Those，then，whosaytheuniverseisoneandpositonekindof
thingasmatter，andascorporealmatterwhichhasspatial
magnitude，evidentlygoastrayinmanyways。Fortheypositthe
elementsofbodiesonly，notofincorporealthings，thoughthereare
alsoincorporealthings。Andintryingtostatethecausesof
generationanddestruction，andingivingaphysicalaccountofall
things，theydoawaywiththecauseofmovement。Further，theyerr
innotpositingthesubstance，i。e。theessence，asthecauseof
anything，andbesidesthisinlightlycallinganyofthesimplebodies
exceptearththefirstprinciple，withoutinquiringhowtheyare
producedoutofoneanothers-Imeanfire，water，earth，andair。For
somethingsareproducedoutofeachotherbycombination，othersby
separation，andthismakesthegreatestdifferencetotheirpriority
andposteriority。For(1)inawaythepropertyofbeingmost
elementaryofallwouldseemtobelongtothefirstthingfromwhich
theyareproducedbycombination，andthispropertywouldbelongto
themostfine-grainedandsubtleofbodies。Forthisreasonthose
whomakefiretheprinciplewouldbemostinagreementwiththis
argument。Buteachoftheotherthinkersagreesthattheelementof
corporealthingsisofthissort。Atleastnoneofthosewhonamedone
elementclaimedthatearthwastheelement，evidentlybecauseofthe
coarsenessofitsgrain。(Oftheotherthreeelementseachhasfound
somejudgeonitsside；forsomemaintainthatfire，othersthat
water，othersthatairistheelement。Yetwhy，afterall，dotheynot
nameearthalso，asmostmendo？Forpeoplesayallthingsareearth
Hesiodsaysearthwasproducedfirstofcorporealthings；soprimitive
andpopularhastheopinionbeen。)Accordingtothisargument，then，
noonewouldberightwhoeithersaysthefirstprincipleisanyof
theelementsotherthanfire，orsupposesittobedenserthanairbut
rarerthanwater。But(2)ifthatwhichislateringenerationis
priorinnature，andthatwhichisconcoctedandcompoundedislater
ingeneration，thecontraryofwhatwehavebeensayingmustbe
true，-watermustbepriortoair，andearthtowater。
Somuch，then，forthosewhopositonecausesuchaswementioned；
butthesameistrueifonesupposesmoreofthese，asEmpedoclessays
matterofthingsisfourbodies。Forhetooisconfrontedby
consequencessomeofwhicharethesameashavebeenmentioned，
whileothersarepeculiartohim。Forweseethesebodiesproduced
fromoneanother，whichimpliesthatthesamebodydoesnotalways
remainfireorearth(wehavespokenaboutthisinourworkson
nature)；andregardingthecauseofmovementandthequestion
whetherwemustpositoneortwo，hemustbethoughttohavespoken
neithercorrectlynoraltogetherplausibly。Andingeneral，change
ofqualityisnecessarilydoneawaywithforthosewhospeakthus，for
ontheirviewcoldwillnotcomefromhotnorhotfromcold。Forifit
didtherewouldbesomethingthatacceptedthecontraries
themselves，andtherewouldbesomeoneentitythatbecamefireand
water，whichEmpedoclesdenies。
AsregardsAnaxagoras，ifoneweretosupposethathesaidthere
weretwoelements，thesuppositionwouldaccordthoroughlywithan
argumentwhichAnaxagorashimselfdidnotstatearticulately，but
whichhemusthaveacceptedifanyonehadledhimontoit。True，
tosaythatinthebeginningallthingsweremixedisabsurdbothon
othergroundsandbecauseitfollowsthattheymusthaveexisted
beforeinanunmixedform，andbecausenaturedoesnotallowany
chancethingtobemixedwithanychancething，andalsobecauseon
thisviewmodificationsandaccidentscouldbeseparatedfrom
substances(forthesamethingswhicharemixedcanbeseparated)；yet
ifoneweretofollowhimup，piecingtogetherwhathemeans，hewould
perhapsbeseentobesomewhatmoderninhisviews。Forwhennothing
wasseparatedout，evidentlynothingcouldbetrulyassertedofthe
substancethatthenexisted。Imean，e。g。thatitwasneitherwhite
norblack，norgreynoranyothercolour，butofnecessitycolourless；
forifithadbeencoloured，itwouldhavehadoneofthesecolours。
Andsimilarly，bythissameargument，itwasflavourless，norhadit
anysimilarattribute；foritcouldnotbeeitherofanyqualityorof
anysize，norcoulditbeanydefinitekindofthing。Forifit
were，oneoftheparticularformswouldhavebelongedtoit，and
thisisimpossible，sinceallweremixedtogether；forthe
particularformwouldnecessarilyhavebeenalreadyseparatedout，but
heallweremixedexceptreason，andthisalonewasunmixedand
pure。Fromthisitfollows，then，thathemustsaytheprinciples
aretheOne(forthisissimpleandunmixed)andtheOther，whichis
ofsuchanatureaswesupposetheindefinitetobebeforeitis
definedandpartakesofsomeform。Therefore，whileexpressinghimself
neitherrightlynorclearly，hemeanssomethinglikewhatthelater
thinkerssayandwhatisnowmoreclearlyseentobethecase。
Butthesethinkersare，afterall，athomeonlyinargumentsabout
generationanddestructionandmovement；foritispracticallyonlyof
thissortofsubstancethattheyseektheprinciplesandthecauses。
Butthosewhoextendtheirvisiontoallthingsthatexist，andof
existingthingssupposesometobeperceptibleandothersnot
perceptible，evidentlystudybothclasses，whichisallthemore
reasonwhyoneshoulddevotesometimetoseeingwhatisgoodintheir
viewsandwhatbadfromthestandpointoftheinquirywehavenow
beforeus。
The’Pythagoreans’treatofprinciplesandelementsstranger
thanthoseofthephysicalphilosophers(thereasonisthattheygot
theprinciplesfromnon-sensiblethings，fortheobjectsof
mathematics，exceptthoseofastronomy，areoftheclassofthings
withoutmovement)；yettheirdiscussionsandinvestigationsareall
aboutnature；fortheygeneratetheheavens，andwithregardto
theirpartsandattributesandfunctionstheyobservethephenomena，
anduseuptheprinciplesandthecausesinexplainingthese，which
impliesthattheyagreewiththeothers，thephysicalphilosophers，
thattherealisjustallthatwhichisperceptibleandcontainedby
theso-called’heavens’。Butthecausesandtheprincipleswhich
theymentionare，aswesaid，sufficienttoactasstepsevenupto
thehigherrealmsofreality，andaremoresuitedtothesethanto
theoriesaboutnature。Theydonottellusatall，however，how
therecanbemovementiflimitandunlimitedandoddandevenare
theonlythingsassumed，orhowwithoutmovementandchangethere
canbegenerationanddestruction，orthebodiesthatmovethroughthe
heavenscandowhattheydo。
Further，ifoneeithergrantedthemthatspatialmagnitude
consistsoftheseelements，orthiswereproved，stillhowwould
somebodiesbelightandothershaveweight？Tojudgefromwhatthey
assumeandmaintaintheyarespeakingnomoreofmathematicalbodies
thanofperceptible；hencetheyhavesaidnothingwhateverabout
fireorearthortheotherbodiesofthissort，Isupposebecausethey
havenothingtosaywhichappliespeculiarlytoperceptiblethings。
Further，howarewetocombinethebeliefsthattheattributes
ofnumber，andnumberitself，arecausesofwhatexistsandhappensin
theheavensbothfromthebeginningandnow，andthatthereisno
othernumberthanthisnumberoutofwhichtheworldiscomposed？When
inoneparticularregiontheyplaceopinionandopportunity，and，a
littleaboveorbelow，injusticeanddecisionormixture，and
allege，asproof，thateachoftheseisanumber，andthatthere
happenstobealreadyinthisplaceapluralityoftheextendedbodies
composedofnumbers，becausetheseattributesofnumberattachto
thevariousplaces，-thisbeingso，isthisnumber，whichwemust
supposeeachoftheseabstractionstobe，thesamenumberwhichis
exhibitedinthematerialuniverse，orisitanotherthanthis？
Platosaysitisdifferent；yetevenhethinksthatboththese
bodiesandtheircausesarenumbers，butthattheintelligiblenumbers
arecauses，whiletheothersaresensible。
LetusleavethePythagoreansforthepresent；foritisenoughto
havetouchedonthemasmuchaswehavedone。Butasforthosewho
posittheIdeasascauses，firstly，inseekingtograspthecauses
ofthethingsaroundus，theyintroducedothersequalinnumberto
these，asifamanwhowantedtocountthingsthoughthewouldnot
beabletodoitwhiletheywerefew，buttriedtocountthemwhen
hehadaddedtotheirnumber。FortheFormsarepracticallyequal
to-ornotfewerthan-thethings，intryingtoexplainwhichthese
thinkersproceededfromthemtotheForms。Fortoeachthingthere
answersanentitywhichhasthesamenameandexistsapartfromthe
substances，andsoalsointhecaseofallothergroupsthereisaone
overmany，whetherthemanyareinthisworldorareeternal。
Further，ofthewaysinwhichweprovethattheFormsexist，
noneisconvincing；forfromsomenoinferencenecessarilyfollows，
andfromsomeariseFormsevenofthingsofwhichwethinkthereare
noForms。Foraccordingtotheargumentsfromtheexistenceofthe
sciencestherewillbeFormsofallthingsofwhichtherearesciences
andaccordingtothe’oneovermany’argumenttherewillbeFormseven
ofnegations，andaccordingtotheargumentthatthereisanobject
forthoughtevenwhenthethinghasperished，therewillbeFormsof
perishablethings；forwehaveanimageofthese。Further，ofthemore
accuratearguments，someleadtoIdeasofrelations，ofwhichwesay
thereisnoindependentclass，andothersintroducethe’thirdman’。
AndingeneraltheargumentsfortheFormsdestroythethings
forwhoseexistencewearemorezealousthanfortheexistenceof
theIdeas；foritfollowsthatnotthedyadbutnumberisfirst，
i。e。thattherelativeispriortotheabsolute，-besidesalltheother
pointsonwhichcertainpeoplebyfollowingouttheopinionsheld
abouttheIdeashavecomeintoconflictwiththeprinciplesofthe
theory。
Further，accordingtotheassumptiononwhichourbeliefinthe
Ideasrests，therewillbeFormsnotonlyofsubstancesbutalsoof
manyotherthings(fortheconceptissinglenotonlyinthecaseof
substancesbutalsointheothercases，andtherearesciencesnot
onlyofsubstancebutalsoofotherthings，andathousandother
suchdifficultiesconfrontthem)。Butaccordingtothenecessities
ofthecaseandtheopinionsheldabouttheForms，ifFormscanbe
sharedintheremustbeIdeasofsubstancesonly。Fortheyarenot
sharedinincidentally，butathingmustshareinitsFormasin
somethingnotpredicatedofasubject(by’beingsharedin
incidentally’Imeanthate。g。ifathingsharesin’doubleitself’，
itsharesalsoin’eternal’，butincidentally；for’eternal’happens
tobepredicableofthe’double’)。ThereforetheFormswillbe
substance；butthesametermsindicatesubstanceinthisandinthe
idealworld(orwhatwillbethemeaningofsayingthatthereis
somethingapartfromtheparticulars-theoneovermany？)。Andifthe
Ideasandtheparticularsthatshareinthemhavethesameform，there
willbesomethingcommontothese；forwhyshould’2’beoneandthe
sameintheperishable2’sorinthosewhicharemanybuteternal，and
notthesameinthe’2’itself’asintheparticular2？Butifthey
havenotthesameform，theymusthaveonlythenameincommon，andit
isasifoneweretocallbothCalliasandawoodenimagea’man’，
withoutobservinganycommunitybetweenthem。
AboveallonemightdiscussthequestionwhatonearththeForms
contributetosensiblethings，eithertothosethatareeternalor
tothosethatcomeintobeingandceasetobe。Fortheycause
neithermovementnoranychangeinthem。Butagaintheyhelpinno
wiseeithertowardstheknowledgeoftheotherthings(fortheyare
noteventhesubstanceofthese，elsetheywouldhavebeeninthem)，
ortowardstheirbeing，iftheyarenotintheparticularswhichshare
inthem；thoughiftheywere，theymightbethoughttobecauses，as
whitecauseswhitenessinawhiteobjectbyenteringintoits
composition。Butthisargument，whichfirstAnaxagorasandlater
Eudoxusandcertainothersused，isveryeasilyupset；foritisnot
difficulttocollectmanyinsuperableobjectionstosuchaview。
But，further，allotherthingscannotcomefromtheFormsinany
oftheusualsensesof’from’。Andtosaythattheyarepatternsand
theotherthingsshareinthemistouseemptywordsandpoetical
metaphors。Forwhatisitthatworks，lookingtotheIdeas？And
anythingcaneitherbe，orbecome，likeanotherwithoutbeingcopied
fromit，sothatwhetherSocratesornotamanSocrateslikemight
cometobe；andevidentlythismightbesoevenifSocrateswere
eternal。Andtherewillbeseveralpatternsofthesamething，and
thereforeseveralForms；e。g。’animal’and’two-footed’andalso
’manhimself’willbeFormsofman。Again，theFormsarepatterns
notonlysensiblethings，butofFormsthemselvesalso；i。e。the
genus，asgenusofvariousspecies，willbeso；thereforethesame
thingwillbepatternandcopy。
