　or　a　low。　True；　greatness　and　smallness　are　not　claimed　to　be　quantities；　but　relations：　but　it　is　by　their　apparent　possession　of　quantity　that　they　are　thought　of　as　relations。　All　this；　however；　needs　more　careful　examination。　　　　　In　sum；　we　hold　that　there　is　no　single　genus　of　Quantity。　Only　number　is　Quantity；　the　rest　＇magnitudes；　space；　time；　motion＇　quantities　only　in　a　secondary　degree。　We　have　therefore　not　strictly　one　genus；　but　one　category　grouping　the　approximate　with　the　primary　and　the　secondary。　　　　　We　have　however　to　enquire　in　what　sense　the　abstract　numbers　are　substances。　Can　it　be　that　they　are　also　in　a　manner　quantitative？　Into　whatever　category　they　fall；　the　other　numbers　＇those　inherent　in　objects＇　can　have　nothing　in　common　with　them　but　the　name。　5。　Speech；　time；　motion…　in　what　sense　are　these　quantities？　　　　　Let　us　begin　with　speech。　It　is　subject　to　measurement；　but　only　in　so　far　as　it　is　sound；　it　is　not　a　quantity　in　its　essential　nature；　which　nature　is　that　it　be　significant；　as　noun　and　verb　are　significant。　The　air　is　its　Matter；　as　it　is　Matter　to　verb　and　noun；　the　components　of　speech。　　　　　To　be　more　precise；　we　may　define　speech　as　an　impact　＇made　upon　the　outer　air　by　the　breath＇；　though　it　is　not　so　much　the　impact　as　the　impression　which　the　impact　produces　and　which；　as　it　were；　imposes　Form　＇upon　the　air＇。　Speech；　thus；　is　rather　an　action　than　a　quantity…　an　action　with　a　significance。　Though　perhaps　it　would　be　truer　to　say　that　while　this　motion；　this　impact；　is　an　action；　the　counter…motion　is　an　experience　＇or　Passion＇；　or　each　may　be　from　different　points　of　view　either　an　action　or　an　experience：　or　we　may　think　of　speech　as　action　upon　a　substrate　＇air＇　and　experience　within　that　substrate。　　　　　If　however　voice　is　not　characteristically　impact；　but　is　simply　air；　two　categories　will　be　involved：　voice　is　significant；　and　the　one　category　will　not　be　sufficient　to　account　for　this　significance　without　associating　with　a　second。　　　　　With　regard　to　time；　if　it　is　to　be　thought　of　as　a　measure；　we　must　determine　what　it　is　that　applies　this　measure。　It　must　clearly　be　either　Soul　or　the　Present　Moment。　If　on　the　contrary　we　take　time　to　be　something　measured　and　regard　it　as　being　of　such　and　such　extension…　a　year；　for　example…　then　we　may　consider　it　as　a　quantity：　essentially　however　time　is　of　a　different　nature；　the　very　fact　that　we　can　attribute　this　or　that　length　to　it　shows　us　that　it　is　not　length：　in　other　words；　time　is　not　Quantity。　Quantity　in　the　strict　sense　is　the　Quantity　not　inbound　with　things；　if　things　became　quantities　by　mere　participation　in　Quantity；　then　Substance　itself　would　be　identical　with　Quantity。　　　　　Equality　and　inequality　must　be　regarded　as　properties　of　Quantity…Absolute；　not　of　the　participants；　or　of　them　not　essentially　but　only　accidentally：　such　participants　as　〃three　yards'　length；〃　which　becomes　a　quantity；　not　as　belonging　to　a　single　genus　of　Quantity；　but　by　being　subsumed　under　the　one　head；　the　one　category。　　　　　6。　In　considering　Relation　we　must　enquire　whether　it　possesses　the　community　of　a　genus；　or　whether　it　may　on　other　grounds　be　treated　as　a　unity。　　　　　Above　all；　has　Relation…　for　example；　that　of　right　and　left；　double　and　half…　any　actuality？　Has　it；　perhaps；　actuality　in　some　cases　only；　as　for　instance　in　what　is　termed　〃posterior〃　but　not　in　what　is　termed　〃prior〃？　Or　is　its　actuality　in　no　case　conceivable？　　　　　What　meaning；　then；　are　we　to　attach　to　double　and　half　and　all　other　cases　of　less　and　more；　to　habit　and　disposition；　reclining；　sitting；　standing；　to　father；　son；　master；　slave；　to　like；　unlike；　equal；　unequal；　to　active　and　passive；　measure　and　measured；　or　again　to　knowledge　and　sensation；　as　related　respectively　to　the　knowable　and　the　sensible？　　　　　Knowledge；　indeed；　may　be　supposed　to　entail　in　relation　to　the　known　object　some　actual　entity　corresponding　to　that　object's　Ideal　Form；　and　similarly　with　sensation　as　related　to　the　sense…object。　The　active　will　perform　some　constant　function　in　relation　to　the　passive；　as　will　the　measure　in　relation　to　the　measured。　　　　　But　what　will　emerge　from　the　relation　of　like　to　like？　Nothing　will　emerge。　Likeness　is　the　inherence　of　qualitative　identity；　its　entire　content　is　the　quality　present　in　the　two　objects。　　　　　From　equality；　similarly；　nothing　emerges。　The　relation　merely　presupposes　the　existence　of　a　quantitative　identity；…　is　nothing　but　our　judgement　comparing　objects　essentially　independent　and　concluding；　〃This　and　that　have　the　same　magnitude；　the　same　quality；　this　has　produced　that；　this　is　superior　to　that。〃　　　　　Again；　what　meaning　can　sitting　and　standing　have　apart　from　sitter　and　stander？　The　term　〃habit〃　either　implies　a　having；　in　which　case　it　signifies　possession；　or　else　it　arises　from　something　had；　and　so　denotes　quality；　and　similarly　with　disposition。　　　　　What　then　in　these　instances　can　be　the　meaning　of　correlatives　apart　from　our　conception　of　their　juxtaposition？　〃Greater〃　may　refer　to　very　different　magnitudes；　〃different〃　to　all　sorts　of　objects：　the　comparison　is　ours；　it　does　not　lie　in　the　things　themselves。　　　　　Right　and　left；　before　and　behind；　would　seem　to　belong　less　to　the　category　of　Relation　than　to　that　of　Situation。　Right　means　〃situated　at　one　point；〃　left　means　〃situated　at　another。〃　But　the　right　and　left　are　in　our　conception；　nothing　of　them　in　the　things　themselves。　　　　　Before　and　after　are　merely　two　times；　the　relation　is　again　of　our　making。　　　　　7。　Now　if　we　do　not　mean　anything　by　Relation　but　are　victims　of　words；　none　of　the　relations　mentioned　can　exist：　Relation　will　be　a　notion　void　of　content。　　　　　Suppose　however　that　we　do　possess　ourselves　of　objective　truth　when　in　comparing　two　points　of　time　we　pronounce　one　prior；　or　posterior；　to　the　other；　that　priority　does　entail　something　distinct　from　the　objects　to　which　it　refers；　admit　an　objective　truth　behind　the　relation　of　left　and　right：　does　this　apply　also　to　magnitudes；　and　is　the　relation　exhibiting　excess　and　deficiency　also　something　distinct　from　the　quantities　involved？　　　　　Now　one　thing　is　double　of　another　quite　apart　from　our　speech　or　thought；　one　thing　possesses　and　another　is　possessed　before　we　notice　the　fact；　equals　do　not　await　our　comparison　but…　and　this　applies　to　Quality　as　well　as　Quantity…　rest　upon　an　identity　existing　between　the　objects　compared：　in　all　the　conditions　in　which　we　assert　Relation　the　mutual　relation　exists　over　and　above　the　objects；　we　perceive　it　as　already　existent；　our　knowledge　is　directed　upon　a　thing；　there　to　be　known…　a　clear　testimony　to　the　reality　of　Relation。　　　　　In　these　circumstances　we　can　no　longer　put　the　question　of　its　existence。　We　have　simply　to　distinguish：　sometimes　the　relation　subsists　while　the　objects　remain　unaltered　and　even　apart；　sometimes　it　depends　upon　their　combination；　sometimes；　while　they　remain　unchanged；　the　relation　utterly　ceases；　or；　as　happens　with　right　and　near；　becomes　different。　These　are　the　facts　which　chiefly　account　for　the　notion　that　Relation　has　no　reality　in　such　circumstances。　　　　　Our　task；　thus；　is　to　give　full　value　to　this　elusive　character　of　Relation；　and；　then　to　enquire　what　there　is　that　is　constant　in　all　these　particular　cases　and　whether　this　constant　is　generic　or　accidental；　and　having　found　this　constant；　we　must　discover　what　sort　of　actuality　it　possesses。　　　　　It　need　hardly　be　said　that　we　are　not　to　affirm　Relation　where　one　thing　is　simply　an　attribute　of　another；　as　a　habit　is　an　attribute　of　a　soul　or　of　a　body；　it　is　not　Relation　when　a　soul　belongs　to　this　individual　or　dwells　in　that　body。　Relation　enters　only　when　the　actuality　of　the　relationships　is　derived　from　no　other　source　than　Relation　itself；　th