WEhavesaidpreviously，inourdistinctionofthevarious
meaningsofwords，that’one’hasseveralmeanings；thethingsthat
aredirectlyandoftheirownnatureandnotaccidentallycalledone
maybesummarizedunderfourheads，thoughthewordisusedinmore
senses。1Thereisthecontinuous，eitheringeneral，or
especiallythatwhichiscontinuousbynatureandnotbycontactnor
bybeingtogether；andofthese，thathasmoreunityandisprior，
whosemovementismoreindivisibleandsimpler。2Thatwhichisa
wholeandhasacertainshapeandformisoneinastillhigher
degree；andespeciallyifathingisofthissortbynature，andnot
byforcelikethethingswhichareunifiedbyglueornailsorby
beingtiedtogether，i。e。ifithasinitselfthecauseofits
continuity。Athingisofthissortbecauseitsmovementisoneand
indivisibleinplaceandtime；sothatevidentlyifathinghasby
natureaprincipleofmovementthatisofthefirstkindi。e。local
movementandthefirstinthatkindi。e。circularmovement，thisis
intheprimarysenseoneextendedthing。Somethings，then，areonein
thisway，quacontinuousorwhole，andtheotherthingsthatareone
arethosewhosedefinitionisone。Ofthissortarethethingsthe
thoughtofwhichisone，i。e。thosethethoughtofwhichis
indivisible；anditisindivisibleifthethingisindivisibleinkind
orinnumber。3Innumber，then，theindividualisindivisible，
and4inkind，thatwhichinintelligibilityandinknowledgeis
indivisible，sothatthatwhichcausessubstancestobeonemustbe
oneintheprimarysense。’One’，then，hasallthesemeanings-the
naturallycontinuousandthewhole，andtheindividualandthe
universal。Andalltheseareonebecauseinsomecasesthemovement，
inothersthethoughtorthedefinitionisindivisible。
Butitmustbeobservedthatthequestions，whatsortofthings
aresaidtobeone，andwhatitistobeoneandwhatisthe
definitionofit，shouldnotbeassumedtobethesame。’One’has
allthesemeanings，andeachofthethingstowhichoneofthesekinds
ofunitybelongswillbeone；but’tobeone’willsometimesmean
beingoneofthesethings，andsometimesbeingsomethingelsewhichis
evennearertothemeaningoftheword’one’whiletheseother
thingsapproximatetoitsapplication。Thisisalsotrueof
’element’or’cause’，ifonehadbothtospecifythethingsofwhich
itispredicableandtorenderthedefinitionoftheword。Forina
sensefireisanelementanddoubtlessalso’theindefinite’or
somethingelseofthesortisbyitsownnaturetheelement，butina
senseitisnot；foritisnotthesamethingtobefireandtobe
anelement，butwhileasaparticularthingwithanatureofitsown
fireisanelement，thename’element’meansthatithasthis
attribute，thatthereissomethingwhichismadeofitasaprimary
constituent。Andsowith’cause’and’one’andallsuchterms。For
thisreason，too，’tobeone’means’tobeindivisible，being
essentiallyonemeansa“this“andcapableofbeingisolatedeitherin
place，orinformorthought’；orperhaps’tobewholeand
indivisible’；butitmeansespecially’tobethefirstmeasureofa
kind’，andmoststrictlyofquantity；foritisfromthisthatit
hasbeenextendedtotheothercategories。Formeasureisthatby
whichquantityisknown；andquantityquaquantityisknowneither
bya’one’orbyanumber，andallnumberisknownbya’one’。
Thereforeallquantityquaquantityisknownbytheone，andthatby
whichquantitiesareprimarilyknownistheoneitself；andsotheone
isthestarting-pointofnumberquanumber。Andhenceintheother
classestoo’measure’meansthatbywhicheachisfirstknown，andthe
measureofeachisaunit-inlength，inbreadth，indepth，in
weight，inspeed。Thewords’weight’and’speed’arecommontoboth
contraries；foreachofthemhastwomeanings-’weight’meansboththat
whichhasanyamountofgravityandthatwhichhasanexcessof
gravity，and’speed’boththatwhichhasanyamountofmovementand
thatwhichhasanexcessofmovement；foreventheslowhasa
certainspeedandthecomparativelylightacertainweight。
Inallthese，then，themeasureandstarting-pointissomething
oneandindivisible，sinceeveninlineswetreatasindivisiblethe
lineafootlong。Foreverywhereweseekasthemeasuresomething
oneandindivisible；andthisisthatwhichissimpleeitherin
qualityorinquantity。Nowwhereitisthoughtimpossibletotake
awayortoadd，therethemeasureisexacthencethatofnumberis
mostexact；forweposittheunitasindivisibleineveryrespect；
butinallothercasesweimitatethissortofmeasure。Forinthe
caseofafurlongoratalentorofanythingcomparativelylargeany
additionorsubtractionmightmoreeasilyescapeournoticethanin
thecaseofsomethingsmaller；sothatthefirstthingfromwhich，
asfarasourperceptiongoes，nothingcanbesubtracted，allmenmake
themeasure，whetherofliquidsorofsolids，whetherofweightor
ofsize；andtheythinktheyknowthequantitywhentheyknowitby
meansofthismeasure。Andindeedtheyknowmovementtoobythesimple
movementandthequickest；forthisoccupiesleasttime。Andsoin
astronomya’one’ofthissortisthestarting-pointandmeasure
fortheyassumethemovementoftheheavenstobeuniformandthe
quickest，andjudgetheothersbyreferencetoit，andinmusicthe
quarter-tonebecauseitistheleastinterval，andinspeechthe
letter。Andalltheseareonesinthissense——notthat’one’is
somethingpredicableinthesamesenseofallofthese，butinthe
sensewehavementioned。
Butthemeasureisnotalwaysoneinnumber——sometimesthereare
several；e。g。thequarter-tonesnottotheear，butasdetermined
bytheratiosaretwo，andthearticulatesoundsbywhichwe
measurearemorethanone，andthediagonalofthesquareanditsside
aremeasuredbytwoquantities，andallspatialmagnitudesreveal
similarvarietiesofunit。Thus，then，theoneisthemeasureofall
things，becausewecometoknowtheelementsinthesubstanceby
dividingthethingseitherinrespectofquantityorinrespectof
kind。Andtheoneisindivisiblejustbecausethefirstofeach
classofthingsisindivisible。Butitisnotinthesamewaythat
every’one’isindivisiblee。g。afootandaunit；thelatteris
indivisibleineveryrespect，whiletheformermustbeplacedamong
thingswhichareundividedtoperception，ashasbeensaid
already-onlytoperception，fordoubtlesseverycontinuousthingis
divisible。
Themeasureisalwayshomogeneouswiththethingmeasured；the
measureofspatialmagnitudesisaspatialmagnitude，andin
particularthatoflengthisalength，thatofbreadthabreadth，that
ofarticulatesoundanarticulatesound，thatofweightaweight，that
ofunitsaunit。Forwemuststatethematterso，andnotsaythat
themeasureofnumbersisanumber；weoughtindeedtosaythisif
weweretousethecorrespondingformofwords，buttheclaimdoesnot
reallycorrespond-itisasifoneclaimedthatthemeasureofunitsis
unitsandnotaunit；numberisapluralityofunits。
Knowledge，also，andperception，wecallthemeasureofthingsfor
thesamereason，becausewecometoknowsomethingbythem-whileas
amatteroffacttheyaremeasuredratherthanmeasureotherthings。
Butitiswithusasifsomeoneelsemeasuredusandwecameto
knowhowbigwearebyseeingthatheappliedthecubit-measureto
suchandsuchafractionofus。ButProtagorassays’manisthe
measureofallthings’，asifhehadsaid’themanwhoknows’or
’themanwhoperceives’；andthesebecausetheyhaverespectively
knowledgeandperception，whichwesayarethemeasuresofobjects。
Suchthinkersaresayingnothing，then，whiletheyappeartobesaying
somethingremarkable。
Evidently，then，unityinthestrictestsense，ifwedefineit
accordingtothemeaningoftheword，isameasure，andmost
properlyofquantity，andsecondlyofquality。Andsomethingswillbe
oneiftheyareindivisibleinquantity，andothersiftheyare
indivisibleinquality；andsothatwhichisoneisindivisible，
eitherabsolutelyorquaone。
Withregardtothesubstanceandnatureoftheonewemustask
inwhichoftwowaysitexists。Thisistheveryquestionthatwe
reviewedinourdiscussionofproblems，viz。whattheoneisandhow
wemustconceiveofit，whetherwemusttaketheoneitselfasbeinga
substanceasboththePythagoreanssayinearlierandPlatoin
latertimes，orthereis，rather，anunderlyingnatureandtheone
shouldbedescribedmoreintelligiblyandmoreinthemannerofthe
physicalphilosophers，ofwhomonesaystheoneislove，another
saysitisair，andanothertheindefinite。
If，then，nouniversalcanbeasubstance，ashasbeensaidour
discussionofsubstanceandbeing，andifbeingitselfcannotbea
substanceinthesenseofaoneapartfromthemanyforitis
commontothemany，butisonlyapredicate，clearlyunityalso
cannotbeasubstance；forbeingandunityarethemostuniversalof
allpredicates。Therefore，ontheonehand，generaarenotcertain
entitiesandsubstancesseparablefromotherthings；andonthe
otherhandtheonecannotbeagenus，forthesamereasonsforwhich
beingandsubstancecannotbegenera。
Further，thepositionmustbesimilarinallthekindsofunity。
Now’unity’hasjustasmanymeaningsas’being’；sothatsinceinthe
sphereofqualitiestheoneissomethingdefinite-someparticularkind
ofthing-andsimilarlyinthesphereofquantities，clearlywemustin
everycategoryaskwhattheoneis，aswemustaskwhattheexistent
is，sinceitisnotenoughtosaythatitsnatureisjusttobeoneor
existent。Butincolourstheoneisacolour，e。g。white，andthenthe
othercoloursareobservedtobeproducedoutofthisandblack，and
blackistheprivationofwhite，asdarknessoflight。Thereforeif
allexistentthingswerecolours，existentthingswouldhavebeena
number，indeed，butofwhat？Clearlyofcolours；andthe’one’would
havebeenaparticular’one’，i。e。white。Andsimilarlyifall
existingthingsweretunes，theywouldhavebeenanumber，buta
numberofquarter-tones，andtheiressencewouldnothavebeennumber；
andtheonewouldhavebeensomethingwhosesubstancewasnottobe
onebuttobethequarter-tone。Andsimilarlyifallexistentthings
hadbeenarticulatesounds，theywouldhavebeenanumberof
letters，andtheonewouldhavebeenavowel。Andifallexistent
thingswererectilinearfigures，theywouldhavebeenanumberof
figures，andtheonewouldhavebeenthetriangle。Andthesame
argumentappliestoallotherclasses。Since，therefore，whilethere
arenumbersandaonebothinaffectionsandinqualitiesandin
quantitiesandinmovement，inallcasesthenumberisanumberof
particularthingsandtheoneisonesomething，anditssubstanceis
notjusttobeone，thesamemustbetrueofsubstancesalso；forit
istrueofallcasesalike。
Thattheone，then，ineveryclassisadefinitething，andin
nocaseisitsnaturejustthis，unity，isevident；butasin
colourstheone-itselfwhichwemustseekisonecolour，sotooin
substancetheone-itselfisonesubstance。Thatinasenseunitymeans
thesameasbeingisclearfromthefactsthatitsmeaningscorrespond
tothecategoriesonetoone，anditisnotcomprisedwithinany
categorye。g。itiscomprisedneitherin’whatathingis’norin
quality，butisrelatedtothemjustasbeingis；thatin’oneman’
nothingmoreispredicatedthanin’man’justasbeingisnothing
apartfromsubstanceorqualityorquantity；andthattobeoneis
justtobeaparticularthing。