presuppose，toguardagainstdialecticalobjections，anyfurther
　　qualificationswhichmightbeadded。This，then，isthemostcertain
　　ofallprinciples，sinceitanswerstothedefinitiongivenabove。For
　　itisimpossibleforanyonetobelievethesamethingtobeandnot
　　tobe，assomethinkHeraclitussays。Forwhatamansays，hedoesnot
　　necessarilybelieve；andifitisimpossiblethatcontrary
　　attributesshouldbelongatthesametimetothesamesubjectthe
　　usualqualificationsmustbepresupposedinthispremisstoo，and
　　ifanopinionwhichcontradictsanotheriscontrarytoit，obviously
　　itisimpossibleforthesamemanatthesametimetobelievethesame
　　thingtobeandnottobe；forifamanweremistakenonthispointhe
　　wouldhavecontraryopinionsatthesametime。Itisforthisreason
　　thatallwhoarecarryingoutademonstrationreduceittothisas
　　anultimatebelief；forthisisnaturallythestarting-pointeven
　　foralltheotheraxioms。
　　Therearesomewho，aswesaid，boththemselvesassertthatit
　　ispossibleforthesamethingtobeandnottobe，andsaythat
　　peoplecanjudgethistobethecase。Andamongothersmanywriters
　　aboutnatureusethislanguage。Butwehavenowpositedthatitis
　　impossibleforanythingatthesametimetobeandnottobe，andby
　　thismeanshaveshownthatthisisthemostindisputableofall
　　principles-Someindeeddemandthateventhisshallbedemonstrated，
　　butthistheydothroughwantofeducation，fornottoknowofwhat
　　thingsoneshoulddemanddemonstration，andofwhatoneshouldnot，
　　argueswantofeducation。Foritisimpossiblethatthereshouldbe
　　demonstrationofabsolutelyeverythingtherewouldbeaninfinite
　　regress，sothattherewouldstillbenodemonstration；butif
　　therearethingsofwhichoneshouldnotdemanddemonstration，these
　　personscouldnotsaywhatprincipletheymaintaintobemore
　　self-evidentthanthepresentone。
　　Wecan，however，demonstratenegativelyeventhatthisviewis
　　impossible，ifouropponentwillonlysaysomething；andifhesays
　　nothing，itisabsurdtoseektogiveanaccountofourviewstoone
　　whocannotgiveanaccountofanything，insofarashecannotdo
　　so。Forsuchaman，assuch，isfromthestartnobetterthana
　　vegetable。NownegativedemonstrationIdistinguishfromdemonstration
　　proper，becauseinademonstrationonemightbethoughttobe
　　beggingthequestion，butifanotherpersonisresponsibleforthe
　　assumptionweshallhavenegativeproof，notdemonstration。The
　　starting-pointforallsuchargumentsisnotthedemandthatour
　　opponentshallsaythatsomethingeitherisorisnotforthisone
　　mightperhapstaketobeabeggingofthequestion，butthatheshall
　　saysomethingwhichissignificantbothforhimselfandforanother；
　　forthisisnecessary，ifhereallyistosayanything。For，ifhe
　　meansnothing，suchamanwillnotbecapableofreasoning，either
　　withhimselforwithanother。Butifanyonegrantsthis，
　　demonstrationwillbepossible；forweshallalreadyhavesomething
　　definite。Thepersonresponsiblefortheproof，however，isnothewho
　　demonstratesbuthewholistens；forwhiledisowningreasonhelistens
　　toreason。Andagainhewhoadmitsthishasadmittedthatsomethingis
　　trueapartfromdemonstrationsothatnoteverythingwillbe’so
　　andnotso’。
　　Firstthenthisatleastisobviouslytrue，thattheword’be’
　　or’notbe’hasadefinitemeaning，sothatnoteverythingwillbe’so
　　andnotso’。Again，if’man’hasonemeaning，letthisbe
　　’two-footedanimal’；byhavingonemeaningIunderstandthis:-if’man’
　　means’X’，thenifAisaman’X’willbewhat’beingaman’meansfor
　　him。Itmakesnodifferenceevenifoneweretosayawordhas
　　severalmeanings，ifonlytheyarelimitedinnumber；fortoeach
　　definitiontheremightbeassignedadifferentword。Forinstance，
　　wemightsaythat’man’hasnotonemeaningbutseveral，oneof
　　whichwouldhaveonedefinition，viz。’two-footedanimal’，whilethere
　　mightbealsoseveralotherdefinitionsifonlytheywerelimitedin
　　number；forapeculiarnamemightbeassignedtoeachofthe
　　definitions。If，however，theywerenotlimitedbutoneweretosay
　　thatthewordhasaninfinitenumberofmeanings，obviously
　　reasoningwouldbeimpossible；fornottohaveonemeaningisto
　　havenomeaning，andifwordshavenomeaningourreasoningwithone
　　another，andindeedwithourselves，hasbeenannihilated；foritis
　　impossibletothinkofanythingifwedonotthinkofonething；but
　　ifthisispossible，onenamemightbeassignedtothisthing。
　　Letitbeassumedthen，aswassaidatthebeginning，thatthe
　　namehasameaningandhasonemeaning；itisimpossible，then，that
　　’beingaman’shouldmeanprecisely’notbeingaman’，if’man’not
　　onlysignifiessomethingaboutonesubjectbutalsohasone
　　significanceforwedonotidentify’havingonesignificance’with
　　’signifyingsomethingaboutonesubject’，sinceonthatassumption
　　even’musical’and’white’and’man’wouldhavehadone
　　significance，sothatallthingswouldhavebeenone；fortheywould
　　allhavehadthesamesignificance。
　　Anditwillnotbepossibletobeandnottobethesamething，
　　exceptinvirtueofanambiguity，justasifonewhomwecall’man’，
　　othersweretocall’not-man’；butthepointinquestionisnot
　　this，whetherthesamethingcanatthesametimebeandnotbea
　　maninname，butwhetheritcaninfact。Nowif’man’and’not-man’
　　meannothingdifferent，obviously’notbeingaman’willmean
　　nothingdifferentfrom’beingaman’；sothat’beingaman’willbe
　　’notbeingaman’；fortheywillbeone。Forbeingonemeans
　　this-beingrelatedas’raiment’and’dress’are，iftheirdefinition
　　isone。Andif’beingaman’and’beinganot-man’aretobeone，they
　　mustmeanonething。Butitwasshownearlier’thattheymean
　　differentthings-Therefore，ifitistruetosayofanythingthat
　　itisaman，itmustbeatwo-footedanimalforthiswaswhat’man’
　　meant；andifthisisnecessary，itisimpossiblethatthesamething
　　shouldnotatthattimebeatwo-footedanimal；forthisiswhat
　　’beingnecessary’means-thatitisimpossibleforthethingnottobe。
　　Itis，then，impossiblethatitshouldbeatthesametimetruetosay
　　thesamethingisamanandisnotaman。
　　Thesameaccountholdsgoodwithregardto’notbeingaman’，
　　for’beingaman’and’beinganot-man’meandifferentthings，since
　　even’beingwhite’and’beingaman’aredifferent；fortheformer
　　termsaremuchmoredifferentsothattheymustafortiorimean
　　differentthings。Andifanyonesaysthat’white’meansoneandthe
　　samethingas’man’，againweshallsaythesameaswhatwassaid
　　before，thatitwouldfollowthatallthingsareone，andnotonly
　　opposites。Butifthisisimpossible，thenwhatwehavemaintained
　　willfollow，ifouropponentwillonlyanswerourquestion。
　　Andif，whenoneasksthequestionsimply，headdsthe
　　contradictories，heisnotansweringthequestion。Forthereis
　　nothingtopreventthesamethingfrombeingbothamanandwhite
　　andcountlessotherthings:butstill，ifoneaskswhetheritisoris
　　nottruetosaythatthisisaman，ouropponentmustgiveananswer
　　whichmeansonething，andnotaddthat’itisalsowhiteand
　　large’。For，besidesotherreasons，itisimpossibletoenumerate
　　itsaccidentalattributes，whichareinfiniteinnumber；lethim，
　　then，enumerateeitherallornone。Similarly，therefore，evenif
　　thesamethingisathousandtimesamanandanot-man，hemustnot，
　　inansweringthequestionwhetherthisisaman，addthatitisalso
　　atthesametimeanot-man，unlessheisboundtoaddalsoallthe
　　otheraccidents，allthatthesubjectisorisnot；andifhedoes
　　this，heisnotobservingtherulesofargument。
　　Andingeneralthosewhosaythisdoawaywithsubstanceand
　　essence。Fortheymustsaythatallattributesareaccidents，andthat
　　thereisnosuchthingas’beingessentiallyaman’or’ananimal’。
　　Forifthereistobeanysuchthingas’beingessentiallyaman’this
　　willnotbe’beinganot-man’or’notbeingaman’yettheseare
　　negationsofit；fortherewasonethingwhichitmeant，andthiswas
　　thesubstanceofsomething。Anddenotingthesubstanceofathing
　　meansthattheessenceofthethingisnothingelse。Butifits
　　beingessentiallyamanistobethesameaseitherbeing
　　essentiallyanot-manoressentiallynotbeingaman，thenitsessence
　　willbesomethingelse。Thereforeouropponentsmustsaythatthere
　　cannotbesuchadefinitionofanything，butthatallattributesare
　　accidental；forthisisthedistinctionbetweensubstanceand
　　accident-’white’isaccidentaltoman，becausethoughheiswhite，
　　whitenessisnothisessence。Butifallstatementsareaccidental，
　　therewillbenothingprimaryaboutwhichtheyaremade，ifthe
　　accidentalalwaysimpliespredicationaboutasubject。The
　　predication，then，mustgoonadinfinitum。Butthisisimpossible；
　　fornotevenmorethantwotermscanbecombinedinaccidental
　　predication。For1anaccidentisnotanaccidentofanaccident，
　　unlessitbebecausebothareaccidentsofthesamesubject。Imean，
　　forinstance，thatthewhiteismusicalandthelatteriswhite，
　　onlybecausebothareaccidentaltoman。But2Socratesis
　　musical，notinthissense，thatbothtermsareaccidentalto
　　somethingelse。Sincethensomepredicatesareaccidentalinthis
　　andsomeinthatsense，athosewhichareaccidentalinthelatter
　　sense，inwhichwhiteisaccidentaltoSocrates，cannotforman
　　infiniteseriesintheupwarddirection；e。g。Socratesthewhitehas
　　notyetanotheraccident；fornounitycanbegotoutofsuchasum。
　　Noragainbwill’white’haveanothertermaccidentaltoit，e。g。
　　’musical’。Forthisisnomoreaccidentaltothatthanthatisto
　　this；andatthesametimewehavedrawnthedistinction，thatwhile
　　somepredicatesareaccidentalinthissense，othersaresointhe
　　senseinwhich’musical’isaccidentaltoSocrates；andtheaccident
　　isanaccidentofanaccidentnotincasesofthelatterkind，but
　　onlyincasesoftheotherkind，sothatnotalltermswillbe
　　accidental。Theremust，then，evensobesomethingwhichdenotes
　　substance。Andifthisisso，ithasbeenshownthatcontradictories
　　cannotbepredicatedatthesametime。
　　Again，ifallcontradictorystatementsaretrueofthesame
　　subjectatthesametime，evidentlyallthingswillbeone。Forthe
　　samethingwillbeatrireme，awall，andaman，ifofeverythingit
　　ispossibleeithertoaffirmortodenyanythingandthispremiss
　　mustbeacceptedbythosewhosharetheviewsofProtagoras。Forif
　　anyonethinksthatthemanisnotatrireme，evidentlyheisnota
　　trireme；sothathealsoisatrireme，if，astheysay，
　　contradictorystatementsarebothtrue。Andwethusgetthedoctrine
　　ofAnaxagoras，thatallthingsaremixedtogether；sothatnothing
　　reallyexists。Theyseem，then，tobespeakingoftheindeterminate，
　　and，whilefancyingthemselvestobespeakingofbeing，theyare
　　speakingaboutnon-being；foritisthatwhichexistspotentially
　　andnotincompleterealitythatisindeterminate。Buttheymust
　　predicateofeverysubjecttheaffirmationorthenegationofevery
　　attribute。Foritisabsurdifofeachsubjectitsownnegationis
　　tobepredicable，whilethenegationofsomethingelsewhichcannotbe
　　predicatedofitisnottobepredicableofit；forinstance，ifitis
　　truetosayofamanthatheisnotaman，evidentlyitisalsotrue
　　tosaythatheiseitheratriremeornotatrireme。If，then，the
　　affirmativecanbepredicated，thenegativemustbepredicabletoo；
　　andiftheaffirmativeisnotpredicable，thenegative，atleast，will
　　bemorepredicablethanthenegativeofthesubjectitself。If，
　　then，eventhelatternegativeispredicable，thenegativeof
　　’trireme’willbealsopredicable；and，ifthisispredicable，the
　　affirmativewillbesotoo。