Authors/Thomas Aquinas/perihermenias/perihermenias II/L10

LECTURE 10

Latin	English
Cajetanus lib. 2 l. 10 n. 1 Postquam determinavit de oppositione modalium, hic determinare intendit de consequentiis earum. Et circa hoc duo facit: primo, tradit veritatem; secundo, movet quandam dubitationem circa determinata; ibi: dubitabit autem et cetera. Circa primum duo facit: primo, ponit consequentias earum secundum opinionem aliorum; secundo, examinando et corrigendo dictam opinionem, determinat veritatem; ibi: ergo impossibile et cetera.	1. Having established the opposition of modals, Aristotle now intends to determine their consequents. He first presents the true doctrine; then, he raises a difficulty where he says, But it may be questioned whether "Possible to be follows upon "necessary to be,” etc. In presenting the true doctrine, he first posits the consequents of the opposition of modals according to the opinion of others; secondly, he determines the truth by examining and correcting their opinion, where he says, Now the impossible and the not impossible follow contradictorily upon the contingent and the possible and the not contingent and the not possible, but inversely, etc.
Cajetanus lib. 2 l. 10 n. 2 Quoad primum considerandum est quod cum quilibet modus faciat duas affirmationes, ut dictum fuit, et duabus affirmationibus opponantur duae negationes, ut etiam dictum fuit in primo; secundum quemlibet modum fient quatuor enunciationes, duae scilicet affirmativae et duae negativae. Cum autem modi sint quatuor, efficientur sexdecim modales: quaternarius enim in seipsum ductus sexdecim constituit. Et quoniam apud omnes, quaelibet cuiusque modi, undecumque incipias, habet unam tantum cuiusque modi se consequentem, ideo ad assignandas consequentias modalium, singulas ex singulis modis accipere oportet et ad consequentiae ordinem inter se adunare.	2. Before we consider these consequents according to the opinion of others, we must first note that since any mode makes two affirmations and there are two negations opposed to these, there will be four enunciations according to any one mode, two affirmatives and two negatives. And since there are four modes, there will be sixteen modals. Among these sixteen, anyone of each mode, from wherever you begin, has only one of each mode following upon it. Hence, to assign the consequents of the modals, we have to take one from each mode and arrange them among themselves to form an order of consequents.
Cajetanus lib. 2 l. 10 n. 3 Et hoc modo fecerunt antiqui, de quibus inquit Aristoteles: consequentiae vero fiunt secundum infrascriptum ordinem, antiquis ita ponentibus. Formaverunt enim quatuor ordines modalium, in quorum quolibet omnes quae se consequuntur collocaverunt. Ut autem confusio vitetur, vocetur, cum Averroe, de caetero, in quolibet modo, affirmativa de dicto, et modo, affirmativa simplex; affirmativa autem de modo et negativa de dicto, affirmativa declinata; negativa vero de modo et non dicto, negativa simplex; negativa autem de utroque, negativa declinata: ita quod modi affirmationem vel negationem simplicitas, dicti vero declinatio denominet. Dixerunt ergo antiqui quod affirmationem simplicem de possibili, scilicet, possibile est esse, sequitur affirmativa simplex de contingenti, scilicet, contingens est esse (contingens enim convertitur cum possibili); et negativa simplex de impossibili, scilicet, non impossibile esse; et similiter negativa simplex de necessario, scilicet, non necesse est esse. Et hic est primus ordo modalium consequentium se. In secundo autem dixerunt quod affirmativas declinatas de possibili et contingenti, scilicet, possibile non esse, et, contingens non esse, sequuntur negativae declinatae de necessario et impossibili, scilicet, non necessarium non esse, et, non impossibile non esse. In tertio vero ordine dixerunt quod negativas simplices de possibili et contingenti, scilicet, non possibile esse, non contingens esse, sequuntur affirmativa declinata de necessario, scilicet, necesse non esse, et affirmativa simplex de impossibili, scilicet, impossibile esse. In quarto demum ordine dixerunt quod negativas declinatas de possibili et contingenti, scilicet, non possibile non esse, et, non contingens non esse, sequuntur affirmativa simplex de necessario, scilicet, necesse esse, et affirmativa declinata de impossibili, scilicet, impossibile est non esse.	3. The modals were ordered in this way by the ancients. They disposed them in four orders placing together in each order those that were a consequent to each other. Aristotle speaks of this order when he says, Logical consequents follow according to the order in the table below, which is the way in which the ancients posited them. Henceforth, however, to avoid confusion let us call the affirmative of dictum and mode in any one mode, the simple affirmative, as it is by Averroes, among others; affirmative of mode and negative of dictum, the declined affirmative; negative of mode and not of dictum, the simple negative; negative of both mode and dictum, the declined negative. Hence, simplicity of mode designates affirmation or negation, and so, too, does declination of dictum. The ancients said, then, that simple affirmation of the contingent, i.e., "contingent to be” follows upon simple affirmation of the possible, i.e., "Possible to be” (for the contingent is converted with the possible); the simple negative of the impossible also follows upon this, i.e., "not impossible to be”; and the simple negative of the necessary, i.e., "not necessary to be.” This is the first order of modal consequents. In the second order they said that the declined negatives of the necessary and impossible, i.e., "not necessary not to be” and "not impossible not to be,” follow upon the declined affirmative of the possible and the contingent, i.e., "possible not to be” and "contingent not to be.” In the third order, according to them, the declined affirmative of the necessary, i.e., "necessary not to be,” and the simple affirmative of of the impossible, i.e., "impossible to be,” follow upon the simple negatives of the possible and the contingent, i.e., "not possible to be” and not contingent to be.” Finally, in the fourth order, the simple affirmative of the necessary, i.e., "necessary to be,” and the declined affirmative of the impossible, i.e., "impossible not to be,” follow upon the declined negatives of the possible and the contingent, i.e., "not possible not to be” and "not contingent not to be.”
Cajetanus lib. 2 l. 10 n. 4 Consideretur autem ex subscriptione appositae figurae, quemadmodum dicimus, ut clarius elucescat depictum. Consequentiae enunciationum modalium secundum quatuor ordines ab antiquis positae et ordinatae. (Figura).	4. To make this ordering more evident, let us consider it with the help of the following table. CONSEQUENTS OF MODAL ENUNCIATIONS IN THE FOUR ORDERS POSITED AND ORDERED BY THE ANCIENTS FIRST ORDER It is possible to be It is contingent to be It is not impossible to be It is not necessary to be SECOND ORDER It is possible not to be It is contingent not to be It is not impossible not to be It is not necessary not to be It is not possible to be It is not contingent to be It is impossible to be It is necessary not to be FOURTH ORDER It is not possible not to be It is not contingent not to be It is impossible not to be It is necessary to be
Cajetanus lib. 2 l. 10 n. 5 Deinde cum dicit: ergo impossibile et non impossibile etc., examinando dictam opinionem, determinat veritatem. Et circa hoc duo facit: quia primo examinat consequentias earum de impossibili; secundo, illarum de necessario; ibi: necessarium autem et cetera. Unde ex praemissa opinione concludens et approbans, dicit: ergo istae, scilicet, impossibile, et, non impossibile, sequuntur illas, scilicet, contingens et possibile, non contingens, et, non possibile, sequuntur, inquam, contradictorie, idest ita ut contradictoriae de impossibili contradictorias de possibili et contingenti consequantur, sed conversim, idest, sed non ita quod affirmatio affirmationem et negatio negationem sequatur, sed conversim, scilicet, quod affirmationem negatio et negationem affirmatio. Et explanans hoc ait: illud enim quod est possibile esse, idest affirmationem possibilis negatio sequitur impossibilis, idest, non impossibile esse; negationem vero possibilis affirmatio sequitur impossibilis. Illud enim quod est, non possibile esse, sequitur ista, impossibile est esse; haec autem, scilicet, impossibile esse, affirmatio est; illa vero, scilicet, non possibile esse, negatio est: hic siquidem modus negatur; ibi, non. Bene igitur dixerunt antiqui in quolibet ordine quoad consequentias illarum de impossibili, quia, ut in suprascripta figura apparet, semper ex affirmatione possibilis negationem impossibilis, et ex negatione possibilis affirmationem impossibilis inferunt.	5. When he says, Now the impossible and the not impossible follow contradictorily upon the contingent and the possible and the not contingent and the not possible, but inversely, etc., he determines the truth by examining the foresaid opinion. First, he examines the consequents of enunciations predicating impossibility; secondly, those predicating necessity, where he says, Now we must consider how enunciations predicating necessity are related to these, etc. From the opinion advanced, then, he concludes with approval that the impossible and the not impossible follow upon the contingent and the possible and the not contingent and the not possible, contradictorily, i.e., the contradictories of the impossible follow upon the contradictories of the possible and the contingent, but inversely, i.e., not so that affirmation follows upon affirmation and negation upon negation, but inversely, i.e., negation follows upon affirmation and affirmation upon negation. He explains this when he says, The negation of "impossible to be” follows upon "possible to be,” i.e., the negation of the impossible, i.e., "not impossible to be,” follows upon the affirmation of the possible, and the affirmation of the impossible follows upon the negation of the possible. For the affirmation, "impossible to be” follows upon the negation, "not possible to be.” In the latter the mode is negated, in the former it is not. Therefore, the ancients were right in saying that in any order, the consequences of enunciations predicating impossibility are as follows: from affirmation of the possible, negation of the impossible is inferred; and from negation of the possible, affirmation of the impossible is inferred. This is apparent in the diagram.
Cajetanus lib. 2 l. 10 n. 6 Deinde cum dicit: necessarium autem etc., intendit examinando determinare consequentias de necessario. Et circa hoc duo facit: primo examinat dicta antiquorum; secundo, determinat veritatem intentam; ibi: at vero neque necessarium et cetera. Circa primum quatuor facit. Primo, declarat quid bene et quid male dictum sit ab antiquis in hac re. Ubi attendendum est quod cum quatuor sint enunciationes de necessario, ut dictum est, differentes inter se secundum quantitatem et qualitatem, adeo ut unam integrent figuram oppositionis iuxta morem illarum de inesse; duae earum sunt contrariae inter se, duae autem illis contrariis contradictoriae, ut patet in hac figura. (Figura). Quia ergo antiqui universales contrarias bene intulerunt ex aliis, contradictorias autem earum, scilicet particulares, male intulerunt; ideo dicit quod considerandum restat de his, quae sunt de necessario, qualiter se habeant in consequendo illas de possibili et non possibili. Manifestum est autem ex dicendis quod non eodem modo istae de necessario illas de possibili consequuntur, quo easdem sequuntur illae de impossibili. Nam omnes enunciationes de impossibili recte illatae sunt ab antiquis. Enunciationes autem de necessario non omnes recte inferuntur: sed duae earum, quae sunt contrariae, scilicet, necesse est esse, et, necesse est non esse, sequuntur, idest recta consequentia deducuntur ab antiquis, in tertio scilicet et quarto ordine; reliquae autem duae de necessario, scilicet, non necesse non esse, et, non necesse esse, quae sunt contradictoriae supradictis, sunt extra consequentias illarum, in secundo scilicet et primo ordine. Unde antiqui in tertio et quarto ordine omnia recte fecerunt; in primo autem et in secundo peccaverunt, non quoad omnia, sed quoad enunciationes de necessario tantum.	6. When he says, Now we must consider how enunciations predicating necessity are related to these, etc., he proposes an examination of the consequents of enunciations predicating necessity in order to determine the truth about them. First he examines what was said by the ancients; secondly, he determines the truth, where he says, But in fact neither " necessary to be” nor "necessary not to be” follow upon "possible to be,” etc. In his examination of the ancients, Aristotle makes four points. First, he shows what was well said by the ancients and what was badly said. It must be noted in regard to this that, as we have said, there are four enunciations predicating necessity, which differ among themselves in quantity and quality, and hence they make up a diagram of opposition in the manner of the absolute enunciations. Two of them are contrary to each other, and two are contradictory to these contraries, as is clear in the diagram below. necessary to be contraries necessary not to be not necessary not to be subcontraries not necessary to be Now the ancients correctly inferred the universal contraries from the possibles, contingents, and impossibles, but incorrectly inferred their contradictories, namely, particulars. This is the reason Aristotle says that it remains to be considered how enunciations predicating necessity are related consequentially to the possible and not possible. From what Aristotle says, it is clear that those predicating necessity do not follow upon the possibles in the same way as those predicating impossibility follow upon the possibles, for all of the enunciations predicating impossibility were correctly inferred by the ancients, but those predicating necessity were not. Two of them, the contraries, "necessary to be” and "necessary not to be,” follow, i.e., correct consequents were deduced by the ancients in the third and fourth orders; the remaining two, "not necessary not to be” and "not necessary to be,” which are contradictories of the contraries, are outside of the consequents of these, i.e., in the second and first orders. Hence, the ancients represented everything correctly in the third and fourth orders, but in the first and second they erred, not with respect to all things, but only with respect to enunciations predicating necessity.
Cajetanus lib. 2 l. 10 n. 7 Secundo cum dicit: non enim est negatio eius etc., respondet cuidam tacitae obiectioni, qua defendi posset consequentia enunciationis de necessario in primo ordine ab antiquis facta. Est autem obiectio tacita talis. Non possibile esse, et, necesse non esse, convertibiliter se sequuntur in tertio ordine iam approbato; ergo, possibile esse, et, non necesse esse, invicem se sequi debent in primo ordine. Tenet consequentia: quia duorum convertibiliter se sequentium contradictoria mutuo se sequuntur; sed illae duae tertii ordinis convertibiliter se sequuntur, et istae duae primi ordinis sunt earum contradictoriae; ergo istae primi ordinis, scilicet, possibile esse, et, non necesse esse, mutuo se sequuntur. Huic, inquam, obiectioni respondet Aristoteles hic interimendo minorem quoad hoc quod assumit, quod scilicet necessaria primi ordinis et necessaria tertii ordinis sunt contradictoriae. Unde dicit: non enim est negatio eius quod est, necesse non esse (quae erat in tertio ordine), illa quae dicit, non necesse est esse, quae sita erat in primo ordine. Et causam subdit, quia contingit utrasque simul esse veras in eodem; quod contradictoriis repugnat. Illud enim idem, quod est necessarium non esse, non est necessarium esse. Necessarium siquidem est hominem non esse lignum et non necessarium est hominem esse lignum. Adverte quod, ut infra patebit, istae duae de necessario, quas posuerunt antiqui in primo et tertio ordine, sunt subalternae (et ideo sunt simul verae), et deberent esse contradictoriae; et ideo erraverunt antiqui.	7. Secondly, he says, For the negation of "necessary not to be” is not "not necessary to be,” since both may be true of the same subject, etc. Here he replies to a tacit objection. This reply could be used to defend the consequent of the enunciation of the necessary made by the ancients in the first order. The tacit objection is this: "not possible to be” and "necessary not to be” follow convertibly in the third order which has already been shown to be correct; therefore, "possible to be” and "not necessary to be” ought to follow upon each other in the first order. The consequent holds; for the contradictories of two that convertibly follow upon each other, mutually follow upon each other; but those two follow upon each other convertibly in the third order and these two in the first order are their contradictories; therefore, those of the first order, i.e., "possible to be” and "not necessary to be,” mutually follow upon each other. Aristotle replies here to this objection by destroying what was assumed in the minor, i.e., that the necessary of the first order and the necessary of the third order are contradictories. He says, For the negation of "necessary not to be” (which is in the third order) is not "not necessary to be” (which has been placed in the first order). He also gives the reason: it is possible for both to be true at once of the same subject, which is repugnant to contradictories. For the same thing which is necessary not to be, is not necessary to be; for example, it is necessary that man not be wood and it is not necessary that man be wood. Notice, as will be clear later, that these two which the ancients posited in the first and third orders, are subalterns and therefore are at once true, whereas they should be contradictories; hence the ancients were in error.
Cajetanus lib. 2 l. 10 n. 8 Boethius autem et Averroes non reprehensive legunt tam hanc, quam praecedentem textus particulam, sed narrative utramque simul iungentes. Narrare enim aiunt Aristotelem qualitatem suprascriptae figurae quoad consequentiam illarum de necessario, postquam narravit quo modo se habuerint illae de impossibili, et dicere quod secundum praescriptam figuram non eodem modo sequuntur illas de possibili illae de necessario, quo sequuntur illae de impossibili. Nam contradictorias de possibili contradictoriae de impossibili sequuntur, licet conversim; contradictoriae autem de necessario non dicuntur sequi illas contradictorias de possibili, sed potius eas sequi dicuntur contrariae de necessario: non inter se contrariae, sed hoc modo, quod affirmationem possibilis negatio de necessario sequi dicitur, negationem vero possibilis non affirmatio de necessario sequi ponitur, quae sit contradictoria illi negativae quae ponebatur sequi ad possibilem, sed talis affirmationis de necessario contrario. Et quod hoc ita fiat in illa figura ut dicimus, patet ex primo et tertio ordine, quorum capita sunt negatio et affirmatio possibilis, et extrema sunt, non necesse esse, et, necesse non esse. Hae siquidem non sunt contradictoriae. Non enim est negatio eius, quae est, necesse non esse, non necesse esse (quoniam contingit eas simul verificari de eodem), sed illa scilicet, necesse non esse, est contraria contradictoriae huius, scilicet, non necesse esse, quae est, necesse est esse. Sed quia sequenti litterae magis consona est introductio nostra, quae etiam Alberto consentit, et extorte videtur ab aliis exponi ly contrariae, ideo prima, iudicio meo, acceptanda est expositio et ad antiquorum reprehensionem referendus est textus.	8. Boethius and Averroes read both this and the preceding part of the text, not reprovingly, but as explanatorily joined together. They say Aristotle explains the quality of the above table with respect to the consequents of enunciations predicating necessity after he has explained in what way those predicating impossibility are related. What Aristotle is saying, then, is that those of the necessary do not follow those of the possible in the same way as those of the impossible follow upon the possible. For contradictories of the impossible follow upon contradictories of the possible, although inversely; but contradictories of the necessary are not said to follow the contradictories of the possible, but rather the contraries of the necessary follow upon them. It is not the contraries among themselves that follow, but contraries in this way: the negation of the necessary is said to follow upon the affirmation of the possible; but what follows on the negation of this possible is not the affirmation of the necessary contradictory to that negative of the necessary following upon the possible, but the contrary of such an affirmation of the necessary. That this is the case is evident in the first and third orders. The sources are negation and affirmation of the possible, and the extremes are "not necessary to be” and "necessary not to be.” But these are not contradictories, for the negation of "necessary not to be” is not "not necessary to be,” for it is possible for them to be at once true of the same thing. "Necessary not to be” is the contrary of the contradictory of "not necessary to be,” which contradictory is "necessary to be.” In my judgment, however, the first exposition should be accepted and this portion of the text taken as a reproof of the ancients, because the contraries seem to be explained in a forced way by others, whereas our introduction is more in accord with what follows in the next part of the text; in addition, it agrees with Albert’s interpretation.
Cajetanus lib. 2 l. 10 n. 9 Tertio cum dicit: causa autem cur etc., manifestat id quod praemiserat, scilicet, quod non simili modo ad illas de possibili sequuntur illae de impossibili et illae de necessario. Antiquorum enim hoc peccatum fuit tam in primo quam in secundo ordine, et quod simili modo intulerunt illas de impossibili et necessario. In primo siquidem ordine, sicut posuerunt negativam simplicem de impossibili, ita posuerunt negativam simplicem de necessario, et similiter in secundo ordine utranque negativam declinatam locaverunt. Hoc ergo quare peccatum sit, et causa autem quare necessarium non sequitur possibile, similiter, idest, eodem modo cum caeteris, scilicet, de impossibili, est, quoniam impossibile redditur idem valens necessario, idest, aequivalet necessario, contrarie, idest, contrario modo sumptum, et non eodem modo. Nam si, hoc esse est impossibile, non inferemus, ergo hoc esse est necesse, sed, hoc non esse est necesse. Quia ergo impossibile et necesse mutuo se sequuntur, quando dicta eorum contrario modo sumuntur, et non quando dicta eorum simili modo sumuntur, sequitur quod non eodem modo ad possibile se habeant impossibile et necessarium, sed contrario modo. Nam ad id possibile quod sequitur dictum affirmatum de impossibili, sequitur dictum negatum de necessario; et e contrario. Quare autem hoc accidit infra dicetur. Erraverunt igitur antiqui quod similes enunciationes de impossibili et necessario in primo et in secundo ordine locaverunt.	9. Thirdly, he says, Now the reason why enunciations predicating necessity do not follow in the same way as the others, etc. Here Aristotle shows why enunciations predicating impossibility and necessity do not follow in a similar way upon those predicating possibility. This was the error made by the ancients in both the first and second orders, for in the first order they posited the simple negative of the impossible, and in a similar way the simple negative of the necessary, and in the second order their declined negatives, the reason being that they inferred those predicating impossibility and necessity in a similar way. The cause of this error, then, and the reason why enunciations predicating necessity do not follow the possible in the same way, i.e., in a similar mode, as the others, i.e., as the impossibles, is that the impossible expresses the same meaning as the necessary, i.e., is equivalent to the necessary, contrarily, i.e., taken in a contrary mode, and not in the same mode. For if something is impossible to be, we do not infer, therefore it is necessary to be, but it is necessary not to be. Since, therefore, the impossible and necessary mutually follow each other when their dictums are taken in a contrary mode—and not when their dictums are taken in a similar mode—it follows that the impossible and necessary are not related in the same way to the possible, but in a contrary way. For the negated dictum of the necessary follows upon that possible which follows the affirmed dictum of the impossible, and contrarily. Why this is so will be explained later. Therefore, the ancients erred when they located similar enunciations of the impossible and necessary in the first and in the second orders.
Cajetanus lib. 2 l. 10 n. 10 Hinc apparet quod supra posita nostra expositio conformior est Aristoteli. Cum enim hunc textum induxerit ad manifestandum illa verba: manifestum est autem quoniam non eodem modo, etc., eo accipiendo sunt sensu illa verba, quo hic per causam manifestantur. Liquet autem quod hic redditur causa dissimilitudinis verae inter necessarias et impossibiles in consequendo possibiles, et non dissimilitudinis falso opinatae ab antiquis: quoniam ex vera causa nonnisi verum concluditur. Ergo reprehendendo antiquos, veram dissimilitudinem inter necessarias, et impossibiles in consequendo possibiles, quam non servaverunt illi, proposuisse tunc intelligendum est, et nunc eam manifestasse. Quod autem dissimilitudo illa, quam antiqui posuerunt inter necessarias et impossibiles, sit falso posita, ex infra dicendis patebit. Ostendetur enim quod contradictorias de possibili contradictoriae de necessario sequuntur conversim; et quod in hoc non differunt ab his quae sunt de impossibili, sed differunt in hoc quod modo diximus, quod possibilium et impossibilium se consequentium dictum est similiter, possibilium autem et necessariorum, se invicem consequentium dictum est contrarium, ut infra clara luce videbitur.	10. Hence it appears that our exposition is more in conformity with Aristotle. For he introduced this text to manifest these words: It is evident that the case here is not the same, etc. By taking this meaning, then, these words are made clear through the cause. Moreover, it is evident that here the cause is given of a true dissimilitude between necessaries and impossibles in following the possibles, and not of a dissimilitude falsely held by the ancients, for from a true cause only the truth is concluded. Therefore in reproving the ancients it must be understood that a true dissimilitude between the necessary and impossible in following the possible, which they did not beed, has been proposed, and now has been made manifest. It will be clear from what will be said later that the dissimilitude posited by the ancients between the necessary and impossible is falsely posited, for it will be shown that contradictories of the necessary follow contradictories of the possible inversely, and that in this they do not differ from enunciations predicating impossibility. They do differ, however, in the way we have indicated, i.e., the dictum of the possibles and of the impossibles following on them is similar, but the dictum of the possibles and of the necessaries following on them is contrary, as will be seen clearly later.
Cajetanus lib. 2 l. 10 n. 11 Quarto cum dicit: aut certe impossibile est etc., manifestat aliud quod proposuerat, scilicet, quod contradictoriae de necessario male situatae sint secundum consequentiam ab antiquis, qui contradictiones necessarii ita ordinaverunt. In primo ordine posuerunt contradictoriam negationem, necesse esse, idest, non necesse esse; et in secundo contradictoriam negationem, necesse non esse, idest, non necesse non esse. Et probat hunc consequentiae modum esse malum in primo ordine. Cognita enim malitia primi, facile est secundi ordinis agnoscere defectum. Probat autem hoc tali ratione ducente ad impossibile. Ad necessarium esse sequitur possibile esse: aliter sequeretur non possibile esse, quod manifeste implicat; ad possibile esse sequitur non impossibile esse, ut patet; ad non impossibile esse, secundum antiquos, sequitur in primo ordine non necessarium esse; ergo de primo ad ultimum, ad necessarium esse sequitur non necessarium esse: quod est inconveniens, quia est manifesta implicatio contradictionis. Relinquitur ergo quod male dictum sit, quod non necessarium esse consequatur in primo ordine. Ait ergo et certe impossibile est poni sic secundum consequentiam, ut antiqui posuerunt, necessarii contradictiones, idest illas duas enunciationes de necessario, quae sunt negationes contradictoriae aliarum duarum de necessario. Nam ad id quod est, necessarium esse, sequitur, possibile est esse: nam si non, idest quoniam si hanc negaveris consequentiam, negatio possibilis sequitur illam, scilicet, necesse esse. Necesse est enim de necessario aut dicere, idest affirmare possibile, aut negare possibile: de quolibet enim est affirmatio vel negatio vera. Quare si dicas quod, ad necesse esse, non sequitur, possibile esse, sed, non possibile est esse; cum haec aequivaleat illi quae dicit, impossibile est esse, relinquitur quod ad, necesse esse, sequitur, impossibile esse, et idem erit, necesse esse et impossibile esse: quod est inconveniens. Bona ergo erat prima illatio, scilicet, necesse est esse, ergo possibile est esse. Tunc ultra. Illud quod est, possibile esse, sequitur, non impossibile esse, ut patet in primo ordine. Ad hoc vero, scilicet, non impossibile esse, secundum antiquos eodem primo ordine, sequitur, non necesse est esse (quare contingit de primo ad ultimum); ad id quod est, necessarium esse, sequitur, non necessarium esse: quod est inconveniens, immo impossibile.	11. Fourthly, when he says, Or is it impossible to arrange the contradictions of enunciations predicating necessity in this way? he manifests another point he had proposed, namely, that contradictories of enunciations predicating necessity were badly placed according to consequence by the ancients when they ordered them thus: the contradictory negation to "necessary to be,” i.e., "not necessary to be,” in the first order, and the contradictory negation to "necessary not to be,” i.e., "not necessary not to be,” in the second. Aristotle only proves that this mode of consequence is incorrect in the first order, for when this is known the mistake in the second order is readily seen. He does this by an argument leading to an impossibility. "Possible to be” follows upon "necessary to be”; otherwise "not possible to be” would follow, which it manifestly implies. "Not impossible to be” follows upon "possible to be” as is evident, and, according to the ancients, in the first order, "not necessary to be” follows upon "not impossible to be.” Therefore, from first to last, "not necessary to be” follows upon "necessary to be,” which is inadmissible because there is an obvious implication of contradiction. Therefore, it is erroneous to say that "not necessary to be” follows in the first order. He says, then, that in fact it is impossible to posit contradictions of the necessary according to consequence as the ancients posited them, i.e., in the first order the contradictory negation of "necessary to be,” i.e., "not necessary to be” and in the second the contradictory negation of "necessary not to be,” i.e., "not necessary not to be.” For "possible to be” follows upon "necessary to be”; if not, i.e., if you deny this consequence, the negation of the possible follows upon "necessary to be,” since the possible must either be asserted of the necessary or denied, the reason being that of anything there is a true affirmation or a true negation. Therefore, if you say that "possible to be” does not follow upon "necessary to be,” but "not possible to be” does follow, then, since the latter is equivalent to the former, i.e., "not possible to be” to "impossible to be,” "impossible to be” follows upon "necessary to be” and the same thing will be "necessary to be” and "impossible to be,” which cannot be admitted. Consequently, the first inference was good, i.e., "It is necessary to be, therefore it is possible to be.” But again, "possible to be” follows upon "not impossible to be,” as is evident in the first order, and according to the ancients, "not necessary to be” follows upon "not impossible to be” in the same first order. Therefore, from first to last we arrive at this: "not necessary to be” follows upon "necessary to be,” which is unlikely, not to say impossible.
Cajetanus lib. 2 l. 10 n. 12 Dubitatur hic: quia in I priorum dicitur quod ad possibile sequitur non necessarium, hic autem dicitur oppositum. Ad hoc est dicendum quod possibile sumitur dupliciter. Uno modo in communi, et sic est quoddam superius ad necessarium et contingens ad utrunque, sicut animal ad hominem et bovem; et sic ad possibile non sequitur non necessarium, sicut ad animal non sequitur non homo. Alio modo sumitur possibile pro una parte possibilis in communi, idest pro possibili seu contingenti, scilicet ad utrunque, scilicet quod potest esse et non esse; et sic ad possibile sequitur non necessarium. Quod enim potest esse et non esse, non necessarium est esse, et similiter non necessarium est non esse. Loquimur ergo hic de possibili in communi, ibi vero in speciali.	12. There is a doubt about this, for in I Priorum [13: 32a 28 and 32b 15], it is said that the not necessary follows upon the possible, while here the opposite is said. The possible, however, is taken in two ways: commonly, and thus it is superior to the necessary and the contingent to either of two alternatives, as is the case with animal in relation to man and cow; taken in this way, the not necessary does not follow upon the possible, just as not-man does not follow upon animal. In another way the possible is taken for one part of the possible commonly, i.e., for the possible or contingent to either of two alternatives, namely, for what can be and not be. The not necessary follows upon the possible taken in this way, for what can be and not be is not necessary to be, and likewise is not necessary not to be. In the Prior Analytics, then, Aristotle is speaking of the possible in particular; here of the possible commonly.
Cajetanus lib. 2 l. 10 n. 13 Deinde cum dicit: at vero neque necessarium etc., determinat veritatem intentam. Et circa hoc tria facit: primo, determinat quae enunciatio de necessario sequatur ad possibile; secundo, ordinat consequentias omnium modalium; ibi: sequuntur enim et cetera. Quoad primum, sicut duabus viis reprehendit antiquos, ita ex illis duobus motivis intentum probat. Et intendit quod, ad possibile esse, sequitur, non necesse non esse. Primum motivum est per locum a divisione. Ad, possibile esse, non sequitur (ut probatum est), non necesse esse, at vero neque, necesse esse, neque, necesse non esse. Reliquum est ergo ut sequatur ad eam, non necesse non esse: non enim dantur plures enunciationes de necessario. Huius communis divisionis primo proponit reliqua duo membra excludenda, dicens: at vero neque necessarium esse, neque necessarium non esse, sequitur ad possibile non esse; secundo probat hoc sic. Nullum formale consequens minuit suum antecedens: tunc enim oppositum consequentis staret cum antecedente; sed utrumque horum, scilicet, necesse esse, et, necesse non esse, minuit possibile esse; ergo, et cetera. Unde, tacita maiore, ponit minoris probationem dicens: illi enim, scilicet, possibile esse, utraque, scilicet, esse et non esse, contingit accidere; horum autem, scilicet, necesse esse et necesse non esse, utrumlibet verum fuerit, non erunt illa duo, scilicet, esse et non esse, vera simul in potentia. Et primum horum explanans ait: cum dico, possibile esse, simul est possibile esse et non esse. Quoad secundum vero subdit. Si vero dicas, necesse esse vel necesse non esse, non remanet utrumque, scilicet, esse et non esse, possibile: si enim necesse est esse, possibilitas ad non esse excluditur; et si necesse est non esse, possibilitas ad esse removetur. Utrumque ergo istorum minuit illud antecedens, possibile esse, quoniam ad esse et non esse se extendit, et cetera. Tertio subdit conclusionem: relinquitur ergo quod, non necessarium non esse, comes est ei quae dicit, possibile esse; et consequenter haec ponenda erit in primo ordine.	13. When he says, But in fact neither "necessary to be” nor "necessary not to be” follow upon "possible to be,” etc., he determines the truth. First he determines which enunciation of the necessary follows upon the possible; secondly, he orders the consequents of all of the modals, where he says, Thus, these contradictions also follow in the way indicated, etc. Aristotle has reproved the ancients in two ways; on the basis of these two he now proves which enunciation of the necessary follows upon the possible. What he intends to show is that "not necessary not to be” follows upon "possible to be.” The first argument is taken from a locus of division. "Not necessary to be” does not follow upon possible to be” (as has been proved), but neither does "necessary to be” nor "necessary not to be.” Therefore, "not necessary not to be” follows upon "possible to be,” since there are no more enunciations of the necessary. He first proposes the remaining two members that are to be excluded from this common division: But in fact neither "necessary to be” nor "necessary not to be” follow upon "possible to be.” Then he proves this: no formal consequent diminishes its antecedent, for if it did, the opposite of the consequent would stand with the antecedent; but both of these, namely, "necessary to be” and "necessary not to be,” diminish possible to be”; therefore, etc. The major is therefore implied and he gives the proof of the minor when he says that "possible to be” admits of two possibilities, namely, "to be” and "not to be”; but of these, namely, "necessary to be” and "necessary not to be” (whichever should be true), these two, "to be” and "not to be,” will not be true at the same time in potency. He explains the first point thus: when I say "possible to be” it is at once possible to be and not to be. With respect to the second, he adds: if you should say, "necessary to be” or "necessary not to be,” both do not remain, i.e., possible to be and not to be do not remain, for if a thing is necessary to be, possibility not to be is excluded, and if it is necessary not to be, possibility to be is removed. Both of these, then, diminish the antecedent, possible to be, for it is extended to "to be” and "not to be,” etc. Thirdly, he concludes: it remains, therefore, that "not necessary not to be” accompanies "possible to be,” and consequently will have to be placed in the first order.
Cajetanus lib. 2 l. 10 n. 14 Occurrit in hac parte dubium circa hoc quod dicit quod, ad possibile non sequitur necessarium, cum superius dixerit quod ad ipsum non sequitur non necessarium. Cum enim necessarium et non necessarium sint contradictoria opposita, et de quolibet sit affirmatio vel negatio vera, non videtur posse evadi quin ad possibile sequatur necessarium, vel, non necessarium. Et cum non sequatur necessarium, sequetur non necessarium, ut dicebant antiqui. Augetur et dubitatio ex eo quod Aristoteles nunc usus est tali argumentationis modo, volens probare quod ad necessarium sequatur possibile. Dixit enim: nam si non negatio possibilis consequatur. Necesse est enim aut dicere aut negare.	14. A difficulty arises at this point with respect to his saying that the necessary does not follow upon the possible, since he has also said that the not necessary does not follow upon it. For the necessary and the not necessary are opposed contradictorily, and since of anything there is a true affirmation or negation, it seems impossible to avoid the conclusion that either the necessary or the not necessary follows upon the possible; and since the necessary does not follow, the not necessary must follow, as the ancients said. Furthermore, the difficulty is augmented by the fact that Aristotle just used such a mode of argumentation when, to prove that the possible follows upon the necessary, he said, for if not, the negation will follow; for it is necessary either to affirm or deny.
Cajetanus lib. 2 l. 10 n. 15 Pro solutione huius, oportet reminisci habitudinis quae est inter possibile et necessarium, quod scilicet possibile est superius ad necessarium, et attendere quod superius potestate continet suum inferius et eius oppositum, ita quod neutrum eorum actualiter sibi vindicat, sed utrunque potest sibi contingere; sicut animali potest accidere homo et non homo: et consequenter inspicere debes quod, eadem est proportio superioris ad habendum affirmationem et negationem unius inferioris, quae est alicuius subiecti ad affirmativam et negativam futuri contingentis. Utrobique enim neutrum habetur, et salvatur potentia ad utrumlibet. Unde, sicut in futuris contingentibus nec affirmatio nec negatio est determinate vera, sed sub disiunctione altera est necessario vera, ut in fine primi conclusum est; ita nec affirmatio nec negatio inferioris sequitur determinate affirmationem vel negationem superioris, sed sub disiunctione altera sequitur necessario. Unde non valet, est animal, ergo est homo, neque, ergo non est homo, sed, ergo est homo vel non est homo. Quia ergo possibile superius est ad necessarium, ideo optime determinavit Aristoteles neutram contradictionis partem de necessario determinate sequi ad possibile. Non tamen dixit quod sub disiunctione neutra sequatur; hoc enim est contra illud primum principium: de quolibet est affirmatio vera vel falsa. Ad id autem quod additur, ex eadem trahitur radice responsio. Quia enim necessarium inferius est ad possibile, et inferius non in potentia sed in actu includit suum superius, necesse est ad inferius determinate sequi suum superius: aliter determinate sequetur eius contradictorium. Unde per dissimilem habitudinem, quae est inter necessarium et possibile et non possibile, ex una parte, et inter possibile et necessarium et non necessarium, ex altera parte, ibi optimus fuit processus ad alteram contradictionis partem determinate, et hic optimus ad neutram determinate.	15. In order to resolve this, we must recall the relationship between the possible and the necessary, namely, that the possible is superior to the necessary. Now the superior potentially contains its own inferior and the opposite of it in such a way that neither of them is actually appropriated by the superior, but each is possible to it; as in the case of man and not-man in relation to animal. We must also consider that the proportion of the superior as related to the affirmation and negation of one inferior is the same (which is the proportion of some subject to the affirmative and negative of a future contingent), for it is had by neither of the two, and the potency to either is kept. Accordingly, as in future contingents neither the affirmation nor the negation is determinately true, but under disjunction one is necessarily true (as was concluded at the end of the first book), so neither the affirmation nor negation of the inferior follows upon the affirmation or negation of the superior determinately, but under disjunction one follows necessarily. This, for instance, is not valid: "It is animal, therefore it is man,” nor is "therefore it is not man” valid, but, "therefore it is man or it is not man.” Since, then, the possible is superior to the necessary, Aristotle has correctly determined that neither part of the contradiction of the necessary determinately follows upon the possible. However, he has not said that under disjunction neither follows; for this would be opposed to the first principle, that of anything there is a true or false affirmation. The response to what was added, beginning with "Furthermore, the difficulty is augmented,” etc., is based upon the same point. Since the necessary is inferior to the possible, and the inferior does not include its superior in potency but in act, the superior must follow determinately upon the inferior; otherwise the contradiction of it would follow determinately. Hence, because of the dissimilar relationship between the necessary and the possible and not possible on the one hand, and between the possible and the necessary and not necessary on the other, the movement of the earlier argument to one part of the contradiction determinately was quite right, and the movement here to neither determinately was quite right.
Cajetanus lib. 2 l. 10 n. 16 Oritur quoque alia dubitatiuncula. Videtur enim quod Aristoteles difformiter accipiat ly possibile in praecedenti textu et in isto. Ibi enim accipit ipsum in communi, ut sequitur ad necessarium; hic videtur accipere ipsum specialiter pro possibili ad utrumlibet, quia dicit quod possibile est simul potens esse et non esse. Et ad hoc dicendum est quod uniformiter usus est possibili. Nec eius verba obstant: quoniam et de possibili in communi verum est dicere quod potest sibi utrunque accidere, scilicet, esse et non esse: tum quia quidquid verificatur de suo inferiori, verificatur etiam de suo superiori, licet non eodem modo; tum quia possibile in communi neutram contradictionis partem sibi determinat, et consequenter utranque sibi advenire compatitur, licet non asserat potentiam ad utranque partem, quemadmodum possibile ad utrunque.	16. There is another slight difficulty, for it seems that Aristotle takes the possible in a different way in the preceding text and in this. There he takes it commonly as it follows upon the necessary; here he seems to take it specifically for the possible that is indifferent to alternatives, since he says that the possible is at once possible to be and not to be. But in fact Aristotle has used the possible uniformly. Nor are his words at variance, for it is also true to say of the possible as common that it admits of both possibilities, i.e., of "to be” and "not to be”; first, because whatever is verified of its inferior is verified also of its superior, although not in the same mode; secondly, because the possible as common determines neither part of the contradiction to itself and consequently admits of either happening, although it does not affirm a potency to each part, as does the possible to either of two alternatives.
Cajetanus lib. 2 l. 10 n. 17 Secundum motivum ad idem, correspondens tacitae obiectioni antiquorum quam supra exclusit, addit cum subdit: hoc enim verum est et cetera. Ubi notandum quod Aristoteles sub illa maiore adducta pro antiquis (scilicet, convertibiliter se consequentium contradictoria se mutuo consequuntur), subsumit minorem: sed horum convertibiliter se sequentium in tertio ordine (scilicet, non possibile esse et necesse non esse), contradictoria sunt, possibile esse et non necesse non esse (quoniam modi negatione eis opponuntur); ergo istae duae (scilicet, possibile esse et non necesse non esse) se consequuntur et in primo locandae sunt ordine. Unde motivum tangens ait: hoc enim, quod dictum est, verum est, idest verum esse ostenditur, et de necesse non esse, idest, et ex illius, scilicet, non necesse non esse, opposita, quae est, necesse non esse. Vel, hoc enim, scilicet, non necesse non esse, verum est, scilicet, contradictorium illius de necesse non esse. Et minorem subdens ait: haec enim, scilicet, non necesse non esse, fit contradictio eius, quae convertibiliter sequitur, non possibile esse. Et explanans hoc in terminis subdit. Illud enim, non possibile esse, quod est caput tertii ordinis, sequitur hoc de impossibili, scilicet, impossibile esse, et haec de necessario, scilicet, necesse non esse, cuius negatio seu contradictoria est, non necesse non esse. Et quia, caeteris paribus, modus negatur, et illa, possibile esse, est (subauditur) contradictoria illius, scilicet, non possibile; igitur ista duo mutuo se consequuntur, scilicet, possibile esse, et, non necesse non esse, tamquam contradictoria duorum se mutuo consequentium.	17. The second grounds for proving the same thing corresponds to the tacit objection of the ancients he excluded above: For this, he says, is true also with respect to "necessary to be,” etc. It should be noted here that Aristotle subsumes under the major cited as a proof for the position of the ancients (namely, contradictories of consequences convertibly following each other mutually follow upon each other) this minor: but the contradictories of those following upon each other convertibly in the third order (i.e., of "not possible to be” and "necessary not to be”) are "possible to be” and "not necessary not to be” (for they are opposed to them by negation of mode); therefore, these two (i.e., "possible to be” and "not necessary not to be”) follow upon each other and are to be placed in the first order. Hence, with respect to the basis of the above argument, he says, For this, i.e., what has been said, is true, i.e., is shown to be true, also with respect to "necessary not to be,” i.e., of the opposite of "not necessary not to be,” i.e., "necessary not to be.” Or, For this, namely, not necessary not to be,” is true, namely, is the true contradictory of necessary not to be.” He gives the minor when he says, For "not necessary not to be” is the contradictory of what follows upon "not possible to be.” Then he states this explicitly: for "not possible to be,” which is the source of the third order is followed by this impossible, namely, "impossible to be,” and by this one of the necessary, namely, "necessary not to be,” of which the negation or contradictory is "not necessary not to be.” And since, other things being equal, the mode is negated, and, "possible to be” is (it is understood) the contradictory of "not possible to be,” therefore, these two mutually follow upon each other, namely, "possible to be” and "not necessary not to be,” as contradictories of the two mutually following upon each other.
Cajetanus lib. 2 l. 10 n. 18 Deinde cum dicit: sequuntur enim etc., ordinat omnes consequentias modalium secundum opinionem propriam; et ait quod, hae contradictiones, scilicet, de necessario, sequuntur illas de possibili, secundum modum praedictum et approbatum illarum de impossibili. Sicut enim contradictorias de possibili contradictoriae de impossibili sequuntur, licet conversim; ita contradictorias de possibili contradictoriae de necessario sequuntur conversim: licet in hoc, ut dictum est, dissimilitudo sit quod, contradictoriarum de possibili et impossibili similiter est dictum, contradictoriarum autem de possibili et necessario contrarium est dictum, ut in sequenti videtur figura: consequentiae enunciationum modalium secundum quatuor ordines ab Aristotele positae et ordinatae. (Figura). Ubi vides quod nulla est inter Aristotelem et antiquos differentia, nisi in duobus primis ordinibus quoad illas de necessario. Praepostero namque situ usi sunt antiqui, eam de necessario, quae locanda erat in primo ordine, in secundo ponentes, et eam quae in secundo ponenda erat, in primo locantes. Et aspice quoque quod convertibiliter se consequentium semper contradictoria se consequi ordinavit. Singulis enim tertii ordinis singulae primi ordinis contradictoriae sunt; et similiter singulae quarti ordinis singulis, quae in secundo sunt, contradictoriae sunt. Quod antiqui non observarunt.	18. When he says, Thus, these contradictions also follow in the way indicated, etc., he orders all of the consequents of modals according to his own opinion. He says, then, that these contradictions, namely, of the necessary, follow those of the possible, according to the foresaid and approved mode of those of the impossible. For just as contradictories of the impossible follow upon contradictories of the possible, although inversely, so contradictories of the necessary follow contradictories of the possible inversely. In the latter, however, as has been said, there is a dissimilarity in that the dictum of the contradictories of the possible and impossible is similar, but the dictum of the contradictories of the possible and necessary is contrary. This can be seen in the following table. CONSEQUENTS OF MODAL ENUNCIATIONS POSITED AND ORDERED BY ARISTOTLE ACCORDING TO FOUR ORDERS FIRST ORDER It is possible to be It is contingent to be It is not impossible to be It is not necessary to be SECOND ORDER It is possible not to be It is contingent not to be It is not impossible not to be It is not necessary not to be It is not possible to be It is not contingent to be It is impossible to be It is necessary not to be FOURTH ORDER It is not possible not to be It is not contingent not to be It is impossible not to be It is necessary to be Here you see that there is no difference between Aristotle and the ancients except in the first two orders with respect to those of the necessary. The ancients inverted the position of these, placing the necessary that should have been placed in the first order in the second order, and the one that should have been in the second in the first. Notice, too, that he has ordered them in such a way that the contradictories of those following upon each other convertibly, always follow each other, for each one in the first order is the contradictory of each one in the third order, and similarly, each of the fourth order the contradictory of each in the second. This the ancients did not observe.