presuppose，toguardagainstdialecticalobjections，anyfurther
qualificationswhichmightbeadded。This，then，isthemostcertain
ofallprinciples，sinceitanswerstothedefinitiongivenabove。For
itisimpossibleforanyonetobelievethesamethingtobeandnot
tobe，assomethinkHeraclitussays。Forwhatamansays，hedoesnot
necessarilybelieve；andifitisimpossiblethatcontrary
attributesshouldbelongatthesametimetothesamesubject(the
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
demonstrationofabsolutelyeverything(therewouldbeaninfinite
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
opponentshallsaythatsomethingeitherisorisnot(forthisone
mightperhapstaketobeabeggingofthequestion)，butthatheshall
saysomethingwhichissignificantbothforhimselfandforanother；
forthisisnecessary，ifhereallyistosayanything。For，ifhe
meansnothing，suchamanwillnotbecapableofreasoning，either
withhimselforwithanother。Butifanyonegrantsthis，
demonstrationwillbepossible；forweshallalreadyhavesomething
definite。Thepersonresponsiblefortheproof，however，isnothewho
demonstratesbuthewholistens；forwhiledisowningreasonhelistens
toreason。Andagainhewhoadmitsthishasadmittedthatsomethingis
trueapartfromdemonstration(sothatnoteverythingwillbe’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
significance(forwedonotidentify’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-footedanimal(forthiswaswhat’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。For(1)anaccidentisnotanaccidentofanaccident，
unlessitbebecausebothareaccidentsofthesamesubject。Imean，
forinstance，thatthewhiteismusicalandthelatteriswhite，
onlybecausebothareaccidentaltoman。But(2)Socratesis
musical，notinthissense，thatbothtermsareaccidentalto
somethingelse。Sincethensomepredicatesareaccidentalinthis
andsomeinthatsense，(a)thosewhichareaccidentalinthelatter
sense，inwhichwhiteisaccidentaltoSocrates，cannotforman
infiniteseriesintheupwarddirection；e。g。Socratesthewhitehas
notyetanotheraccident；fornounitycanbegotoutofsuchasum。
Noragain(b)will’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
ispossibleeithertoaffirmortodenyanything(andthispremiss
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。
