Afurtherdifficultyisraisedbythefactthatallknowledgeis
ofuniversalsandofthe’such’，butsubstanceisnotauniversal，but
israthera’this’-aseparablething，sothatifthereisknowledge
aboutthefirstprinciples，thequestionarises，howarewetosuppose
thefirstprincipletobesubstance？
Further，isthereanythingapartfromtheconcretethingbywhich
Imeanthematterandthatwhichisjoinedwithit，ornot？Ifnot，
wearemetbytheobjectionthatallthingsthatareinmatterare
perishable。Butifthereissomething，itmustbetheformorshape。
Nowitishardtodetermineinwhichcasesthisexistsapartandin
whichitdoesnot；forinsomecasestheformisevidentlynot
separable，e。g。inthecaseofahouse。
Further，aretheprinciplesthesameinkindorinnumber？Ifthey
areoneinnumber，allthingswillbethesame。
Sincethescienceofthephilosophertreatsofbeingquabeing
universallyandnotinrespectofapartofit，and’being’hasmany
sensesandisnotusedinoneonly，itfollowsthatifthewordis
usedequivocallyandinvirtueofnothingcommontoitsvarious
uses，beingdoesnotfallunderonescienceforthemeaningsofan
equivocaltermdonotformonegenus；butifthewordisusedin
virtueofsomethingcommon，beingwillfallunderonescience。The
termseemstobeusedinthewaywehavementioned，like’medical’and
’healthy’。Foreachofthesealsoweuseinmanysenses。Termsare
usedinthiswaybyvirtueofsomekindofreference，intheone
casetomedicalscience，intheothertohealth，inothersto
somethingelse，butineachcasetooneidenticalconcept。Fora
discussionandaknifearecalledmedicalbecausetheformer
proceedsfrommedicalscience，andthelatterisusefultoit。Anda
thingiscalledhealthyinasimilarway；onethingbecauseitis
indicativeofhealth，anotherbecauseitisproductiveofit。And
thesameistrueintheothercases。Everythingthatis，then，issaid
to’be’inthissameway；eachthingthatisissaidto’be’because
itisamodificationofbeingquabeingorapermanentora
transientstateoramovementofit，orsomethingelseofthesort。
Andsinceeverythingthatismaybereferredtosomethingsingleand
common，eachofthecontrarietiesalsomaybereferredtothefirst
differencesandcontrarietiesofbeing，whetherthefirst
differencesofbeingarepluralityandunity，orlikenessand
unlikeness，orsomeotherdifferences；letthesebetakenasalready
discussed。Itmakesnodifferencewhetherthatwhichisbereferredto
beingortounity。Foreveniftheyarenotthesamebutdifferent，at
leasttheyareconvertible；forthatwhichisoneisalsosomehow
being，andthatwhichisbeingisone。
Butsinceeverypairofcontrariesfallstobeexaminedbyoneand
thesamescience，andineachpaironetermistheprivativeofthe
otherthoughonemightregardingsomecontrariesraisethequestion，
howtheycanbeprivatelyrelated，viz。thosewhichhavean
intermediate，e。g。unjustandjust-inallsuchcasesonemustmaintain
thattheprivationisnotofthewholedefinition，butoftheinfima
species。ifthejustmanis’byvirtueofsomepermanentdisposition
obedienttothelaws’，theunjustmanwillnotineverycasehave
thewholedefinitiondeniedofhim，butmaybemerely’insomerespect
deficientinobediencetothelaws’，andinthisrespecttheprivation
willattachtohim；andsimilarlyinallothercases。
Asthemathematicianinvestigatesabstractionsforbefore
beginninghisinvestigationhestripsoffallthesensible
qualities，e。g。weightandlightness，hardnessanditscontrary，and
alsoheatandcoldandtheothersensiblecontrarieties，andleaves
onlythequantitativeandcontinuous，sometimesinone，sometimesin
two，sometimesinthreedimensions，andtheattributesofthesequa
quantitativeandcontinuous，anddoesnotconsidertheminanyother
respect，andexaminestherelativepositionsofsomeandthe
attributesofthese，andthecommensurabilitiesand
incommensurabilitiesofothers，andtheratiosofothers；butyetwe
positoneandthesamescienceofallthesethings——geometry——the
sameistruewithregardtobeing。Fortheattributesofthisinso
farasitisbeing，andthecontrarietiesinitquabeing，itisthe
businessofnoothersciencethanphilosophytoinvestigate；forto
physicsonewouldassignthestudyofthingsnotquabeing，butrather
quasharinginmovement；whiledialecticandsophisticdealwiththe
attributesofthingsthatare，butnotofthingsquabeing，andnot
withbeingitselfinsofarasitisbeing；thereforeitremains
thatitisthephilosopherwhostudiesthethingswehavenamed，inso
farastheyarebeing。Sinceallthatisisto’be’invirtueof
somethingsingleandcommon，thoughthetermhasmanymeanings，and
contrariesareinthesamecasefortheyarereferredtothefirst
contrarietiesanddifferencesofbeing，andthingsofthissortcan
fallunderonescience，thedifficultywestatedatthebeginning
appearstobesolved，-Imeanthequestionhowtherecanbeasingle
scienceofthingswhicharemanyanddifferentingenus。
Sinceeventhemathematicianusesthecommonaxiomsonlyina
specialapplication，itmustbethebusinessoffirstphilosophyto
examinetheprinciplesofmathematicsalso。Thatwhenequalsaretaken
fromequalstheremaindersareequal，iscommontoallquantities，but
mathematicsstudiesapartofitspropermatterwhichithasdetached，
e。g。linesoranglesornumbersorsomeotherkindofquantity-not，
however，quabeingbutinsofaraseachofthemiscontinuousin
oneortwoorthreedimensions；butphilosophydoesnotinquire
aboutparticularsubjectsinsofaraseachofthemhassomeattribute
orother，butspeculatesaboutbeing，insofaraseachparticular
thingis-Physicsisinthesamepositionasmathematics；for
physicsstudiestheattributesandtheprinciplesofthethingsthat
are，quamovingandnotquabeingwhereastheprimaryscience，we
havesaid，dealswiththese，onlyinsofarastheunderlyingsubjects
areexistent，andnotinvirtueofanyothercharacter；andsoboth
physicsandmathematicsmustbeclassedaspartsofWisdom。
Thereisaprincipleinthings，aboutwhichwecannotbedeceived，
butmustalways，onthecontraryrecognizethetruth，-viz。thatthe
samethingcannotatoneandthesametimebeandnotbe，oradmitany
othersimilarpairofopposites。Aboutsuchmattersthereisno
proofinthefullsense，thoughthereisproofadhominem。Foritis
notpossibletoinferthistruthitselffromamorecertainprinciple，
yetthisisnecessaryifthereistobecompletedproofofitinthe
fullsense。Buthewhowantstoprovetotheasserterofopposites
thatheiswrongmustgetfromhimanadmissionwhichshallbe
identicalwiththeprinciplethatthesamethingcannotbeandnot
beatoneandthesametime，butshallnotseemtobeidentical；for
thusalonecanhisthesisbedemonstratedtothemanwhoasserts
thatoppositestatementscanbetrulymadeaboutthesamesubject。
Those，then，whoaretojoininargumentwithoneanothermusttosome
extentunderstandoneanother；forifthisdoesnothappenhoware
theytojoininargumentwithoneanother？Thereforeeverywordmust
beintelligibleandindicatesomething，andnotmanythingsbutonly
one；andifitsignifiesmorethanonething，itmustbemadeplainto
whichofthesethewordisbeingapplied。He，then，whosays’this
isandisnot’denieswhatheaffirms，sothatwhattheword
signifies，hesaysitdoesnotsignify；andthisisimpossible。
Thereforeif’thisis’signifiessomething，onecannottrulyassert
itscontradictory。
Further，ifthewordsignifiessomethingandthisisasserted
truly，thisconnexionmustbenecessary；anditisnotpossiblethat
thatwhichnecessarilyisshouldevernotbe；itisnotpossible
thereforetomaketheopposedaffirmationsandnegationstrulyof
thesamesubject。Further，iftheaffirmationisnomoretruethanthe
negation，hewhosays’man’willbenomorerightthanhewhosays
’not-man’。Itwouldseemalsothatinsayingthemanisnotahorse
onewouldbeeithermoreornotlessrightthaninsayingheisnot
aman，sothatonewillalsoberightinsayingthatthesameperson
isahorse；foritwasassumedtobepossibletomakeopposite
statementsequallytruly。Itfollowsthenthatthesamepersonisa
manandahorse，oranyotheranimal。
While，then，thereisnoproofofthesethingsinthefull
sense，thereisaproofwhichmaysufficeagainstonewhowillmake
thesesuppositions。AndperhapsifonehadquestionedHeraclitus
himselfinthiswayonemighthaveforcedhimtoconfessthatopposite
statementscanneverbetrueofthesamesubjects。But，asitis，he
adoptedthisopinionwithoutunderstandingwhathisstatement
involves。Butinanycaseifwhatissaidbyhimistrue，noteven
thisitselfwillbetrue-viz。thatthesamethingcanatoneandthe
sametimebothbeandnotbe。Foras，whenthestatementsare
separated，theaffirmationisnomoretruethanthenegation，inthe
sameway-thecombinedandcomplexstatementbeinglikeasingle
affirmation-thewholetakenasanaffirmationwillbenomoretrue
thanthenegation。Further，ifitisnotpossibletoaffirmanything
truly，thisitselfwillbefalse-theassertionthatthereisnotrue
affirmation。Butifatrueaffirmationexists，thisappearsto
refutewhatissaidbythosewhoraisesuchobjectionsandutterly
destroyrationaldiscourse。
ThesayingofProtagorasisliketheviewswehavementioned；he
saidthatmanisthemeasureofallthings，meaningsimplythatthat
whichseemstoeachmanalsoassuredlyis。Ifthisisso，itfollows
thatthesamethingbothisandisnot，andisbadandgood，and
thatthecontentsofallotheroppositestatementsaretrue，because
oftenaparticularthingappearsbeautifultosomeandthecontraryof
beautifultoothers，andthatwhichappearstoeachmanisthe
measure。Thisdifficultymaybesolvedbyconsideringthesourceof
thisopinion。Itseemstohaveariseninsomecasesfromthe
doctrineofthenaturalphilosophers，andinothersfromthefactthat
allmenhavenotthesameviewsaboutthesamethings，buta
particularthingappearspleasanttosomeandthecontraryofpleasant
toothers。
Thatnothingcomestobeoutofthatwhichisnot，but
everythingoutofthatwhichis，isadogmacommontonearlyallthe
naturalphilosophers。Since，then，whitecannotcometobeifthe
perfectlywhiteandinnorespectnot-whiteexistedbefore，thatwhich
becomeswhitemustcomefromthatwhichisnotwhite；sothatit
mustcometobeoutofthatwhichisnotsotheyargue，unlessthe
samethingwasatthebeginningwhiteandnot-white。Butitisnot
hardtosolvethisdifficulty；forwehavesaidinourworkson
physicsinwhatsensethingsthatcometobecometobefromthat
whichisnot，andinwhatsensefromthatwhichis。
Buttoattendequallytotheopinionsandthefanciesofdisputing
partiesischildish；forclearlyoneofthemmustbemistaken。And
thisisevidentfromwhathappensinrespectofsensation；forthe
samethingneverappearssweettosomeandthecontraryofsweetto
others，unlessintheonecasethesense-organwhichdiscriminatesthe
aforesaidflavourshasbeenpervertedandinjured。Andifthisisso
theonepartymustbetakentobethemeasure，andtheothermustnot。
Andsaythesameofgoodandbad，andbeautifulandugly，andall
othersuchqualities。Fortomaintaintheviewweareopposingisjust
likemaintainingthatthethingsthatappeartopeoplewhoputtheir
fingerundertheireyeandmaketheobjectappeartwoinsteadofone
mustbetwobecausetheyappeartobeofthatnumberandagainone
fortothosewhodonotinterferewiththeireyetheoneobject
appearsone。