« * DE INTERPR.XII-XIV: SUMMARY XXIII I. ‘Pos¬ verbs answer ‘falsely’‘how?’ [3]. determineand sibly’ the question ‘... ‘truly’ ‘...can’), doesand not’), that’) called .(= ‘it is wrongly modesbyclauses [4-6]. (=tlebecause their Aristo¬ are of positioninflectable) modes Nominal winch be resolved (= true (“casuales” in modal biales(proper)kindscan casualesmodes: four of secundum[7]. “adver¬ adverbs; and secundum positionem chose ‘possible’ into sensum Aristotle cquipollence modes andrelated ‘necessary’each“ ”, four ‘im¬ ‘pos¬ -- X1I-X1V “ possible’(essentiallyby and ” “ [8], eachother), interpretatione= ” other different ” sible’ ‘contingent’ reducedand because CHAPTERS fromchose be modes Abailard’sprinted Abai¬ and : firstOF THE COMMENTARYthe volume whichnominal they SUMMARY ON half can give Thewhole of breaks present De contains adverbial modes thelard’s 3.1-29.15).offchaptersabout Geyer’s through He adverbial modes 497.20 in rise and affirmations, predicate,and commentary edition 483.30-has to alwaysnegationsthan modes introductionSince way (pp. uncertainty predicatewhile nominal brackets determinationsdeterminations(i.e. to the the secundum of : predicate text numbers editionsquare paragraphs the of more [9-11].this portion followingThewith on refer grammatically), subjectare beingsensum whichin whole “ secundum partly a be found the divided our the [12], modal have are but theto the constructionemcase”, con¬ proposi¬ Acommon summarythein to twoare stitutedby differ adverbialnominal chapters chapters two propositions“ thanThus modal includes modifiedverb The three these chapters, ” hi to propositions,the introductoryto ARISTOTLE’S thoseconsiderationsubject [13-14]; and gram¬ (“ we problems de in deserve,dealing the intotreatise modalII. PRELIMINARIESdeals I. (‘de inesse =and chapter tionsseparatefrom quantifiedsyllogisms, The modalproper,[15];therefore, be (simple which Aristotlethe the arisinga puro nominalwhen proposition ”) modal text. matical,more of ”, subject considermixed subject III. does [16]. subject xn-xiv. commentary xu-ÿÿÿ, to [1-2].[1]. grammaticalAristotlesimple with propositions; withpropositions. “ contraposition)simple canunlessincisi comparablethe oncommentaryDIFFERENT a as on usedoft of modal of inesse’)concerning [2],op simple those propositions,subject [17].proper deal by conversionstheall-containingfail examplesis as XII commentary Aristotle their propositionssuggested some does, with is in modal propositions Modal propositions, when used; A. contrary on fallaciousnotfailures with to Whyand puro as by I. [3-17], nor here, “PERSONAL”; (“ propositions [1-93]. other due Abailard modal are or ; propositionstwo out Conversions I. in “DE apparent an modes not I. on which B. MODES;Proper adverbs arguments SUBJECT, PREDICATE, FOUR MODES; RE”,I. are THEIR RELEVANCE term ANALYSES ” xiii QUANTIFICATION, MODALOR PROPOSITIONS PER OF to C. DIVISIONEM CONVERTIBILITY : are “ ANDDE TO Two E. xiv

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- < » ¡i XXIV INTRODUCTION INTERPR.DE XII-XIV: SUMMARY XXV SENSU”, “PER “IMPERSONAL”);I. EQUIPOLLENCE OR [18-32], I. [33-39],Aristotle CONPOSITIONEM” D. BETWEENNON-QUANTIFIED thechosemodes PROBLEMS Modal PROPOSITIONS MODAL [33]. ON IMPERSONALanalysedPROPOSITIONS(“ ”) each propositions be exponi as sayingsome¬ related other de and LE. (“ “ sensumost i' eithercan thing ”)subject (“ each has ‘possible’ thing of de of Taken necessary’modereeach subject,affirmationand implies thea the aconsists ofthede to as sensu! ”” “de” one and possible’‘not ‘necessary’ sensu”):referring firsttiling, or predicate word negation for [34], (verbin the case re and the sentence is compound “de ‘not implies (“mood), the thus being divided one of the thing the the theretheir equipollences verb per divisionem ”) the second(“ fromthe [19], of contrary, affirmationsTaken as + plus [18];case asmany andnegations; twice [35], the subject of re [36-37],tableare each the thingtothe verbis thepredicate reallyconpositionemexample contrary wherethe Aristotelian the ordersimplies and is in per name ”), quan¬ “de proposition” of different[38],fourareorder the propositionsthe be orders other mood an modal, threeevery and bound by [39], - impersonal- De in rules Inferenceis together tifiedpersonalproperly [20-22],(while reducibleimpersonals set secundum sensu only; clumsypersonals) and“ appli¬ definite here naturalem [23], in are“secundumEQUIPOLLENCE ” converted,are other out [40-46],consequentiam necessity-of-not-beingor reducedPriscian’s[24],anot way cannotPropositions comitationem personals convertible impersonals ”, be are Limitedabout affirmative in resolution available [25]. “ quantified subjectof Usual of clause- subject,There four andfor eachequipollence [40], for pre¬ PRO¬ four can Impersonal impersonal the negative propositions” [41], mode cation modal propositions I.POSITIONS BETWEENdistributed eight orders conversionssubject, and QUANTIFIEDare particular of are de the notE. MODAL Fallaciesof to ‘possible’,predicates,‘necessary’,‘p’ossibileallow [27], [26]; four universal, propositionsall some sensu eachof quantifiedand having” propositionsrelation dicatenecessaryto for may statedthis ‘est’ fourre of the whileimpersonalsintoAristotle group ofordersfour failures asconfusionthe fai¬ fact thisinhere the seemas ‘true’ “de failures[42-43]; byseems[28-29], quantified between “ est’) ” be in due [44-45],INFERENTIAL validimpersonal, when andpeculiarde same[46], king hand, reallyma¬itself de which(“ other [30],impersonalconditionin is for argumentations,andpropositions; similar RE” proposition(‘good’,predication the inferences personalparticularization, universalization modal propositionsnon- tire to doesnot ‘necessary’ [31], sensu de ”) do‘possible’accompanied apparentlures intellectus “DE [47] bea etc.),to predicatingim¬ propositionsin Meaning some ofvice in adjectives used óf A infiniti¬ re de are [47-54], may ‘useful’,and be to impersonal proposi¬ and ‘possible’is ‘impossible’ still signify admit On concipiendi’by “ ” in “DEsensu and (examples co-signify, subject though in implies sense)while only - F. [48-49]). bring [32], ” “ “ to “ versa etc.,forname; forms, same I. de the the the de oneBETWEEN tionsthe Someandthem, aboutinfinitive‘modusand ” referenceRELATIONS” Affirmation leads [50]; (in Priscian’sis Becauseof modal propositions negation of invalid Modals ” notthe : re things changing the ves accusative?(= must - de Why a different modals AND or not SENSU temporal sensu is transitive to ” PROPOSITIONSre sensu not same “ ”, “determination connectionin “ contraryMODAL with with not are or are apparent in from ” timeor

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- — · » XXVI INTRODUCTION DE XXVII [51]. failures INTERPR.XII-XIV: SUMMARY failure [52].inferences I. Possible posedof Other apparent ‘necessary’ex¬ applicationthe distinctionbetween consequence[74]. ‘post’ Affirmation (ornegation) of ‘Ante’ implies (or of “de‘necessary’ and [75]. and [53]. affirmation negation)of modals in Validity[54], ‘necesse de ex “ propositions” Necessity determinations [76-83]. sensu‘inpossibile’ of inference “ actu ” modalex natura ” from “ non’ with ‘necessary’: re” meanings of‘necessary’the Three [76]. [55- affected ‘possible’,meaning when — MODAL by occurs is thedeterminationapparently to [77-78].and differentCom¬ behaviour 93]. proposi¬ [56] parison with ‘Necessary’implies G. clause intrasumpta”DETERMINATIONSmodalsubject propo¬ true impossible implies I. is [55];PROPOSITIONS the the the ‘possible’deter¬ a WITH of usually (unless is [79]. itself the clausesverband has as verb implied of and thedoes [80],imply does Determinadoof with different ofits the determination“while ‘et’- determining[57-58] a be verbs ”, real contrary necessity tionby“ their a taken . implication mination other,imply temporalModal[81] determined [82]. sition negative)of extrasumptasamemodal [59]. boththis any negation ‘quando’-value,necessity Truthtruth propositionsBoethius confines the verifiesvalue, the two ‘dum’ The temporals[83]. “ implies, are implied Difference determined possibility ‘necessary’” [60], of modalsa modals determi¬[84-86]. determinado ; modal isproposition dal between mo¬‘not-being intrasumpta not Determined and about “ determination A round . make propositions with in by, the without Modalto butother - (i. Modes not of withanalysed hypotheticalthe[61], determined If the of plus propositionstemporalsway plus preted temporal-hypothetical,them [84-85]. simplecase determination;necessity) possibility; not ‘dum...’falsesamecategorical[62]. in othetical withoutsometimes‘being’; equipollenceinter¬ ‘im¬ by nations, sometimesthoseaffect Inferencetheyfollow ‘non’the [86].‘necessary’ [63],as” as possible’ if ‘possible’ modals to compoundsproblem‘Et’ modal a and the maythebetween determined modalof for non-hyp Aÿand asmodal, pattern may the [87- fact for the secondsubject-infinitivese. subjects of about determination93].as astogether with and a shbject them true,propositionthe well This[87-90], de¬ [64-75].propositions,betweena not as statingeither [64], is of a the makespossibleof rules possibleof doubles ‘A possible of [93]). ‘A ‘A the be [91-92] (allowing proposition always non-A’)non-A’[65-66]. The prove‘only’ the sense), is (in also be (the non-determinedthose because truewhileimplies ‘non-A’ theseor for or modals therest as COMMENTARY be [67-68]. non-A’ truly valid rules be somehow absurdity trueis termined exception absurd,that[69].onlyomnitemporalor and infinitiveswhen [70]. by with cases of one for temporalinfinitives seems ‘et’-[71-72], two for true may pro¬ [94]. Real validDifference possible present- not same is forimplies ‘dum’ without That [94-129]. value present a andclausethe [73]. proposition two after between‘A past in ‘Dum’this analysed Uniqueness [95]. this A to Commentary precedesbetween to two futureis determiningto Aristotle’s future is for consequences whatfor presentwhilenon-A’ of II. a a [94-198]. accepting when A. modal Sum¬ or chapters follows positions ofof with what Conditionthe PROPOSITIONS on present;not what ConnectionNEGATION II. section MODALmaryon CHAPTER OF a ON argument XII into - text true : xii-xm,

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- — . — XII-XIV: SUMMARY I. «DE INTERPR. XXIX XXVIII COMMENTARY INTRODUCTIONrule — general for propositions BE¬ corrects The making negative [96-106]. II. INFERENCES [130-198].Aristotle ‘necesse’ B. CHAPTERwrong inferences possibile ‘esse’ ‘non-esse’ ON xm: between and [130-160], rule according[96]. TWEEN PROPOSITIONS ’ The which is the MODAL (‘non’ negation ‘inferences by of Right and interpretation the[97].rule Order [130],Aristotle for the purpose wrongattached copula)of of provisionallyattachedto does distinguish Aristotle [98] criticizingAristotle’sset between right of sections[131], of [132], [99] between examples Connectionabove and here Aristotleconcernedis ‘pos¬ indiscriminate and [100], out mistakes Details‘necessary’ Aristotle’swith interpretation,simpleor and gives predicatewrong both it •correcting‘Possible’ equipollent,[133]. to place sible’ of contrarily[134] ‘non’not [101]. compound compound- and ‘impossible’,contradictorily [135]. withthepredicatesa beand Explanation not [102], a the text: and ‘contradictorily’ ‘contrarily’ [136]. Alterna¬ [103-105], consciously ‘non’,How- text rightwrong in whateverexplained. are ‘possible’and ‘impossible’ [148— clusionsverb applicationAristotle position‘possible’:of draws‘possible’his [106]. of ‘possible’explained between [137-139]. can putesse’in of rule esse’ passegesexposed meanings Relation‘necessary’ tila The of of [140]. compared wordswrong [107-115]. tive and with ‘PossibileWrongnegation between con¬ [107]. relationandconversim [141-145].Aristotle’s analysed to between” Mean¬ [147]. and [146]. and [161— on and be[108-110]; “ of“ Express passages ‘non always. interpreted of the esse’ Connection by [111-112], inferencesanalysis Aristotle’s fault actualfactallows be both ing Logical ‘necesse [113-114].is the verb is Analysis 151]. esse’arguments[152-153]. proofesse’ inconsistencyesse’ Properthat mentionedcan [115]. ‘Necesseof syllogism The Aristotle’swhatnegationsnegativesyllogism modal butapplicationesse’ orderof of in [154-155];esse’[157-160], the be two togetherimpossibiliuspropositions of ‘necesse used by necessary ‘possibile possibile ” the ‘possibile [156]. possible ofesse’:of [116].of possibileConnectionof kind implicationand rule [117].true [116-129]. Simil¬ stotle about Ari¬ also by contrariesof about of ‘non Meaning ‘non [118]. extra Discussionstatement Doubtsfollows only arly of wrong because follow of proved esse’ [119]). be gationalwaysfor other true predicatenot Ne¬ do 166]. est Thisused “ modals “ [120].‘non’ what¬ from implication [162], esse’ of to two (Alternative starting ‘possible’non [161]. estthis ‘ ‘pos¬ attached“determinantes Aristotle‘possible’,had this ambivalence cannotbe[121]. predicateesse’This, ” ‘necessary’precedes ‘possible meaning true possibile[122].esse’ can possible’previous ‘neces¬ ” the [123-124];. non ‘possible’, does of Alter¬ non est ‘necessary’[163].the esse’ whole ‘possibilethe becomes ‘Possibilethe how ’ a is the is attached, be¬ can agree if [164]. of [127], ‘possibilepassages with in alsoimplyof‘possibile’[165-166]. al¬ propositionaffirmative;applies veritatemAristotle’snegation ‘non[125-126]. it reasons for imply whatof drat [167-198], [128-129]. is sible shouldSolution‘not should ‘Ne¬ negativenegativebetween To relation sary’doesdoubt:not’implycesse’with meanings imply part its not doubts:possibility‘possibile’, ever of ” Aristotle’s argument: Connectionthat justified: neitherjustified: ruleinterpretations modals must iffollows Second[167]. and general possibile modals other Explanation of non. not’; does reason is implyFirst or ‘non negative this native Connection nonThe between Therule for of Two imply reason to ‘ ’ ambivalent and words ways of it not est est it but ’ non it tween - Connection‘ account to cannot

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