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。