t b RobinS Prior Analytics ARISTOLE Prior Analytics translated, wi thi ntroducti on,notes,and commentary,by RobinSmith HackettPublishing Company Indi anapolisICambridge Aristotle: 384322 B.c. Copyright 1989 by Robi n Smi th Al lrights reserved Pri nted i n the Uni ted States of America Cover and interior design by L.Daniel Ki rkl i n For further i nformation, please address the publisher Hackett Publ i shi ng Company,I nc. POBox 44937 Indi anapol i s,I ndiana 46204 Library of Congress Cataloging-in-PublicatonData Ari stotle. [ Prior analytics.Engl i sh] Prior analytics I Ari stotle ;translated, with i ntroduction, notes, and commentary by Robi n Smith. p.em.Bi bl iography:p. I ncludes i ndex. ISBN 0-87220-064-7 1. Logic-Early works to 1800.I. Title. B440. ASS651989 160dc1988-39877 CIP The paper used i n thi s publ ication meets the mi ni mum requi rements of American National Standard for Information Sciences-Permanence of Paper for Pri nted Li brary Materials, ANSI 239.48- 1984. Preface Introduction Pror Analytics BookA BookB NotestoBookA NotestoBookB AppendixI Contents Vll Xlll 1 65 105 183 AList oftheDeductiveFormsinPror AnalyticsA4-22229 Appendix II DeviationsfromRoss's(OCT)Text236 Glossary239 Bibliography24 4 IndexLocorum249 General Index252 InMemoriam Charles Allen Carson 1928-1989 PREFACE NoothertreatiseonformallogiciscomparabletoAristotle'sPror Analytics.Thisistruei nthefrstpl acebecausenootherlogici anoccupiesaposi tioninhi storyatal l comparabletoAristotle.Hewasnot onlythefrstformallogi ci an, he was also one of the greatest: themost compel l i ngevidenceforthi sassessmenti shi sstartl i ng appearanceon thestageofhi story,wi thnorealpredecessor.Buthi storicalacci dent hasaddedmuchtothei mportanceoftheProrAnalytics.Formany generations,Aristotel i anlogic (oratleastwhatpassedforAristotel i an logic) wasi denticallylogic:thus, Kant coul d say,i n the Crtique ofPure Reason,thattheenti refeldoflogichadnotmadeasi ngleadvance si nceAristotle'sgreattreatise.Fewwoul dconcuri nsuchanopi ni on today,but theeffect of thePror Analyticsi n formi ng our phi losophical heritageis di ffcul t to exaggerate. Atthesameti me, itmightbearguedthattheworkhasl i ttlephi losophicali nteresttoday.Duri ngthel astcentury,formallogichas reachedextremelyhi ghlevelsoftechnicalsophistication, andphi losophicaldi scussionof itsunderlyingconceptshasadvancedcommensurately.Asaresul t, i tmi ghtbesuggestedthatwhateveradmi ration wemayhavetodayforAristotle'sachievement, neverthelesshehas l i ttleto teachusthat wecannotlearnbetter fromour contemporaries. When we consider the effort that i srequi redto study asysteminmany respectsawkwardandunfami l i arfromamodernpoi ntofview,the di ffcul ti esoccasionedbyAristotle'signoranceofmuchofwhatwe havesi ncelearned about deductivesystems,andthemany probl ems of i nterpretation which arise wi thanyworkproducedinanother l anguage andinanothercul tureatadi stanceofovertwomi l l enni a, thePror Analyticsmayseemtobeof valueonlytothephi losophicalanti quary. Ido not thi nk thi s i s afai r assessment. Inpart,Iwoul drespond wi th the same defensemany hi storians of phi l osophy giveforthe practice of thei r craft:Aristotlei samajorpartof ourphi losophicalancestry,and we cometounderstandourselvesbetterbystudying ouridealorigi ns.I nl argerpart,however,Iwoul dsuggestthatwesti l l mayhavesomethi ng tolearnfromthi s oldGreek.If hei signorant of our vast body of VII VIIIPREFACE metalogic,hei salsounencumberedbyourmanynewly-bornprejudices.Someti mes, wefndhi s approachto aquesti on, once we come to understandi tinour ownterms,isafreshone:occasional ly,hemight evenberight. The proof,of course,must bei n the experienci ng. The Translation.Transl ati on i s al most bynaturearrogant: the translator acts as akindof i mpersonator of the author,andthereader hasno goodmeansof defenseagai nstafalserepresentati on. Inthecaseof a workl i ketheProrAnalytics,thereisatemptationtoevenfurther arrogance.Aristotle'sGreeki sfrequentlycl i pped,di ffcul tofconstruction,awkward,ambi guous,orobscure.Thetranslatorissorely temptedtogivehi mahandincomi ngacrossbetterinEngl i sh: to resolvetheambi gui ti es,cleanupthemessy constructions,flloutwhat isabbreviated(or evenabsent), smoothouttheawkwardparts.Whi le abouti t, onecouldalso gi ve thereader abi t of hel p wi thafewrather ful l renderi ngsofdi ffcul ttermsorphrases,creati ngatextthatembodi es a certai n amount of commentaryi n its i nterstices. Thereareoccasionswhenthissort oftranslationisappropriate,but i ti snotwhatIhaveai medat. Ihavetriedi nsteadtogivethephi losophicallyi nformedreader whodoesnotknowGreekavehicle for the studyofAristotle' sPror Analytics.Tothatend, Ihaveattemptedto leaveasmuchof thei nterpretativeworkaspossi bleundone.Oneway todothat istofol lowthemodelof Robert Grossetesteandconstruct a sortof functionalmappi ngof Aristotle'sGreeki ntoEnglish(orrather i ntoabarbaroussort of constructi on made of English words). But this, Ibel i eve,i si nmanycasesjustnottotransl ateatall. TheGreekless reader,presented wi th suchasubl i teralstri ng of English vocabul ary,is often prompted to ask:Wel l,whatever could that mean? WhatIhavetri edtodoi nsteadi stostri keacompromi se.The Englishofmytranslati onisi ntendedtobeEngl i sh, thoughIhave soughttoavoidmaki ngitmoreelegantthanAristotle'sGreek.When Aristotlei shardtoconstrue,Ihaveundertakentotranslatehimwith di ffcul tEnglish.However,Ihavemadei ntel l i gi bi l i tytakeprecedence overthegoalofreproduci ngthecharacterofAristotle'sGreekin Engl i sh, somethi ng whichprobablycannotbedone.Whenalternative i nterpretationsofthetextarepossi ble, Ihave,of course,chosenthe oneIfndmostl i kely( thoughinsomefortunatecases,Ihavebeen abletoreproduceanambiguity of GreeksyntaxinEngl i sh); however, intheNotesIalertthereadertothosepossi bi l i ti eswhichIhave PREFACEIX closedoffinthetranslationi tself.Whenacertai ntransl ati onofa technicaltermiswel l -establ i shed, Ihavemoreoftenthannotopted fori t, eventhoughthesetradi ti onal renderi ngsaresometimesless thanopti mal,simplytomakemyversionuseful : readersmustotherwisehaveaglossaryconverti ngmyrenderi ngsi ntotheestabli shed onesi nordertomakesenseofthesecondaryl i terature.Ihave, however,avoidedoneunnecessarybarbari sm: Iusuallytranslate huparche pant as'belongstoevery'rather than'belongstoal l ' (whi ch,i nthepresentsense, hasnoEnglishuseoutsidedi scussionsofthe syl logistic:see Geach 1972, 69).TheText.Thetranslati onisgenerallybasedonRoss'stext;variations fromhi sreadi ngs,wheretheyarei mportant, aredi scussedinthe Notes(al i stofvari ationsfromRossi sgivenasAppendi xII). In vi rtuallyeverysuchcase, mydi fferenceswi thRossleantowardseditorial conservati sm: Ihavetriedtofndacoherentsenseforthebestattestedreadi ng,andIhavetakentheposi ti onthatAri stotlesometimesnods.Iretai nthetradi ti onal divi si oni ntoChapters,which ( thoughcompletelywi thoutanci entauthority)isaconveni entand generallyreasonablewayofsubdivi di ngthetext.Li nereferencesi n themarginaret o thestandardedi tion( Bekker).Squarebracketsenclosepassageswhich, al thoughwel l -attestedinthemanuscri pts,neverthelessseemtobespurious.Iuseanglebracketstomarkboth edi torialaddi tionstoAristotle'stext( i . e. , correctionstothemanuscripts) andi nterpretative addi tions tothe transl ati on.TheNotes.TheNotesarenoti ntendedasacomprehensivecommentary,butratherasanaidtothereaderwithmoreknowledgeof logicandphi losophythanofGreek.Mygoalhasbeentoprovide otherswithaPror Analyticsthat can actuallybeusedforserious study. Accordi ngly,Ihavetriedtomakeclearwhatiscontroversi al orproblematicaboutthetextand,totheextentpossi ble, togetoutofthe reader'sway.Thishassometi mesledmetoi ncl uderatherlengthy di scussionsof thegrammaticalandtextualproblemssurroundi ng certai npassages,whichmayseemoddinaworki ntendedtobei ntel l i gi bl e tothosewhodonotknowGreek. Buti ti spreciselyforthat sort of reader that these poi ntsrequi rethe ful l est di scussion. Such areader has no text beyondthetransl ati on andcannot seethroughthefni shed producttoitsoftenmurkyorigi ns.WhatIhavedonei sreconstruct XPREFACE someofthemessy,eventendentiousprocesswherebyrenderi ngs cometobechosen; IhopethatIhaveatthesameti memanagedto undermi ne my own appearance of authori ty. Ihavealsotriedtoalertthereadertodi ffcul ti esinunderstandi ng thetext andtogivesome broadpictureof therangeof opi ni on among scholars,al thoughthisi snecessari lyselectiveandomitsmentionof manyissues.Insomecases,Idonottakeaposi ti onmysel f,butin othersIdo: thereader isbetterarmedagai nstmyprejudicesbybeing i nformedof whattheyare.Ononepoi nt, Ihavearguedforarather specifclineof i nterpretati on. Iseethe Pror Analyticsas organi zedi n a certai nwaytosupportthegoalsofthePosteror.Thenatureofmy viewisspelledoutintheIntroduction,andthedetai l s aredefendedi n variouspl aces,asappropri ate,throughoutt heNotes.Onceagai n, I believethatifmyreadersareawareofmyownexegeticalhobbyhorses,theywi l l beinabetterposi ti ontodefendthemselvesagainst any di storting effects. TheIntroduction.TheProrAnalyticsisatechnicalwork,anda di ffcul t one.Someframework for viewing i ts theoriesisnecessary,and wemust(asAristotlesays)begi nwithwhati sfami l i artous.Ihave therefore offered, intheIntroduction,amodel for Aristotle'sdeductive systeminthestyleof mathematicallogic.Thismayberegardedasa bi t of temporalprovi nci al i sm: perhapsina centuryortwo,itmayseem asquainttofuturereadersasmi d-ni neteenthcenturyaccountsdoto us.But attheleast,i t offersapoi nt of departurefromwhichtobegi n.Ici tethetwo Books of thePror Analyticssi mplyasAandB( 'A23'means' BookA,Chapter23' ). OtherworksofAri stotl earegiven English( ratherthanLati n) ti tles.Referencestocommentariesand othertranslati onsarei dentifedbythecommentator'snameandpage number only; other l i teraturei s ci tedbyauthorandyear.Thedetails, i n eachcase,arefoundi ntheBi bl i ography.AsfortheBi bl i ography,it shouldberegardedsi mply asthel i st of works Imenti on ( thoughIalso i ncl ude afewgeneral works on Ari stotle).Acknowledgments.AgrantfromtheBureauof GeneralResearchof KansasStateUni versi typrovi dedsupportfortheacqui si ti on of materials andexpenses of manuscript preparati on; Iacknowledgethi s with thanks. Anumber of personshavegenerouslyhelpedme wi thvarious stagesofthework.Robert Turnbullofferedadviceandencouragement astheprojectwastaki ngi ni ti al shape.johnCorcoranhasformany PREFACEXI yearstriedtokeepmythoughtsaboutAristotle'sl ogi ccoherent; he readthroughtheenti remanuscri pti ndraftandsuggestedseveral correctionsi ntheNotes.Asi fthatwerenotgenerosityenough,he andWoosukPark eachtooki t onthemselvestoreadthewholebook i npageproofs,suggesti ngsti l l further changesandfndi nganynumber of errorsIhadoverlooked. Al l anBackki ndl yal l owedmetosee partsof themanuscriptof hisbookOnReduplicationwhi l ei t wassti l li npress.Iprevai l edratherheavilyonCharl esM.Youngtotransmi t metheresul tsof searchesof theThesaursLingaeGraecaeby way of electroni cmai l . Anynumberof mycolleaguesi nancientphi losophy have toleratedmybadgeri ng them about whether theythoughtthisor that construaltobepossi ble.PaigeNicholsassi stedwi ththepreparationofthemanuscript(oneresultof whi chi sthatshei snow,Iam qui tesure,theonl yl i vi nghumanbei ngtohavereadaloudthewhole oftheProrAnalyticsi nanyl anguage). JamesHul l ett, Frances Hackett,DanKi rkl i n, andthestaffof HackettPubl i shi ngCompany haveexceededanyauthor'sreasonableexpectationsofwhatapubl i sher oughtto be.Iamespeciallyi ndebtedtoMichaelFrede, who,asthesecond reader of themanuscri pt forHackett Publ i shi ng Company,made afar moresignifcantcontri buti ontothefnal workthanthatoffcewould suggest.HereadthroughtheNotesi ntwo draftsandthetranslationi n three.The wealthof carefulanddetailedcommentsheprovidedsaved mefrommany errorsandbaddecisionsandkept thi s book frombei ng muchworse: theforceof thetypi caldecl arati on of modesty by whi ch anauthorretainsonl y theresponsibilityforawork'sfaul tsandascribes creditforitsvirtuestoothersisperhapsattenuatedfromoveruse,but in this case I canthink of no other way to express thetruth.As this book wasi n i ts fnal stages,mybrother,Dr.Charles A.Carson, succumbedi n alengthystrugglewith cancer.Charles was alwaysagreat lover of words(thoughhislanguagewasLati n, notGreek);Iwouldlike mybokto serveasa smallmemorialtohis exempl arylife. INTRODUCTION TheContentof thePrior Analtics.FromAristotle'sviewpoi nt, the Pror Analticsi s si mply the frst part of the Analytics:thesecondpart is theworkknowntousasthePosterorAnalytics.Thesubjectofthe. latterisproofordemonstration(apodexis),thatis, argumentation whichproducessci entifcunderstandi ng(epistemi.Aristotlemakesi t clearfromthe start thatthi sisal so thesubjectof theenti reAnalytics, andthusofits frstpart,thePror.Aristotleconceives of ademonstrativescienceasasystemof demonstrations,whichinturnareatypeof deduction(sulogsmos).Accordi ngly,theProrAnalyticsgivesanaccount of deductionsingeneralandthePosteror di scussesthespecifc character of those deductions which aredemonstrations.Althoughtherelationshi p of the two parts of the Analticsappearsto bestraightforwardenoughonthi saccount, controversi eshavearisen abouti tsdetailsandi tshi story.Inmanyrespects,thePror Analyticsis themorehighly developed work:i n the Posteror,Aristotle often seems ignorant of technicalresults contai nedi ni t. Somescholarshaveargued that thephi losophicalenvi ronmentsof thetwoparts are also di fferent.To menti onthemosti mportant suchstudy,Fri edrichSol msenundertooktorecoverthecourseof hi storicaldevelopment of Aristotle'slogicaldoctrinesusingjaeger'sviewthatAristotleevolvedfromanearly Platonic stancei n phi losophy to amatureposi tionhostileto Pl atoni sm.HeconcludedthatthePosteror Analyticswas the earl i er workandthat i t refectedamorepri mi tivestageof thetheory of deductionthanthat found i n the Pror.Controversy aboutthi s poi nt is sti l lnot ended.Ati ssueherearetwo poi nts. Oneisthehi storicalquesti on of when thevariouspartsoftheAnalyticswerecomposedandhowtheyul timatelytookshapei ntheformpreservedforus. Theotheri show closelythePosterorAnalyticsdependsonthetheoriesofthePror.I cannotdi scusstheseissuesadequatelyhere,butnei therdoIwishto ignorethem. Instead,let me alert thereader tomy owni nterpretation,whichistosomeextentdefendedi ntheNotes.ItakethePror Analyticstobewhat Aristotlesaysiti s: atheoreticalprel i mi narytothe Posteror.Ital mostfol lowsfromthi sthatthedoctri nesofthePror weredevelopedafterthoseinthePosterorhadtakenatleasti ni ti alXI I IXIVINTRODUCTION shape.Infact,Ibel ievetheconnectiontakesamorei nteresting form.Aristotle'spurposei nthePosteor Analytcsisnotsi mpl ytopresenta viewof scientifcunderstandi ngbutalso,evenprimari ly,toshowthat i t i s the correct one.Thisleadshimto what Iwoul d regard asthemost origi nal andbri l l i anti nsightintheenti rework:Aristotlemadeproofs themselvesanobjectof studyinordertoanswerquestionsaboutthe possiblestructuresof demonstrativesciences.Thisiswhatledhimto developthetheoryofdeductionsi nthePror Analytics,ratheri nthe samewaythatHi l bert'sdesi retoresolvecertai nmathematicalquestions l edtohi s concept of proof theory.Theresul t isthatthecontents oftheProrAnalyticsarei nl argemeasuredesignedthroughoutwith theproof-theoreti c concerns of the Posteror i n mi nd.Pror AnaltAdescribesitself morethan onceashavingatripartite goal : todetermi ne'howeverydeductioncomesabout, ' todefnea ' route'(hodos)wherebydeductionsmaybefound, andtoexpl ai nhow totransformanygivendeductioni ntoadeduction' i nthefgures. 'Thefrst of theseprojectsisaccompl i shedi n Chapters1-26andthe secondin27-31(wi th31acommentonthei nadequacyof Platonic Divisionasanal ternativeprocedure). Thethi rdprojectoccupies 32-45( i tscompl etionisannouncedatthebegi nni ngof 46,51b3-5): Chapter 46 appearstobeal argelyi ndependent study wi thno obvious relationto therest of the Pror Analytics. ProrAnalyticsBi smoredi ffcul ttocharacterizewi thconfdence. Thei nternal structureofBookAmakesitappearthatAristotlehas achi evedallhisannouncedgoals,withtheexceptionofafewareas ( mostnotablyconcerni ngargumentsfromassumptions)whichhehas i ndicatedasneedi ngfurtherstudy.BookB,therefore,hasbeenseen asacollection of afterthoughts.Italsol ackstheperiodic statements of goalsandsummari es of accompl i shmentswhichmaketheorgani zation of Book Arel atively easy to see.Inaddi ti on, some of the contents of B (forinstanceB5-7,15)seemtobeformal or technical studi es withno real connectiontotheanalysis of arguments.Infuencedby aremark i n theTopics(VIII. 14,163a29-30), commentatorshavesometimesfavoredtheopi ni onthatAristotle'spurposeinmuchofBisasortof logical'gymnastics,' offeri ng exercises to develop the student'sfaci l i ty. Asanexplanationforthestudi esinBookB,thi sisveryunsati sfyi ng; itisalsounnecessary,fortherearebetteralternatives.Itryto showintheNotesthateachsectionofBookBservesoneoftwo purposes: ei therittriestoexpl ai nexistingtechnicalnotionsfromthe study of di alecticintermsof thetheoryof thefguresof Book A(and INTRODUCTIONX thus furtherstheproject of A 32-44 ),orituses the theory of fguresto answersomeproof-theoreticquestionraisedinthePosterorAnaltics (andthuscontributestotheoveral l goalofthePror Analytics).The frst of thesepurposesi s best i l l ustratedbythefnalChapters (22-27),buti tal soappliestoB16-18andtheshortnotesonargumentative practicei nB19-20.Thesecondpurposei sinevidencethroughout theabstractmetalogicalstudiesi nB2-15.Fori nstance,B5-7 providesthebackgroundforresolvingaquestionraisedinPosteror AnalyticsA3,whi leB2-4isi nspi redbyPosteror Analtics1.12.(There arealsoi nternalrelationsof dependencywi thi nBookBitself:B2-4, fori nstance,provides part of thebasis for B15,andboththese,inturn,arei mportanttoB21). Aparticul arlystri ki ngcasei sB21, whi. chi s paralleltoPosteror Analytics1.16-17butclearlyrefectsahigherlevel of developmentof Aristotle'stheoryof deducti on. (SeetheNotesfor detai led suggestions concerni ng specifc passages. ) Aristotle's Theor of Deduction.Therewasonceati me when Aristotle'slogic wasperceived(bothbyits adherents andbyits detractors) as aseriousrivaltomodernmathematicallogic.Thoseti mesareforthe most partpast.Interpretersnowi nvokethetechni quesandresul tsof symbolic logic asamatter of coursei ntryi ngtounderstandAristotle's deductivesystemandhi s viewsonlogicalquestions. Thi sisnottosay thatAristotlehasturnedouttobeamathematicallogici an: tothe contrary,muchrecent work has shown justhow di fferent hei s from hi s twentieth-centurycounterpartsi nmanyrespects.However,thedi sputewhetherlogiciansoughttotakeasthei rmodel PrncipiaMathematicaortheProrAnaltics-rrather,somereformul ati onofits doctrinesi nthestyleof 'tradi ti onal ' logic-hasnowbeenrepl acedin most quartersbytheprojectofunderstandi ng justwhatAristotleaccomplished.Thegreatrichnessandpowerofmodernformaltheories,together withthesubstantialunderstandi ngofthei rnaturesandproperti es whi chhasbeenaccumul atedoverthelastcentury,oftenpermi tusto seemoreclearlythepropertiesofAristotle'sownconstruction. Of course,cautionisnecessaryi n any suchi nterpretati on: Aristotle'sways of thi nki ng areoftenal i entomajor phi losophical currents of thetwentiethcentury,someti mesmuchmoresothanat frst appears.Iwilltry toofferaserviceableviewofAristotle'sdeductivesystemthrougha twenti eth-centurylens.Thecenterpieceof thattheoryisthesulogsmos:thededuction. (I XIINTRODUCTION avoidtheEngli shcognate'syllogi sm' forahostofreasons,mostcentrallythatithas cometohaveaset of associations qui teout of placei n transl ati ngori nterpreti ngAristotle. )Ari stotledefnesthi stermqui te generallyinawaythat woul d apply to a widerangeof validarguments. However,Pror AnalyticsA4-22deals onl y wi thamuchnarrower class of arguments,correspondi ng(atleasti n someapproximateway) tothe 'syllogi sms' of tradi tional logictexts:asulogimoscontainstwopremisesandaconcl usi on, eachof whichisa'categorical'sentence,witha totalofthreeters,oneof which(themiddle)occursineachpremi se butnotintheconcl usi on. Thisrestrictionisnotamatterof changei n defnition,si nceAristotlelatertakessomepainstoarguethatevery sulogmosisi nsomewayreducibletoanargumentfromthisnarrower class.(OneofthereasonsIavoidtranslating sulogmosas'syl logism'is toprevent givingthisi mportant claimtheappearanceof triviali ty. ) Thequestionjustwhata sulogismosisinmoderntermshasbeena matterofcontroversysinceLukasiewicz'spioneeringstudyArstotle's Sylogistic frmtheStandpoint of ModerForal Logic.Tradi ti onallogic hadtakensyl logi sms tobe arguments composedof severalstatements;Lukasiewicz arguedi nsteadthat a syllogism i s actually a certai n type of condi tionalproposi ti onalform, havingasitsantecedenttheconj unction of thepremises andasits consequent theconcl usi on. Hi s conceptiondi ffersfromthetradi tionalnotioni ntwoways:frst, i nregarding thesyllogismasasi nglestatement, andsecond, i nregardi ngi tas utterlydevoidofmaterialcontent, consistingonl yoffreetermvariablesandlogical constants.Hetheni nterpreted Aristotle'stheory as an axiomatizeddeductivesystemi nwhichthesyllogisticmoodsare theorems. Lukasiewicz's i nterpretation has not l acked either for strong adherents ( i ncl udi ngBochenskiandPatzig)orfordeterminedcri tics.Someof thesecri tics,whilegenerallyaccepti ngtheappropriatenessofreinterpretingAristotlei nmodernterms,haveneverthelessrejectedcertai naspectsofhisview.JohnCorcoranandTimothySmi leyhave proposedthatanAristotel i ansyllogismisbetterunderstoodasadeductionthanasaproposi ti on. Corcoraninparticularhasshownqui te clearlyhow,taki ngsyllogismstobedeductionsandrepresenti ngthe syllogisticasanaturaldeductionsystem, i tispossi bletogiveaformal modelnotonl yforAristotle'ssystembutalsofortheproofsheoffers for his resul ts.Lukasiewicz doestheformer,but notthelatter:i nstead, hepresupposesthewholeoftheproposi tionalcalcul usaspartofhis formalmodelandthenfaul tsAristotleforfai l i ngtorecogni zethi sas necessary. INTRODUCTIONXI IIwi l lnot attempt to resolvethi s controversyhere: readers who want aful l erpictureof just whatisatissueshouldconsul tthe worksi nthe Bibl iography.I nstead,Iwillpresentani nterpretationthatessenti al l y fol lowsCorcoran. One pri nci palvi rtue of Corcoran'sapproach, whi ch i s especiallyi mportanti nthecontext of atransl ati onof thePror Analytics,isthatitpermitsaformalmodelwhi chstaysvery closetoAri stotle'sactualtext,si nceital lowsustoreadformal l yprecisenatural deductions straight out of it. CategoricalSentences.Aristotle'stheoryofdeductionsreliesona theory of statements whichisonl y giveninbri ef termsintheAnaltics (i t is foundi n more complete form i n OnInterretation,al though Aristotledoesnotactuallyreferustothat account). Accordi ng tothat theory, everydeclarativesentence(logosapophantikos),orsentencecapableof beingtrueorfalse,isei theranafraton(kataphasi)oradeial (apophasis)orthecombinationof severalsuchsentences. Anaffrmationis asentenceinwhichapredicateisaffrmedofasubject,fori nstance, 'Socratesiswise, ''Platowalks' ; adenialisasentencei nwhicha predicateisdeni edofasubject, fori nstance,'Socratesisnotwi se, ''Platodoesnotwal k. ' Unl ikemodernformallogic,whichwouldtreat deni alsassententi allycompound( i . e. , thenegationsof afrmati ons),Aristotle regards them as structurally paral l elto affrmations.In thesentences just described, thepredicate andthesubject areof di fferentlogicaltype(thepredicatemustbeageneralterm, whereas thesubjectisasi ngul ar term). But Aristotleextendsthissameanalysis toanother classof sentences,i nwhichbothsubjectandpredicateare generaltermsandcertai naddi tionalsyntacticelementsappear.I n these cateorcal setences,as they aretradi ti onal l y cal l ed(though notby Aristotle), the subject may beaffrmed or denied ei ther of thewholeof thesubject(expressedbytheuseof'every'or'no' ) orofpartofi t (expressedby the use of 'some'or 'not every' ). Fori nstance,i f 'mortal' isaffrmedof thewhol e of'man,'wehavetheaffrmation' Everyman ismortal ' ; if i tisdeni edof thewhole,wehave'Nomani smortal' ;i f affrmed of a part, 'Somemani s mortal ' ;and i f deni ed of apart, 'Some manisnotmortal . ' (Thi sextensioni sbynomeansphi losophically unproblematicfromamodernpoi nt of view:seeGeach1972,44-61. ) Inaccordancewi thtradi ti on, wemayrepl ace'of thewhole'wi th' uni versal' and' of apart'wi th'particul ar'andcallaffrmationsanddeni als afratie andneatie sentences,respectively.Thi sthen gives us fournewtypesofcategoricalsentences: universalaffrmative,uni versal negative,particul araffrmative,andparticul arnegative.Iwillavai lXI I I INTRODUCTION myselfofanothervenerabletradi ti onandrefertothesefourtypes respectively as a, e, i,and o sentences. Ani mportantthesisof On Interretationisthat categorical sentences maybeassociatedi ntopai rsi nauni queway,suchthatexactlyone member of eachpairi strueandonefalse.Ari stotlecallssuchapaira 'contradiction'(antphai);followingmodernusage,Iwillsaythateach member of suchapai ri s the contradictoroftheother.Ingeneral,the contradictoryofacategoricalsentenceisacategoricalsentencehaving thesamesubjectandpredicateanddiferingonlyintype.Specifcally, anasentencehasasitscontradictorythecorrespondi ng osentence,and ane sentenceanisentence.Forexample,theasentence'Everymanis mortal'i s the contradictory of theo sentence'Somemanisnot mortal , 'whi l e the e sentence' No manismortal'and the i sentence'Someman ismortal'arecontradictoriesof oneanother.Itshouldal so benoted thatAristotleregardscorrespondi ngaande sentencesasi nconsistent, thoughnot contradictori es: bothcannotbetruetogether,though both may befalse. The exampl es givenso far refect Aristotle'sanalysisi n On Interretation.However,i nthePror Analtics,henormallymakesuseof adi fferent (andqui teartifci al )i di omforexpressi ngcategoricalsentences. I n placeof 'Every Xis Y, 'he says'Ybelongstoevery X'(andsi mi larly fortheremai ni ngcategoricals). Itshouldalsobenotedthatheregul arl y uses twoforms forparticul ar negatives: 'not to every'and'not to some. 'Eventhoughhetreatstheseasequival entforms,Ari stotle someti mescarriesanargumentthroughtwice,frsti nvol vingoneof the forms andthenwiththeother form substituted for i t.The Figures.The system which Aristotle studi es i nvestigates deductionshavingaspremisestwocategoricalsentenceswhichshareone term.Thiscanhappeni nthreeways:thetermi ncommonmaybe subj ectof onepremiseandpredicateoftheother,predicateof both premises,or subject of both. Aristotlerefersto each of theseasa figure (schema)andcallsthetermwhichbothpremisessharethemiddle (meson) andthe other two terms etremes(okra).If themi ddleissubject of onepremi seandpredicateof theother,thepremisesarei nthe frt fgre;ifitispredicateofboth, i nthesecond fgure;i fitissubjectof both, the thirdfgure. Asdescribed,thesethreefguresrepresentanexhaustiveclassifcationofpremi sepai rs: i ftwocategoricalsentencesshareexactlyone INTRODUCTIONXIX term,thenthattermmustbepredicateofboth, subjectofboth, or predicateofoneandsubjectoftheother.However,therei sacomplication. Forthosecasesi nwhichthereisaconcl usi on, Ari stotle normallystatesthepremi sesi nafxedorder: thatpremisewhi ch containsthepredicateof the conclusionisfrst. Consequently,hehas special designations for each of the extremes and each of thepremi ses:theextremewhi chappearsaspredicateof theconcl usi on, andthereforei nthefrstpremi se,isthe major extreme(mezon akron),or si mply the firt(rton),andthecorrespondi ngpremiseisthemajor premise, whiletheothertermistheminor etreme(eatonakron),orthethird (trton)orlast(eschaton).Theprecisewayi nwhichAristotledefnes these terms isunclear andperhaps confused (see the di scussionsi n the Notes concerni ng the defni tion of each fgure).In A4-6,Aristotleexami nesvariouscombi nationsof twopremises havi ngexactlyonetermi ncommonanddeterminesforeachpair whether adeductionhavingathi rdcategoricalsentenceasconcl usi on ispossible.Whenadeductionispossible,heprovesthisfactbytel l i ng ushowtoconstruct one.Whenadeductionisnotpossi bl e, heproves thisfactbyofferi ngacountermodel, thatis, concreteexamplesto showthatpremisesoftherelevanttypesareconsi stentwi thany conceivabletypeof concl usi on. Letusfrstconsiderthestructureof his deductivesystem, usi ng aformalmodeli nthestyleof mathematical logic, andthen turn to hi s countermodel techni que.AForalModel.Asi mpl emodelforAristotle'stheorymaybeconstructed asfol lows.Takeasthepri mi ti vesymbols the constants a, e, i, o and asupply of variables A,B,C,. . . (itmakes no di fferenceforthis exposition whether the supply of variablesisfni teor i nfni te: Aristotle wouldarguethati tmustbefni te). A sentenceof thesystemi sastring consi sti ng of avariable,aconstant, anda(di sti nct)variable,forexample,AaC,DiA.Thefrstvariablei nasentenceisitspredicate,the seconditssubject(obviously,theseformulashaveastheiri ntended i nterpretationthecategoricalsentencesdi scussedabove). Weal so need adefni ti on of the contradictor ofas fol l ows: 1.The contradictory of AaBis AoB 2.The contradictory of AeB is AiB 3.Thecontradictoryofthecontradictoryof asentenceisthatsentenceitself. XINTRODUCTION Final ly,weneedaset of converion inferece rles: 4.BeA=>AeB 5. BiA =>AiB 6.BaA=>AiB Wemaynowdefneadeductionasfollows.First,wedefnecomplete deduction.Acompletedeductionisanysubstitutioni nstanceof anyof thefol lowi ng(Iuse'1'toseparatetheconclusionof adeductionfrom itspremises):7. AaB,BaG 8.AeB,BaG 9.AaB,BiG 10. AeB,BiG 1AaG 1Ae 1AiG 1AoG (Barbara) (Gearent) (Dari) (Fero) 7-10areof coursethefour frst-fguremoods(Ihaveaddedthetraditionalmedievalmnemoni cnamesforconveni ence:seethedi scussion i n Appendi x 1).Wenowdefne completed deduction:Acompleteddeductionisasequencesl ... snof sentenceswhichmeetsei therofthe fol lowi ng condi ti ons:I . For eachi such that 2