Authors/Thomas Aquinas/perihermenias/perihermenias II

Commentary by Thomas Aquinas; finished by Cardinal Cajetan. Translated by Jean T. Oesterle Milwaukee: Marquette University Press, 1962

LECTURE 1

Latin	English
Aquinas lib. 2 l. 1 n. 1 Postquam philosophus in primo libro determinavit de enunciatione simpliciter considerata; hic determinat de enunciatione, secundum quod diversificatur per aliquid sibi additum. Possunt autem tria in enunciatione considerari: primo, ipsae dictiones, quae praedicantur vel subiiciuntur in enunciatione, quas supra distinxit per nomina et verba; secundo, ipsa compositio, secundum quam est verum vel falsum in enunciatione affirmativa vel negativa; tertio, ipsa oppositio unius enunciationis ad aliam. Dividitur ergo haec pars in tres partes: in prima, ostendit quid accidat enunciationi ex hoc quod aliquid additur ad dictiones in subiecto vel praedicato positas; secundo, quid accidat enunciationi ex hoc quod aliquid additur ad determinandum veritatem vel falsitatem compositionis; ibi: his vero determinatis etc.; tertio, solvit quamdam dubitationem circa oppositiones enunciationum provenientem ex eo, quod additur aliquid simplici enunciationi; ibi: utrum autem contraria est affirmatio et cetera. Est autem considerandum quod additio facta ad praedicatum vel subiectum quandoque tollit unitatem enunciationis, quandoque vero non tollit, sicut additio negationis infinitantis dictionem. Circa primum ergo duo facit: primo, ostendit quid accidat enunciationibus ex additione negationis infinitantis dictionem; secundo, ostendit quid accidat circa enunciationem ex additione tollente unitatem; ibi: at vero unum de pluribus et cetera. Circa primum duo facit: primo, determinat de enunciationibus simplicissimis, in quibus nomen finitum vel infinitum ponitur tantum ex parte subiecti; secundo, determinat de enunciationibus, in quibus nomen finitum vel infinitum ponitur non solum ex parte subiecti, sed etiam ex parte praedicati; ibi: quando autem est tertium adiacens et cetera. Circa primum duo facit: primo, proponit rationes quasdam distinguendi tales enunciationes; secundo, ponit earum distinctionem et ordinem; ibi: quare prima est affirmatio et cetera. Circa primum duo facit: primo, ponit rationes distinguendi enunciationes ex parte nominum; secundo, ostendit quod non potest esse eadem ratio distinguendi ex parte verborum; ibi: praeter verbum autem et cetera. Circa primum tria facit: primo, proponit rationes distinguendi enunciationes; secundo, exponit quod dixerat; ibi: nomen autem dictum est etc.; tertio, concludit intentum; ibi: erit omnis affirmatio et cetera.	1. In the first book, the Philosopher has dealt with the enunciation considered simply. Now he is going to treat of the enunciation as it is diversified by the addition of something to it. There are three things that can be considered in the enunciation: first, the words that are predicated or subjected, which he has already distinguished into names and verbs; secondly, the composition, according to which there is truth or falsity in the affirmative or negative enunciation; finally, the opposition of one enunciation to another. This book is divided into three parts which are related to these three things in the enunciation. In the first, he shows what happens to the enunciation when something is added to the words posited as the subject or predicate; in the second, what happens when something is added to determine the truth or falsity of the composition. He begins this where he says, Having determined these things, we must consider in what way negations and affirmations of the possible and not possible, etc. In the third part he solves a question that arises about the oppositions of enunciations in which something is added to the simple enunciation. This he takes up where he says, There is a question as to whether the contrary of an affirmation is a negation, or whether the contrary of an affirmation is another affirmation, etc. With respect to additions made to the words used in the enunciation, it should be noted that an addition made to the predicate or the subject sometimes destroys the unity of the enunciation, and sometimes not, the latter being the case in which the addition is a negative making a word infinite. Consequently, he first shows what happens to the enunciation when the added negation makes a word infinite. Secondly, he shows what happens when an addition destroys the unity of the enunciation where he says, Neither the affirmation nor the negation which affirms or denies one predicate of many subjects or many predicates of one subject is one, unless something one is constituted from the many, etc. In relation to the first point he first investigates the simplest of enunciations, in which a finite or infinite name is posited only on the part of the subject. Then he considers the enunciation in which a finite or infinite name is posited not only on the part of the subject, but also on the part of the predicate, where he says, But when "is” is predicated as a third element in the enunciation, etc. Apropos of these simple enunciations, he proposes certain grounds for distinguishing such enunciations and then gives their distinction and order where he says, Therefore the primary affirmation and negation is "Man is,” "Man is not,” etc. And first he gives the grounds for distinguishing enunciations on the part of the name; secondly, he shows that there are not the same grounds for a distinction on the part of the verb, where he says, There can be no affirmation or negation without a verb, etc. First, then, he proposes the grounds for distinguishing these enunciations; secondly, he explains this where he says, we have already stated what a name is, etc.; finally, he arrives at the conclusion he intended where he says, every affirmation will be made up of a name and a verb, or an infinite name and a verb.
Aquinas lib. 2 l. 1 n. 2 Resumit ergo illud, quod supra dictum est de definitione affirmationis, quod scilicet affirmatio est enunciatio significans aliquid de aliquo; et, quia verbum est proprie nota eorum quae de altero praedicantur, consequens est ut illud, de quo aliquid dicitur, pertineat ad nomen; nomen autem est vel finitum vel infinitum; et ideo, quasi concludens subdit quod quia affirmatio significat aliquid de aliquo, consequens est ut hoc, de quo significatur, scilicet subiectum affirmationis, sit vel nomen, scilicet finitum (quod proprie dicitur nomen, ut in primo dictum est), vel innominatum, idest infinitum nomen: quod dicitur innominatum, quia ipsum non nominat aliquid cum aliqua forma determinata, sed solum removet determinationem formae. Et ne aliquis diceret quod id quod in affirmatione subiicitur est simul nomen et innominatum, ad hoc excludendum subdit quod id quod est, scilicet praedicatum, in affirmatione, scilicet una, de qua nunc loquimur, oportet esse unum et de uno subiecto; et sic oportet quod subiectum talis affirmationis sit vel nomen, vel nomen infinitum.	2. First of all, he goes back to what was said above in defining affirmation, namely, that affirmation is an enunciation signifying something about something; and, since it is peculiar to the verb to be a sign of what is predicated of another, it follows that that about which something is said pertains to the name; but the name is either finite or infinite; therefore, as if drawing a conclusion, he says that since affirmation signifies something about something it follows that that about which something is signified, i.e., the subject of an affirmation, is either a finite name (which is properly called a name), or unnamed, i.e., an infinite name. It is called "unnamed” because it does not name something with a determinate form but removes the determination of form. And lest anyone think that what is subjected in an affirmation is at once a name and unnamed, he adds, and one thing must be signified about one thing in an affirmation, i.e., in the enunciation, of which we are speaking now; and hence the subject of such an affirmation must be either the name or the infinite name.
Aquinas lib. 2 l. 1 n. 3 Deinde cum dicit: nomen autem etc., exponit quod dixerat, et dicit quod supra dictum est quid sit nomen, et quid sit innominatum, idest infinitum nomen: quia, non homo, non est nomen, sed est infinitum nomen, sicut, non currit, non est verbum, sed infinitum verbum. Interponit autem quoddam, quod valet ad dubitationis remotionem, videlicet quod nomen infinitum quodam modo significat unum. Non enim significat simpliciter unum, sicut nomen finitum, quod significat unam formam generis vel speciei aut etiam individui, sed in quantum significat negationem formae alicuius, in qua negatione multa conveniunt, sicut in quodam uno secundum rationem. Unum enim eodem modo dicitur aliquid, sicut et ens; unde sicut ipsum non ens dicitur ens, non quidem simpliciter, sed secundum quid, idest secundum rationem, ut patet in IV metaphysicae, ita etiam negatio est unum secundum quid, scilicet secundum rationem. Introducit autem hoc, ne aliquis dicat quod affirmatio, in qua subiicitur nomen infinitum, non significet unum de uno, quasi nomen infinitum non significet unum.	3. When he says, we have already stated what a name is, etc., he relates what he has previously said. We have already stated, he says, what a name is and what that which is unnamed is, i.e., the infinite name. "Non-man” is not a name but an infinite name, and "non-runs” is not a verb but an infinite verb. Then he interposes a point that is useful for the preclusion of a difficulty, i.e., that an infinite name in a certain way does signify one thing. It does not signify one thing simply as the finite name does, which signifies one form of a genus or species, or even of an individual; rather it signifies one thing insofar as it signifies the negation of a form, in which negation many things are united, as in something one according to reason. For something is said to be one in the same way it is said to be a being. Hence, just as nonbeing is said to be being, not simply, but according to something, i.e., according to reason, as is evident in IV Metaphysicae [21: 1003b 6], so also a negation is one according to something, i.e., according to reason. Aristotle introduces this point so that no one will say that an affirmation in which an infinite name is the subject does not signify one thing about one subject on the grounds that an infinite name does not signify something one.
Aquinas lib. 2 l. 1 n. 4 Deinde cum dicit: erit omnis affirmatio etc., concludit propositum scilicet quod duplex est modus affirmationis. Quaedam enim est affirmatio, quae constat ex nomine et verbo; quaedam autem est quae constat ex infinito nomine et verbo. Et hoc sequitur ex hoc quod supra dictum est quod hoc, de quo affirmatio aliquid significat, vel est nomen vel innominatum. Et eadem differentia potest accipi ex parte negationis, quia de quocunque contingit affirmare, contingit et negare, ut in primo habitum est.	4. When he says, every affirmation will be made up of a name and a verb or an infinite name and a verb, he concludes that the mode of affirmation is twofold. One consists of a name and a verb, the other of an infinite name and a verb. This follows from what has been said, namely, that that about which an affirmation signifies something is either a name or unnamed. The same difference can be taken on the part of negation, for of whatever something can be affirmed it can be denied, as was said in the first book.
Aquinas lib. 2 l. 1 n. 5 Deinde cum dicit: praeter verbum etc., ostendit quod differentia enunciationum non potest sumi ex parte verbi. Dictum est enim supra quod, praeter verbum nulla est affirmatio vel negatio. Potest enim praeter nomen esse aliqua affirmatio vel negatio, videlicet si ponatur loco nominis infinitum nomen: loco autem verbi in enunciatione non potest poni infinitum verbum, duplici ratione. Primo quidem, quia infinitum verbum constituitur per additionem infinitae particulae, quae quidem addita verbo per se dicto, idest extra enunciationem posito, removet ipsum absolute, sicut addita nomini, removet formam nominis absolute: et ideo extra enunciationem potest accipi verbum infinitum per modum unius dictionis, sicut et nomen infinitum. Sed quando negatio additur verbo in enunciatione posito, negatio illa removet verbum ab aliquo, et sic facit enunciationem negativam: quod non accidit ex parte nominis. Non enim enunciatio efficitur negativa nisi per hoc quod negatur compositio, quae importatur in verbo: et ideo verbum infinitum in enunciatione positum fit verbum negativum. Secundo, quia in nullo variatur veritas enunciationis, sive utamur negativa particula ut infinitante verbum vel ut faciente negativam enunciationem; et ideo accipitur semper in simpliciori intellectu, prout est magis in promptu. Et inde est quod non diversificavit affirmationem per hoc, quod sit ex verbo vel infinito verbo, sicut diversificavit per hoc, quod est ex nomine vel infinito nomine. Est autem considerandum quod in nominibus et in verbis praeter differentiam finiti et infiniti est differentia recti et obliqui. Casus enim nominum, etiam verbo addito, non constituunt enunciationem significantem verum vel falsum, ut in primo habitum est: quia in obliquo nomine non concluditur ipse rectus, sed in casibus verbi includitur ipsum verbum praesentis temporis. Praeteritum enim et futurum, quae significant casus verbi, dicuntur per respectum ad praesens. Unde si dicatur, hoc erit, idem est ac si diceretur, hoc est futurum; hoc fuit, hoc est praeteritum. Et propter hoc, ex casu verbi et nomine fit enunciatio. Et ideo subiungit quod sive dicatur est, sive erit, sive fuit, vel quaecumque alia huiusmodi verba, sunt de numero praedictorum verborum, sine quibus non potest fieri enunciatio: quia omnia consignificant tempus, et alia tempora dicuntur per respectum ad praesens.	5. When he says, There can be no affirmation or negation without a verb, etc., he intends to show that enunciations cannot be differentiated on the part of the verb. He made the point earlier that there is no affirmation or negation without a verb. However there can be an affirmation or negation without a name, i.e., when an infinite name is posited in place of a name.” An infinite verb, on the other hand, cannot be posited in an enunciation in place of a verb, and this for two reasons. First of all, the infinite verb is constituted by the addition of an infinite particle which, when added to a verb said by itself (i.e., posited outside of the enunciation), removes it absolutely, just as it removes the form of the name absolutely when added to it. Therefore, outside of the enunciation, the infinite verb, as well as the infinite name, can be taken in the mode of one word. But when a negation is added to the verb in an enunciation it removes the verb from something and thus makes the enunciation negative, which is not the case with respect to the name. For an enunciation is made negative by denying the composition which the verb introduces; hence, an infinite verb posited in the enunciation becomes a negative verb. Secondly, whichever way we use the negative particle, whether as making the verb infinite or as making a negative enunciation, the truth of the enunciation is not changed. The negative particle, therefore, is always taken in the more absolute sense, as being clearer. This, then, is why Aristotle does not diversify the affirmation as made up of a verb or infinite verb, but as made up of a name or an infinite name. It should also be noted that besides the difference of finite and infinite there is the difference of nominative and oblique cases. The cases of names even with a verb added do not constitute an enunciation signifying truth or falsity, as was said in the first book, for the nominative is not included in an oblique name. The verb of present time, however, is included in the cases of the verb, for the past and future, which the cases of the verb signify, are said with respect to the present. Whence, ‘if we say, "This will be,” it is the same as if we were to say, "This is future”; and "This has been” the same as "This is past.” A name, then, and a case of the verb do constitute an enunciation. Therefore Aristotle adds that "is,” or "will be,” or "was,” or any other verb of this kind that we use are of the number of the foresaid verbs without which an enunciation cannot be made, since they all signify with time and past and future time are said with respect to the present.
Aquinas lib. 2 l. 1 n. 6 Deinde cum dicit: quare prima erit affirmatio etc., concludit ex praemissis distinctionem enunciationum in quibus nomen finitum vel infinitum ponitur solum ex parte subiecti, in quibus triplex differentia intelligi potest: una quidem, secundum affirmationem et negationem; alia, secundum subiectum finitum et infinitum; tertia, secundum subiectum universaliter, vel non universaliter positum. Nomen autem finitum est ratione prius infinito sicut affirmatio prior est negatione; unde primam affirmationem ponit, homo est, et primam negationem, homo non est. Deinde ponit secundam affirmationem, non homo est, secundam autem negationem, non homo non est. Ulterius autem ponit illas enunciationes in quibus subiectum universaliter ponitur, quae sunt quatuor, sicut et illae in quibus est subiectum non universaliter positum. Praetermisit autem ponere exemplum de enunciationibus, in quibus subiicitur singulare, ut, Socrates est, Socrates non est, quia singularibus nominibus non additur aliquod signum. Unde in huiusmodi enunciationibus non potest omnis differentia inveniri. Similiter etiam praetermittit exemplificare de enunciationibus, quarum subiecta particulariter ponuntur, quia tale subiectum quodammodo eamdem vim habet cum subiecto universali, non universaliter sumpto. Non ponit autem aliquam differentiam ex parte verbi, quae posset sumi secundum casus verbi, quia sicut ipse dicit, in extrinsecis temporibus, idest in praeterito et in futuro, quae circumstant praesens, est eadem ratio sicut et in praesenti, ut iam dictum est.	6. When he says, Therefore the primary affirmation and negation is, etc., he infers from the premises the distinction of enunciations in which the finite and infinite name is posited only on the part of the subject. Among these there is a threefold difference to be noted: the first, according to affirmation and negation; the second, according to finite and infinite subject; the third, according as the subject is posited universally or not universally. Now the finite name is prior in notion to the infinite name just as affirmation is prior to negation. Accordingly, he posits "Man is” as the first affirmation and "Man is not” as the first negation. Then he posits the second affirmation, "Non-man is,” and the second negation, "Non-man is not.” Finally he posits the enunciations in which the subject is universally posited. These are four, as are those in which the subject is not universally posited. The reason he does not give examples of the enunciation with a singular subject, such as "Socrates is” and "Socrates is not,” is that no sign is added to singular names, and hence not every difference can be found in them. Nor does he give examples of the enunciation in which the subject is taken particularly, for such a subject in a certain way has the same force as a universal subject not universally taken. He does not posit any difference on the part of the verb according to its cases because, as he himself says, affirmations and negations in regard to extrinsic times, i.e., past and future time which surround the prcsent, are similar to these, as has already been said.

LECTURE 2

Latin	English
Aquinas lib. 2 l. 2 n. 1 Postquam philosophus distinxit enunciationes, in quibus nomen finitum vel infinitum ponitur solum ex parte subiecti, hic accedit ad distinguendum illas enunciationes, in quibus nomen finitum vel infinitum ponitur ex parte subiecti et ex parte praedicati. Et circa hoc duo facit; primo, distinguit huiusmodi enunciationes; secundo, manifestat quaedam quae circa eas dubia esse possent; ibi: quoniam vero contraria est et cetera. Circa primum duo facit: primo, agit de enunciationibus in quibus nomen praedicatur cum hoc verbo, est; secundo de enunciationibus in quibus alia verba ponuntur; ibi: in his vero in quibus et cetera. Distinguit autem huiusmodi enunciationes sicut et primas, secundum triplicem differentiam ex parte subiecti consideratam: primo namque, agit de enunciationibus in quibus subiicitur nomen finitum non universaliter sumptum; secundo de illis in quibus subiicitur nomen finitum universaliter sumptum; ibi: similiter autem se habent etc.; tertio, de illis in quibus subiicitur nomen infinitum; ibi: aliae autem habent ad id quod est non homo et cetera. Circa primum tria facit: primo, proponit diversitatem oppositionis talium enunciationum; secundo, concludit earum numerum et ponit earum habitudinem; ibi: quare quatuor etc.; tertio, exemplificat; ibi: intelligimus vero et cetera. Circa primum duo facit: primo, proponit quod intendit; secundo, exponit quoddam quod dixerat; ibi: dico autem et cetera.	1. After distinguishing enunciations in which either a finite or an infinite name is posited only on the part of the subject, the Philosopher begins here to distinguish enunciations in which either a finite or an infinite name is posited as the subject and as the predicate. First he distinguishes these enunciations, and then he manifests certain things that might be doubtful in relation to them where he says, Since the negation contrary to "Every animal is just,” is the one signifying "No animal is just,” etc. With respect to their distinction he first deals with enunciations in which the name is predicated with the verb "is”; secondly, with those in which other verbs are used, where he says, In enunciations in which "is” does not join the predicate to the subject, for example, when the verb "matures” or "walks” is used, etc.” He distinguishes these enunciations as he did the primary enunciations, according to a threefold difference on the part of the subject, first treating those in which the subject is a finite name not taken universally, secondly, those in which the subject is a finite name taken universally where he says, The same is the case when the affirmation is of a name taken universally, etc.” Thirdly, he treats those in which an infinite name is the subject, where he says, and there are two other pairs, if something is added to non-man” as a subject, etc. With respect to the first enunciations [in which the subject is a finite name not taken universally] he proposes a diversity of oppositions and then concludes as to their number and states their relationship, where he says, In this case, therefore, there will be four enunciations, etc. Finally, he exemplifies this with a table.
Aquinas lib. 2 l. 2 n. 2 Circa primum duo oportet intelligere: primo quidem, quid est hoc quod dicit, est tertium adiacens praedicatur. Ad cuius evidentiam considerandum est quod hoc verbum est quandoque in enunciatione praedicatur secundum se; ut cum dicitur, Socrates est: per quod nihil aliud intendimus significare, quam quod Socrates sit in rerum natura. Quandoque vero non praedicatur per se, quasi principale praedicatum, sed quasi coniunctum principali praedicato ad connectendum ipsum subiecto; sicut cum dicitur, Socrates est albus, non est intentio loquentis ut asserat Socratem esse in rerum natura, sed ut attribuat ei albedinem mediante hoc verbo, est; et ideo in talibus, est, praedicatur ut adiacens principali praedicato. Et dicitur esse tertium, non quia sit tertium praedicatum, sed quia est tertia dictio posita in enunciatione, quae simul cum nomine praedicato facit unum praedicatum, ut sic enunciatio dividatur in duas partes et non in tres.	2. In relation to the first point two things have to be understood. First, what is meant by "is” is predicated as a third element in the enunciation. To clarify this we must note that the verb "is” itself is sometimes predicated in an enunciation, as in "Socrates is.” By this we intend to signify that Socrates really is. Sometimes, however, "is” is not predicated as the principal predicate, but is joined to the principal predicate to connect it to the subject, as in "Socrates is white.” Here the intention is not to assert that Socrates really is, but to attribute whiteness to him by means of the verb "is.” Hence, in such enunciations "is” is predicated as added to the principal predicate. It is said to be third, not because it is a third predicate, but because it is a third word posited in the enunciation, which together with the name predicated makes one predicate. The enunciation is thus divided into two parts and not three.
Aquinas lib. 2 l. 2 n. 3 Secundo, considerandum est quid est hoc, quod dicit quod quando est, eo modo quo dictum est, tertium adiacens praedicatur, dupliciter dicuntur oppositiones. Circa quod considerandum est quod in praemissis enunciationibus, in quibus nomen ponebatur solum ex parte subiecti, secundum quodlibet subiectum erat una oppositio; puta si subiectum erat nomen finitum non universaliter sumptum, erat sola una oppositio, scilicet est homo, non est homo. Sed quando est tertium adiacens praedicatur, oportet esse duas oppositiones eodem subiecto existente secundum differentiam nominis praedicati, quod potest esse finitum vel infinitum; sicut haec est una oppositio, homo est iustus, homo non est iustus: alia vero oppositio est, homo est non iustus, homo non est non iustus. Non enim negatio fit nisi per appositionem negativae particulae ad hoc verbum est, quod est nota praedicationis.	3. Secondly, we must consider what he means by when "is” is predicated as a third element in the enunciation, in the mode in which we have explained, there are two oppositions. In the enunciations already treated, in which the name is posited only on the part of the subject, there was one opposition in relation to any subject. For example, if the subject was a finite name not taken universally there was only one opposition, "Man is,” "Man is not.” But when "is” is predicated in addition there are two oppositions with regard to the same subject corresponding to the difference of the predicate name, which can be finite or infinite. There is the opposition of "Man is just,” "Man is not just,” and the opposition, "Man is non-just,” "Man is not non-just.” For the negation is effected by applying the negative particle to the verb "is,” which is a sign of a predication.
Aquinas lib. 2 l. 2 n. 4 Deinde cum dicit: dico autem, ut est iustus etc., exponit quod dixerat, est tertium adiacens, et dicit quod cum dicitur, homo est iustus, hoc verbum est, adiacet, scilicet praedicato, tamquam tertium nomen vel verbum in affirmatione. Potest enim ipsum est, dici nomen, prout quaelibet dictio nomen dicitur, et sic est tertium nomen, idest tertia dictio. Sed quia secundum communem usum loquendi, dictio significans tempus magis dicitur verbum quam nomen, propter hoc addit, vel verbum, quasi dicat, ad hoc quod sit tertium, non refert utrum dicatur nomen vel verbum.	4. When he says, I mean by this that in an enunciation such as"Man is just,” etc., he explains what he means by when "is” is predicated as a third element in the enunciation. When we say "Man is just,” the verb "is” is added to the predicate as a third name or verb in the affirmation. Now "is,” like any other word, may be called a name, and thus it is a third name, i.e., word. But because, according to common usage, a word signifying time is called a verb rather than a name Aristotle adds here, or verb, as if to say that with respect to the fact that it is a third thing, it does not matter whether it is called a name or a verb.
Aquinas lib. 2 l. 2 n. 5 Deinde cum dicit: quare quatuor erunt etc., concludit numerum enunciationum. Et primo, ponit conclusionem numeri; secundo, ponit earum habitudinem; ibi: quarum duae quidem etc.; tertio, rationem numeri explicat; ibi: dico autem quoniam est et cetera. Dicit ergo primo quod quia duae sunt oppositiones, quando est tertium adiacens praedicatur, cum omnis oppositio sit inter duas enunciationes, consequens est quod sint quatuor enunciationes illae in quibus est, tertium adiacens, praedicatur, subiecto finito non universaliter sumpto. Deinde cum dicit: quarum duae quidem etc., ostendit habitudinem praedictarum enunciationum ad invicem; et dicit quod duae dictarum enunciationum se habent ad affirmationem et negationem secundum consequentiam, sive secundum correlationem, aut analogiam, ut in Graeco habetur, sicut privationes; aliae vero duae minime. Quod quia breviter et obscure dictum est, diversimode a diversis expositum est.	5. He goes on to say, In this case, therefore, there will be four enunciations, etc. Here he concludes to the number of the enunciations, first giving the number, and then their relationship where he says, two of which will correspond in their sequence, in respect of affirmation and negation, with the privations but two will not. Finally, he explains the reason for the number where he says, I mean that the "is” will be added either to "just” or to "non-just,” etc. He says first, then, that since there are two oppositions when "is” is predicated as a third element in the enunciation, and since every opposition is between two enunciations, it follows that there are four enunciations in which "is” is predicated as a third element when the subject is finite and is not taken universally. When he says, two of which will correspond in their sequence, etc., he shows their relationship. Two of these enunciations are related to affirmation and negation according to consequence (or according to correlation or proportion, as it is in the Greek) like privations; the other two are not. Because this is said so briefly and obscurely, it has been explained in diverse ways.
Aquinas lib. 2 l. 2 n. 6 Ad cuius evidentiam considerandum est quod tripliciter nomen potest praedicari in huiusmodi enunciationibus. Quandoque enim praedicatur nomen finitum, secundum quod assumuntur duae enunciationes, una affirmativa et altera negativa, scilicet homo est iustus, et homo non est iustus; quae dicuntur simplices. Quandoque vero praedicatur nomen infinitum, secundum quod etiam assumuntur duae aliae, scilicet homo est non iustus, homo non est non iustus; quae dicuntur infinitae. Quandoque vero praedicatur nomen privativum, secundum quod etiam sumuntur duae aliae, scilicet homo est iniustus, homo non est iniustus; quae dicuntur privativae.	6. Before we take up the various explanations of this passage there is a general point in relation to it that needs to be clarified. In this kind of enunciation a name can be predicated in three ways. We can predicate a finite name and by this we obtain two enunciations, one affirmative and one negative, "Man is just” and "Man is not just.” These are called simple enunciations. Or, we can predicate an infinite name and by this we obtain two other enunciations, "Man is non-just” and "Man is not non-just,” These are called infinite enunciations. Finally, we can predicate a privative name and again we will have two, "Man is unjust” and "Man is not unjust.” These are called privative.
Aquinas lib. 2 l. 2 n. 7 Quidam ergo sic exposuerunt, quod duae enunciationes earum, quas praemiserat scilicet illae, quae sunt de infinito praedicato, se habent ad affirmationem et negationem, quae sunt de praedicato finito secundum consequentiam vel analogiam, sicut privationes, idest sicut illae, quae sunt de praedicato privativo. Illae enim duae, quae sunt de praedicato infinito, se habent secundum consequentiam ad illas, quae sunt de finito praedicato secundum transpositionem quandam, scilicet affirmatio ad negationem et negatio ad affirmationem. Nam homo est non iustus, quae est affirmatio de infinito praedicato, respondet secundum consequentiam negativae de praedicato finito, huic scilicet homo non est iustus. Negativa vero de infinito praedicato, scilicet homo non est non iustus, affirmativae de finito praedicato, huic scilicet homo est iustus. Propter quod Theophrastus vocabat eas, quae sunt de infinito praedicato, transpositas. Et similiter etiam affirmativa de privativo praedicato respondet secundum consequentiam negativae de finito praedicato, scilicet haec, homo est iniustus, ei quae est, homo non est iustus. Negativa vero affirmativae, scilicet haec, homo non est iniustus, ei quae est, homo est iustus. Disponatur ergo in figura. Et in prima quidem linea ponantur illae, quae sunt de finito praedicato, scilicet homo est iustus, homo non est iustus. In secunda autem linea, negativa de infinito praedicato sub affirmativa de finito et affirmativa sub negativa. In tertia vero, negativa de privativo praedicato similiter sub affirmativa de finito et affirmativa sub negativa: ut patet in subscripta figura. (Figura). Sic ergo duae, scilicet quae sunt de infinito praedicato, se habent ad affirmationem et negationem de finito praedicato, sicut privationes, idest sicut illae quae sunt de privativo praedicato. Sed duae aliae quae sunt de infinito subiecto, scilicet non homo est iustus, non homo non est iustus, manifestum est quod non habent similem consequentiam. Et hoc modo exposuit herminus hoc quod dicitur, duae vero, minime, referens hoc ad illas quae sunt de infinito subiecto. Sed hoc manifeste est contra litteram. Nam cum praemisisset quatuor enunciationes, duas scilicet de finito praedicato et duas de infinito, subiungit quasi illas subdividens, quarum duae quidem et cetera. Duae vero, minime; ubi datur intelligi quod utraeque duae intelligantur in praemissis. Illae autem quae sunt de infinito subiecto non includuntur in praemissis, sed de his postea dicetur. Unde manifestum est quod de eis nunc non loquitur.	7. Now the passage in question has been explained by some in the following way. Two of the enunciations he has given, those with an infinite predicate, are related to the affirmation and negation of the finite predicate according to consequence or analogy, as are privations, i.e., as those with a privative predicate. For the two with an infinite predicate are related according to consequence to those with a finite predicate but in a transposed way, namely, affirmation to negation and negation to affirmation. That is, "Man is non-just,” the affirmation of the infinite predicate, corresponds according to consequence to the negative of the finite predicate, i.e., to "Man is not just”; the negative of the infinite predicate, "Man is not non-just,” corresponds to the affirmative of the finite predicate, i.e., to "Man is just.” Theophrastus for this reason called those with the infinite predicate, "transposed.” The affirmative with a privative predicate also corresponds according to consequence to the negative with a finite predicate, i.e., "Man is unjust” to "Man is not just”; and the negative of the privative predicate to the affirmative of the finite predicate, "Man is not unjust” to "Man is just.” These enunciations can therefore be placed in a table in the following way: Man is just Man is not non-just Man is not unjust Man is not just Man is non-just Man is unjust This makes it clear that two, those with the infinite predicate, are related to the affirmation and negation of the finite predicate in the way privations are, i.e., as those that have a privative predicate. It is also evident that there are two others that do not have a similar consequence, i.e., those with an infinite subject, "Non-man is just” and "Non-man is not just.” This is the way Herminus explained the words but two will not, i.e., by referring it to enunciations with an infinite subject. This, however, is clearly contrary to the words of Aristotle, for after giving the four enunciations, two with a finite predicate and two with an infinite predicate, he adds two of which... but two will not, as though he were subdividing them, which can only mean that both pairs are comprised in what he is saying. He does not include among these the ones with an infinite subject but will mention them later. It is clear, then, that he is not speaking of these here.
Aquinas lib. 2 l. 2 n. 8 Et ideo, ut Ammonius dicit, alii aliter exposuerunt, dicentes quod praedictarum quatuor propositionum duae, scilicet quae sunt de infinito praedicato, sic se habent ad affirmationem et negationem, idest ad ipsam speciem affirmationis et negationis, ut privationes, idest ut privativae affirmationes seu negationes. Haec enim affirmatio, homo est non iustus, non est simpliciter affirmatio, sed secundum quid, quasi secundum privationem affirmatio; sicut homo mortuus non est homo simpliciter, sed secundum privationem; et idem dicendum est de negativa, quae est de infinito praedicato. Duae vero, quae sunt de finito praedicato, non se habent ad speciem affirmationis et negationis secundum privationem, sed simpliciter. Haec enim, homo est iustus, est simpliciter affirmativa, et haec, homo non est iustus, est simpliciter negativa. Sed nec hic sensus convenit verbis Aristotelis. Dicit enim infra: haec igitur quemadmodum in resolutoriis dictum est, sic sunt disposita; ubi nihil invenitur ad hunc sensum pertinens. Et ideo Ammonius ex his, quae in fine I priorum dicuntur de propositionibus, quae sunt de finito vel infinito vel privativo praedicato, alium sensum accipit.	8. Since this exposition is not consonant with Aristotle’s words, others, Ammonius says, have explained this in another way. According to them, two of the four propositions, those of the infinite predicate, are related to affirmation and negation, i.e., to the species itself of affirmation and negation, as privations, that is, as privative affirmations and negations. For the affirmation, "Man is non-just,” is not an affirmation simply, but relatively, as though according to privation; as a dead man is not a man simply, but according to privation. The same thing applies to the negative enunciation with an infinite predicate. However, the two enunciations having finite predicates are not related to the species of affirmation and negation according to privation, but simply, for the enunciation "Man is just” is simply affirmative and "Man is not just” is simply negative. But this meaning does not correspond to the words of Aristotle either, for he says further on: This, then, is the way these are arranged, as we have said in the Analytics, but there is nothing in that text pertaining to this meaning. Ammonius, therefore, interprets this differently and in accordance with what is said at the end of I Priorum [46: 51b 5] about propositions having a finite or infinite or privative predicate.
Aquinas lib. 2 l. 2 n. 9 Ad cuius evidentiam considerandum est quod, sicut ipse dicit, enunciatio aliqua virtute se habet ad illud, de quo totum id quod in enunciatione significatur vere praedicari potest: sicut haec enunciatio, homo est iustus, se habet ad omnia illa, de quorum quolibet vere potest dici quod est homo iustus; et similiter haec enunciatio, homo non est iustus, se habet ad omnia illa, de quorum quolibet vere dici potest quod non est homo iustus. Secundum ergo hunc modum loquendi, manifestum est quod simplex negativa in plus est quam affirmativa infinita, quae ei correspondet. Nam, quod sit homo non iustus, vere potest dici de quolibet homine, qui non habet habitum iustitiae; sed quod non sit homo iustus, potest dici non solum de homine non habente habitum iustitiae, sed etiam de eo qui penitus non est homo: haec enim est vera, lignum non est homo iustus; tamen haec est falsa, lignum est homo non iustus. Et ita negativa simplex est in plus quam affirmativa infinita; sicut etiam animal est in plus quam homo, quia de pluribus verificatur. Simili etiam ratione, negativa simplex est in plus quam affirmativa privativa: quia de eo quod non est homo non potest dici quod sit homo iniustus. Sed affirmativa infinita est in plus quam affirmativa privativa: potest enim dici de puero et de quocumque homine nondum habente habitum virtutis aut vitii quod sit homo non iustus, non tamen de aliquo eorum vere dici potest quod sit homo iniustus. Affirmativa vero simplex in minus est quam negativa infinita: quia quod non sit homo non iustus potest dici non solum de homine iusto, sed etiam de eo quod penitus non est homo. Similiter etiam negativa privativa in plus est quam negativa infinita. Nam, quod non sit homo iniustus, potest dici non solum de homine habente habitum iustitiae, sed de eo quod penitus non est homo, de quorum quolibet potest dici quod non sit homo non iustus: sed ulterius potest dici de omnibus hominibus, qui nec habent habitum iustitiae neque habent habitum iniustitiae.	9. To make Ammonius’ explanation clear, it must be noted that, as Aristotle himself says, the enunciation, by some power, is related to that of which the whole of what is signified in the enunciation can be truly predicated. The enunciation, "Man is just,” for example, is related to all those of which in any way "is a just man” can be truly said. So, too, the enunciation "Man is not just” is related to all those of which in any way "is not a just man” can be truly said. According to this mode of speaking it is evident, then, that the simple negative is wider than the infinite affirmative which corresponds to it. Thus, "is a non-just man” can truly be said of any man who does not have the habit of justice; but "is not a just man” can be said not only of a man not having the habit of justice, but also of what is not a man at all. For example, it is true to say "Wood is not a just man,” but false to say, "Wood is a non-just man.” The simple negative, then, is wider than the infinite affirmative-just as animal is wider than man, since it is verified of more. For a similar reason the simple negative is wider than the privative affirmative, for "is an unjust man” cannot be said of what is not man. But the infinite affirmative is wider than the private affirmative, for "is a non-just man” can be truly said of a boy or of any man not yet having a habit of virtue or vice, but "is an unjust man” cannot. And the simple affirmative is narrower than the infinite negative, for "is not a non-just man” can be said not only of a just man, but also of what is not man at all. Similarly, the privative negative is wider than the infinite negative. For "is not an unjust man” can be said not only of a man having the habit of justice and of what is not man at all—of which "is not a non-just man” can be said—but over and beyond this can be said about all men who neither have the habit of justice nor the habit of injustice.
Aquinas lib. 2 l. 2 n. 10 His igitur visis, facile est exponere praesentem litteram hoc modo. Quarum, scilicet quatuor enunciationum praedictarum, duae quidem, scilicet infinitae, se habebunt ad affirmationem et negationem, idest ad duas simplices, quarum una est affirmativa et altera negativa, secundum consequentiam, idest in modo consequendi ad eas, ut privationes, idest sicut duae privativae: quia scilicet, sicut ad simplicem affirmativam sequitur negativa infinita, et non convertitur (eo quod negativa infinita est in plus), ita etiam ad simplicem affirmativam sequitur negativa privativa, quae est in plus, et non convertitur. Sed sicut simplex negativa sequitur ad infinitam affirmativam; quae est in minus, et non convertitur; ita etiam negativa simplex sequitur ad privativam affirmativam, quae est in minus, et non convertitur. Ex quo patet quod eadem est habitudo in consequendo infinitarum ad simplices quae est etiam privativarum.	10. With these points in mind it is easy to explain the present sentence in Aristotle. Two of which, i.e., the infinites, will be related to the simple affirmation and negation according to consequence, i.e., in their mode of following upon the two simple enunciations, the infinitives will be related as are privations, i.e., as the two privative enunciations. For just as the infinite negative follows upon the simple affirmative, and.is not convertible with it (because the infinite negative is wider), so also the privative negative which is wider follows upon the simple affirmative and is not convertible. But just as the simple negative follows upon the infinite affirmative, which is narrower and is not convertible with it, so also the simple negative follows upon the privative affirmative, which is narrower and is not convertible. From this it is clear that there is the same relationship, with respect to consequence, of infinites to simple enunciations as there is of privatives.
Aquinas lib. 2 l. 2 n. 11 Sequitur, duae autem, scilicet simplices, quae relinquuntur, remotis duabus, scilicet infinitis, a quatuor praemissis, minime, idest non ita se habent ad infinitas in consequendo, sicut privativae se habent ad eas; quia videlicet, ex una parte simplex affirmativa est in minus quam negativa infinita, sed negativa privativa est in plus quam negativa infinita: ex alia vero parte, negativa simplex est in plus quam affirmativa infinita, sed affirmativa privativa est in minus quam infinita affirmativa. Sic ergo patet quod simplices non ita se habent ad infinitas in consequendo, sicut privativae se habent ad infinitas.	11. He goes on to say, but two, i.e., the simple entinciations that are left after the two infinite enunciations have been taken care of, will not, i.e., are not related to infinites according to consequence as privatives are related to them, because, on the one hand, the simple affirmative is narrower than the infinite negative, and the privative negative wider than the infinite negative; and on the other hand, the simple negative is wider than the infinite affirmative, and the privative affirmative narrower than the infinite affirmative. Thus it is clear that simple entinciations are riot related to infinites in respect to consequence as privatives are related to infinites.
Aquinas lib. 2 l. 2 n. 12 Quamvis autem secundum hoc littera philosophi subtiliter exponatur, tamen videtur esse aliquantulum expositio extorta. Nam littera philosophi videtur sonare diversas habitudines non esse attendendas respectu diversorum; sicut in praedicta expositione primo accipitur similitudo habitudinis ad simplices, et postea dissimilitudo habitudinis respectu infinitarum. Et ideo simplicior et magis conveniens litterae Aristotelis est expositio Porphyrii quam Boethius ponit; secundum quam expositionem attenditur similitudo et dissimilitudo secundum consequentiam affirmativarum ad negativas. Unde dicit: quarum, scilicet quatuor praemissarum, duae quidem, scilicet affirmativae, quarum una est simplex et alia infinita, se habebunt secundum consequentiam ad affirmationem et negationem; ut scilicet ad unam affirmativam sequatur alterius negativa. Nam ad affirmativam simplicem sequitur negativa infinita; et ad affirmativam infinitam sequitur negativa simplex. Duae vero, scilicet negativae, minime, idest non ita se habent ad affirmativas, ut scilicet ex negativis sequantur affirmativae, sicut ex affirmativis sequebantur negativae. Et quantum ad utrumque similiter se habent privativae sicut infinitae.	12. But although this explains the words of the Philosopher in a subtle manner the explanation appears a bit forced. For the words of the Philosopher seem to say that diverse relationships will not apply in respect to diverse things; however, in the exposition we have just seen, first there is an explanation of a similitude of relationship to simple enunciations and then an explanation of a dissimilitude of relationship in respect to infinites. The simpler exposition of this passage of Aristotle by Porphyry, which Boethius gives, is therefore more apposite. According to Porphyry’s explanation there is similitude and dissimilitude according to consequence of affirmatives and negatives. Thus Aristotle is saying: Of which, i.e., the four enunciations we are discussing, two, i.e., affirmatives, one simple and the other infinite, will be related according to consequence in regard to affirmation and negation, i.e., so that upon one affirmative follows the other negative, for the infinite negative follows upon the simple affirmative and the simple negative upon the infinite affirmative. But two, i.e., the negatives, will not, i.e., are not so related to affirmatives, i.e., so that affirmatives follow from negatives. And with respect to both, privatives are related in the same way as the infinites.
Aquinas lib. 2 l. 2 n. 13 Deinde cum dicit: dico autem quoniam etc., manifestat quoddam quod supra dixerat, scilicet quod sint quatuor praedictae enunciationes: loquimur enim nunc de enunciationibus, in quibus hoc verbum est solum praedicatur secundum quod est adiacens alicui nomini finito vel infinito: puta secundum quod adiacet iusto; ut cum dicitur, homo est iustus, vel secundum quod adiacet non iusto; ut cum dicitur, homo est non iustus. Et quia in neutra harum negatio apponitur ad verbum, consequens est quod utraque sit affirmativa. Omni autem affirmationi opponitur negatio, ut supra in primo ostensum est. Relinquitur ergo quod praedictis duabus enunciationibus affirmativis respondet duae aliae negativae. Et sic consequens est quod sint quatuor simplices enunciationes.	13. Then Aristotle says, I mean that the "is” will be added either to "just” or to "non-just,” etc. Here he shows how, under these circumstances, we get four enunciations. We are speaking now of enunciations in which the verb "is” is predicated as added to some finite or infinite name, for instance as it adjoins "just” in "Man is just,” or "non-just” in "Man is non-just.” Now since the negation is not applied to the verb in either of these, each is affirmative. However, there is a negation opposed to every affirmation as was shown in the first book. Therefore, two negatives correspond to the two foresaid affirmative enunciations, making four simple enunciations.
Aquinas lib. 2 l. 2 n. 14 Deinde cum dicit: intelligimus vero etc., manifestat quod supra dictum est per quandam figuralem descriptionem. Dicit enim quod id, quod in supradictis dictum est, intelligi potest ex sequenti subscriptione. Sit enim quaedam quadrata figura, in cuius uno angulo describatur haec enunciatio, homo est iustus, et ex opposito describatur eius negatio quae est, homo non est iustus; sub quibus scribantur duae aliae infinitae, scilicet homo est non iustus, homo non est non iustus. (Figura). In qua descriptione apparet quod hoc verbum est, affirmativum vel negativum, adiacet iusto et non iusto. Et secundum hoc diversificantur quatuor enunciationes.	14. Then he says, The following diagram will make this clear. Here he manifests what he has said by a diagrammatic description; for, as he says, what has been stated can be understood from the following diagram. Take a four-sided figure and in one corner write the enunciation "Man is just.” Opposite it write its negation "Man is not just,” and under these the two infinite enunciations, "Man is non-just,” "Man is not non-just.” Man is just Man is not non-just Man is not just Man is non-just It is evident from this table that the verb "is” whether affirmative or negative is adjoined to "just” and "non-just.” It is according to this that the four enunciations are diversified.
Aquinas lib. 2 l. 2 n. 15 Ultimo autem concludit quod praedictae enunciationes disponuntur secundum ordinem consequentiae, prout dictum est in resolutoriis, idest in I priorum. Alia littera habet: dico autem, quoniam est aut homini aut non homini adiacebit, et in figura, est, hoc loco homini et non homini adiacebit. Quod quidem non est intelligendum, ut homo, et non homo accipiatur ex parte subiecti, non enim nunc agitur de enunciationibus quae sunt de infinito subiecto. Unde oportet quod homo et non homo accipiantur ex parte praedicati. Sed quia philosophus exemplificat de enunciationibus in quibus ex parte praedicati ponitur iustum et non iustum, visum est Alexandro, quod praedicta littera sit corrupta. Quibusdam aliis videtur quod possit sustineri et quod signanter Aristoteles nomina in exemplis variaverit, ut ostenderet quod non differt in quibuscunque nominibus ponantur exempla.	15. Finally, he concludes that these enunciations are disposed aaccording to an order of consequence that he has stated in the Analytics, i.e., in I Priorum [46: 51b 5]. There is a variant reading of a previous portion of this text, namely, I mean that "is” will be added either to "man” or to non-man,” and in the diagram "is” is added to "man” and "non-man. This cannot be understood to mean that "man” and "non-man” are taken on the part of the subject; for Aristotle is not treating here of enunciations with an infinite subject and hence "man” and "non-man” must be taken on the part of the predicate. This variant text seemed to Alexander to be corrupt, for the Philosopher has been explicating enunciations in which "just” and "non-just” are posited on the part of the predicate. Others think it can be sustained and that Aristotle has intentionally varied the names to show that it makes no difference what names are used in the examples.

LECTURE 3

Latin	English
Cajetanus lib. 2 l. 3 n. 1 Postquam philosophus distinxit enunciationes in quibus subiicitur nomen infinitum non universaliter sumptum, hic intendit distinguere enunciationes, in quibus subiicitur nomen finitum universaliter sumptum. Et circa hoc tria facit: primo, ponit similitudinem istarum enunciationum ad infinitas supra positas; secundo, ostendit dissimilitudinem earumdem; ibi: sed non similiter etc.; tertio, concludit numerum oppositionum inter dictas enunciationes; ibi: hae duae igitur et cetera. Dicit ergo primo quod similes sunt enunciationes, in quibus est nominis universaliter sumpti affirmatio.	1. Having distinguished enunciations in which the subject is an infinite name not taken universally, Aristotle now distinguishes enunciations in which the subject is a finite name taken universally. He first proposes a similarity between these enunciations and the infinite enunciations already discussed, and then shows their difference where he says, But it is not possible, in the same way as in the former case, that those on the diagonal both be true, etc. Finally, he concludes with the number of oppositions there are between these enunciations where he says, These two pairs, then, are opposed, etc. He says first, then, that enunciations in which the affirmation is of a name taken universally are similar to those already discussed.
Cajetanus lib. 2 l. 3 n. 2 Quoad primum notandum est quod in enunciationibus indefinitis supra positis erant duae oppositiones et quatuor enunciationes, et affirmativae inferebant negativas, et non inferebantur ab eis, ut patet tam in expositione Ammonii, quam Porphyrii. Ita in enunciationibus in quibus subiicitur nomen finitum universaliter sumptum inveniuntur duae oppositiones et quatuor enunciationes: et affirmativae inferunt negativas et non e contra. Unde similiter se habent enunciationes supradictae, si nominis in subiecto sumpti fiat affirmatio universaliter. Fient enim tunc quatuor enunciationes: duae de praedicato finito, scilicet omnis homo est iustus, et eius negatio quae est non omnis homo est iustus; et duae de praedicato infinito, scilicet omnis homo est non iustus, et eius negatio quae est, non omnis homo est non iustus. Et quia quaelibet affirmatio cum sua negatione unam integrat oppositionem, duae efficiuntur oppositiones, sicut et de indefinitis dictum est. Nec obstat quod de enunciationibus universalibus loquens particulares inseruit; quoniam sicut supra de indefinitis et suis negationibus sermonem fecit, ita nunc de affirmationibus universalibus sermonem faciens de earum negationibus est coactus loqui. Negatio siquidem universalis affirmativae non est universalis negativa, sed particularis negativa, ut in I libro habitum est.	2. It is to be noted in relation to Aristotle’s first point that in indefinite enunciations there were two oppositions and four enunciations, the affirmatives inferring the negatives and not being inferred by them, as is clear in the exposition of Ammonius as well as of Porphyry. In enunciations in which the finite name universally taken is the subject there are also two oppositions and four eminciations, the affirmatives inferring the negatives and not the contrary. Hence, enunciations are related in a similar way if the affirmation is made universally of the name taken as the subject. For again, four enunciations will be made, two with a finite predicate-"Every man is just,” and its negation, "Not every man is just”-and two with an infinite predicate-"Every man is non-just” and its negation, "Not every man is non-just.” And since any affirmation together with its negation makes one whole opposition, two oppositions are made, as was also said of indefinite enunciations. There might seem to be an objection to his use of particulars when speaking of universal enunciations, but this cannot be objected to, for just as in dealing with indefinite enunciations he spoke of their negations, so now in dealing with universal affirmatives be is forced to speak of their negations. The negation of the universal affirmative, however, is not the do universal but the particular negative as was stated in the first book.
Cajetanus lib. 2 l. 3 n. 3 Quod autem similis sit consequentia in istis et supradictis indefinitis patet exemplariter. Et ne multa loquendo res clara prolixitate obtenebretur, formetur primo figura de indefinitis, quae supra posita est in expositione Porphyrii, scilicet ex una parte ponatur affirmativa finita, et sub ea negativa infinita, et sub ista negativa privativa. Ex altera parte primo negativa finita, et sub ea affirmativa infinita, et sub ea affirmativa privativa. Deinde sub illa figura formetur alia figura similis illi universaliter: ponatur scilicet ex una parte universalis affirmativa de praedicato finito, et sub ea particularis negativa de praedicato infinito, et ad complementum similitudinis sub ista particularis negativa de praedicato privativo; ex altera vero parte ponatur primo particularis negativa de praedicato infinito, et sub ea universalis affirmativa de praedicato finito, et sub ista universalis affirmativa de praedicato privativo, hoc modo: (Figura). Quibus ita dispositis, exerceatur consequentia semper in ista proxima figura, sicut supra in indefinitis exercita est: sive sequendo expositionem Ammonii, ut infinitae se habeant ad finitas, sicut privativae se habent ad ipsas finitas; finitae autem non se habeant ad infinitas medias, sicut privativae se habent ad ipsas infinitas: sive sectando expositionem Porphyrii, ut affirmativae inferant negativas, et non e contra. Utrique enim expositioni suprascriptae deserviunt figurae, ut patet diligenter indaganti. Similiter ergo se habent enunciationes istae universales ad indefinitas in tribus, scilicet in numero propositionum, et numero oppositionum, et modo consequentiae.	3. A table will make it evident that the consequence is similar in these and in indefinite eminciations. And lest what is clear be made obscure by prolixity let us first make a diagram of the indefinites posited in the last lesson, based upon the exposition of Porphyry. Place the finite affirmative on one side and under it the infinite negative, and under this the privative negative. On the other side put the finite negative first, under it the infinite affirmative, and under this the privative affirmative. Then under this diagram make another similar to it but of universals. On one side put the universal affirmative of the finite predicate, under it the particular negative of the infinite predicate, and to complete the parallel put the particular negative of the privative predicate under this. On the other side, first put the particular negative of the infinite predicate, under it the universal affirmative of the finite predicate,” and under this the universal affirmative of the privative predicate. Thus: DIAGRAM OF THE INDEFINITES Man is just Man is not just Man is not non-just Man is non-just Man is not unjust Man is unjust DIAGRAM OF THE UNIVERSALS Every man is just Not every man is just. Not every man is non-just Every man is non-just Not every man is unjust Every man is unjust In this disposition of enunciations, the consequence always follows in the second diagram just as it followed in regard to indefinites in the first diagram. This is true if we follow the exposition of Ammonius in which infinites are related to finites as privatives are related to the same finites, and the finites not related to the infinite middle enunciatious as privatives are related to those infinites. It is equally true if we follow the exposition of Porphyry, in which affirmatives infer negatives and not vice versa. That the tables serve both expositions will be clear to one studying them. These universal enunciations, therefore, are related in like manner to indefinite entinciations in three things: the number of propositions, the number of oppositions, and the mode of consequence.
Cajetanus lib. 2 l. 3 n. 4 Deinde cum dicit: sed non similiter angulares etc., ponit dissimilitudinem inter istas universales et supradictas indefinitas, in hoc quod angulares non similiter contingit veras esse. Quae verba primo exponenda sunt secundum eam, quam credimus esse ad mentem Aristotelis, expositionem; deinde secundum alios. Angulares enunciationes in utraque figura suprascripta vocat eas quae sunt diametraliter oppositae, scilicet affirmativam finitam ex uno angulo, et affirmativam infinitam sive privativam ex alio angulo: et similiter negativam finitam ex uno angulo, et negativam infinitam vel privativam ex alio angulo.	4. When he says, But it is not possible, in the same way as in the former case, that those on the diagonal both be true, etc., he proposes a difference between the universals and the indefinites, i.e., that it is not possible for the diagonals to be true in the case of universals. First we will explain these words according to the exposition we believe Aristotle had in mind, then according to the opinion of others. Aristotle means by diagonal eminciations those that are diametrically opposed in the diagram above, i.e., the finite affirmative in one corner and the infinite affirmative or the privative in the other; and the finite negative in one corner and the, infinite negative or privative in the other.
Cajetanus lib. 2 l. 3 n. 5 Enunciationes ergo in qualitate similes angulares vocatae, eo quod angulares, idest diametraliter distant, dissimilis veritatis sunt apud indefinitas et universales. Angulares enim indefinitae tam in diametro affirmationum, quam in diametro negationum possunt esse simul verae, ut patet in suprascripta figura indefinitarum. Et hoc intellige in materia contingenti. Angulares vero in figura universalium non sic se habent, quoniam angulares secundum diametrum affirmationum impossibile est esse simul veras in quacumque materia. Angulares autem secundum diametrum negationum quandoque possunt esse simul verae, quando scilicet fiunt in materia contingenti: in materia enim necessaria et remota impossibile est esse ambas veras. Haec est Boethii, quam veram credimus, expositio.	5. Enunciations that are similar in quality, and called diagonal because diametrically distant, are dissimilar in truth, tben, in the case of indefinites and universals. The indefinites on the corners, both oil the diagonal of affirmations and the diagonal of negations can be simultaneously true, as is evident in the table of the indefinite entinciations. This is to be understood in regard to contingent matter. But diagonals of universals are not so related, for angtilars on the diagonal of affirmations cannot be simultaneously true in any matter. Those on the diagonal of negations, however, can sometimes be true simultaneously, i.e., when they are in contingerlt matter. In necessary and rernote matter it is impossible for both of these to be true. This is the exposition of Boethitis, which we believe to be the true one.
Cajetanus lib. 2 l. 3 n. 6 Herminus autem, Boethio referente, aliter exponit. Licet enim ponat similitudinem inter universales et indefinitas quoad numerum enunciationum et oppositionum, oppositiones tamen aliter accipit in universalibus et aliter in indefinitis. Oppositiones siquidem indefinitarum numerat sicut et nos numeravimus, alteram scilicet inter finitas affirmativam et negativam, et alteram inter infinitas affirmativam et negativam, quemadmodum nos fecimus. Universalium vero non sic numerat oppositiones, sed alteram sumit inter universalem affirmativam finitam et particularem negativam finitam, scilicet omnis homo est iustus, non omnis homo est iustus, et alteram inter eamdem universalem affirmativam finitam et universalem affirmativam infinitam, scilicet omnis homo est iustus, omnis homo est non iustus. Inter has enim est contrarietas, inter illas vero contradictio. Dissimilitudinem etiam universalium ad indefinitas aliter ponit. Non enim nobiscum fundat dissimilitudinem inter angulares universalium et indefinitarum supra differentiam quae est inter angulares universalium affirmativas et negativas, sed supra differentiam quae est inter ipsas universalium angulares inter se ex utraque parte. Format namque talem figuram, in qua ex una parte sub universali affirmativa finita, universalis affirmativa infinita est; et ex alia parte sub particulari negativa finita, particularis negativa infinita ponitur; sicque angulares sunt disparis qualitatis, et similiter indefinitarum figuram format hoc modo: (Figura). Quibus ita dispositis, ait in hoc stare dissimilitudinem, quod angulares indefinitarum mutuo se invicem compellunt ad veritatis sequelam, ita quod unius angularis veritas suae angularis veritatem infert undecumque incipias. Universalium vero angulares non se mutuo compellunt ad veritatem, sed ex altera parte necessitas deficit illationis. Si enim incipias ab aliquo universalium et ad suam angularem procedas, veritas universalis non ita potest esse simul cum veritate angularis, quod compellit eam ad veritatem: quia si universalis est vera, sua universalis contraria erit falsa: non enim possunt esse simul verae. Et si ista universalis contraria est falsa, sua contradictoria particularis, quae est angularis primae universalis assumptae, erit necessario vera: impossibile est enim contradictorias esse simul falsas. Si autem incipias e converso ab aliqua particularium et ad suam angularem procedas, veritas particularis ita potest stare cum veritate suae angularis, quod tamen non necessario infert eius veritatem: quia licet sequatur: particularis est vera; ergo sua universalis contradictoria est falsa; non tamen sequitur ultra: ista universalis contradictoria est falsa; ergo sua universalis contraria, quae est angularis particularis assumpti, est vera. Possunt enim contrariae esse simul falsae.	6. Herminus, however, according to Boethius, explains this in another way. He takes the oppositions in one way in universals and in another in indefinites, although he holds that there is a likeness between universals and indefinites with respect to the n timber of enunciations and of oppositions. He arrives at the oppositions of indefinites we have, i.e., one between the affirmative and negative finites, and the other between the affirmative and negative infinites. But he disposes the oppositions of universals in another way, taking one between the finite universal affirmative and finite particular negative, "Every man is just” and "Not every man is just,” and the other between the same finite universal affirmative and the infinite universal affirmative, "Every man is just” and "Every man is non-just.” Between the latter there is contrariety, between the former contradiction. He also proposes the dissimilarity between universals and indefinites in another way. He does not base the dissimilarity between diagonals of universals and indefinites on the difference between affirinative and negative diagonals of universals, as we do, but on the difference between the diagonals of universals on both sides among themselves. Hence he forms his diagram in this way: under the finite universal affirmative be places the infinite universal affirmative, and on the other side, under the finite particular negative the infinite particular negative. Thus the diagonals are of different quality. He also diagrams the indefinites in this way. Every man is just ? contradictories ? Not every man is just contraries subcontraries Every man is non-just ? contradictories ? Not every man is non-just Man is just Man is non-just Man is not just Man is not non-just With enunciations disposed in this way he says their difference is this: that in indefinite enunciations, one on the diagonal is true as a necessary consequence of the truth of the other, so that the truth of one enunciation infers the truth of its diagonal from wherever you begin * But there is no such mutual necessary consequence in universals—from the truth of one on a diagonal to the other—since the necessity of inference fails in part. If you begin from any of the universals and proceed to its diagonal, the truth of the universal cannot be simultaneous with the truth of its diagonal so as to compel it to truth. For if the universal is true its universal contrary will be false, since they cannot be at once true; and if this universal contrary is false, its particular contradictory, which is the diagonal of the first universal assumed, will necessarily be true, since it is impossible for contradictories to be at once false; but if, conversely, you begin with a particular enunciation and proceed to its diagonal, the truth of the particular can so stand with the truth of its diagonal that it does not infer its truth necessarily. For this follows: the particular is true, therefore its universal contradictory is false. But this does not follow: this universal contradictory is false, therefore its universal contrary, which is the diagonal of the particular assumed, is true. For contraries can be at once false.
Cajetanus lib. 2 l. 3 n. 7 Sed videtur expositio ista deficere ab Aristotelis mente quoad modum sumendi oppositiones. Non enim intendit hic loqui de oppositione quae est inter finitas et infinitas, sed de ea quae est inter finitas inter se, et infinitas inter se. Si enim de utroque modo oppositionis exponere volumus, iam non duas, sed tres oppositiones inveniemus: primam inter finitas, secundam inter infinitas, tertiam quam ipse herminus dixit inter finitam et infinitam. Figura etiam quam formavit, conformis non est ei, quam Aristoteles in fine I priorum formavit, ad quam nos remisit, cum dixit: haec igitur quemadmodum in resolutoriis dictum est, sic sunt disposita. In Aristotelis namque figura, angulares sunt affirmativae affirmativis, et negativae negativis.	7. But the way in which oppositions are taken in this exposition does not seem to be what Aristotle had in mind. He did not intend to speak here of the opposition between finites and infinites, but of the opposition between finites themselves and infinites themselves. For if we meant to explain each mode of opposition, there would not be two but three oppositions: first, between finites; second, between infinites; and third, the one Herminus states between finite and infinite. Even the diagram Herminus makes is not like the one Aristotle makes at the end of I Priorum, to which Aristotle himself referred us in the last lesson when he said, This, then, is the way these are arranged, as we have said in the Analytics; for in Aristotle’s diagram affirmatives are diagonal to affirmatives and negatives to negatives.
Cajetanus lib. 2 l. 3 n. 8 Deinde cum dicit: hae igitur duae etc., concludit numerum propositionum. Et potest dupliciter exponi; primo, ut ly hae demonstret universales, et sic est sensus, quod hae universales finitae et infinitae habent duas oppositiones, quas supra declaravimus; secundo, potest exponi ut ly hae demonstret enunciationes finitas et infinitas quoad praedicatum sive universales sive indefinitas, et tunc est sensus, quod hae enunciationes supradictae habent duas oppositiones, alteram inter affirmationem finitam et eius negationem, alteram inter affirmationem infinitam et eius negationem. Placet autem mihi magis secunda expositio, quoniam brevitas cui Aristoteles studebat, replicationem non exigebat, sed potius quia enunciationes finitas et infinitas quoad praedicatum secundum diversas quantitates enumeraverat, ad duas oppositiones omnes reducere, terminando earum tractatum, voluit.	8. Then Aristotle says, These two pairs, then, are opposed, etc. Here he concludes to the number of propositions. What he says here can be interpreted in two ways. In the first way, "these” designates universals, and thus the meaning is that the finite and infinite universals have two oppositions, which we have explained above. In the second, "these” designates enunciations which are finite and infinite with respect to the predicate, whether universal or indefinite, and then the meaning is that these enunciations have two oppositions, one between the finite affirmation and its negation and the other between the infinite affirmation and its negation. The second exposition seems more satisfactory to me, for the brevity for which, Aristotle strove allows for no repetition; hence, in terminating his treatment of the enunciations he had enumerated—those with a finite and infinite predicate according to diverse quantities—he meant to reduce all the oppositions to two.
Cajetanus lib. 2 l. 3 n. 9 Deinde cum dicit: aliae autem ad id quod est etc., intendit declarare diversitatem enunciationum de tertio adiacente, in quibus subiicitur nomen infinitum. Et circa hoc tria facit: primo, proponit et distinguit eas; secundo, ostendit quod non dantur plures supradictis; ibi: magis autem etc.; tertio, ostendit habitudinem istarum ad alias; ibi: hae autem extra et cetera. Ad evidentiam primi advertendum est tres esse species enunciationum de inesse, in quibus explicite ponitur hoc verbum est. Quaedam sunt, quae subiecto sive finito sive infinito nihil habent additum ultra verbum, ut, homo est, non homo est. Quaedam vero sunt quae subiecto finito habent, praeter verbum, aliquid additum sive finitum sive infinitum, ut, homo est iustus, homo est non iustus. Quaedam autem sunt quae subiecto infinito, praeter verbum, habent aliquid additum sive finitum sive infinitum, ut, non homo est iustus, non homo est non iustus. Et quia de primis iam determinatum est, ideo de ultimis tractare volens, ait: aliae autem sunt, quae habent aliquid, scilicet praedicatum, additum supra verbum est, ad id quod est, non homo, quasi ad subiectum, idest ad subiectum infinitum. Dixit autem quasi, quia sicut nomen infinitum deficit a ratione nominis, ita deficit a ratione subiecti. Significatum siquidem nominis infiniti non proprie substernitur compositioni cum praedicato quam importat, est, tertium adiacens. Enumerat quoque quatuor enunciationes et duas oppositiones in hoc ordine, sicut in superioribus fecit. Distinguit etiam istas ex finitate vel infinitate praedicata. Unde primo, ponit oppositiones inter affirmativam et negativam habentes subiectum infinitum et praedicatum finitum, dicens: ut, non homo est iustus, non homo non est iustus. Secundo, ponit oppositionem alteram inter affirmativam et negativam, habentes subiectum infinitum et praedicatum infinitum, dicens: ut, non homo est non iustus, non homo non est non iustus.	9. When he says, and there, are two other pairs if something is added to "non-man” as a subject, etc., he shows the diversity of enunciations when "is” is added as a third element and the subject is an infinite name. First, he proposes and distinguishes them; secondly, he shows that there are no more opposites than these where he says, There will be no more opposites than these; thirdly, he shows the relationship of these to the others where he says, The latter, however, are separate from the former and distinct from them, etc. With respect to the first point, it should be noted that there are three species of absolute [de inesse] enunciations in which the verb "is” is posited explicitly. Some have nothing added to the subject—which can be either finite or infinite—beyond the verb, as in "Man is,” "Non-man is.” Some have, besides the verb, something either finite or infinite added to a finite subject, as in "Man is just,” "Man is non-just.” Finally, some have, besides the verb, something either finite or infinite added to an infinite subject, as in "Non-man is just,” "Non-man is non-just.” He has already treated the first two and now intends to take tip the last ones. And there are two other pairs, he says, that have something, namely a predicate. added beside the verb "is” to "non-man” as if to a subject, i.e., to an infinite subject. He says "as if” because the infinite name falls short of the notion of a subject insofar as it falls short of the notion of a name. Indeed, the signification of an infinite name is not properly submitted to composition with the predicate, which "is,” the third element added, introduces. Aristotle enumerates four enunciations and two oppositions in this order as he did in the former. In addition he distinguishes these from the former finiteness and infinity. First, he posits the opposition between affirmative and negative enunciations with an infinite subject and a finite predicate, "Non-man is just,” "Non-man is not just.” Then he posits another opposition between those with an infinite subject and an infinite predicate, "Non-man is non-just,” "Non-man is not non-just.
Cajetanus lib. 2 l. 3 n. 10 Deinde cum dicit: magis autem plures etc., ostendit quod non dantur plures oppositiones enunciationum supradictis. Ubi notandum est quod enunciationes de inesse, in quibus explicite ponitur hoc verbum est, sive secundum, sive tertium adiacens, de quibus loquimur, non possunt esse plures quam duodecim supra positae; et consequenter oppositiones earum secundum affirmationem et negationem non sunt nisi sex. Cum enim in tres ordines divisae sint enunciationes, scilicet in illas de secundo adiacente, in illas de tertio subiecti finiti, et in illas de tertio subiecti infiniti, et in quolibet ordine sint quatuor enunciationes; fiunt omnes enunciationes duodecim, et oppositiones sex. Et quoniam subiectum earum in quolibet ordine potest quadrupliciter quantificari, scilicet universalitate, particularitate, et singularitate et indefinitione; ideo istae duodecim multiplicantur in quadraginta octo. Quater enim duodecim quadraginta octo faciunt. Nec possibile est plures his imaginari. Et licet Aristoteles nonnisi viginti harum expresserit, octo in primo ordine, octo in secundo, et quatuor in tertio, attamen per eas reliquas voluit intelligi. Sunt autem sic enumerandae et ordinandae secundum singulos ordines, ut affirmationi negatio prima ex opposito situetur, ut oppositionis intentum clarius videatur. Et sic contra universalem affirmativam non est ordinanda universalis negativa, sed particularis negativa, quae est illius negatio; et e converso, contra particularem affirmativam non est ordinanda particularis negativa, sed universalis negativa quae est eius negatio. Ad clarius autem intuendum numerum, coordinandae sunt omnes, quae sunt similis quantitatis, simul in recta linea, distinctis tamen ordinibus tribus supradictis. Quod ut clarius elucescat, in hac subscripta videatur figura: (Figura). Quod autem plures his non sint, ex eo patet quod non contingit pluribus modis variari subiectum et praedicatum penes finitum et infinitum, nec pluribus modis variantur finitum et infinitum subiectum. Nulla enim enunciatio de secundo adiacente potest variari penes praedicatum finitum vel infinitum, sed tantum penes subiectum quod sufficienter factum apparet. Enunciationes autem de tertio adiacente quadrupliciter variari possunt, quia aut sunt subiecti et praedicati finiti, aut utriusque infiniti, aut subiecti finiti et praedicati infiniti, aut subiecti infiniti et praedicati finiti. Quarum nullam praetermissam esse superior docet figura.	10. Then he says, There will be no more opposites than these. Here he points out that there are no more oppositions of enunciations than the ones be has already given. We should note, then, that simple [or absolute] enunciations—of which we have been speaking—in which the verb "is” is explicitly posited whether it is the second or third element added, cannot be more than the twelve posited. Consequently, their oppositions according to affirmation and negation are only six. For enunciations are divided into three orders: those with the second element added, those with the third element added to a finite subject, and those with the third element added to an infinite subject; and in any order there are four enunciations. And since their subject in any order can be quantified in four ways, i.e., by universality, particularity, singularity, and indefiniteness, these twelve will be increased to fortyeight (four twelves being forty-eight). Nor is it possible to imagine more than these. Aristotle has only expressed twenty of these, eight in the first order, eight in the second, and four in the third, but through them be intended the rest to be understood. They are to be enumerated and disposed according to each order so that the primary negation is placed opposite an affirmation in order to make the relation of opposition more evident. Thus, the universal negative should not be ordered as opposite to the universal affirmative, but the particular negative, which is its negation. Conversely, the particular negative should not be ordered as opposite to the particular affirmative, but the universal negative, which is its negation. For a clearer look at their number all those of similar quantity should be co-ordered in a straight line and in the three distinct orders given above. The following diagram will make this clear. FIRST ORDER Socrates is Socrates is not Non-Socrates is Non-Socrates is not Some man is Some man is not Some non-man is Some non-man is not Man is Man is not Non-man is Non-man is not Every man is No man is Every non-man is No non-man is SECOND ORDER Socrates is just Socrates is not just Socrates is non-just Socrates is not non-just Some man is just Some man is not just Some man is non-just Some man is not non-just Man is just Man is not just Man is non-just Man is not non-just Every man is just No man is just Every man is non-just No man is non-just THIRD ORDER Non-Socrates is just Non-Socrates is not just Non-Socrates is non-just Non-Socrates is not non-just Some non-man is just Some non-man is not just Some non-man is non-just Some non-man is not non-just Non-man is just Non-man is not just Non-man is non-just Non-man is not non-just Every non-man is just No non-man is just Every non-man is non-just No non-man is non-just It is evident that there are no more than these, for the subject and the predicate cannot be varied in any other way with respect to finite and infinite. Nor can the finite and infinite subject be varied in any other way, for the enunciation with a second adjoining element cannot be varied with a finite and infinite predicate but only in respect to the subject. This is clear enough. But enunciations with a third adjoining element can be varied in four ways: they may have either a finite subject and predicate, or an infinite subject and predicate, or a finite subject and infinite predicate, or an infinite subject and finite predicate. These variations are all evident in the above table.
Cajetanus lib. 2 l. 3 n. 11 Deinde cum dicit: hae autem extra illas etc., ostendit habitudinem harum quas in tertio ordine numeravimus ad illas, quae in secundo sitae sunt ordine, et dicit quod istae sunt extra illas, quia non sequuntur ad illas, nec e converso. Et rationem assignans subdit: ut nomine utentes eo quod est non homo, idest ideo istae sunt extra illas, quia istae utuntur nomine infinito loco nominis, dum omnes habent subiectum infinitum. Notanter autem dixit enunciationes subiecti infiniti uti ut nomine, infinito nomine, quia cum subiici in enunciatione proprium sit nominis, praedicari autem commune nomini et verbo, omne subiectum enunciationis ut nomen subiicitur.	11. Then when he says, The latter, however, are separate from the former and distinct from them, etc., he shows the relationship of those we have put in the third order to those in the second order. The former, he says, are distinct from the latter because they do not follow upon the latter, nor conversely. He assigns the reason when he adds: because of the use of "non-man” as a name, i.e., the former are separate from the latter because the former use an infinite name in place of a name, since they all have an infinite subject. It should be noted that he says enunciations of an infinite subject use an infinite name as a name; for to be subjected in an enunciation is proper to a name, to be predicated common to a name and a verb, and therefore every subject of an enunciation is subjected as a name.
Cajetanus lib. 2 l. 3 n. 12 Deinde cum dicit: in his vero in quibus est etc., determinat de enunciationibus in quibus ponuntur verba adiectiva. Et circa hoc tria facit: primo, distinguit eas; secundo, respondet cuidam tacitae quaestioni; ibi: non enim dicendum est etc.; tertio, concludit earum conditiones; ibi: ergo et caetera eadem et cetera. Ad evidentiam primi resumendum est, quod inter enunciationes in quibus ponitur est secundum adiacens, et eas in quibus ponitur est tertium adiacens talis est differentia quod in illis, quae sunt de secundo adiacente, simpliciter fiunt oppositiones, scilicet ex parte subiecti tantum variati per finitum et infinitum; in his vero, quae habent est tertium adiacens dupliciter fiunt oppositiones, scilicet et ex parte praedicati et ex parte subiecti, quia utrumque variari potest per finitum et infinitum. Unde unum ordinem tantum enunciationum de secundo adiacente fecimus, habentem quatuor enunciationes diversimode quantificatas et duas oppositiones. Enunciationes autem de tertio adiacente oportuit partiri in duos ordines, quia sunt in eis quatuor oppositiones et octo enunciationes, ut supra dictum est. Considerandum quoque est quod enunciationes, in quibus ponuntur verba adiectiva, quoad significatum aequivalent enunciationibus de tertio adiacente, resoluto verbo adiectivo in proprium participium et est, quod semper fieri licet, quia in omni verbo adiectivo clauditur verbum substantivum. Unde idem significant ista, omnis homo currit, quod ista, omnis homo est currens. Propter quod Boethius vocat enunciationes cum verbo adiectivo de secundo adiacente secundum vocem, de tertio autem secundum potestatem, quia potest resolvi in tertium adiacens, cui aequivalet. Quoad numerum autem enunciationum et oppositionum, enunciationes verbi adiectivi formaliter sumptae non aequivalent illis de tertio adiacente, sed aequivalent enunciationibus, in quibus ponitur est secundum adiacens. Non possunt enim fieri oppositiones dupliciter in enunciationibus adiectivis, scilicet ex parte subiecti et praedicati, sicut fiebant in substantivis de tertio adiacente, quia verbum, quod praedicatur in adiectivis, infinitari non potest. Sed oppositiones adiectivarum fiunt simpliciter, scilicet ex parte subiecti tantum variati per infinitum et finitum diversimode quantificati, sicut fieri didicimus supra in enunciationibus substantivis de secundo adiacente, eadem ducti ratione, quia praeter verbum nulla est affirmatio vel negatio, sicut praeter nomen esse potest. Quia autem in praesenti tractatu non de significationibus, sed de numero enunciationum et oppositionum sermo intenditur, ideo Aristoteles determinat diversificandas esse enunciationes adiectivas secundum modum, quo distinctae sunt enunciationes in quibus ponitur est secundum adiacens. Et ait quod in his enunciationibus, in quibus non contingit poni hoc verbum est formaliter, sed aliquod aliud, ut, currit, vel, ambulat, idest in enunciationibus adiectivis, idem faciunt quoad numerum oppositionum et enunciationum sic posita, scilicet nomen et verbum, ac si est secundum adiacens subiecto nomini adderetur. Habent enim et istae adiectivae, sicut illae, in quibus ponitur est, duas oppositiones tantum, alteram inter finitas, ut, omnis homo currit, omnis homo non currit, alteram inter infinitas quoad subiectum, ut, omnis non homo currit, omnis non homo non currit.	12. Next he takes up enunciations in which adjective verbs are posited, when he says, In enunciations in which "is” does not join the predicate to the subject, etc. First, he distinguishes these adjective verbs; secondly, he answers an implied question where he says, We must not say "non-every man,” etc.; thirdly, he concludes with their conditions where he says, All else in the enunciations in which "is” does not join the predicate to the subject will be the same, etc. It is necessary to note here that there is a difference between enunciations in which "is” is posited as a second adjoining element and those in which it is posited as a third element. In those with "is” as a second element oppositions are simple, i.e., varied only on the part of the subject by finite and infinite. In those having "is” as a third element oppositions are made in two ways—on the part of the predicate and on the part of the subject—for both can be varied by finite and infinite. Hence we made only one order of enunciations with "is” as the second element. It had four enunciations quantified in diverse ways, and two oppositions. But enunciations with "is” as a third element must be divided into two orders, because in them there are four oppositions and eight enunciations, as we said above. Enunciations with adjective verbs are made equivalent in signification to enunciations with "is” as the third element by resolving the adjective verb into its proper participle and "is,” which may always be done because a substantive verb is contained in every adjective verb. For example, "Every man runs” signifies the same thing as "Every man is running.” Because of this Boethius calls enunciations having an adjective verb "eminciations of the second adjoining element according to vocal sound, but of the third adjoining element according to power.” He designates them in this manner because they can be resolved into enunciations with a third adjoining element to which they are equivalent. With respect to the number and oppositions of enunciations, those with an adjective verb, formally taken, are not equivalent to those with a third adjoining element but to those in which "is” is posited as the second element. For oppositions cannot be made in two ways in adjectival enunciations as they are in the case of substantival enunciations with a third adjoining element, namely, on the part of the subject and predicate, because the verb which is predicated in adjectival enunciations cannot be made infinite. Hence oppositions of adjectival enunciations are made simply, i.e., only by the subject quantified in diverse ways being varied by finite and infinite, as was done above in substantival enunciations with a second adjoining element, and for the same reason, i.e., there can be no affirmation or negation without a verb but there can be without a name. Since the present treatment is not of significations but of the number of enunciations and oppositions, Aristotle determines that adjectival enunciations are to be diversified according to the mode in which enunciations with "is” as the second adjoining element are distinguished. And he says that in enunciations in which the verb "is” is not posited formally, but some other verb, such as "matures” or "walks,” i.e., in adjectival enunciations, the name and verb form the same scheme with respect to the number of oppositions and enunciations as when is as a second adjoining element is added to the name as a subject. For these adjectival enunciations, like the ones in which "is” is posited, have only two oppositions, one between the finites, as in "Every man runs,” "Not every man runs,” the other between the infinites with respect to subject, as in "Every non-man runs,” "Not every non-man runs.”
Cajetanus lib. 2 l. 3 n. 13 Deinde cum dicit: non enim dicendum est etc., respondet tacitae quaestioni. Et circa hoc facit duo: primo, ponit solutionem quaestionis; deinde, probat eam; ibi: manifestum est autem et cetera. Est ergo quaestio talis: cur negatio infinitans numquam addita est supra signo universali aut particulari, ut puta, cum vellemus infinitare istam, omnis homo currit, cur non sic infinitata est, non omnis homo currit, sed sic, omnis non homo currit? Huic namque quaestioni respondet, dicens quod quia nomen infinitabile debet significare aliquid universale, vel singulare; omnis autem et similia signa non significant aliquid universale aut singulare, sed quoniam universaliter aut particulariter; ideo non est dicendum, non omnis homo, si infinitare volumus (licet debeat dici, si negare quantitatem enunciationis quaerimus), sed negatio infinitans ad ly homo, quod significat aliquid universale, addenda est, et dicendum, omnis non homo.	13. Then he answers an implied question when he says, We, must not say "non-every man” but must add the negation to man, etc. First he states the solution of the question, then he proves it where he says, This is evident from the following, etc. The question is this: Why is the negation that makes a word infinite never added to the universal or particular sign? For example, when we wish to make "Every man runs” infinite, why do we do it in this way "Every non-man runs,” and not in this, "Non-every man runs.” He answers the question by saying that to be capable of being made infinite a name has to signify something universal or singular. "Every” and similar signs, however, do not signify something universal or singular, but that something is taken universally or particularly. Therefore, we should not say "non-every man” if we wish to infinitize (although it may be used if we wish to deny the quantity of an enunciation), but must add the infinitizing negation to "man,” which signifies something universal, and say "every non-man.”
Cajetanus lib. 2 l. 3 n. 14 Deinde cum dicit: manifestum est autem ex eo quod est etc., probat hoc quod dictum est, scilicet quod omnis et similia non significant aliquod universale, sed quoniam universaliter tali ratione. Illud, in quo differunt enunciationes praecise differentes per habere et non habere ly omnis, est non universale aliquod, sed quoniam universaliter; sed illud in quo differunt enunciationes praecise differentes per habere et non habere ly omnis, est significatum per ly omnis; ergo significatum per ly omnis est non aliquid universale, sed quoniam universaliter. Minor huius rationis, tacita in textu, ex se clara est. Id enim in quo, caeteris paribus, habentia a non habentibus aliquem terminum differunt, significatum est illius termini. Maior vero in littera exemplariter declaratur sic. Illae enunciationes homo currit, et omnis homo currit, praecise differunt ex hoc, quod in una est ly omnis, et in altera non. Tamen non ita differunt ex hoc, quod una sit universalis, alia non universalis. Utraque enim habet subiectum universale, scilicet ly homo, sed differunt, quia in ea, ubi ponitur ly omnis, enunciatur de subiecto universaliter, in altera autem non universaliter. Cum enim dico, homo currit, cursum attribuo homini universali, sive communi, sed non pro tota humana universitate; cum autem dico, omnis homo currit, cursum inesse homini pro omnibus inferioribus significo. Simili modo declarari potest de tribus aliis, quae in textu adducuntur, scilicet, homo non currit, respectu suae universalis universaliter, omnis homo non currit: et sic de aliis. Relinquitur ergo, quod, omnis et nullus et similia signa nullum universale significant, sed tantummodo significant, quoniam universaliter de homine affirmant vel negant.	14. Where he says, This is evident from the following, etc., he proves that "every” and similar words do not signify a universal but that a universal is taken universally. His argument is the following: That by which enunciations having or not having the "every” differ is not the universal; rather, they differ in that the universal is taken universally. But that by which enunciations having and not having the "every” differ is signified by the "every.” Therefore, that which is signified by the "every” is not a universal but that the universal is taken universally. The minor of the argument is evident, though not explicitly given in the text: that in which the having of some term differs from the not having of it, other things being equal, is the signification of that term. The major is made evident by examples. The enunciations "Man matures” and "Every man matures” differ precisely by the fact that in one there is an "every,” in the other not. However, they do not differ in such a way by this that one is universal, the other not universal, for both have the universal subject, "man”; they differ because in the one in which "every” is posited, the enunciation is of the subject universally, but in the other not universally. For when I say, "Man matures,” I attribute maturing to "man” as universal or common but not to man as to the whole human race; when I say, "Every man matures,” however, I signify maturing to be present to man according to all the inferiors. This is evident, too, in the three other examples of enunciations in Aristotle’s text. For example, "Non-man matures” when its universal is taken universally becomes "Every non-man matures,” and so of the others. It follows, therefore, that "every” and "no” and similar signs do not signify a universal but only signify that they affirm or deny of man universally.
Cajetanus lib. 2 l. 3 n. 15 Notato hic duo: primum est quod non dixit omnis et nullus significat universaliter, sed quoniam universaliter; secundum est, quod addit, de homine affirmant vel negant. Primi ratio est, quia signum distributivum non significat modum ipsum universalitatis aut particularitatis absolute, sed applicatum termino distributo. Cum enim dico, omnis homo, ly omnis denotat universitatem applicari illi termino homo, ita quod Aristoteles dicens quod omnis significat quoniam universaliter, per ly quoniam insinuavit applicationem universalitatis importatam in ly omnis in actu exercito, sicut et in I posteriorum, in definitione scire applicationem causae notavit per illud verbum quoniam, dicens: scire est rem per causam cognoscere, et quoniam illius est causa. Ratio autem secundi insinuat differentiam inter terminos categorematicos et syncategorematicos. Illi siquidem ponunt significata supra terminos absolute; isti autem ponunt significata sua supra terminos in ordine ad praedicata. Cum enim dicitur, homo albus, ly albus denominat hominem in seipso absque respectu ad aliquod sibi addendum. Cum vero dicitur, omnis homo, ly omnis etsi hominem distribuat, non tamen distributio intellectum firmat, nisi in ordine ad aliquod praedicatum intelligatur. Cuius signum est, quia, cum dicimus, omnis homo currit, non intendimus distribuere hominem pro tota sua universitate absolute, sed in ordine ad cursum. Cum autem dicimus, albus homo currit, determinamus hominem in seipso esse album et non in ordine ad cursum. Quia ergo omnis et nullus, sicut et alia syncategoremata, nil aliud in enunciatione faciunt, nisi quia determinant subiectum in ordine ad praedicatum, et hoc sine affirmatione et negatione fieri nequit; ideo dixit quod nil aliud significant, nisi quoniam universaliter de nomine, idest de subiecto, affirmant vel negant, idest affirmationem vel negationem fieri determinant, ac per hoc a categorematicis ea separavit. Potest etiam referri hoc quod dixit, affirmant vel negant, ad ipsa signa, scilicet omnis et nullus, quorum alterum positive distribuit, alterum removendo.	15. Two things should be noted here: first, that Aristotle does not say "every” and "no” signify universally, but that the universal is taken universally; secondly, that he adds, they affirm or deny of man. The reason for the first is that the distributive sign does not signify the mode of universality or of particularity absolutely, but the mode applied to a distributed term. When I say, "every man” the "every” denotes that universality is applied to the term "man.” Hence, when Aristotle says "every” signifies that a universal is taken universally, by the "that” he conveys the application in actual exercise of the universality denoted by the "every,” just as in I Posteriorum [2: 71b 10] in the definition of "to know,” namely, To know scientifically is to know a thing through its cause and that this is its cause, he signifies by the word "that” the application of the cause. The reason for the second is to imply the difference between categorematic and syneategorematic terms. The former apply what is signified to the terms absolutely; the latter apply what they signify to the terms in relation to the predicates. For example, in "white man” the "white” denominates man in himself apart from any regard to something to be added; but in "every man,” although the "every” distributes man,” the distribution does not confirm the intellect unless it is under stood in relation to some predicate. A sign of this is that when we say "Every man runs” we do not intend to distribute "man” in its whole universality absolutely, but only in relation to "running.” When we say "White man runs,” on the other hand, we designate man in himself as "white” and not in relation to "running.” Therefore, since "every” and "no” and the other syncategorematic terms do nothing except determine the subject in relation to the predicate in the enunciation, and this cannot be done without affirmation and negation, Aristotle says that they only signify that the affirmation or negation is of a name, i.e., of a subject, universally, i.e., they prescribe the affirmation or negation that is being formed, and by this he separates them from categorematic terms. They affirm, or deny can also be referred to the signs themselves i.e., "every” and "no,” one of which distributes positively, the other distributes by removing.
Cajetanus lib. 2 l. 3 n. 16 Deinde cum dicit: ergo et caetera eadem etc., concludit adiectivarum enunciationum conditiones. Dixerat enim quod adiectivae enunciationes idem faciunt quoad oppositionum numerum, quod substantivae de secundo adiacente; et hoc declaraverat, oppositionum numero exemplariter subiuncto. Et quia ad hanc convenientiam sequitur convenientia quoad finitationem praedicatorum, et quoad diversam subiectorum quantitatem, et earum multiplicationem ex ductu quaternarii in seipsum, et si qua sunt huiusmodi enumerata; ideo concludit: ergo et caetera, quae in illis servanda erant, eadem, idest similia istis apponenda sunt.	16. When he says All else in enunciations in which "is”does not join the predicate to the subject, etc., he concludes the treatment of the conditions of adjectival enunciations. He has already stated that adjectival enunciations are the same with respect to the number of oppositions as substantival enunciations with "is” as the second element, and has clarified this by a table showing the number of oppositions. Now, since upon this conformity follows conformity both with respect to finiteness of predicates and with respect to the diverse quantity of subjects, and also-if any enunciations of this kind are enumerated—their multiplication in sets of four, he concludes, Therefore also the other things, which are to be observed in them, are to be considered the same, i.e., similar to these.

LECTURE 4

Latin	English
Cajetanus lib. 2 l. 4 n. 1 Postquam determinatum est de diversitate enunciationum, hic intendit removere quaedam dubia circa praedicta. Et circa hoc facit sex secundum numerum dubiorum, quae suis patebunt locis. Quia ergo supra dixerat quod in universalibus non similiter contingit angulares esse simul veras, quia affirmativae angulares non possunt esse simul verae, negativae autem sic; poterat quispiam dubitare, quae est causa huius diversitatis. Ideo nunc illius dicti causam intendit assignare talem, quia, scilicet, angulares affirmativae sunt contrariae inter se; contrarias autem in nulla materia contingit esse simul veras. Angulares autem negativae sunt subcontrariae illis oppositae; subcontrarias autem contingit esse simul veras. Et circa haec duo facit: primo, declarat conditiones contrariarum et subcontrariarum; secundo, quod angulares affirmativae sint contrariae et quod angulares negativae sint subcontrariae; ibi: sequuntur vero et cetera. Dicit ergo resumendo: quoniam in primo dictum est quod enunciatio negativa contraria illi affirmativae universali, scilicet, omne animal est iustum, est ista, nullum animal est iustum; manifestum est quod istae non possunt simul, idest in eodem tempore, neque in eodem ipso, idest de eodem subiecto esse verae. His vero oppositae, idest subcontrariae inter se, possunt esse simul verae aliquando, scilicet in materia contingenti, ut, quoddam animal est iustum, non omne animal est iustum.	1. Having treated the diversity of enunciations Aristotle now answers certain questions about them. He takes up six points related to the number of difficulties. These will become evident as we come to them. Since he has said that in universal enunciations the diagonals in one case cannot be at once true but can be in another, for the diagonal affirmatives cannot be at once true but the negatives can,” someone might raise a question as to the cause of this diversity. Therefore, it is his intention now to assign the cause of this: namely, that the diagonal affirmatives are contrary to each other, and contraries cannot be at once true in any matter; but the diagonal negatives are subcontraries opposed to these and can be at once true. In relation to this he first states the conditions for contraries and subcontraries. Then he shows that diagonal affirmatives are contraries and that diagonal negatives are subcontraries where he says, Now the enunciation "No man is just” follows upon the enunciation "Every man is nonjust,” etc. By way of resumé, therefore, he says that in the first book it was said that the negative enunciation contrary to the universal affirmative "Every animal is just” is "No animal is just.” It is evident that these cannot be at once true, i.e., at the same time, nor of the same thing, i.e., of the same subject. But the opposites of these, i.e., the subcontraries, can sometimes be at once true, i.e., in contingent matter, as in "Some animal is just” and "Not every animal is just.”
Cajetanus lib. 2 l. 4 n. 2 Deinde cum dicit: sequuntur vero etc., declarat quod angulares affirmativae supra positae sint contrariae, negativae vero subcontrariae. Et primum quidem ex eo quod universalis affirmativa infinita et universalis negativa simplex aequipollent; et consequenter utraque earum est contraria universali affirmativae simplici, quae est altera angularis. Unde dicit quod hanc universalem negativam finitam, nullus homo est iustus, sequitur aequipollenter illa universalis affirmativa infinita, omnis homo est non iustus. Secundum vero declarat ex eo quod particularis affirmativa finita et particularis negativa infinita aequipollent. Et consequenter utraque earum est subcontraria particulari negativae simplici, quae est altera angularis, ut in figura supra posita inspicere potes. Unde subdit quod illam particularem affirmativam finitam, aliquis homo est iustus, opposita sequitur aequipollenter (opposita intellige non istius particularis, sed illius universalis affirmativae infinitae), non omnis homo est non iustus. Haec enim est contradictoria eius. Ut autem clare videatur quomodo supra dictae enunciationes sint aequipollentes, formetur figura quadrata, in cuius uno angulo ponatur universalis negativa finita, et sub ea contradictoria particularis affirmativa finita; ex alia vero parte locetur universalis affirmativa infinita, et sub ea contradictoria particularis negativa infinita, noteturque contradictio inter angulares et collaterales inter se, hoc modo: (Figura). His siquidem sic dispositis, patet primo ipsarum universalium mutua consequentia in veritate et falsitate, quia si altera earum est vera, sua angularis contradictoria est falsa; et si ista est falsa, sua collateralis contradictoria, quae est altera universalis, erit vera, et similiter procedit quoad falsitatem particularium. Deinde eodem modo manifestatur mutua sequela. Si enim altera earum est vera, sua angularis contradictoria est falsa, ista autem existente falsa, sua contradictoria collateralis, quae est altera particularis erit vera; simili quoque modo procedendum est quoad falsitatem.	2. When he says, Now the enunciation, "No man is just” follows upon the enunciation "Every man is nonjust,” etc., he shows that the diagonal affirmatives previously posited are contraries, the negatives subcontraries. First he manifests this from the fact that the infinite universal affirmative and the simple universal negative are equal in meaning, and consequently each of them is contrary to the simple universal affirmative, which is the other diagonal. Hence, he says that the infinite universal affirmative "Every man is non-just” follows upon the finite universal negative "No man is just,” equivalently. Secondly he shows this from the fact that the finite particular affirmative and the infinite particular negative are equal in meaning, and consequently each of these is subcontrary to the simple particular negative, which is the other diagonal. This you can see in the previous diagram. He says, then, that the opposite "Not every man is non-just” follows upon the finite particular "Some man is just” equivalently (understand "the opposite” not of this particular but of the infinite universal affirmative, for this is its contradictory). In order to see clearly how these enunciations are equivalent, make a four-sided figure, putting the finite universal negative in one corner and under it the contradictory, the finite particular affirmative. On the other side, put the infinite universal affirmative and under it the contradictory, the infinite particular negative. Now indicate the contradiction between diagonals and the contradiction between collaterals. No man is just equivalents Every man is non-just contradictories contradictories Some man is just equivalents Not every man is non-just This arrangement makes the mutual consequence of the universals in truth and falsity evident, for if one of them is true, its diagonal contradictory is false; and if this is false, its collateral contradictory, which is the other universal, will be true. With respect to the falsity of the particulars the procedure is the same. Their mutual consequence is made evident in the same way, for if one of them is true, its diagonal contradictory is false, and if this is false, its contradictory collateral, which is the other particular, will be true; the procedure is the same with respect to falsity.
Cajetanus lib. 2 l. 4 n. 3 Sed est hic unum dubium. In I enim priorum, in fine, Aristoteles ex proposito determinat non esse idem iudicium de universali negativa et universali affirmativa infinita; et superius in hoc secundo, super illo verbo: quarum duae se habent secundum consequentiam, duae vero minime, Ammonius, Porphyrius, Boethius et sanctus Thomas dixerunt quod negativa simplex sequitur affirmativam infinitam, sed non e converso. Ad hoc dicendum est, secundum Albertum, quod negativam finitam sequitur affirmativa infinita subiecto constante; negativa vero simplex sequitur affirmativam absolute. Unde utrumque dictum verificatur, et quod inter eas est mutua consequentia cum subiecti constantia, et quod inter eas non est mutua consequentia absolute. Potest dici secundo, quod supra locuti sumus de infinita enunciatione quoad suum totalem significatum ad formam praedicati reductum; et secundum hoc, quia negativa finita est superior affirmativa infinita, ideo non erat mutua consequentia: hic autem loquimur de ipsa infinita formaliter sumpta. Unde s. Thomas tunc adducendo Ammonii expositionem dixit, secundum hunc modum loquendi: negativa simplex, in plus est quam affirmativa infinita. Textus vero I priorum ultra praedicta loquitur de finita et infinita in ordine ad syllogismum. Manifestum est autem quod universalis affirmativa sive finita sive infinita non concluditur nisi in primo primae. Universalis autem negativa quaecumque concluditur et in secundo primae, et primo et secundo secundae.	3. However, a question arises with respect to this. At the end of I Priorum [46: 51b 5], Aristotle determines from what he has proposed that the judgment of the universal negative and the infinite universal affirmative is not the same. Furthermore, in the second book of the present work, in relation to the phrase Of which two are related according to consequence, two are not. Ammonius, Porphyry, Boethius, and St. Thomas say that the simple negative follows upon the infinite affirmative and not conversely.” Albert answers this latter difficulty by pointing out that the infinite affirmative follows upon the finite negative when the subject is constant, but the simple negative follows upon the affirmative absolutely. Hence both positions are verified, for with a constant subject there is a mutual consequence between them, but there is not a mutual consequence between them absolutely. We could also answer this difficulty in this way. In Book II, Lesson 2 we were speaking of the infinite enunciation with the whole of what it signified reduced to the form of the predicate, and according to this there was not a mutual consequence, since the finite negative is superior to the infinite affirmative. But here we are speaking of the infinite itself formally taken. Hence St. Thomas, when he introduced the exposition of Ammonius in his commentary on the above passage, said that according to this mode of speaking the simple negative is wider than the infinite affirmative. In the above mentioned text in I Priorum [46: 52a 36], Aristotle is speaking of finite and infinite enunciations in relation to the syllogism. It is evident, however, that the universal affirmative, whether finite or infinite is only inferred in the first mode of the first figure, while any universal negative whatever is inferred in the second mode of the first figure and in the first and second modes of the second figure.
Cajetanus lib. 2 l. 4 n. 4 Deinde cum dicit: manifestum est autem etc., movet secundum dubium de vario situ negationis, an scilicet quoad veritatem et falsitatem differat praeponere et postponere negationem. Oritur autem haec dubitatio, quia dictum est nunc quod non refert quoad veritatem si dicatur, omnis homo est non iustus, aut si dicatur, omnis homo non est iustus; et tamen in altera postponitur negatio, in altera praeponitur, licet multum referat quoad affirmationem et negationem. Hanc, inquam, dubitationem solvere intendens cum distinctione, respondet quod in singularibus enunciationibus eiusdem veritatis sunt singularis negatio et infinita affirmatio eiusdem, in universalibus autem non est sic. Si enim est vera negatio ipsius universalis non oportet quod sit vera infinita affirmatio universalis. Negatio enim universalis est particularis contradictoria, qua existente vera, non est necesse suam subalternam, quae est contraria suae contradictoriae esse veram. Possunt enim duae contrariae esse simul falsae. Unde dicit quod in singularibus enunciationibus manifestum est quod, si est verum negare interrogatum, idest, si est vera negatio enunciationis singularis, de qua facta est interrogatio, verum etiam est affirmare, idest, vera erit affirmatio infinita eiusdem singularis. Verbi gratia: putasne Socrates est sapiens? Si vera est ista responsio, non; Socrates igitur non sapiens est, idest, vera erit ista affirmatio infinita, Socrates est non sapiens. In universalibus vero non est vera, quae similiter dicitur, idest, ex veritate negationis universalis affirmativae interrogatae non sequitur vera universalis affirmativa infinita, quae similis est quoad quantitatem et qualitatem enunciationi quaesitae; vera autem est eius negatio, idest, sed ex veritate responsionis negativae sequitur veram esse eius, scilicet universalis quaesitae negationem, idest, particularem negativam. Verbi gratia: putasne omnis homo est sapiens? Si vera est ista responsio, non; affirmativa similis interrogatae quam quis ex hac responsione inferre intentaret est illa: igitur omnis homo est non sapiens. Haec autem non sequitur ex illa negatione. Falsum est enim hoc, scilicet quod sequitur ex illa responsione; sed inferendum est, igitur non omnis homo sapiens est. Et ratio utriusque est, quia haec particularis ultimo illata est opposita, idest contradictoria illi universali interrogatae quam respondens falsificavit; et ideo oportet quod sit vera. Contradictoriarum enim si una est falsa, reliqua est vera. Illa vero, scilicet universalis affirmativa infinita primo illata, est contraria illi eidem universali interrogatae. Non est autem opus quod si universalium altera sit falsa, quod reliqua sit vera. In promptu est autem causa huius diversitatis inter singulares et universales. In singularibus enim varius negationis situs non variat quantitatem enunciationis; in universalibus autem variat, ut patet. Ideo fit ut non sit eadem veritas negantium universalem in quarum altera praeponitur, in altera autem postponitur negatio, ut de se patet.	4. When he says, And it is also clear with respect to the singular that if a question is asked and a negative answer is the true one, there is also a true affirmation, etc., he presents a difficulty relating to the varying position of the negation, i.e., whether there is a difference as to truth and falsity when the negation is a part of the predicate or a part of the verb. This difficulty arises from what he has just said, namely, that it is of no consequence as to truth or falsity whether you say, "Every man is non-just” or "Every man is not just”; yet in one case the negation is a part of the predicate, in the other part of the copula, and this makes a great deal of difference with respect to affirmation and negation. To solve this problem Aristotle makes a distinction: in singular enunciations, the singular negation and infinite affirmation of the same subject are of the same truth, but in universals this is not so. For if the negation of the universal is true it is not necessary that the infinite affirmation of the universal is true. The negation of the universal is the contradictory particular, but if it is true [i.e., the contradictory particular] it is not necessary that the subaltern, which is the contrary of the contradictory, be true, for two contraries can be at once false. Hence he says that in singular enunciations it is evident that if it is true to deny the thing asked, i.e., if the negation of a singular enunciation, which has been made into an interrogation, is true, there will also be a true affirmation, i.e., the infinite affirmation of the same singular will be true. For example, if the question "Do you think Socrates is wise?” has "No” as a true response, then "Socrates is non-wise,” i.e., the infinite affirmation "Socrates is non-wise” will be true. But in the case of universals the affirmative inference is not true, i.e., from the truth of a negation to a universal affirmative question, the truth of the infinite universal affirmative (which is similar in quantity and quality to the enunciation asked) does not follow. But the negation is true, i.e., from the truth of the negative response it follows that its negation is true, i.e., the negation of the universal asked, which is the particular negative. Consider, for example, the question "Do you think every man is wise?” If the response "No” is true, one would be tempted to infer the affirmative similar to the question asked, i.e., then "Every man is non-wise.” This, however, does not follow from the negation, for this is false as it follows from that response. Rather, what must be inferred is "Then not every man is wise.” And the reason for both is that the particular enunciation inferred last is the opposite, i.e., the contradictory of the universal question, which, being falsified by the negative response, makes the contradictory of the universal affirmative true, for of contradictories, if one is false the other is true. The infinite universal affirmative first inferred, however, is contrary to the same universal question. Should it not also be true? No, because it is not necessary in the case of universals that if one is false the other is true. The cause of the diversity between singulars and universals is now clear. In singulars the varying position of the negation does not vary the quantity of the enunciation ‘ but in universals it does. Therefore there is not the same truth in enunciations denying a universal when in one the negation is a part of the predicate and in the other a part of the verb.
Cajetanus lib. 2 l. 4 n. 5 Deinde cum dicit: illae vero secundum infinita etc., solvit tertiam dubitationem, an infinita nomina vel verba sint negationes. Insurgit autem hoc dubium, quia dictum est quod aequipollent negativa et infinita. Et rursus dictum est nunc quod non refert in singularibus praeponere et postponere negationem: si enim infinitum nomen est negatio, tunc enunciatio, habens subiectum infinitum vel praedicatum, erit negativa et non affirmativa. Hanc dubitationem solvit per interpretationem, probando quod nec nomina nec verba infinita sint negationes, licet videantur. Unde duo circa hoc facit: primo, proponit solutionem dicens: illae vero, scilicet dictiones, contraiacentes: verbi gratia: non homo, et, homo non iustus et iustus. Vel sic: illae vero, scilicet dictiones, secundum infinita, idest secundum infinitorum naturam, iacentes contra nomina et verba (utpote quae removentes quidem nomina et verba significant, ut non homo et non iustus et non currit, quae opponuntur contra ly homo ly iustus et ly currit), illae, inquam, dictiones infinitae videbuntur prima facie esse quasi negationes sine nomine et verbo ex eo quod comparatae nominibus et verbis contra quae iacent, ea removent, sed non sunt secundum veritatem. Dixit sine nomine et verbo quia nomen infinitum, nominis natura caret, et verbum infinitum verbi natura non possidet. Dixit quasi, quia nec nomen infinitum a nominis ratione, nec verbum infinitum a verbi proprietate omnino semota sunt. Unde, si negationes apparent, videbuntur sine nomine et verbo non omnino sed quasi. Deinde probat distinctiones infinitas non esse negationes tali ratione. Semper est necesse negationem esse veram vel falsam, quia negatio est enunciatio alicuius ab aliquo; nomen autem infinitum non dicit verum vel falsum; igitur dictio infinita non est negatio. Minorem declarat, quia qui dixit, non homo, nihil magis de homine dixit quam qui dixit, homo. Et quoad significatum quidem clarissimum est: non homo, namque, nihil addit supra hominem, imo removet hominem. Quoad veritatis vero vel falsitatis conceptum, nihil magis profuit qui dixit, non homo, quam qui dixit, homo, si aliquid aliud non addatur, imo minus verus vel falsus fuit, idest magis remotus a veritate et falsitate, qui dixit, non homo, quam qui dixit, homo: quia tam veritas quam falsitas in compositione consistit; compositioni autem vicinior est dictio finita, quae aliquid ponit, quam dictio infinita, quae nec ponit, nec componit, idest nec positionem nec compositionem importat.	5. Then he says, The antitheses in infinite names and verbs, as in " non-man” and "nonjust,” might seem to be negations without a name or a verb, etc. Here he raises the third difficulty, i.e., whether infinite names or verbs are negations. This question arises from his having said that the negative and infinite are equivalent and from having just said that in singular enunciations it makes no difference whether the negative is a part of the predicate or a part of the verb. For if the infinite name is a negation, then the enunciation having an infinite subject or predicate will be negative and not affirmative. He resolves this question by an interpretation which proves that neither infinite names nor verbs are negations although they seem to be. First he proposes the solution saying, The antitheses in infinite names and verbs, i.e., words contraposed, e.g., "non-man,” and "non-just man” and "just man”; or this may be read as, Those (namely, words) corresponding to infinites, i.e., corresponding to the nature of infinites, placed in opposition to names or verbs (namely, removing what the names and verbs signify, as in "non-man,” "non-just,” and "non-runs,” which are opposed to "man,” "just” and "runs”), would seem at first sight to be quasi-negations without Dame and verb, because, as related to the names and verbs before which they are placed, they remove them; they are not truly negations however. He says without a name or a verb because the infinite name lacks the nature of a name and the infinite verb does not have the nature of a verb. He says quasi because the infinite name does not fall short of the notion of the name in every way, nor the infinite verb of the nature of the verb. Hence, if it is thought that they are negations, they will be regarded as without a name or a verb, not in every way but as though they were without a name or a verb. He proves that infinitizing signs of separation are not negations by pointing out that it is always necessary for the negation to be true or false since a negation is an enunciation of something separated from something. The infinite name, however, does not assert what is true or false. Therefore the infinite word is not a negation. He manifests the minor when he says that the one who says "non-man” says nothing more of man than the one who says "man.” Clearly this is so with respect to what is signified, for "non-man” adds nothing beyond "man”; rather, it removes "man.” Moreover, with respect to a conception of truth or falsity, it is of no more use to say "non-man” than to say "man” if something else is not added; rather, it is less true or false, i.e., one who says non-man is more removed from truth and falsity than one who says man,” for both truth and falsity depend on composition, and the finite word which posits something is closer to composition than the infinite word, which neither posits nor composes, i.e., it implies neither positing nor composition.
Cajetanus lib. 2 l. 4 n. 6 Deinde cum dicit: significat autem etc., respondet quartae dubitationi, quomodo scilicet intelligatur illud verbum supradictum de enunciationibus habentibus subiectum infinitum: hae autem extra illas, ipsae secundum se erunt. Et ait quod intelligitur quantum ad significati consequentiam, et non solum quantum ad ipsas enunciationes formaliter. Unde duas habentes subiectum infinitum, universalem scilicet affirmativam et universalem negativam adducens, ait quod neutra earum significat idem alicui illarum, scilicet habentium subiectum finitum. Haec enim universalis affirmativa, omnis non homo est iustus, nulli habenti subiectum finitum significat idem: non enim significat idem quod ista, omnis homo est iustus; neque quod ista, omnis homo est non iustus. Similiter opposita negatio et universalis negativa habens subiectum infinitum, quae est contrarie opposita supradictae, scilicet omnis non homo non est iustus, nulli illarum de subiecto finito significat idem. Et hoc clarum est ex diversitate subiecti in istis et in illis.	6. When he says, Moreover, "Every non-man is just does not signify the same thing as any of the other enunciations, etc., he answers a fourth difficulty, i.e., how the earlier statement concerning enunciations having an infinite subject is to be understood. The statement was that these stand by themselves and are distinct from the former [in consequence of using the name "non-man”]. This is to be understood not just with respect to the enunciations themselves formally, but with respect to the consequence of what is signified. Hence, giving two examples of enunciations with an infinite subject, the universal affirmative and universal negative,” he says that neither of these signifies the same thing as any of those, namely of those having a finite subject. The universal affirmative "Every non-man is just” does not signify the same thing as any of the enunciations with a finite subject; for it does not signify "Every man is just” nor "Every man is non-just.” Nor do the opposite negation, or the universal negative having an infinite subject which is contrarily opposed to the universal affirmative, signify the same thing as enunciations with a finite subject; i.e., "Not every non-man is just” and "No non-man is just,” do not signify the same thing as any of those with a finite subject. This is evident from the diversity of subject in the latter and the former.
Cajetanus lib. 2 l. 4 n. 7 Deinde cum dicit: illa vero quae est etc., respondet quintae quaestioni, an scilicet inter enunciationes de subiecto infinito sit aliqua consequentia. Oritur autem dubitatio haec ex eo, quod superius est inter eas ad invicem assignata consequentia. Ait ergo quod etiam inter istas est consequentia. Nam universalis affirmativa de subiecto, et praedicato infinitis et universalis negativa de subiecto infinito, praedicato vero finito, aequipollent. Ista namque, omnis non homo est non iustus, idem significat illi, nullus non homo est iustus. Idem autem est iudicium de particularibus indefinitis et singularibus similibus supradictis. Cuiuscunque enim quantitatis sint, semper affirmativa de utroque extremo infinita et negativa subiecti quidem infiniti, praedicati autem finiti, aequipollent, ut facile potes exemplis videre. Unde Aristoteles universales exprimens, caeteras ex illis intelligi voluit.	7. When he says, But "Every non-man is non-just” signifies the same thing as "No non-man is just,” he answers a fifth difficulty, i.e., is there a consequence among enunciations with an infinite subject? This question arises from the fact that consequences were assigned among them earlier.” He says, therefore, that there is a consequence even among these, for the universal affirmative with an infinite subject and predicate and the universal negative with an infinite subject but a finite predicate are equivalent, i.e., "Every non-man is non-just” signifies the same thing as "No non-man is just.” This is also the case in particular infinites and singulars which are similar to the foresaid, for no matter what their quantity, the affirmative with both extremes infinite and the negative with an infinite subject and a finite predicate are always equivalent, as may be easily seen by examples. Hence, Aristotle in giving the universals intends the others to be understood from these.
Cajetanus lib. 2 l. 4 n. 8 Deinde cum dicit: transposita vero nomina etc., solvit sextam dubitationem, an propter nominum vel verborum transpositionem varietur enunciationis significatio. Oritur autem haec quaestio ex eo, quod docuit transpositionem negationis variare enunciationis significationem. Aliud enim dixit significare, omnis homo non est iustus, et aliud, non omnis homo est iustus. Ex hoc, inquam, dubitatur, an similiter contingat circa nominum transpositionem, quod ipsa transposita enunciationem varient, sicut negatio transposita. Et circa hoc duo facit: primo, ponit solutionem dicens, quod transposita nomina et verba idem significant: verbi gratia, idem significat, est albus homo, et, est homo albus, ubi est transpositio nominum. Similiter transposita verba idem significant, ut, est albus homo, et, homo albus est.	8. When he says, When the names and verbs are transposed, the enunciations signify the same thing, etc., he resolves a sixth difficulty: whether the signification of the enunciation is varied because of the transposition of names or verbs. This question arises from his having shown that the transposition of the negation varies the signification of the enunciation. "Every man is non-just,” he said, does not signify the same thing as "Not every man is just.” This raises the question as to whether a similar thing happens when we transpose names. Would this vary the enunciation as the transposed negation does? First he states the solution, saying that transposed names and verbs signify the same thing, e.g., "Man is white” signifies the same thing as "White is man.” Transposed verbs also signify the same thing, as in "Man is white” and "Man white is.”
Cajetanus lib. 2 l. 4 n. 9 Deinde cum dicit: nam si hoc non est etc., probat praedictam solutionem ex numero negationum contradictoriarum ducendo ad impossibile, tali ratione. Si hoc non est, idest si nomina transposita diversificant enunciationem, eiusdem affirmationis erunt duae negationes; sed ostensum est in I libro, quod una tantum est negatio unius affirmationis; ergo a destructione consequentis ad destructionem antecedentis transposita nomina non variant enunciationem. Ad probationis autem consequentiae claritatem formetur figura, ubi ex uno latere locentur ambae suprapositae affirmationes, transpositis nominibus; et ex altero contraponantur duae negativae, similes illis quoad terminos et eorum positiones. Deinde, aliquantulo interiecto spatio, sub affirmativis ponatur affirmatio infiniti subiecti, et sub negativis illius negatio. Et notetur contradictio inter primam affirmationem et duas negationes primas, et inter secundam affirmationem et omnes tres negationes, ita tamen quod inter ipsam et infimam negationem notetur contradictio non vera, sed imaginaria. Notetur quoque contradictio inter tertiam affirmationem et tertiam negationem inter se. Hoc modo: (Figura). His ita dispositis, probat consequentiam Aristoteles sic. Illius affirmationis, est albus homo, negatio est, non est albus homo; illius autem secundae affirmationis, quae est, est homo albus, si ista affirmatio non est eadem illi supradictae affirmationi, scilicet, est albus homo, propter nominum transpositionem, negatio erit altera istarum, scilicet aut, non est non homo albus, aut, non est homo albus. Sed utraque habet affirmationem oppositam alia ab illa assignatam, scilicet, est homo albus. Nam altera quidem dictarum negationum, scilicet, non est non homo albus, negatio est illius quae dicit, est non homo albus; alia vero, scilicet, non est homo albus, negatio est eius affirmationis, quae dicit, est albus homo, quae fuit prima affirmatio. Ergo quaecunque dictarum negationum afferatur contradictoria illi mediae, sequitur quod sint duae unius, idest quod unius negationis sint duae affirmationes, et quod unius affirmationis sint duae negationes: quod est impossibile. Et hoc, ut dictum est, sequitur stante hypothesi erronea, quod illae affirmationes sint propter nominum transpositionem diversae.	9. Then he proves the solution from the number of contradictory negations when he says, For if this is not the case there will be more than one negation of the same enunciation, etc. He does this by a reduction to the impossible and his reasoning is as follows. If this is not so, i.e., if transposed names diversify enunciations, there will be two negations of the same affirmation. But in the first book it was shown that there is only one negation of one affirmation. Going, then, from the destruction of the consequent to the destruction of the antecedent, transposed names do not vary the enunciation. To clarify the proof of the consequent, make a figure in which both of the affirmations posited above, with the names transposed are located on one side. Put the two negatives similar to them in respect to terms and position on the opposite side. Then leaving a little space, under the affirmatives put the affirmation with an infinite subject and under the negatives the negation of it. Mark the contradiction between the first affirmation and the first two negations and between the second affirmation and all three negations, but in the latter case mark the contradiction between it and the lowest negation as not true but imaginary. Mark, also, the contradiction between the third affirmation and negation. (1) Man is white ————contradictories———— Man is not white (2) White is man ————contradictories———— White is not man (3) Non-man is white ————contradictories———— Non-man is not white Now we can see how Aristotle proves the consequent. The negation of the affirmation "Man is white” is "Man is not white.” But if the second affirmation, "White is man,” is not the same as "Man is white,” because of the transposition of the names, its negation, [i.e., of "White is man”] will be either of these two: "Non-man is not white,” or "White is not man.” But each of these has another opposed affirmation than that assigned, namely, than "White is man.” For one of the negations, namely, "Non-man is not white,” is the negation of "Non-man is white”; the other, "White is not man” is the negation of the affirmation "Man is white,” which was the first affirmation. Therefore whatever negation is given as contradictory to the middle enunciation, it follows that there are two of one, i.e., two affirmations of one negation, and two negations of one affirmation, which is impossible. And this, as has been said, follows upon an erroneously set up hypothesis, i.e., that these affirmations are diverse because of the transposition of names.
Cajetanus lib. 2 l. 4 n. 10 Adverte hic primo quod Aristoteles per illas duas negationes, non est non homo albus, et, non est homo albus, sub disiunctione sumptas ad inveniendam negationem illius affirmationis, est homo albus, caeteras intellexit, quasi diceret: aut negatio talis affirmationis acceptabitur illa quae est vere eius negatio, aut quaecunque extranea negatio ponetur; et quodlibet dicatur, semper, stante hypothesi, sequitur unius affirmationis esse plures negationes, unam veram quae est contradictoria suae comparis habentis nomina transposita, et alteram quam tu ut distinctam acceptas, vel falso imaginaris; et e contra multarum affirmationum esse unicam negationem, ut patet in opposita figura. Ex quacunque enim illarum quatuor incipias, duas sibi oppositas aspicis. Unde notanter concludit indeterminate: quare erunt duae unius.	10. Notice first that Aristotle through these two negations, "Non-man is not white” and "White is not man,” taken under disjunction to find the negation of the affirmation "Man is white,” has comprehended other things. It is as though he said: The negation which will be taken will either be the true negation of such an affirmation or some extraneous negation; and whichever is taken, it always follows, given the hypothesis, that there are many negations of one affirmation—one which is the contradictory of it, having equal truth with the one having its name transposed, and the other which you accept as distinct, or you imagine falsely. And conversely, there is a single negation of many affirmations, as is clear in the diagram. Hence, from whichever of these four you begin, you see two opposed to it. It is significant, therefore, that Aristotle concludes indeterminately: Therefore, there will be two [negations] of one [affirmation].
Cajetanus lib. 2 l. 4 n. 11 Nota secundo quod Aristoteles contempsit probare quod contradictoria primae affirmationis sit contradictoria secundae, et similiter quod contradictoria secundae affirmationis sit contradictoria primae. Hoc enim accepit tamquam per se notum, ex eo quod non possunt simul esse verae neque simul falsae, ut manifeste patet praeposito sibi termino singulari. Non stant enim simul aliquo modo istae duae, Socrates est albus homo, Socrates non est homo albus. Nec turberis quod eas non singulares proposuit. Noverat enim supra dictum esse in primo quae affirmatio et negatio sint contradictoriae et quae non, et ideo non fuit sollicitus de exemplorum claritate. Liquet ergo ex eo quod negationes affirmationum de nominibus transpositis non sunt diversae quod nec ipsae affirmationes sunt diversae et sic nomina et verba transposita idem significant.	11. Note secondly that Aristotle does not consider it important to prove that the contradictory of the first affirmation is the contradictory of the second, and similarly that the contradictory of the second affirmation is the contradictory of the first. This he accepts as self-evident since they can neither be true at the same time nor false at the same time. This is manifestly clear when a singular term is placed first, for "Socrates is a white man” and "Socrates is not a white man” cannot be maintained at the same time in any mode. You should not be disturbed by the fact that he does not propose these singulars here, for he was undoubtedly aware that he had already stated in the first book which affirmation and negation are contradictories and which not and for this reason felt that a careful elaboration of the examples was not necessary here. It is therefore evident that since negations of affirmations with transposed names are not diverse the affirmations themselves are not diverse, and hence transposed names and verbs signify the same thing.
Cajetanus lib. 2 l. 4 n. 12 Occurrit autem dubium circa hoc, quia non videtur verum quod nominibus transpositis eadem sit affirmatio. Non enim valet: omnis homo est animal; ergo omne animal est homo. Similiter, transposito verbo, non valet: homo est animal rationale; ergo homo animal rationale est, de secundo adiacente. Licet enim nugatio committatur, tamen non sequitur primam. Ad hoc est dicendum quod sicut in rebus naturalibus est duplex transmutatio, scilicet localis, scilicet de loco ad locum, et formalis de forma ad formam; ita in enunciationibus est duplex transmutatio, situalis scilicet, quando terminus praepositus postponitur, et e converso, et formalis, quando terminus, qui erat praedicatum efficitur subiectum, et e converso vel quomodolibet, simpliciter et cetera. Et sicut quandoque fit in naturalibus transmutatio pure localis, puta quando res transfertur de loco ad locum, nulla alia variatione facta; quandoque autem fit transmutatio secundum locum, non pura sed cum variatione formali, sicut quando transit de loco frigido ad locum calidum: ita in enunciationibus quandoque fit transmutatio pure situalis, quando scilicet nomen vel verbum solo situ vocali variatur; quandoque autem fit transmutatio situalis et formalis simul, sicut contingit cum praedicatum fit subiectum, vel cum verbum tertium adiacens fit secundum. Et quoniam hic intendit Aristoteles de transmutatione nominum et verborum pure situali, ut transpositionis vocabulum praesefert, ideo dixit quod transposita nomina et verba idem significant, insinuare volens quod, si nihil aliud praeter transpositionem nominis vel verbi accidat in enunciatione, eadem manet oratio. Unde patet responsio ad instantias. Manifestum est namque quod in utraque non sola transpositio fit, sed transmutatio de subiecto in praedicatum, vel de tertio adiacente in secundum. Et per hoc patet responsio ad similia.	12. A doubt does arise, however, about the point Aristotle is making here, for it does not seem true that with transposed names the affirmation is the same. This, for example, is not valid: "Every man is an animal”; therefore, "Every animal is a man.” Nor is the following example with a transposed verb valid: "Man is a rational animal and (taking "is” as the second element), therefore "Man animal rational is”; for although it is nugatory as a whole combination, nevertheless it does not follow upon the first. The answer to this is as follows. just as there is a twofold transmutation in natural things, i.e., local, from place to place, and formal, from form to form, so in enunciations there is a twofold transmutation: a positional transmutation when a term placed before is placed after, and conversely, and a formal transmutation when a term that was a predicate is made a subject, and conversely, or in whatever mode, simply, etc. And just as in natural things sometimes a purely local transmutation is made (for instance, when a thing is transferred from place to place, with no other variation made) and sometimes a transmutation is made according to place—not simply but with a formal variation (as when a thing passes from a cold place to a hot place), so in enunciations a transmutation is sometimes made which is purely positional, i.e., when the name and verb are varied only in vocal position, and sometimes a transmutation is made which is at once formal and positional, as when the predicate becomes the subject, or the verb which is the third element added becomes the second. Aristotle’s purpose here was to treat of the purely positional transmutation of names and verbs, as the vocabulary of the transposition indicates; when he says, then, that transposed names and verbs signify the same thing, he intends to imply that if nothing other than the transposition of name and verb takes place in the enunciation, what is said remains the same. Hence, the response to the present objection is clear, for in both examples there is not only a transposition but a transmutation of subject to predicate in one case, and from an enunciation with a third element to one with a second element in the other. The response to similar questions is evident from this.

LECTURE 5

Latin	English
Cajetanus lib. 2 l. 5 n. 1 Postquam Aristoteles determinavit diversitatem enunciationis unius provenientem ex additione negationis infinitatis, hic intendit determinare quid accidat enunciationi ex hoc quod additur aliquid subiecto vel praedicato tollens eius unitatem. Et circa hoc duo facit: quia primo, determinat diversitatem earum; secundo, consequentias earum; ibi: quoniam vero haec quidem et cetera. Circa primum duo facit: primo, ponit earum diversitatem; secundo, probat omnes enunciationes esse plures; ibi: si ergo dialectica et cetera. Dicit ergo quoad primum, resumendo quod in primo dictum fuerat, quod affirmare vel negare unum de pluribus, vel plura de uno, si ex illis pluribus non fit unum, non est enunciatio una affirmativa vel negativa. Et declarando quomodo intelligatur unum debere esse subiectum aut praedicatum, subdit quod unum dico non si nomen unum impositum sit, idest ex unitate nominis, sed ex unitate significati. Cum enim plura conveniunt in uno nomine, ita quod ex eis non fiat unum illius nominis significatum, tunc solum vocis unitas est. Cum autem unum nomen pluribus impositum est, sive partibus subiectivis, sive integralibus, ut eadem significatione concludat, tunc et vocis et significati unitas est, et enunciationis unitas non impeditur.	1. After the Philosopher has treated the diversity in an enunciation arising from the addition of the infinite negation, he explains what happens to an enunciation when something is added to the subject or predicate which takes away its unity. He first determines their diversity, and then proves that all the enunciations are many where he says, In fact, if dialectical interrogation is a request for an answer, etc. Secondly, he determines their consequences, where he says, Some things predicated separately are such that they unite to form one predicate, etc. He begins by taking up something he said in the first book: there is not one affirmative enunciation nor one negative enunciation when one thing is affirmed or denied of many or many of one, if one thing is not constituted from the many. Then he explains what he means by the subject or predicate having to be one where he says, I do not use "one” of those things which, although one name may be imposed, do not constitute something one, i.e., a subject or predicate is one, not from the unity of the name, but from the unity of what is signified. For when many things are brought together under one name in such a way that what is signified by that name is not one, then the unity is only one of vocal sound. But when one name has been imposed for many, whether for subjective or for integral parts, so that it encloses them in the same signification, then there is unity both of vocal sound and what is signified. In the latter case, unity of the enunciation is not impeded.
Cajetanus lib. 2 l. 5 n. 2 Secundum quod subiungit: ut homo est fortasse animal et mansuetum et bipes obscuritate non caret. Potest enim intelligi ut sit exemplum ab opposito, quasi diceret: unum dico non ex unitate nominis impositi pluribus ex quibus non fit tale unum, quemadmodum homo est unum quoddam ex animali et mansueto et bipede, partibus suae definitionis. Et ne quis crederet quod hae essent verae definitionis nominis partes, interposuit, fortasse. Porphyrius autem, Boethio referente et approbante, separat has textus particulas, dicens quod Aristoteles hucusque declaravit enunciationem illam esse plures, in qua plura subiicerentur uni, vel de uno praedicarentur plura, ex quibus non fit unum. In istis autem verbis: ut homo est fortasse etc., intendit declarare enunciationem aliquam esse plures, in qua plura ex quibus fit unum subiiciuntur vel praedicantur; sicut cum dicitur, homo est animal et mansuetum et bipes, copula interiecta, vel morula, ut oratores faciunt. Ideo autem addidisse aiunt, fortasse, ut insinuaret hoc contingere posse, necessarium autem non esse.	2. Then he adds, For example, man probably is an animal and biped and civilized. This, however, is obscure, for it can be understood as all example of the opposite, as if he were saying, "I do not mean by ‘one’ such a ‘one’ as the unity of the name imposed upon many from which one thing is not constituted, for instance, ‘man’ as ‘one’ from the parts of the definition, animal and civilized and biped.” And to prevent anyone from thinking these are true parts of the definition of the name he interposes perhaps. Porphyry, however, referred to with approval by Boethius, separates these parts of the text. He says Aristotle first states that that enunciation is many in which many are subjected to one, or many are predicated of one, when one thing is not constituted from these. And when he says, For example, man perhaps is, etc., he intends to show that an enunciation is many when many from which one thing is constituted are subjected or predicated, as in the example "Man is an animal and civilized and biped,” with copulas interjected or a pause such as orators make. He added perhaps, they say, to imply that this could happen, but it need not.
Cajetanus lib. 2 l. 5 n. 3 Possumus in eamdem Porphyrii, Boethii et Alberti sententiam incidentes subtilius textum introducere, ut quatuor hic faciat. Et primo quidem, resumit quae sit enunciatio in communi dicens: enunciatio plures est, in qua unum de pluribus, vel plura de uno enunciantur. Si tamen ex illis pluribus non fit unum, ut in primo dictum et expositum fuit. Deinde dilucidat illum terminum de uno, sive unum, dicens: dico autem unum, idest, unum nomen voco, non propter unitatem vocis, sed significationis, ut supra dictum est. Deinde tertio, dividendo declarat, et declarando dividit, quot modis contingit unum nomen imponi pluribus ex quibus non fit unum, ut ex hoc diversitatem enunciationis multiplicis insinuet. Et ponit duos modos, quorum prior est, quando unum nomen imponitur pluribus ex quibus fit unum, non tamen in quantum ex eis fit unum. Tunc enim, licet materialiter et per accidens loquendo nomen imponatur pluribus ex quibus fit unum, formaliter tamen et per se loquendo nomen unum imponitur pluribus, ex quibus non fit unum: quia imponitur eis non in quantum ex eis est unum, ut fortasse est hoc nomen, homo, impositum ad significandum animal et mansuetum et bipes, idest, partes suae definitionis, non in quantum adunantur in unam hominis naturam per modum actus et potentiae, sed ut distinctae sint inter se actualitates. Et insinuavit quod accipit partes definitionis ut distinctas per illam coniunctionem, et per illud quoque adversative additum: sed si ex his unum fit, quasi diceret, cum hoc tamen stat quod ex eis unum fit. Addidit autem, fortasse, quia hoc nomen, homo, non est impositum ad significandum partes sui definitivas, ut distinctae sunt. Sed si impositum esset aut imponeretur, esset unum nomen pluribus impositum ex quibus non fit unum. Et quia idem iudicium est de tali nomine, et illis pluribus; ideo similiter illae plures partes definitivae possunt dupliciter accipi. Uno modo, per modum actualis et possibilis, et sic unum faciunt; et sic formaliter loquendo vocantur plura, ex quibus fit unum, et pronunciandae sunt continuata oratione, et faciunt enunciationem unam dicendo, animal rationale mortale currit. Est enim ista una sicut et ista, homo currit. Alio modo, accipiuntur praedictae definitionis partes ut distinctae sunt inter se actualitates, et sic non faciunt unum: ex duobus enim actibus ut sic, non fit unum, ut dicitur VII metaphysicae; et sic faciunt enunciationes plures et pronunciandae sunt vel cum pausa, vel coniunctione interposita, dicendo, homo est animal et mansuetum et bipes; sive, homo est animal, mansuetum, bipes, rhetorico more. Quaelibet enim istarum est enunciatio multiplex. Et similiter ista, Socrates est homo, si homo est impositum ad illa, ut distinctae actualitates sunt, significandum. Secundus autem modus, quo unum nomen impositum est pluribus ex quibus non fit unum, subiungitur, cum dicit: ex albo autem et homine et ambulante etc., idest, alio modo hoc fit, quando unum nomen imponitur pluribus, ex quibus non potest fieri unum, qualia sunt: homo, album, et ambulans. Cum enim ex his nullo modo possit fieri aliqua una natura, sicut poterat fieri ex partibus definitivis, clare liquet quod nomen aliquod si eis imponeretur, esset nomen non unum significans, ut in primo dictum fuit de hoc nomine, tunica, imposito homini et equo.	3. While agreeing with the opinion of Porphyry, Boethius, and Albert, we think a more subtle construction can be made of the text. According to it Aristotle makes four points here. First, he reviews what an enunciation is in general when he says, The enunciation is many in which one is enunciated of many or many of one, unless from the many something one is constituted... as he stated and explained in the first book. Secondly, he clarifies the term "one,” when he says, I do not use "one” of those things, etc., i.e., I call a name one, not by reason of the unity of vocal sound, but of signification, as was said above. Thirdly, he manifests (by dividing) and divides (by manifesting) the number of ways in which one name may be imposed on many things from which one thing is not constituted. From this he implies the diversity of the multiple enunciation. And he posits two ways in which one name may be imposed on many things from which one thing is not constituted: first, when one name is imposed upon many things from which one thing is constituted but not as one thing is constituted from them. In this case, materially and accidentally speaking, the name is imposed on many from which one thing is constituted, but it is formally and per se imposed on many from which one thing is not constituted; for it is not imposed upon them in the respect in which they constitute one thing; as perhaps the name "man” is imposed to signify animal and civilized and biped (i.e., parts of its definition) not as they are united in the one nature of man in the mode of act and potency, but as they are themselves distinct actualities. Aristotle implies that he is taking these parts of the definition as distinct by the conjunctions and by also adding adversatively, but if there is something one formed from these, Neither the Greek nor the Latin text of Aristotle has the "if” that Cajetan puts into this phrase.The correct reading is "...but there is something one formed from these.” Close as if to say, "when however it holds that one thing is constituted from these.” He adds perhaps because the name "man” is not imposed to signify its definitive parts as they are distinct. But if it had been so imposed or were imposed, it would be one name imposed on many things from which no one thing is constituted. And since the judgment with respect to such a name and those many things is the same, the many definitive parts can also be taken in two ways: first, in the mode of the actual and possible, and thus they constitute one thing, and formally speaking are called many from which one thing is constituted, and they are to be pronounced in continuous speech and they make one enunciation, for example, "A mortal rational animal is running.” For this is one enunciation, just as is "Man is running.” In the second way, the foresaid parts of the definition are taken as they are distinct actualities, and thus they do not constitute one thing, for one thing is not constituted from two acts as such, as Aristotle says in VII Metaphysicae [13: 1039a 5]. In this case they constitute many enunciations and are pronounced either with conjunctions interposed or with a pause in the rhetorical manner, for example, "Man is an animal and civilized and biped” or "Man is an animal–civilized–biped.” Each of these is a multiple enunciation. And so is the enunciation, "Socrates is a man” if "man” is imposed to signify animal, civilized, and biped as they are distinct actualities. Aristotle takes up the second way in which one name is imposed on many from which one thing is not constituted where he says, whereas from "white” and "man” and "walking” there is not [something one formed]. Since in no way can any one nature be constituted from "man,” white,” and "walking” (as there can be from the definitive parts), it is evident that if a name were imposed on these it would be a name that does not signify one thing, as was said in the first book of the name "cloak” imposed for man and horse.
Cajetanus lib. 2 l. 5 n. 4 Habemus ergo enunciationis pluris seu multiplicis duos modos, quorum, quia uterque fit dupliciter, efficiuntur quatuor modi. Primus est, quando subiicitur vel praedicatur unum nomen impositum pluribus, ex quibus fit unum, non in quantum sunt unum; secundus est, quando ipsa plura ex quibus fit unum, in quantum sunt distinctae actualitates, subiiciuntur vel praedicantur; tertius est, quando ibi est unum nomen impositum pluribus ex quibus non fit unum; quartus est, quando ista plura ex quibus non fit unum, subiiciuntur vel praedicantur. Et notato quod cum enunciatio secundum membra divisionis illius, qua divisa est, in unam et plures, quadrupliciter variari possit, scilicet cum unum de uno praedicatur, vel unum de pluribus, vel plura de uno, vel plura de pluribus; postremum sub silentio praeterivit, quia vel eius pluralitas de se clara est, vel quia, ut inquit Albertus, non intendebat nisi de enunciatione, quae aliquo modo una est, tractare. Demum concludit totam sententiam, dicens: quare nec si aliquis affirmet unum de his pluribus, erit affirmatio una secundum rem: sed vocaliter quidem erit una, significative autem non una, sed multae fient affirmationes. Nec si e converso de uno ista plura affirmabuntur, fiet affirmatio una. Ista namque, homo est albus, ambulans et musicus, importat tres affirmationes, scilicet, homo est albus et est ambulans et est musicus, ut patet ex illius contradictione. Triplex enim negatio illi opponitur correspondens triplici affirmationi positae.	4. We have, therefore, two modes of the many (i.e., the multiple enunciation) and since both are constituted in two ways, there will be four modes: first, when one name imposed on many from which one thing is constituted is subjected or predicated as though the name stands for many; the second, when the many from one which one thing is constituted are subjected or predicated as distinct actualities; the third, when one name is imposed for a many from which nothing one is constituted; the fourth, when many which do not constitute one thing are subjected or predicated. Note that the enunciation, according to the members of the division by which it has been divided into one and many, can be varied in four ways, i.e., one is predicated of one, one of many, many of one, and many of many. Aristotle has not spoken of the last one, either because its plurality is clear enough or because, as Albert says, he only intends to treat of the enunciation which is one in some way. Finally [fourthly], he concludes with this summary: Consequently, if someone affirms something one of these latter there will not be one affirmation according to the thing: vocally it will be one; significatively, it will not be one, but many. And conversely, if the many are affirmed of one subject, there will not be one affirmation. For example, "Man is white, walking, and musical” implies three affirmations, i.e., "Man is white” and "is walking” and "is musical,” as is clear from its contradiction, for a threefold negation is opposed to it, corresponding to the threefold affirmation.
Cajetanus lib. 2 l. 5 n. 5 Deinde cum dicit: si ergo dialectica etc., probat a posteriori supradictas enunciationes esse plures. Circa quod duo facit: primo, ponit rationem ipsam ad hoc probandum per modum consequentiae; deinde probat antecedens dictae consequentiae; ibi: dictum est autem de his et cetera. Quoad primum talem rationem inducit. Si interrogatio dialectica est petitio responsionis, quae sit propositio vel altera pars contradictionis, nulli enunciationum supradictarum interrogative formatae erit responsio una; ergo nec ipsa interrogatio est una, sed plures. Cuius rationis primo ponit antecedens: si ergo et cetera. Ad huius intelligendos terminos nota quod idem sonant enunciatio, interrogatio et responsio. Cum enim dicitur, caelum est animatum, in quantum enunciat praedicatum de subiecto, enunciatio vocatur; in quantum autem quaerendo proponitur, interrogatio; ut vero quaesito redditur, responsio appellatur. Idem ergo erit probare non esse responsionem unam, et interrogationem non esse unam, et enunciationem non esse unam. Adverte secundo interrogationem esse duplicem. Quaedam enim est utram partem contradictionis eligendam proponens; et haec vocatur dialectica, quia dialecticus habet viam ex probabilibus ad utramque contradictionis partem probandam. Altera vero determinatam ad unum responsionem exoptat; et haec est interrogatio demonstrativa, eo quod demonstrator in unum determinate tendit. Considera ulterius quod interrogationi dialecticae dupliciter responderi potest. Uno modo, consentiendo interrogationi, sive affirmative sive negative; ut si quis petat, caelum est animatum? Et respondeatur, est; vel, Deus non movetur? Et respondeatur, non: talis responsio vocatur propositio. Alio modo, potest responderi interimendo; ut si quis petat, caelum est animatum? Et respondeatur, non; vel Deus non movetur? Et respondeatur, movetur: talis responsio vocatur contradictionis altera pars, eo quod affirmationi negatio redditur et negationi affirmatio. Interrogatio ergo dialectica est petitio annuentis responsionis, quae est propositio, vel contradicentis, quae est altera pars contradictionis secundum supradictam Boethii expositionem.	5. Then when he says, In fact, if dialectical interrogation is a request for an answer, etc., he proves a posteriori that the foresaid enunciations are many. First he states an argument to prove this by way of the consequent; then he proves the antecedent of the given consequent where he says, But we have spoken about these things in the Topics, etc. Now if dialectical questioning is a request for an answer, either a proposition or one part of a contradiction, none of the foresaid enunciations, put in the form of a question, will have one answer. Therefore, the question is not one, but many. Aristotle first states the antecedent of the argument, if dialectical interrogation is a request for an answer, etc. To understand this it should be noted that an enunciation, a question, and an answer sound the same. For when we say, "The region of heaven is animated,” we call it an enunciation inasmuch as it enunciates a predicate of a subject, but when it is proposed to obtain an answer we call it an interrogation, and as applied to what was asked we call it a response. Therefore, to prove that there is not one response or one question or one enunciation will be the same thing. It should also be noted that interrogation is twofold. One proposes either of the two parts of a contradiction to choose from. This is called dialectical interrogation because the dialectician knows the way to prove either part of a contradiction from probable positions. The other kind of interrogation seeks one determinate response. This is the demonstrative interrogation, for the demonstrator proceeds determinately toward a single alternative. Note, finally, that it is possible to reply to a dialectical question in two ways. We may consent to the question, either affirmatively or negatively; for example, when someone asks, "Is the region of heaven animated,” we may respond, "It is,” or to the question "Is not God moved,” we may say, "No.” Such a response is called a proposition. The second way of replying is by destroying; for example, when someone asks "Is the region of heaven animated?” and we respond, "No,” or to the question, "Is not God moved?” we respond, "He is moved.” Such a response is called the other part of a contradiction, because a negation is given to an affirmation and an affirmation to a negation. Dialectical interrogation, then, according to the exposition just given, which is that of Boethius, is a request for the admission of a response which is a proposition, or which is one part of a contradiction.
Cajetanus lib. 2 l. 5 n. 6 Deinde subdit probationem consequentiae, cum ait: propositio vero unius contradictionis est et cetera. Ubi notandum est quod si responsio dialectica posset esse plures, non sequeretur quod responsio enunciationis multiplicis non posset esse dialectica; sed si responsio dialectica non potest esse nisi una enunciatio, tunc recte sequitur quod responsio enunciationis pluris, non est responsio dialectica, quae una est. Notandum etiam quod si enunciatio aliqua plurium contradictionum pars est, una non esse comprobatur: una enim uni tantum contradicit. Si autem unius solum contradictionis pars est, una est eadem ratione, quia scilicet unius affirmationis unica est negatio, et e converso. Probat ergo Aristoteles consequentiam ex eo quod propositio, idest responsio dialectica unius contradictionis est, idest una enunciatio est affirmativa vel negativa. Ex hoc enim, ut iam dictum est, sequitur quod nullius enunciationis multiplicis sit responsio dialectica, et consequenter nec una responsio sit. Nec praetereas quod cum propositionem, vel alteram partem contradictionis, responsionemque praeposuerit dialecticae interrogationis, de sola propositione subiunxit, quod est una; quod ideo fecit, quia illius alterius vocabulum ipsum unitatem praeferebat. Cum enim alteram contradictionis partem audis, unam affirmationem vel negationem statim intelligis. Adiunxit autem antecedenti ly ergo, vel insinuans hoc esse aliunde sumptum, ut postmodum in speciali explicabit, vel, permutato situ, notam consequentiae huius inter antecedens et consequens locandam, antecedenti praeposuit; sicut si diceretur, si ergo Socrates currit, movetur; pro eo quod dici deberet, si Socrates currit, ergo movetur. Sequitur deinde consequens: non erit una responsio ad hoc; et infert principalem conclusionem subdens, quod neque una erit interrogatio et cetera. Si enim responsio non potest esse una, nec interrogatio ipsa una erit.	6. He adds the proof of the consequent when he says, and a proposition is a part of one contradiction. In relation to this it should be noted that if a dialectical response could be many, it would not follow that a response to a multiple enunciation would not be dialectical. However, if the dialectical response can only be one enunciation then it follows that a response to a plural enunciation is not a dialectical response, for it is one [i.e., it inclines to one part of a contradiction at a time]. It should also be noted that if an enunciation is a part of many contradictions, it is thereby proven not to be one, for one contradicts only one. But if an enunciation is a part of only one contradiction, it is one by the same reasoning, i.e., because there is only one negation of one affirmation, and conversely. Hence Aristotle proves the consequent from the fact that the proposition, i.e., the dialectical response, is a part of one contradiction, i.e., it is one affirmative or one negative enunciation. It follows from this, as has been said, that there is no dialectical response of a multiple enunciation, and consequently not one response. It should not be overlooked that when he designates a proposition or one part of a contradiction as the response to a dialectical interrogation, it is only of the proposition that he adds that it is one, because the very wording shows the unity of the other. For when you hear one part of a contradiction, you immediately understand one affirmation or negation. He puts the "therefore” with the antecedent, either implying that this is taken from another place and he will explain in particular afterward, or having changed the structure, he places the sign of the consequent, which should be between the antecedent and consequent before the antecedent, as when one says, "Therefore if Socrates runs, he is moved,” for "If Socrates runs, therefore he is moved.” Then the consequent follows: there will not be one answer to this, etc.; and the inference of the principal conclusion, for there would not be a single question. For if the response cannot be one, the question will not be one.
Cajetanus lib. 2 l. 5 n. 7 Quod autem addidit: nec si sit vera, eiusmodi est. Posset aliquis credere, quod licet interrogationi pluri non possit dari responsio una, quando id de quo quaestio fit non potest de omnibus illis pluribus affirmari vel negari (ut cum quaeritur, canis est animal? Quia non potest vere de omnibus responderi, est, propter caeleste sidus, nec vere de omnibus responderi, non est, propter canem latrabilem, nulla possit dari responsio una); attamen quando id quod sub interrogatione cadit potest vere de omnibus affirmari aut negari, tunc potest dari responsio una; ut si quaeratur, canis est substantia? Quia potest vere de omnibus responderi, est, quia esse substantiam omnibus canibus convenit, unica responsio dari possit. Hanc erroneam existimationem removet dicens: nec si sit vera, idest, et dato quod responsio data enunciationi multiplici de omnibus verificetur, nihilominus non est una, quia unum non significat, nec unius contradictionis est pars, sed plures responsio illa habet contradictorias, ut de se patet.	7. He adds, even if there is a true answer, because someone might think that although one response cannot be given to a plural interrogation when the question concerns something that cannot be affirmed or denied of all of the many (for example, when someone asks, "Is a dog an animal?” no one response can be given, for we cannot truly say of every dog that it is an animal because of the star by that name; nor can we truly say of every dog that it is not an animal, because of the barking dog), nevertheless one response could be given when that which falls tinder the interrogation can be truly said of all. For example, when someone asks, "Is a dog a substance?” a single response can be given because it can truly he said of every dog that it is a substance, for to be a substance belongs to all dogs. Aristotle adds the phrase, even if there is a true answer, to remove such an erroneous judgment. For even if the response to the multiple enunciation is verified of all, it is nonetheless not one, since it does not signify one thing, nor is it a part of one contradiction. Rather, as is evident, this response has many contradictories.
Cajetanus lib. 2 l. 5 n. 8 Deinde cum dicit: dictum est autem de his in Topicis etc., probat antecedens dupliciter: primo, auctoritate eorum quae dicta sunt in Topicis; secundo, a signo. Et circa hoc duo facit. Primo, ponit ipsum signum, dicens: quod similiter etc., cum auctoritate topicorum, manifestum est, scilicet, antecedens assumptum, scilicet quod dialectica interrogatio est petitio responsionis affirmativae vel negativae. Quoniam nec ipsum quid est, idest ex eo quod nec ipsa quaestio quid est, est interrogatio dialectica: verbi gratia; si quis quaerat, quid est animal? Talis non quaerit dialectice. Deinde subiungit probationem assumpti, scilicet quod ipsum quid est, non est quaestio dialectica; et intendit quod quia interrogatio dialectica optionem respondenti offerre debet, utram velit contradictionis partem, et ipsa quaestio quid est talem libertatem non proponit (quia cum dicimus, quid est animal? Respondentem ad definitionis assignationem coarctamus, quae non solum ad unum determinata est, sed etiam omni parte contradictionis caret, cum nec esse, nec non esse dicat); ideo ipsa quaestio quid est, non est dialectica interrogatio. Unde dicit: oportet enim ex data, idest ex proposita interrogatione dialectica, hunc respondentem eligere posse utram velit contradictionis partem, quam contradictionis utramque partem interrogantem oportet determinare, idest determinate proponere, hoc modo: utrum hoc animal sit homo an non: ubi evidenter apparet optionem respondenti offerri. Habes ergo pro signo cum quaestio dialectica petat responsionem propositionis, vel alterius contradictionis partem, elongationem quaestionis quid est a quaestionibus dialecticis.	8. Where he says, But we have spoken about these things in the Topics, etc., he proves the antecedent in two ways. First, he proves it on the basis of what was said in the Topics; secondly, by a sign. The sign is given first where he says, Similarly it is clear that the question "What is it?” is not a dialectical one, etc. That is, given the doctrine in the Topics, it is clear (i.e., assuming the antecedent that the dialectical interrogation is a request for an affirmative or negative response) that the question "What is it?” is not a dialectical interrogation, e.g., when someone asks, "What is an animal?” he does not interrogate dialectically. Secondly, he gives the proof of what was assumed, namely, that the question "What is it?” is not a dialectical question. He states that a dialectical interrogation must offer to the one responding the option of whichever part of the contradiction he wishes. The question "What is it?” does not offer such liberty, for in saying "What is an animal?” the one responding is forced to assign a definition, and a definition is not only determined to one but is also entirely devoid of contradiction, since it affirms neither being nor non-being. Therefore, the question "What is it?” is not a dialectical interrogation. Whence he says, For the dialectical interrogation must provide, i.e., from the proposed dialectical interrogation the one responding must be able to choose whichever part of the contradiction he wishes, which parts of the contradiction the interrogator must specify, i.e., he must propose the question in this way: "Is this animal man or not?” wherein the wording of the question clearly offers an option to the one answering. Therefore, you have as a sign that a dialectical question is seeking a response of a proposition or of one part of a contradiction, the setting apart of the question "What is it?” from dialectical questions.

LECTURE 6

Latin	English
Cajetanus lib. 2 l. 6 n. 1 Postquam declaravit diversitatem multiplicis enunciationis, intendit determinare de earum consequentiis. Et circa hoc duo facit, secundum duas dubitationes quas solvit. Secunda incipit; ibi: verum autem est dicere et cetera. Circa primum tria facit: primo, proponit quaestionem; secundo, ostendit rationabilitatem quaestionis; ibi: si enim quoniam etc.; tertio, solvit eam; ibi: eorum igitur et cetera. Est ergo dubitatio prima: quare ex aliquibus divisim praedicatis de uno sequitur enunciatio, in qua illamet unita praedicantur de eodem, et ex aliquibus non. Unde haec diversitas oritur? Verbi gratia; ex istis, Socrates est animal et est bipes; sequitur, ergo Socrates est animal bipes; et similiter ex istis, Socrates est homo et est albus; sequitur, ergo Socrates est homo albus. Ex illis vero, Socrates est bonus, et est citharoedus; non sequitur, ergo est bonus citharoedus. Unde proponens quaestionem inquit: quoniam vero haec, scilicet praedicta, ita praedicantur composita, idest coniuncta, ut unum sit praedicamentum quae extra praedicantur, idest, ut ex eis extra praedicatis unite fiat praedicatio, alia vero praedicata non sunt talia, quae est inter differentia; unde talis innascitur diversitas? Et subdit exempla iam adducta, et ad propositum applicata: quorum primum continet praedicata ex quibus fit unum per se, scilicet, animal et bipes, genus et differentia; secundum autem praedicata ex quibus fit unum per accidens, scilicet, homo albus; tertium vero praedicata ex quibus neque unum per se neque unum per accidens inter se fieri sequitur; ut, citharoedus et bonus, ut declarabitur.	1. Having explained the diversity of the multiple enunciation Aristotle now proposes to determine the consequences of this. He treats this in relation to two questions which he solves. The second begins where he says, On the other hand, it is also true to say predicates of something singly, etc. With respect to the other question, first he proposes it, then he shows that the question is a reasonable one where he says, For if we hold that whenever each is truly said of a subject, both together must also be true, many absurdities will follow, etc. Finally, he solves it where he says, Those things that are predicated—taken in relation to that to which they are joined in predication, etc. The first question is this: Why is it that from some things predicated divisively of a subject an enunciation follows in which they are predicated of the same subject unitedly, and from others not? What is the reason for this diversity? For example, from "Socrates is an animal and he is biped” follows, "Therefore, Socrates is a biped animal”; and similarly, from "Socrates is a man and he is white” follows, "Therefore, Socrates is a white man.” But from "Socrates is good and he is a lute player,” the enunciation, "Therefore, he is a good lute player” does not follow. Hence in proposing the question Aristotle says, Some things, i.e., predicates, are so predicated when combined, that there is one predicate from what is predicated separately, i.e., from some things that are predicated separately, a united predication is made but from others this is riot so. What is the difference between these; whence does such a diversity arise? He adds the examples which we have already cited and applied to the question. Of these examples, the first contains predicates from which something one per se is formed, i.e., "animal” and "biped,” a genus and difference; the second contains predicates from which something accidentally one is formed, namely, "white man”; the third contains predicates from which neither one per se nor one accidentally is formed, "lute player” and "good,” as will be explained.
Cajetanus lib. 2 l. 6 n. 2 Deinde cum dicit: si enim quoniam etc., declarat veritatem diversitatis positae, ex qua rationabilis redditur quaestio: si namque inter praedicata non esset talis diversitas, irrationabilis esset dubitatio. Ostendit autem hoc ratione ducente ad inconveniens, nugationem scilicet. Et quia nugatio duobus modis committitur, scilicet explicite et implicite; ideo primo deducit ad nugationem explicitam, secundo ad implicitam; ibi: amplius, si Socrates et cetera. Ait ergo quod si nulla est inter quaecumque praedicata differentia, sed de quolibet indifferenter censetur quod quia alterutrum separatum dicitur, quod utrumque coniunctim dicatur, multa inconvenientia sequentur. De aliquo enim homine, puta Socrate, verum est separatim dicere quod, homo est, et albus est; quare et omne, idest et coniunctim dicetur, Socrates est homo albus. Rursus et de eodem Socrate potest dici separatim quod, est homo albus, et quod, est albus; quare et omne, idest, igitur coniunctim dicetur, Socrates est homo albus albus: ubi manifesta est nugatio. Rursus si de eodem Socrate iterum dicas separatim quod, est homo albus albus, verum dices et congrue quod est albus, et secundum hoc, si iterum hoc repetes separatim, a veritate simili non discedes, et sic in infinitum sequetur, Socrates est homo albus, albus, albus in infinitum. Simile quod ostenditur in alio exemplo. Si quis de Socrate dicat quod, est musicus, albus, ambulans, cum possit et separatim dicere quod, est musicus, et quod, est albus, et quod, est ambulans; sequetur, Socrates est musicus, albus, ambulans, musicus, albus, ambulans. Et quia pluries separatim, in eodem tamen tempore, enunciari potest, procedit nugatio sine fine. Deinde deducit ad implicitam nugationem, dicens, cum de Socrate vere dici possit separatim quod, est homo, et quod, est bipes, si coniunctim inferre licet, sequetur quod, Socrates sit homo bipes. Ubi est implicita nugatio. Bipes enim circumloquens differentiam hominis actu et intellectu clauditur in hominis ratione. Unde ponendo loco hominis suam rationem (quod fieri licet, ut docet Aristoteles II topicorum), apparebit manifeste nugatio. Dicetur enim: Socrates est homo, idest, animal bipes, bipes. Quoniam ergo plurima inconvenientia sequuntur si quis ponat complexiones, idest, adunationes praedicatorum fieri simpliciter, idest, absque diversitate aliqua, manifestum est ex dictis; quomodo autem faciendum est, nunc, idest, in sequentibus dicemus. Et nota quod iste textus non habetur uniformiter apud omnes quoad verba, sed quia sententia non discrepat, legat quicunque ut vult.	2. When he says, For if we hold that whenever each is truly said of a subject, both together must also be true, etc., he shows that there truly is such a diversity among predicates and in so doing renders the question reasonable, for if there were not such a diversity among predicates the question would be pointless. He shows this by reasoning lead-ing to an absurdity, i.e., to something nugatory. Now, something nugatory is effected in two ways, explicitly and implicitly. Therefore, he first makes a deduction to the explicitly nugatory, secondly to the implicitly, where he says, Furthermore, if Socrates is Socrates and a man, Socrates is a Socrates man, etc. If, he says, there is no difference between predicates, and it is supposed of any of them indifferently that because both are said separately both may he said conjointly, many absurdities will follow. For of some man, say Socrates, it is true to say separately that he is a man and he is white; therefore both -together, i.e., we may also say conjointly, "Socrates is a white man.” Again, of the same Socrates we can say separately that he is a white man and that he is white, and both together, i.e., therefore conjointly, "Socrates is a white white man.” Here the nugatory expression is evident. Further, if of the same Socrates that you again say separately is a white white man it will be true and consistent to say that he is white, and according to this, if again repeating this separately, you will not deviate from a similar truth, and this will follow to infinity, then Socrates is a white white white man to infinity. The same thing can be shown by another example, If someone says of Socrates that he is musical, white, and walking, since it is also possible to say separately that he is musical, and that he is white, and that he is walking, it will follow that Socrates is musical, white, walking, musical, white, walking. And since these can be enunciated many times separately, yet at the same time, the nugatory statement proceeds without end. Then he makes a deduction to the implicitly nugatory. Since it can be truly said of Socrates separately that he is man and that he is biped, it will follow that Socrates is a biped man, if it is licit to infer conjointly. This is implicitly nugatory because the "biped,” which indirectly expresses the difference of man in act and in understanding, is included in the notion of man. Hence, if we posit the definition of man in place of "man” (which it is licit to do, as Aristotle teaches in II Topicorum [2: 110a 5]) the nugatory character of the enunciation will be evident, for when we say "Socrates is a biped man,” we are saying "Socrates is a biped biped animal.” From what has been said it is evident that many absurdities follow if anyone proposes that combinations, i.e., unions of predicates, be made simply, i.e., without any distinction. Now, i.e., in what follows, we will state how this must be settled. This particular text is not uniformly worded in the manuscripts, but since no discrepancy of thought is involved one may read it as he wishes.
Cajetanus lib. 2 l. 6 n. 3 Deinde cum dicit: eorum igitur etc., solvit propositam quaestionem. Et circa hoc duo facit: primo, respondet instantiis in ipsa propositione quaestionis adductis; secundo, satisfacit instantiis in probatione positis; ibi: amplius nec quaecumque et cetera. Circa primum duo facit: primo namque, declarat veritatem; secundo, applicat ad propositas instantias; ibi: quocirca et cetera. Determinat ergo dubitationem tali distinctione. Praedicatorum sive subiectorum plurium duo sunt genera: quaedam sunt per accidens, quaedam per se. Si per accidens, hoc dupliciter contingit, vel quia ambo dicuntur per accidens de uno tertio, vel quia alterum de altero mutuo per accidens praedicatur. Quando illa plura divisim praedicata sunt per accidens quovis modo, ex eis non sequitur coniunctim praedicatum; quando autem sunt per se, tum ex eis sequitur coniuncte praedicatum. Unde continuando se ad praecedentia ait: eorum igitur quae praedicantur, et de quibus praedicantur, idest subiectorum, quaecumque dicuntur secundum accidens (et per hoc innuit oppositum membrum, scilicet per se), vel de eodem, idest accidentaliter concurrunt ad unius tertii denominationem, vel alterutrum de altero, idest accidentaliter mutuo se denominant (et per hoc ponit membra duplicis divisionis), haec, scilicet plura per accidens, non erunt unum, idest non inferent praedicationem coniunctam.	3. When he says, Those things that are predicated—taken in relation to that to which they are joined in predication, etc., he solves the proposed question. First he makes an answer with respect to the instances cited in proposing the question; secondly, he solves the problem as related to the instances posited in his proof where he says, Furthermore, predicates that are present in one another cannot be combined simply. In relation to the first answer, he states the true position first and then applies it to the instances where he says, This is the reason "good” and "shoemaker” cannot be combined simply, etc. He settles the question with this distinction: there are two kinds of multiple predicates and subjects. Some are accidental, some per se. If they are accidental this occurs in two ways, either because both are said accidentally of a third thing or because they are predicated of each other accidentally. Now when the many predicated divisively are in any way accidental, a conjoined predicate does not follow from them; but when they are per se, a conjoined predicate does follow from them. In answering the question, therefore, Aristotle connects what he is saying with what has gone before: Of those things that are predicated and those of which they are predicated, i.e., subjects, whichever are said accidentally (by which he intimates the opposite member, i.e., per se), either of the same subject, i.e., they unite accidentally for the denomination of one third thing, or of one another, i.e., they denominate each other accidentally (and by this he posits the members of a two-fold division), these (i.e., these many accidentally) will not be one, i.e., do not produce a conjoined predication.
Cajetanus lib. 2 l. 6 n. 4 Et explanat utrumque horum exemplariter. Et primo, primum, quando scilicet illa plura per accidens dicuntur de tertio, dicens: ut si homo albus est et musicus divisim. Sed non est idem, idest non sequitur adunatim, ergo homo est musicus albus. Utraque enim sunt accidentia eidem tertio. Deinde explanat secundum, quando solum illa plura per accidens de se mutuo praedicantur, subdens: nec si album musicum verum est dicere, idest, et etiamsi de se invicem ista praedicantur per accidens ratione subiecti in quo uniuntur, ut dicatur, homo est albus, et est musicus, et album est musicum, non tamen sequitur quod album musicum unite praedicetur, dicendo, ergo homo est albus musicus. Et causam assignat, quia album dicitur de musico per accidens, et e converso.	4. He explains both of these by examples. First, the many said accidentally of a third; for example, man is white and musical divisively. But they are not the same, i.e., it does not follow unitedly that "Man is musical white” for both are accidental to the same third thing. Then he explains the second member by an example. In it the many are predicated only of one another. Even if it were true to say white is musical, i.e., even if these are predicated accidentally of each other by reason of the subject in which they are united, so that we may say "Man is white and he is musical, and white is musical,” it still does not follow that "musical white” is predicated as a unity when we say, "Therefore, man is musical white.” He gives as the cause of this that "white” is said of "musical” accidentally and conversely.
Cajetanus lib. 2 l. 6 n. 5 Notandum est hic quod cum duo membra per accidens enumerasset, unico tamen exemplo utrumque membrum explanavit, ut insinuaret quod distinctio illa non erat in diversa praedicata per accidens, sed in eadem diversimode comparata; album enim et musicum, comparata ad hominem, sub primo cadunt membro; comparata autem inter se, sub secundo. Diversitatem ergo comparationis pluralitate membrorum, identitatem autem praedicatorum unitate exempli astruxit.	5. It must be noted here that although he has enumerated two accidental members, he explains both members by this single example so as to imply that the distinction is not one of different accidental predicates, but of the same predicates compared in different ways. "White” and "musical” compared to "man” fall under the first member, but compared with each other, under the second. Hence he has provided diversity of comparison by the plurality of the members, but identity of predicates by the unity of the example.
Cajetanus lib. 2 l. 6 n. 6 Advertendum est ulterius, ad evidentiam divisionis factae in littera, quod, secundum accidens, potest dupliciter accipi. Uno modo, ut distinguitur contra perseitatem posterioristicam, et sic non sumitur hic: quoniam cum dicitur plura praedicata secundum accidens, aut ly secundum accidens determinaret coniunctionem inter se, et sic manifeste esset falsa regula; quoniam inter prima praedicata, animal bipes, seu, animal rationale, est praedicatio secundum accidens hoc modo (differentia enim in nullo modo perseitatis praedicatur de genere, et tamen Aristoteles in textu dicit ea non esse praedicata per accidens, et asserit quod est optima illatio, est animal et bipes, ergo est animal bipes); aut determinaret coniunctionem illarum ad subiectum, et sic etiam inveniretur falsitas in regula: bene namque dicitur, paries est coloratus, et est visibilis, et tamen coloratum visibile non per se inest parieti. Alio modo, accipitur ly secundum accidens, ut distinguitur contra hoc quod dico, ratione sui, seu, non propter aliud, et sic idem sonat, quod, per aliud: et hoc modo accipitur hic. Quaecunque enim sunt talis naturae quod non ratione sui iunguntur, sed propter aliud, ab illatione coniuncta deficere necesse est, ex eo quod coniuncta illatio unum alteri substernit, et ratione sui ea adunata denotat ut potentiam et actum. Est ergo sensus divisionis, quod praedicatorum plurium, quaedam sunt per accidens, quaedam per se, idest, quaedam adunantur inter se ratione sui, quaedam propter aliud. Ea quae per se uniuntur inferunt coniunctum, ea autem quae propter aliud, nequaquam.	6. To make this division evident it must also be noted that accidentally can be taken in two ways. It may be taken as it is distinguished from "posterioristic perseity.” This is not the way it is taken here, for "many predicates accidentally” would then mean that the "accidentally” determines a conjunction between predicates, and thus the rule would clearly be false, for the first predicates he gave as examples are predicated accidentally in this way, namely, "biped animal,” or "rational animal” (for a difference is not predicated of a genus in any mode of perseity, and yet Aristotle says in the text that these are not predicated accidentally, and has asserted that "He is an animal and biped, therefore he is a biped animal” is a good inference). Or it would mean that the "accidentally” determines a conjunction of the predicates with the subject, and thus also the rule would be false, for it is valid to say, "The wall is colored and it is visible,” yet visible colored is not per se in the wall. Accidentally” taken in the second way is distinguished from what I call "on its own account,” i.e., not because of something else; "accidentally” then means "through another.” This is the way it is taken here, for whatever are of such a nature that they are joined because of something else, and not on their own account, do not admit of conjoined inference, because a conjoined inference subjects one to the other, and denotes the things united on their own account as potency and act. Therefore, the sense of the division is this: of many predicates, some are accidental, some per se, i.e., some are united among themselves on their own account, some on account of another. Those that are per se united infer conjointly; those that are united on account of another do not infer conjointly in any way.
Cajetanus lib. 2 l. 6 n. 7 Deinde cum dicit: quocirca nec citharoedus etc., applicat declaratam veritatem ad partes quaestionis. Et primo, ad secundam partem, quia scilicet non sequitur: est bonus et est citharoedus; ergo est bonus citharoedus, dicens: quocirca nec citharoedus bonus etc.; secundo, ad aliam partem quaestionis, quare sequebatur: est animal et est bipes; ergo est animal bipes: et ait: sed animal bipes et cetera. Et subiungit huius ultimi dicti causam, quia, animal bipes, non sunt praedicata secundum accidens coniuncta inter se aut in tertio, sed per se. Et per hoc explanavit alterum membrum primae divisionis, quod adhuc positum non fuerat explicite. Adverte quod Aristoteles, eamdem tenens sententiam de citharoedo et bono et musico et albo, conclusit quod album et musicum non inferunt coniunctum praedicatum; ideo nec citharoedus et bonus inferunt citharoedus bonus simpliciter, idest coniuncte. Est autem ratio dicti, quia licet musica et albedo dissimiles sint bonitati et arti citharisticae in hoc, quod bonitas nata est denominare et subiectum tertium, puta hominem et ipsam artem citharisticam (propter quod falsitas manifeste cernitur, quando dicitur: est bonus et citharoedus; ergo bonus citharoedus), musica vero et albedo subiectum tertium natae sunt denominare tantum, et non se invicem (propter quod latentior est casus cum proceditur: est albus et est musicus; ergo est musicus albus), licet, inquam, in hoc sint dissimiles, et propter istam dissimilitudinem processus Aristotelis minus sufficiens videatur; attamen similes sunt in hoc quod, si servetur identitas omnimoda praedicatorum quam servari oportet, si illamet divisa debent inferri coniunctim, sicut musica non denominat albedinem, neque contra, ita nec bonitas, de qua fit sermo, cum dicitur, homo est bonus, denominat artem citharisticam, neque e converso. Cum enim bonum sit aequivocum, licet a consilio, alia ratione dicitur de perfectione citharoedi, et alia de perfectione hominis. Quando namque dicimus, Socrates est bonus, intelligimus bonitatem moralem, quae est hominis bonitas simpliciter (analogum siquidem simpliciter positum sumitur pro potiori); cum autem infertur, citharoedus bonus, non bonitatem moris sed artis praedicas: unde terminorum identitas non salvatur; sufficienter igitur et subtiliter Aristoteles eamdem de utrisque protulit sententiam, quia eadem est haec, et ibi ratio et cetera.	7. When he says, This is the reason "good” and "shoemaker” cannot be combined simply, etc., he applies the truth he has stated to the parts of the question. He applies it first to the second part, i.e., why this does not follow: "He is good and he is a shoemaker, therefore he is a good shoemaker.” Then he applies it to the other part of the question, i.e., why this follows: "He is an animal and he is biped, therefore he is a biped animal.” He adds the reason in the case of the latter: "biped” and "animal” are not predicates accidentally conjoined among themselves, nor in a third thing, but per se. This also explains the other member of the first division which has not yet been explicitly posited. Notice that he maintains the same judgment is to be made about lute player and good, and musical and white. He has concluded that "white” and "musical” do not infer a conjoined predicate; hence neither do "lute player” and "good” infer "good lute player” simply, i.e., conjointly. There is a reason for saying this. For although there is a difference between musical and white, and goodness and the art of luteplaying, they are also similar. Let us consider their difference first. Goodness is of such a nature that it denominates both a third subject, namely, man, and the art of lute-playing. This is the reason the falsity is clearly discernible when we say "He is good and a lute player, therefore he is a good lute player.” Musical and whiteness, on the other band, are of such a nature that they denominate only a third subject, and not each other, and hence, the error is less obvious in "He is white and be is musical, therefore he is musical white.” Now it is this difference that makes Aristotle’s process of reasoning appear somewhat inconclusive. However, they are similar. For if identity of predicates is kept in every way that is required for the same things divided to be inferred conjointly, then, just as "musical” does not denominate "whiteness,” nor the contrary, so neither does "goodness,” of which we are speaking when we say "Man is good,” denominate the art of lute-playing,,nor conversely. For "good” is equivocal—by choice though—and therefore is said of the perfection of the lute player by means of one notion and of the perfection of man by means of another. For example, when we say, "Socrates is good” we understand moral goodness, which is the goodness of man absolutely (for the analogous term posited simply, stands for what is mainly so); but when good lute player is inferred, it is not the goodness of morality that is predicated but the goodness of art; whence identity of the terms is not saved. Therefore, Aristotle has adequately and subtly expressed the same judgment about both, i.e., "white” and "musical,” and "good” and "lute player,” for the reason here is the same as there.
Cajetanus lib. 2 l. 6 n. 8 Nec praetereundum est quod, cum tres consequentias adduxit quaestionem proponendo, scilicet; est animal et bipes; ergo est animal bipes: et, est homo et albus; ergo est homo albus: et, est citharoedus et bonus; ergo est homo albus: et, est citharoedus et bonus; ergo est bonus citharoedus; et duas primas posuerat esse bonas, tertiam vero non; huius diversitatis causam inquirere volens, cur solvendo quaestionem nullo modo meminerit secundae consequentiae, sed tantum primae et tertiae. Indiscussum namque reliquit an illa consequentia sit bona an mala. Et ad hoc videtur mihi dicendum quod ex his paucis verbis etiam illius consequentiae naturam insinuavit. Profundioris enim sensus textus capax apparet cum dixit quod, non sunt unum album et musicum etc., ut scilicet non tantum indicet quod expositum est, sed etiam eius causam, ex qua natura secundae consequentiae elucescit. Causa namque quare album et musicum non inferunt coniunctam praedicationem est, quia in praedicatione coniuncta oportet alteram partem alteri supponi, ut potentiam actui, ad hoc ut ex eis fiat aliquo modo unum, et altera a reliqua denominetur (hoc enim vis coniunctae praedicationis requirit, ut supra diximus de partibus definitionis); album autem et musicum secundum se non faciunt unum per se, ut patet, neque unum per accidens. Licet enim ipsa ut adunantur in subiecto uno sint unum subiecto per accidens, tamen ipsamet quae adunantur in uno, tertio subiecto, non faciunt inter se unum per accidens: tum quia neutrum informat alterum (quod requiritur ad unitatem per accidens aliquorum inter se, licet non in tertio); tum quia non considerata subiecti unitate, quae est extra eorum rationes, nulla remanet inter ea unitatis causa. Dicens ergo quod album et musicum non sunt unum, scilicet inter se, aliquo modo, causam expressit quare coniunctim non infertur ex eis praedicatum. Et quia oppositorum eadem est disciplina, insinuavit per illamet verba bonitatem illius consequentiae. Ex eo enim quod homo et albus se habent sicut potentia et actus (et ita albedo informet, denominet atque unum faciat cum homine ratione sui), sequitur quod ex divisis potest inferri coniuncta praedicatio; ut dicatur: est homo et albus; ergo est homo albus. Sicut per oppositum dicebatur quod ideo musicum et album non inferunt coniunctum praedicatum quia neutrum alterum informabat.	8. There is another point that must be mentioned. Aristotle in proposing the question draws three consequences: "He is an animal and biped, therefore he is a biped animal” and "He is a man and white, therefore he is a white man” and "He is a lute player and good, therefore he is a good lute player.” Then he states that the first two consequences are good, the third not. His intention was to inquire into the cause of this diversity, but in solving the question he mentions only the first and third consequences, leaving the goodness or badness of the second consequence undiscussed. Why is this? I would say in answer to this that in these few words he has also implied the nature of the second consequence, for there is a more profound meaning to the statement in the text that whiteness and being musical is not one. It is a meaning that not only indicates what has already been explained but also its cause, and from this the nature of the second consequence is apparent. For the reason "white” and "musical” do not infer a conjoined predication is that in conjoined predication one part must be subjected to the other as potency to act such that in some way one thing is formed from them and one is denominated from the other (for the force of the conjoined predication requires this, as we have said above concerning the parts of the definition). "White” and "musical,” however, do not in themselves form one thing per se, as is evident, nor do they form one thing accidentally. For while it is true that as united in a subject they are one in subject accidentally, nevertheless things that are united in one third subject do not form one thing accidentally among themselves: first, because neither informs the other (which is required for accidental unity of things among themselves, although not in a third thing); secondly, because, considered apart from the unity of a subject, which is outside of their notions, there is no cause of unity between them. Therefore, when Aristotle says that whiteness and being musical are not one, i.e., among themselves, in some measure he expresses the reason why a predicate is not conjointly inferred from them. And since the same discipline extends to opposites, the goodness of the second consequence is implied by these words. That is, man and white are related as potency and act (and so, on its own account whiteness informs, denominates, and forms one thing with ‘man’); therefore from these taken divisively a conjoined predication can be inferred, i.e., "He is man and white, therefore be is a white man”; just as, in the opposite case, it was said that "musical” and "white” do not infer a conjoined predicate because neither informs the other.
Cajetanus lib. 2 l. 6 n. 9 Nec obstat quod album faciat unum per accidens cum homine: non enim dictum est quod unitas per accidens aliquorum impedit ex diversis inferre coniunctum, sed quod unitas per accidens aliquorum ratione tertii tantum est illa quae impedit. Talia enim quae non sunt unum per accidens nisi ratione tertii, inter se nullam habent unitatem; et propterea non potest inferri coniunctum, ut dictum est, quod unitatem importat. Illa vero quae sunt unum per accidens ratione sui, seu inter se, ut, homo albus, cum coniuncta accipiuntur, unitate necessaria non carent, quia inter se unitatem habent. Notanter autem apposui ly tantum: quoniam si aliqua duo sunt unum per accidens, ratione tertii subiecti scilicet, sed non tantum ex hoc habent unitatem, sed etiam ratione sui, ex hoc quod alterum reliquum informat, ex istis divisis non prohibetur inferri coniunctum. Verbi gratia, optime dicitur: est quantum et est coloratum; ergo est quantum coloratum: quia color informat quantitatem.	9. There is no opposition between the position just stated and the fact that white forms an accidental unity with man. For we did not say that accidental unity of certain things impedes inferring a conjunction from divided things,” but that accidental unity of certain things only by reason of a third thing is the one that impedes. Things that are one accidentally only by reason of a third thing have no unity among them selves; and for this reason a conjunction, which implies unity, cannot be inferred, as we have said. But things that are one accidentally on their own account, i.e., among themselves, as for example, "white man,” when taken conjointly, have the necessary unity because they have unity among themselves. Notice that I have added "only.” The reason is that if any two C are one accidentally, namely, by reason of a third subject, and they not only have unity from this but also on their own account (because one informs the other), then from these taken divisively a conjoined inference can be made. For example, we can infer, "It is a quantity and it is colored, therefore it is a colored quantity,” because color informs quantity.
Cajetanus lib. 2 l. 6 n. 10 Potes autem credere quod secunda illa consequentia, quam non explicite confirmavit Aristoteles respondendo, sit bona et ex eo quod ipse proponendo quaestionem asseruit bonam, et ex eo quod nulla instantia reperitur. Insinuavit autem et Aristoteles quod sola talis unitas impedit illationem coniunctam, quando dixit quaecumque secundum accidens dicuntur vel de eodem vel alterutrum de altero. Cum enim dixit, secundum accidens de eodem, unitatem eorum ex sola adunatione in tertio posuit (sola enim haec per accidens praedicantur de eodem, ut dictum est); cum autem addidit, vel alterutrum de altero, mutuam accidentalitatem ponens, ex nulla parte inter se unitatem reliquit. Utraque ergo per accidens adducta praedicata, in tertio scilicet vel alterutrum, quae impediant illationem coniunctam, nonnisi in tertio unitatem habent.	10. You can hold as true that this second consequence is good even though Aristotle has not explicitly confirmed it by returning to it, both from the fact that in proposing the question he has claimed it as good and also because there is no instance opposed to it. Moreover, Aristotle has implied that it is only such unity that impedes the conjoined inference where he says: which are said accidentally, either of the same subject or of one another. By accidentally of the same subject, he posits their unity to be only from union in a third thing (for only these are predicated accidentally of the same subject, as was said). When he adds, or of one another—positing mutual accidentality—no unity at all is left between them. Therefore, both kinds of accidental predicates, namely, in a third thing or in one another, that impede a conjoined inference have unity only in a third thing.
Cajetanus lib. 2 l. 6 n. 11 Deinde cum dicit: amplius nec etc., satisfacit instantiis in probatione adductis, et in illis in quibus explicita committebatur nugatio, et in illis in quibus implicita; et ait quod non solum inferre ex divisis coniunctum non licet quando praedicata illa sunt per accidens, sed nec etiam quaecunque insunt in alio: idest, sed nec hoc licet quando praedicata includunt se, ita quod unum includatur in significato formali alterius intrinsece, sive explicite, ut album in albo, sive implicite, ut animal et bipes in homine. Quare neque album frequenter dictum divisim infert coniunctum, neque homo divisim ab animali vel bipede enunciatum, animal bipes, coniunctum cum homine infert; ut dicatur, ergo Socrates est homo bipes, vel animal homo. Insunt enim in hominis ratione, animal et bipes actu et intellectu, licet implicite. Stat ergo solutio quaestionis in hoc, quod unitas plurium per accidens in tertio tantum et nugatio, impediunt ex divisis inferri coniunctum; et consequenter, ubi neutrum horum invenitur, ex divisis licebit inferre coniunctum. Et hoc intellige quando divisae sunt simul verae de eodem et cetera.	11. Then when he says, Furthermore, predicates that are present in one another cannot be combined simply, etc., he gives the solution for the instances (both the explicitly nugatory and the implicitly nugatory) cited in the proof. It is not only not licit, he says, to infer a union from divided predicates when these are accidental, but it is not licit when the predicates are present in one another. That is, it is not licit to infer a conjoined predicate from divided predicates when the predicates include one another in such a way that one is included in the formal signification of another intrinsically, or explicitly, as "white” in white,” or implicitly, as "animal” and "biped” in "man.” Therefore, white” said repeatedly and divisively does not infer a conjoined predication, nor does "man” divisively enunciated from "animal” or "biped” infer "biped” or "animal” conjoined with man, such that we could say, "Therefore, Socrates is a biped-man” or "animal-man.” For animal and biped are included in the notion of man in act and in understanding, although implicitly. The solution of the question, then, is this: the inferring of a conjunction from divided predicates is impeded when there is unity of the many accidentally only in a third thing and when there is a nugatory result. Consequently, where neither of these is found it will be licit to infer a conjunction from divided predicates. It is to be understood that this applies when the divided predicates are at once true of the same subject.

LECTURE 7

Latin	English
Cajetanus lib. 2 l. 7 n. 1 Postquam expedita est prima dubitatio, tractat secundam dubitationem. Et circa hoc tria facit: primo, movet ipsam quaestionem; secundo, solvit eam; ibi: sed quando in adiecto etc., tertio, ex hoc excludit quemdam errorem; ibi: quod autem non est et cetera. Est ergo quaestio: an ex enunciatione habente praedicatum coniunctum, liceat inferre enunciationes dividentes illud coniunctum; et est quaestio contraria superiori. Ibi enim quaesitum est an ex divisis inferatur coniunctum; hic autem quaeritur an ex coniuncto sequantur divisa. Unde movendo quaestionem dicit: verum autem aliquando est dicere de aliquo et simpliciter, idest divisim, quod scilicet prius dicebatur coniunctim, ut quemdam hominem album esse hominem, aut quoddam album hominem album esse, idest ut ex ista, Socrates est homo albus, sequitur divisim, ergo Socrates est homo, ergo Socrates est albus. Non autem semper, idest aliquando autem ex coniuncto non inferri potest divisim; non enim sequitur, Socrates est bonus citharoedus, ergo est bonus. Unde haec est differentia, quod quandoque licet et quandoque non. Et adverte quod notanter adduxit exemplum de homine albo, inferendo utramque partem divisim, ut insinuaret quod intentio quaestionis est investigare quando ex coniuncto potest utraque pars divisim inferri, et non quando altera tantum.	1. Aristotle now takes up the second question in relation to multiple enunciations. He first presents it, and then solves it where he says, When something opposed is present in the adjunct, from which a contradiction follows, it will not be true to predicate them singly, but false, etc. Finally, he excludes an error where he says, In the case of non-being, however, it is not true to say that because it is a matter of opinion, it is something, etc. The second question is this: Is it licit to infer from an enunciation having a conjoined predication, enunciations dividing that conjunction? This question is the contrary of the first question. The first asked whether a conjoined predicate could be inferred from divided predicates; the present one asks whether divided predicates follow from conjoined predicates. When he presents the question he says, on the other hand, it is also true to say predicates of something singly, i.e., what was previously said conjointly may be said divisively; for example, that some white man is a man, or that some white man is white. That is, from "Socrates is a white man,” follows divisively, "Therefore Socrates is a man,” "There fore Socrates is white.” However, this is not always the case, i.e., some times it is not possible to infer divisively from conjoined predicates, for this does not follow: "Socrates is a good lute player, therefore he is good.” Hence, sometimes it is licit, sometimes not. Note that in inferring each part divisively he takes as an ex ample "white man.” This is significant, for by it he means to imply that his intention is to investigate when each part can be inferred divisively from a conjoined predicate, and not when only one of the two can be inferred.
Cajetanus lib. 2 l. 7 n. 2 Deinde cum dicit: sed quando in adiecto etc., solvit quaestionem. Et duo facit: primo, respondet parti negativae quaestionis, quando scilicet non licet; secundo, ibi: quare in quantiscumque etc., respondet parti affirmativae, quando scilicet licet. Circa primum considerandum quod quia dupliciter contingit fieri praedicatum coniunctum, uno modo ex oppositis, alio modo ex non oppositis, ideo duo facit: primo, ostendit quod numquam ex praedicato coniuncto ex oppositis possunt inferri eius partes divisim; secundo, quod nec hoc licet universaliter in praedicato coniuncto ex non oppositis, ibi: vel etiam quando et cetera. Ait ergo quod quando in termino adiecto inest aliquid de numero oppositorum, ad quae sequitur contradictio inter ipsos terminos, non verum est, scilicet inferre divisim, sed falsum. Verbi gratia cum dicitur, Caesar est homo mortuus, non sequitur, ergo est homo: quia ly mortuus, adiacens homini, oppositionem habet ad hominem, quam sequitur contradictio inter hominem et mortuum: si enim est homo, non est mortuus, quia non est corpus inanimatum; et si est mortuus, non est homo, quia mortuum est corpus inanimatum. Quando autem non inest, scilicet talis oppositio, verum est, scilicet inferre divisim. Ratio autem quare, quando est oppositio in adiecto, non sequitur illatio divisa est, quia alter terminus ex adiecti oppositione corrumpitur in ipsa enunciatione coniuncta. Corruptum autem seipsum absque corruptione non infert, quod illatio divisa sonaret.	2. When he says, When something opposed is present in the adjunct, etc., he solves the question, first by responding to the negative part of the question, i.e., when it is not licit; secondly, to the affirmative part, i.e., when it is licit, where he says, Therefore, in whatever predications no contrariety is present when definitions are put in place of the names, and wherein predicates are predicated per se and not accidentally, etc. It should be noted, in relation to the negative part of the question, that a conjoined predicate may be formed in two ways: from opposites and from non-opposites. Therefore, he shows first that the parts in a conjoined predicate of opposites can never be inferred divisively. Secondly, he shows that this is not licit universally in a conjoined predicate of non-opposites, where he says, Or, rather, when something opposed is present in it, it is never true; but when something opposed is not present, it is not always true. Aristotle says, then, that when something that is an opposite is contained in the adjacent term, which results in a contradiction between the terms themselves, it is not true, namely, to infer divisively, but false. For example, when we say, "Caesar is a dead man,” it does not follow, "Therefore he is a man,” because the contradiction between 11 man” and "dead” which results from adding the "dead” to "man” is opposed to man, for if he is a man he is not dead, because he is not an inanimate body; and if he is dead he is not a man, because as dead he is an inanimate body. When something opposed is not present, i.e., there is no such opposition, it is true, i.e., it is true to infer divisively. The reason a divided inference does not follow when there is opposition in the added term is that in a conjoined enunciation the other term is destroyed by the opposition of the added term. But that which has been destroyed is not inferred apart from the destruction, which is what the divided inference would signify.
Cajetanus lib. 2 l. 7 n. 3 Dubitatur hic primo circa id quod supponitur, quomodo possit vere dici, Caesar est homo mortuus, cum enunciatio non possit esse vera, in qua duo contradictoria simul de aliquo praedicantur. Hoc enim est primum principium. Homo autem et mortuus, ut in littera dicitur, contradictoriam oppositionem includunt, quia in homine includitur vita, in mortuo non vita. Dubitatur secundo circa ipsam consequentiam, quam reprobat Aristoteles: videtur enim optima. Cum enim ex enunciatione praedicante duo contradictoria possit utrumque inferri (quia aequivalet copulativae), aut neutrum (quia destruit seipsam), et enunciatio supradicta terminos oppositos contradictorie praedicet, videtur sequi utraque pars, quia falsum est neutram sequi.	3. Two questions arise at this point. The first concerns something assumed here: how can it ever be true to make such a statement as "Caesar is a dead man,” since an enunciation cannot be true in which two contradictories are predicated at the same time of something (for this is a first principle). But "man” and "dead,” as is said in the text, include contradictory opposition, for in man is included life, and in dead, non-life. The second question concerns the consequent that Aristotle rejects, which appears to be good. The enunciation given as an example predicates terms that are opposed contradictorily. But from an enunciation predicating two contradictory terms, either both can be inferred (because it is equivalent to a copulative enunciation), or neither (because it destroys itself); therefore both parts seem to follow, since it is false that neither follows.
Cajetanus lib. 2 l. 7 n. 4 Ad hoc simul dicitur quod aliud est loqui de duobus terminis secundum se, et aliud de eis ut unum stat sub determinatione alterius. Primo namque modo, homo et mortuus, contradictionem inter se habent, et impossibile est quod simul in eodem inveniantur. Secundo autem modo, homo et mortuus, non opponuntur, quia homo transmutatus iam per determinationem corruptivam importatam in ly mortuus, non stat pro suo significato secundum se, sed secundum exigentiam termini additi, a quo suum significatum distractum est. Ad utrunque autem insinuandum Aristoteles duo dixit, et quod habent oppositionem quam sequitur contradictio, attendens significata eorum secundum se, et quod etiam ex eis formatur una vera enunciatio cum dicitur, Socrates est homo mortuus, attendens coniunctionem eorum alterius corruptivam. Unde patet quid dicendum sit ad dubitationes. Ad utramque siquidem dicitur, quod non enunciantur duo contradictoria simul de eodem, sed terminus ut stat sub distractione, seu transmutatione alterius, cui secundum se esset contradictorius.	4. These two questions can be answered simultaneously. It is one thing to speak of two terms in themselves, and another to speak of them as one stands under the determination of another. Taken in the first way, "man” and "dead” have a contradiction between them and it is impossible that they be found in the same thing at the same time. In the second way, however, "man” and "dead” are not opposed, since "man,” changed by the destructive element introduced by "dead,” no longer stands for what it signifies as such, but as determined by the term added, by which what is signified is removed. Aristotle, in order to imply both, says two things: that they have the opposition upon which contradiction follows if you regard what they signify in themselves; and, that one true enunciation is formed from them as in "Socrates is a dead man,” if you regard their conjunction as destructive of one of them. Accordingly, the answer to the two questions is evident. In a case such as this two contradictories are not enunciated of the same thing at the same time, but one term as it stands under dissolution or transmutation from the other, to which by itself it would be contradictory.
Cajetanus lib. 2 l. 7 n. 5 Dubitatur quoque circa id quod ait: inest aliquid oppositorum quae consequitur contradictio; superflue enim videtur addi illa particula, quae consequitur contradictio. Omnia enim opposita consequitur contradictio, ut patet discurrendo in singulis; pater enim est non filius, et album non nigrum, et videns non caecum et cetera. Et ad hoc dicendum est quod opposita possunt dupliciter accipi: uno modo formaliter, idest secundum sua significata; alio modo denominative, seu subiective. Verbi gratia, pater et filius possunt accipi pro paternitate et filiatione, et possunt accipi pro eo qui denominatur pater vel filius. Rursus cum omnis distinctio fiat oppositione aliqua, ut dicitur in X metaphysicae, supponatur omnino distincta esse opposita. Dicendum ergo est quod, licet ad omnia opposita seu distincta contradictio sequatur inter se formaliter sumpta, non tamen ad omnia opposita sequitur contradictio inter ipsa denominative sumpta. Quamvis enim pater et filius mutuam sui negationem inferant inter se formaliter, quia paternitas est non filiatio, et filiatio est non paternitas; in relatione tamen ad denominatum, contradictionem non necessario inferunt. Non enim sequitur, Socrates est pater; ergo non est filius; nec e converso. Ut persuaderet igitur Aristoteles quod non quaecunque opposita colligata impediunt divisam illationem (quia non illa quae habent contradictionem annexam formaliter tantum, sed illa quae habent contradictionem et formaliter et secundum rem denominatam), addidit: quae consequitur contradictio, in tertio scilicet denominato. Et usus est satis congrue vocabulo, scilicet, consequitur: contradictio enim ista in tertio est quodammodo extra ipsa opposita.	5. There is also a question about something else that Aristotle says, namely, something opposed is present... from which a contradiction follows. The phrase from which a contradiction follows seems to be superfluous, for contradiction follows upon all opposites, as is evident in discoursing about singulars; for a father is not a son, and white is not black, and one seeing is not blind, etc. Opposites, however, can be taken in two ways: formally, i.e., according to what they signify, and denominatively, or subjectively. For example, father and son can be taken for paternity and filiation, or they can be taken for the one who is denominated a father or a son. But, again, since every distinction is made by some opposition, as is said in X Metaphysicae [3: 1054a 20], it could be supposed that opposites are wholly distinct. It must be pointed out, therefore, that although contradiction follows between all opposites or distinct things formally taken, nevertheless, contradiction does not follow upon all opposites denominatively taken. Father and son formally taken infer a mutual negation of one another, for paternity is not filiation and filiation is not paternity, but in respect to what is denominated they do not necessarily infer a contradiction. It does not follow, for example, that "Socrates is a father; therefore he is not a son,” nor conversely. Aristotle, therefore, in order to establish that not all combined opposites prevent a divided inference (since those having a contradiction applying only formally do not prevent a divided inference, but those having a contradiction both formally and according to the thing denominated do prevent a divided inference) adds, from which a contradiction follows, namely, in the third thing denominated. And appropriately enough he uses the word follows, for the contradiction in " the third thing denominated is in a certain way outside of the opposites themselves.
Cajetanus lib. 2 l. 7 n. 6 Deinde cum dicit: vel etiam quando est etc., declarat quod ex non oppositis in tertio coniunctis secundum unum praedicatum, non universaliter possunt inferri partes divisim. Et primo, hoc proponit quasi emendans quod immediate dixerat, subiungens: vel etiam quando est, scilicet oppositio inter terminos coniunctos, falsum est semper, scilicet inferre divisim; quasi diceret: dixi quod quando inest oppositio, non verum sed falsum est inferre divisim; quando autem non inest talis oppositio, verum est inferre divisim. Vel etiam ut melius dicatur, quod quando est oppositio, falsum est semper, quando autem non inest talis oppositio, non semper verum est. Et sic modificavit supradicta addendo ly semper, et, non semper. Et subdens exemplum quod non semper ex non oppositis sequatur divisio, ait: ut, Homerus est aliquid ut poeta; ergo etiam est? Non. Ex hoc coniuncto, est poeta, de Homero enunciato, altera pars, ergo Homerus est, non sequitur; et tamen clarum est quod istae duae partes colligatae, est et poeta, non habent oppositionem, ad quam sequitur contradictio. Igitur non semper ex non oppositis coniunctis illatio divisa tenet et cetera.	6. When he says, Or, rather, when something opposed is present in it, it is never true, etc., he explains that the parts cannot universally be inferred divisively in the case of a conjoined predicate in which there is a non-opposite as the third thing denominated. He proposes this—Or, rather, when something opposed is contained in it, i.e., opposition between the terms conjoined—as if amending what he has just said, namely, it is always false, i.e., to infer divisively. What he is saying, then, is this: I have said that when there is inherent opposition it is not true but false to infer divisively; but when there is not such opposition it is true to infer divisively; or, even better, when there is opposition it is always false but when there is not such opposition it is not always true. That is, he modifies what he first said by the addition of "always” and "not always.” Then he adds an example to show that division does not always follow from non-opposites: For example, Homer is something, say, a poet. Is it therefore true to say also that Homer "is,” or not? From the conjoined predicate, is a poet, enunciated of Homer, one part, Therefore Homer is, does not follow; yet it is evident that these two conjoined parts, "is” and "poet,” do not have the opposition upon which contradiction follows. Therefore, in the case of conjoined non-opposites a divided inference does not always hold.
Cajetanus lib. 2 l. 7 n. 7 Deinde cum dicit: secundum accidens etc., probat hoc, quod modo dictum est, ex eo quod altera pars istius compositi, scilicet, est, in antecedente coniuncto praedicatur de Homero secundum accidens, idest ratione alterius, quoniam, scilicet poeta, praedicatur de Homero, et non praedicatur secundum se ly est de Homero; quod tamen infertur, cum concluditur: ergo Homerus est. Considerandum est hic quod ad solvendam illam conclusionem negativam, scilicet,- non semper ex non oppositis coniunctis infertur divisim,- sufficit unam instantiam suae oppositae universali affirmativae afferre. Et hoc fecit Aristoteles adducendo illud genus enunciationum, in quo altera pars coniuncti est aliquid pertinens ad actum animae. Loquimur enim modo de Homero vivente in poematibus suis in mentibus hominum. In his siquidem enunciationibus partes coniunctae non sunt oppositae in tertio, et tamen non licet inferre utramque partem divisim. Committitur enim fallacia secundum quid ad simpliciter. Non enim valet, Caesar est laudatus, ergo est: et simile est de esse in effectu dependente in conservari. Quomodo autem intelligenda sit ratio ad hoc adducta ab Aristotele in sequenti particula dicetur.	7. When he says, The "is” here is predicated accidentally of Homer, he proves what he has said. One part of this composite, namely, "is,” is predicated of Homer in the antecedent conjunction accidentally, i.e., by reason of another, namely, with regard to the "poet” which is predicated of Homer; it is not predicated as such of Homer. Nevertheless, this is what is inferred when one concludes "Therefore Homer is.” To validate his negative conclusion, namely, that it is not always true to infer divisively from conjoined non-opposites, it was sufficient to give one instance of the opposite of the universal affirmative. To do this Aristotle introduces that genus of enunciation in which one part of the conjunction is something pertaining to an act of the mind (for we are speaking only of Homer living in his poems in the minds of men). In such enunciations the parts conjoined are not opposed in the third thing denominated; nevertheless it is not licit to infer each part divisively, for the fallacy of going from the relative to the absolute will be committed. For example, it is not valid to say, "Caesar is praiseworthy, therefore he is,” which is a parallel case, i.e., of an effect whose existence requires maintenance. Aristotle will explain in the following sections of the text how the reasoning in the above text is to be understood.
Cajetanus lib. 2 l. 7 n. 8 Deinde cum dicit: quare in quantiscunque etc., respondet parti affirmativae quaestionis, quando scilicet ex coniunctis licet inferre divisim. Et ponit duas conditiones oppositas supradictis debere convenire in unum, ad hoc ut possit fieri talis consequentia; scilicet, quod nulla inter partes coniuncti oppositio sit, et quod secundum se praedicentur. Unde dicit inferendo ex dictis: quare in quantiscunque praedicamentis, idest praedicatis ordine quodam adunatis, neque contrarietas aliqua, in cuius ratione ponitur contradictio in tertio (contraria enim sunt quae mutuo se ab eodem expellunt), aut universaliter nulla oppositio inest, ex qua scilicet sequatur contradictio in tertio, si definitiones pro nominibus sumantur. Dixit hoc, quia licet in quibusdam non appareat oppositio, solis nominibus positis, sicut, homo mortuus, et in quibusdam appareat, ut, vivum mortuum; hoc tamen non obstante, si, positis nominum definitionibus loco nominum, oppositio appareat, inter opposita collocamus. Sicut, verbi gratia, homo mortuus, licet oppositionem non praeseferat, tamen si loco hominis et mortui eorum definitionibus utamur, videbitur contradictio. Dicemus enim corpus animatum rationale, corpus inanimatum irrationale. In quantiscunque, inquam, coniunctis nulla est oppositio, et secundum se, et non secundum accidens praedicantur, in his verum erit dicere et simpliciter, idest divisim quod fuerat coniunctim enunciatum.	8. When he says, Therefore, in whatever predications no contrariety is present when definitions are put in place of the names, etc., he replies to the affirmative part of the question, i.e., when it is licit to infer divisively from conjoined predicates. He maintains that two conditions—opposed to what has been said earlier in this portion of the text—must combine in one enunciation in order that such a consequence be effected: there must be no opposition between the parts conjoined, and they must be predicated per se. He says, then, inferring from what has been said: Therefore, in whatever predicaments, i.e., predicates joined in a certain order, no contrariety, in virtue of which contradiction is posited in the third thing denominated (for contraries mutually remove each other from the same thing), is present, or universally, no opposition is present, i.e., upon which a contradiction follows in the third thing denominated, when definitions are taken in place of the names.... He says this because it may be the case that the opposition is not apparent from the names alone, as in "dead man,” and again it may be, as in "living dead,” but whether apparent or not it will be evident that we are putting together opposites if we posit the definitions of the names in place of the names. For example, in the case of "dead man,” if we replace "man” and "dead,” with their definitions, the contradiction will be evident, for what we are saying is "rational animate body, irrational inanimate body.” In whatever conjoined predicates, then, there is no opposition, and wherein predicates are predicated per se and not accidentally, in these it will also be true to predicate them singly, i.e., say divisively what had been enunciated conjointly.
Cajetanus lib. 2 l. 7 n. 9 Ad evidentiam secundae conditionis hic positae, nota quod ly secundum se potest dupliciter accipi: uno modo positive, et sic dicit perseitatem primi, secundi, universaliter, quarti modi; alio modo negative, et sic idem sonat quod non per aliud. Rursus considerandum est quod cum Aristoteles dixit de praedicato coniuncto quod, secundum se praedicetur, ly secundum se potest ad tria referri, scilicet, ad partes coniuncti inter se, ad totum coniunctum respectu subiecti, et ad partes coniuncti respectu subiecti. Si ergo accipiatur ly secundum se positive, licet non falsus, extraneus tamen a mente Aristotelis reperitur sensus ad quodcunque illorum trium referatur. Licet enim valeat, est homo risibilis, ergo est homo et est risibilis, et, est animal rationale, ergo est animal et est rationale; tamen his oppositae inferunt similes consequentias. Dicimus enim, est albus musicus, ergo est musicus et est albus: ubi nulla est perseitas, sed est coniunctio per accidens, tam inter partes inter se, quam inter totum et subiectum, quam etiam inter partes et subiectum. Liquet igitur quod non accipit Aristoteles ly secundum se positive, ex eo quod vana fuisset talis additio, quae ab oppositis non facit in hoc differentiam. Ad quid enim addidit, secundum se, et non, secundum accidens, si tam illae quae sunt secundum se, modo exposito, quam illae quae sunt secundum accidens ex coniuncto, inferunt divisum? Si vero accipiatur secundum se, negative, idest, non per aliud, et referatur ad partes coniuncti inter se, falsa invenitur regula. Nam non licet dicere, est bonus citharoedus; ergo est bonus et citharoedus; et tamen ars citharizandi et bonitas eius sine medio coniunguntur. Et similiter contingit, si referatur ad totum coniunctum respectu subiecti, ut in eodem exemplo apparet. Totum enim hoc, citharoedus bonus, non propter aliud convenit homini; et tamen non infert, ut dictum est, divisionem. Superest ergo ut ad partem coniuncti respectu subiecti referatur, et sit sensus: quando aliqua coniunctim praedicata, secundum se, idest, non per aliud, praedicantur, idest, quod utraque pars praedicatur de subiecto non propter alteram, sed propter seipsam et subiectum, tunc ex coniuncto infertur divisa praedicatio.	9. In order to make this second condition clear, it should be noted that "per se” can be taken in two ways: positively, and thus it refers to "perseity” of the first, of the second, and of the fourth mode universally; or negatively, and thus it means the same as not through something else. It should also be noted that when Aristotle says of a conjoined predicate that it is predicated "per se,” the "per se” can be referred to three things: to the parts of the conjunction among themselves, to the whole conjunction with respect to the subject, and to the parts of the conjoined predicate with respect to the subject. Now if "per se” is taken positively, although it will not be false, nevertheless in reference to any of these three the meaning will be found to be foreign to the mind of Aristotle. For, although these are valid: "He is a risible man, therefore he is man and he is risible” and "He is a rational animal, therefore he is animal and he is rational,” nevertheless the opposite kind of predication infers consequences in a similar way. For example, there is no 11 perseity” in "He is a white musician, therefore he is white and he is a musician”; rather, there is an accidental conjunction, not only between the parts among themselves and between the whole and the subject, but even between the parts and the subject. It is evident, therefore, that Aristotle is not taking "per se” positively, for an addition that does not differentiate this kind of predication from the opposed kind of predication would be useless. Why add "per se and not accidentally,” if both those that are per se in the way explained and those that are conjoined accidentally infer divisively? If "per se” is taken negatively, i.e., as not through another, and is referred to the parts of the conjoined predicate among themselves, the rule is found to be false. It is not licit, for example, to say, "He is a good lute player, therefore he is good and a lute player”; yet the art of lute-playing and its goodness are conjoined without anything as a medium. And the case is the same if it is referred to the whole conjoined predicate with respect to the subject, as is clear in the same example, for the whole, "good lute player,” does not belong to man on account of another, and yet it does not infer the division, as has already been said. Therefore, "per se” is referred to the parts of the conjoined predicate with respect to the subject and the meaning is: when the predicates are conjointly predicated per se, i.e., not through another, i.e., each part is predicated of the subject, not on account of another but on account of itself and the subject, then a divided predication is inferred from the conjoined predication.
Cajetanus lib. 2 l. 7 n. 10 Et hoc modo exponunt Averroes et Boethius; et vera invenitur regula, ut inductive facile manifestari potest, et ratio ipsa suadet. Si enim partes alicuius coniuncti praedicati ita inhaerent subiecto quod neutra propter alteram insit, earum separatio nihil habet quod veritatem impediat divisarum. Est et verbis Aristotelis consonus sensus iste. Quoniam et per hoc distinguit inter enunciationes ex quibus coniunctum infert divisam praedicationem, et eas quibus haec non inest consequentia. Istae siquidem ultra habentes oppositiones in adiecto, sunt habentes praedicatum coniunctum, cuius una partium alterius est ita determinatio, quod nonnisi per illam subiectum respicit, sicut apparet in exemplo ab Aristotele adducto, Homerus est poeta. Est siquidem ibi non respicit Homerum ratione ipsius Homeri, sed praecise ratione poesis relictae; et ideo non licet inferre, ergo Homerus est. Et simile est in negativis. Si quis enim dicat, Socrates non est paries, non licet inferre, ergo Socrates non est, eadem ratione, quia esse non est negatum de Socrate, sed de pariete in Socrate.	10. This is the way in which Averroes and Boethius explain this and, explained in this way, a true rule is found, as can easily be manifested inductively; moreover, the reasoning is compelling. For, if the parts of some conjoined predicate so inhere in the subject that neither is in it on account of another, their separation produces nothing that could impede the truth of the divided predicates. And this meaning is consonant with the words of Aristotle, for by this he also distinguishes between enunciations in which the conjoined predicate infers a divided predicate, and those in which this consequence is not inherent. For besides the predicates having opposition in the additional determining element, there are those with a conjoined predicate wherein one part is a determination of the other in such a way that only through it does it regard the subject, as is evident in Aristotle’s example, "Homer is a poet.” The "is” does not regard Homer by reason of Homer himself, but precisely by reason of the poetry he left. Hence it is not licit to infer, "Therefore Homer is.” The same is true with respect to negative enunciations of this type, for it is not licit to infer from "Socrates is not a wall,” "Therefore Socrates is not.” And the reason is the same: "to be” is not denied of Socrates, but of "wallness” in Socrates.
Cajetanus lib. 2 l. 7 n. 11 Et per hoc patet qualiter sit intelligenda ratio in textu superiore adducta. Accipitur enim ibi, secundum se negative, modo hic exposito, et secundum accidens, idest propter aliud. In eadem ergo significatione est usus ly secundum accidens, solvendo hanc et praecedentem quaestionem: utrobique enim intellexit secundum accidens, idest, propter aliud, coniuncta, sed ad diversa retulit. Ibi namque ly secundum accidens determinabat coniunctionem duorum praedicatorum inter se; hic vero determinat partem coniuncti praedicati in ordine ad subiectum. Unde ibi, album et musicum, inter ea quae secundum accidens sunt, numerabantur; hic autem non.	11. Accordingly, it is evident how the reasoning in the text above is to be understood. "Per se” is taken negatively in the way explained here, and "accidentally” as "on account of another.” The "accidentally” is used with the same signification in solving this and the preceding question. In both he understands "accidentally” to mean conjoined on account of another, but it is referred to diverse things. In the preceding question "accidentally” determines the way in which two predicates are conjoined among themselves; in the latter question it determines the way in which the part of the conjoined predicate is ordered to the subject. Hence, in the former, "white” and "musician” are numbered among the things that are accidental, but in the latter they are not.
Cajetanus lib. 2 l. 7 n. 12 Sed occurrit circa hanc expositionem dubitatio non parva. Si enim ideo non licet ex coniuncto inferre divisim, quia altera pars coniuncti non respicit subiectum propter se, sed propter alteram partem (ut dixit Aristoteles de ista enunciatione, Homerus est poeta), sequetur quod numquam a tertio adiacente ad secundum erit bona consequentia: quia in omni enunciatione de tertio adiacente, est respicit subiectum propter praedicatum et non propter se et cetera.	12. This exposition seems a bit dubious, however. For if it is not licit to infer divisively from a conjoined predicate because one part of the conjoined predicate does not regard the subject on account of itself but on account of another part (as Aristotle says of the enunciation, "Homer is a poet”), it will follow that there will never be a good consequence from the third determinant to the second, since in every enunciation with a third determinant, "is” regards the subject on account of the predicate and not on account of itself.
Cajetanus lib. 2 l. 7 n. 13 Ad huius difficultatis evidentiam, nota primo hanc distinctionem. Aliud est tractare regulam, quando ex tertio adiacente infertur secundum et quando non, et aliud quando ex coniuncto fit illatio divisa et quando non. Illa siquidem est extra propositum, istam autem venamur. Illa compatitur varietatem terminorum, ista non. Si namque unus terminorum, qui est altera pars coniuncti, secundum significationem seu suppositionem varietur in separatione, non infertur ex coniuncto praedicato illudmet divisim, sed aliud. Nota secundo hanc propositionem: cum ex tertio adiacente infertur secundum, non servatur identitas terminorum. Liquet ista quoad illum terminum, est. Dictum siquidem fuit supra a sancto Thoma, quod aliud importat est secundum adiacens, et aliud est tertium adiacens. Illud namque importat actum essendi simpliciter, hoc autem habitudinem inhaerentiae vel identitatis praedicati ad subiectum. Fit ergo varietas unius termini cum ex tertio adiacente infertur secundum, et consequenter non fit illatio divisi ex coniuncto. Unde praelucet responsio ad obiectionem, quod, licet ex tertio adiacente quandoque possit inferri secundum, numquam tamen ex tertio adiacente licet inferri secundum tamquam ex coniuncto divisum, quia inferri non potest divisim, cuius altera pars ipsa divisione perit. Negetur ergo consequentia obiectionis et ad probationem dicatur quod, optime concludit quod talis illatio est illicita infra limites illationum, quae ex coniuncto divisionem inducunt, de quibus hic Aristoteles loquitur.	13. To make this difficulty clear, we must first note a distinction. It is one thing to treat of the rule when inferring a second determinant from a third determinant, and when not; it is quite another thing when a divided inference is made from a conjoined predicate, and when not. The former is an additional point; the latter is the question we have been inquiring about. The former is compatible with variety of the terms, the latter not. For if one of the terms which is one part of a conjoined predicate will be varied according to signification, or supposition when taken separately, it is not inferred divisively from the conjoined predicate, but the other is. Secondly, note this proposition: when a second determinant is inferred from a third, identity of the terms is not kept. This is evident with respect to the term "is.” Indeed, St. Thomas said above that "is” as the second determinant implies one thing and "is” as the third determinant another. The former implies the act of being simply, the latter implies the relationship of inherence, or identity of the predicate with the subject. Therefore, when the second determinant is inferred from the third, one term is varied and consequently an inference is not made of the divided from the conjoined. Accordingly, the response to the objection is clear, for although the second determinant can sometimes be inferred from the third, it is never licit for the second to be inferred from the third as divided from conjoined, because you cannot infer divisively when one part is destroyed by that very division. Therefore, let the consequence of the objection be denied and for proof let it be said that the conclusion that such an inference is illicit under the limits of inferences which induce division from a conjoined predicate-is good, for this is what Aristotle is speaking of here.
Cajetanus lib. 2 l. 7 n. 14 Sed contra hoc instatur. Quia etiam tanquam ex coniuncto divisa fit illatio, Socrates est albus, ergo est, per locum a parte in modo ad suum totum, ubi non fit varietas terminorum. Et ad hoc dicitur quod licet homo albus sit pars in modo hominis (quia nihil minuit de hominis ratione albedo, sed ponit hominem simpliciter), tamen est album non est pars in modo ipsius est, eo quod pars in modo est universale cum conditione non minuente, ponente illud simpliciter. Clarum est autem quod album minuit rationem ipsius est, et non ponit ipsum simpliciter: contrahit enim ad esse secundum quid. Unde apud philosophos, cum fit aliquid album, non dicitur generari, sed generari secundum quid.	14. But the objection is raised against this that in the case of "Socrates is white, therefore be is,” a divided inference can be made as from a conjoined predicate, in virtue of the argument that we can go from what is in the mode of part to its whole as long as the terms remain the same. The answer to this is as follows. It is true that white man is a part in the mode of man (because white diminishes nothing of the notion of man but posits man simply); is white, however, is not a part in the mode of is, because a part in the mode of its whole is a universal, the condition not diminishing the positing of it simply. But it is evident that white diminishes the notion of is, and does not posit it simply, for it contracts it to relative being. Whence when something becomes white, philosophers do not say that it is generated, but generated relatively.
Cajetanus lib. 2 l. 7 n. 15 Sed instatur adhuc quia secundum hoc, dicendo, est animal, ergo est, fit illatio divisa per eumdem locum. Animal enim non minuit rationem ipsius est. Ad hoc est dicendum quod ly est, si dicat veritatem propositionis, manifeste peccatur a secundum quid ad simpliciter. Si autem dicat actum essendi, illatio est bona, sed non est de tertio, sed de secundo adiacente.	15. In accordance with this, the objection is raised that in saying "It is an animal, therefore it is,” a divided inference is made in virtue of the same argument; for animal does not diminish the notion of is itself. The answer to this is that if the is asserts the truth of a proposition, the fallacy is committed of going from the relative to the absolute; if the is asserts the act of being, the inference is good, but it is of the second determinant, not of the third.
Cajetanus lib. 2 l. 7 n. 16 Potest ulterius dubitari circa principale: quia sequitur, est quantum coloratum, ergo est quantum, et, est coloratum; et tamen coloratum respicit subiectum mediante quantitate: ergo non videtur recta expositio supra adducta. Ad hoc et similia dicendum est quod coloratum non ita inest subiecto per quantitatem quod sit eius determinatio et ratione talis determinationis subiectum denominet, sicut bonitas artem citharisticam determinat; cum dicitur, est citharoedus bonus; sed potius subiectum ipsum primo coloratum denominatur, quantum vero secundario coloratum dicitur, licet color media quantitate suscipiatur. Unde notanter supra diximus, quod tunc altera pars coniuncti praedicatur per accidens, quando praecise denominat subiectum, quia denominat alteram partem. Quod nec in similibus instantiis invenitur.	16. There is another doubt, this time about the principle in the exposition; for this follows, "It is a colored quantity, therefore it is a quantity and it is colored”; but "colored” regards the subject through the medium of quantity; therefore the exposition given above does not seem to be correct. The answer to this and to similar objections is that "colored” is not so present in a subject by means of quantity that it is its determination, and by reason of such a determination denominates the subject; as goodness,” for instance, determines the art of lute-playing when we say "He is a good lute player.” Rather, the subject itself is first denominated "colored” and quantity is called "colored” secondarily, although color is received through the medium of quantity. Hence, we made a point of saying earlier that one part of a conjoined predicate is predicated accidentally when it denominates the subject precisely because it denominates the other part.93 This is not the case here nor in similar instances.
Cajetanus lib. 2 l. 7 n. 17 Deinde cum dicit: quod autem non est etc., excludit quorumdam errorem qui, quod non est, esse tali syllogismo concludere satagebant: quod est, opinabile est. Quod non est, est opinabile. Ergo quod non est, est. Hunc siquidem processum elidit Aristoteles destruendo primam propositionem, quae partem coniuncti in subiecto divisim praedicat, ac si diceret: est opinabile, ergo est. Unde assumendo subiectum conclusionis illorum ait: quod autem non est; et addit medium eorum, quoniam opinabile est; et subdit maiorem extremitatem, non est verum dicere, esse aliquid. Et causam assignat, quia talis opinatio non propterea est, quia illud sit, sed potius quia non est.	17. When he says, In the case of non-being, however, it is not true to say that it is something, etc., he excludes the error of those who were satisfied to conclude that what is not, is. This is the syllogism they use: "That which is, is ‘opinionable’; that which is not, is ‘opinionable’; therefore what is not, is.” Aristotle destroys this process of reasoning by destroying the first proposition, which predicates divisively a part of what is conjoined in the subject, as if it said "It is ‘opinionable,’ therefore it is.” Hence, assuming the subject of their conclusion, he says, In the case of that which is not, however; and he adds their middle term, because it is a matter of opinion; then he adds the major extreme, it is not true to say that it is something. He then assigns the cause: it is not because it is but rather because it is not, that there is such opinion.

LECTURE 8

Latin	English
Cajetanus lib. 2 l. 8 n. 1 Postquam determinatum est de enunciationibus, quarum partibus aliud additur tam remanente quam variata unitate, hic intendit declarare quid accidat enunciationi, ex eo quod aliquid additur, non suis partibus, sed compositioni eius. Et circa hoc duo facit: primo, determinat de oppositione earum; secundo, de consequentiis; ibi: consequentiae vero et cetera. Circa primum duo facit: primo, proponit quod intendit; secundo, exequitur; ibi: nam si eorum et cetera. Proponit ergo quod iam perspiciendum est, quomodo se habeant affirmationes et negationes enunciationum de possibili et non possibili et cetera. Et causam subdit: habent enim multas dubitationes speciales. Sed antequam ulterius procedatur, quoniam de enunciationibus, quae modales vocantur, sermo inchoatur, praelibandum est esse quasdam modales enunciationes, et qui et quot sunt modi reddentes propositiones modales; et quid earum sit subiectum et quid praedicatum; et quid sit ipsa enunciatio modalis; quisque sit ordo earum ad praecedentes; et quae necessitas sit specialem faciendi tractatum de his.	1. Now that he has treated enunciations in which something added to the parts leaves the unity intact on the one hand, and varies it on the other, Aristotle begins to explain what happens to the enunciation when something is added, not to its parts, but to its composition. First, he explains their opposition; secondly, he treats of the consequences of their opposition where he says, Logical sequences result from modals ordered thus, etc. With respect to the first point, he proposes the question he intends to consider and then begins his consideration where he says, Let us grant that of mutually related enunciations, contradictories are those opposed to each other, etc. He proposes that we must now investigate the way in which affirmations and negations of the possible and not possible are related. He gives the reason when he adds, for the question has many special difficulties. However, before we proceed with the consideration of enunciations that are called modal, we must first see that there are such things as modal enunciations, and which and how many modes render propositions modal; we must also know what their subject is and their predicate, what the modal enunciation itself is, what the order is between modal enunciations and the enunciations already treated, and finally, why a special treatment of them is necessary.
Cajetanus lib. 2 l. 8 n. 2 Quia ergo possumus dupliciter de rebus loqui; uno modo, componendo rem unam cum alia, alio modo, compositionem factam declarando qualis sit, insurgunt duo enunciationum genera; quaedam scilicet enunciantes aliquid inesse vel non inesse alteri, et hae vocantur de inesse, de quibus superius habitus est sermo; quaedam vero enunciantes modum compositionis praedicati cum subiecto, et hae vocantur modales, a principaliori parte sua, modo scilicet. Cum enim dicitur, Socratem currere est possibile, non enunciatur cursus de Socrate, sed qualis sit compositio cursus cum Socrate, scilicet possibilis. Signanter autem dixi modum compositionis, quoniam modus in enunciatione positus duplex est. Quidam enim determinat verbum, vel ratione significati ipsius verbi ut Socrates currit velociter, vel ratione temporis consignificati, ut Socrates currit hodie; quidam autem determinat compositionem ipsam praedicati cum subiecto; sicut cum dicitur, Socratem currere est possibile. In illis namque determinatur qualis cursus insit Socrati, vel quando; in hac autem, qualis sit coniunctio cursus cum Socrate. Modi ergo non illi qui rem verbi, sed qui compositionem determinant, modales enunciationes reddunt, eo quod compositio veluti forma totius totam enunciationem continet.	2. We can speak about things in two ways: in one, composing one thing with another; in the other, declaring the kind of composition that exists between the two things. To signify these two ways of speaking about things we form two kinds of enunciations. One kind enunciates that something belongs or does not belong to something. These are called absolute [de inesse] enunciations; these we have already discussed. The other enunciates the mode of composition of the predicate with the subject. These are called modal, from their principal part, the mode. For when we say, "That Socrates run is possible,” it is not the running of Socrates that is enunciated but the kind of composition there is between running and Socrates-in this case, possible. I have said "mode of composition” expressly, for there are two kinds of mode posited in the enunciation. One modifies the verb, either with respect to what it signifies, as in "Socrates runs swiftly,” or with respect to the time signified along with the verb, as in "Socrates runs today.” The other kind modifies the very composition of the predicate with the subject, as in the example, "That Socrates run is possible.” The former determines how or when running is in Socrates; the latter determines the kind of conjunction there is between running and Socrates. The former, which affects the actuality of the verb, does not make a modal enunciation. Only the modes that affect the composition make a modal enunciation, the reason being that the composition, as the form of the whole, contains the whole enunciation.
Cajetanus lib. 2 l. 8 n. 3 Sunt autem huiusmodi modi quatuor proprie loquendo, scilicet possibile et impossibile, necessarium et contingens. Verum namque et falsum, licet supra compositionem cadant cum dicitur, Socratem currere est verum, vel hominem esse quadrupedem est falsum, attamen modificare proprie non videntur compositionem ipsam. Quia modificari proprie dicitur aliquid, quando redditur aliquale, non quando fit secundum suam substantiam. Compositio autem quando dicitur vera, non aliqualis proponitur, sed quod est: nihil enim aliud est dicere, Socratem currere est verum, quam quod compositio cursus cum Socrate est. Et similiter quando est falsa, nihil aliud dicitur, quam quod non est: nam nihil aliud est dicere, Socratem currere est falsum, quam quod compositio cursus cum Socrate non est. Quando vero compositio dicitur possibilis aut contingens, iam non ipsam esse, sed ipsam aliqualem esse dicimus: cum siquidem dicitur, Socratem currere est possibile, non substantificamus compositionem cursus cum Socrate, sed qualificamus, asserentes illam esse possibilem. Unde Aristoteles hic modos proponens, veri et falsi nullo modo meminit, licet infra verum et non verum inferat, propter causam ibi assignandam.	3. This kind of mode, properly speaking, is fourfold: possible, impossible, necessary, and contingent. True and false are not included because, strictly speaking, they do not seem to modify the composition even though they fall upon the composition itself, as is evident in "That Socrates runs is true,” and "That man is four-footed is false.” For something is said to be modified in the proper sense of the term when it is caused to be in a certain way, not when it comes to be according to its substance. Now, when a composition is said to be true it is not proposed that it is in a certain way, but that it is. To say, "That Socrates runs is true,” for example, is to say that the composition of running with Socrates is. The case is similar when it is false, for what is said is that it is not; for example, to say, "That Socrates runs is false” is to say that the composition of running with Socrates is not. On the other hand, when the composition is said to be possible or contingent, we are not saying that it is but that it is in a certain way. For example, when we say, "That Socrates run is possible,” we do not make the composition of running with Socrates substantial, but we qualify it, asserting that it is possible. Consequently, Aristotle in proposing the modes, does not mention the true and false at all, although later on he infers the true and the not true, and assigns the reason for it where he does this.
Cajetanus lib. 2 l. 8 n. 4 Et quia enunciatio modalis duas in se continet compositiones, alteram inter partes dicti, alteram inter dictum et modum, intelligendum est eam compositionem modificari, idest, quae est inter partes dicti, non eam quae est inter modum et dictum. Quod sic perpendi potest. Huius enunciationis modalis, Socratem esse album est possibile, duae sunt partes; altera est, Socratem esse album, altera est, possibile. Prima dictum vocatur, eo quod est id quod dicitur per eius indicativam, scilicet, Socrates est albus: qui enim profert hanc, Socrates est albus, nihil aliud dicit nisi Socratem esse album: secunda vocatur modus, eo quod modi adiectio est. Prima compositionem quandam in se continet ex Socrate et albo; secunda pars primae opposita compositionem aliquam sonat ex dicti compositione et modo. Prima rursus pars, licet omnia habeat propria, subiectum scilicet, et praedicatum, copulam et compositionem, tota tamen subiectum est modalis enunciationis; secunda autem est praedicatum. Dicti ergo compositio subiicitur et modificatur in enunciatione modali. Qui enim dicit, Socratem esse album est possibile, non significat qualis est coniunctio possibilitatis cum hoc dicto, Socratem esse album, sed insinuat qualis sit compositio partium dicti inter se, scilicet albi cum Socrate, scilicet quod est compositio possibilis. Non dicit igitur enunciatio modalis aliquid inesse, vel non inesse, sed dicti potius modum enunciat. Nec proprie componit secundum significatum, quia compositionis non est compositio, sed rerum compositioni modum apponit. Unde nihil aliud est enunciatio modalis, quam enunciatio dicti modificativa.	4. Since the modal enunciation contains two compositions, one between the parts of what is said, the other between what is said and the mode, it must be understood that it is the former composition that is modified, i.e., the composition between the parts of what is said, not the composition between what is said and the mode. This can be seen in an example. In the modal enunciation, "That Socrates be white is possible,” there are two parts: one, "That Socrates be white,” the other, "is possible.” The first is called the dictum because it is that which is asserted by the indicative, namely, "Socrates is white”; for in saying "Socrates is white” we are simply saying, "That Socrates be white.” The second part is called the mode because it is the addition of a restriction. The first part of the modal enunciation consists of a certain composition of Socrates and white; the second part, opposed to the first, 4 indicates a composition from the composition of dictum and mode. Again, the first part, although it has all the properties of an enunciation—subject, predicate, copula, and composition—is, in its entirety, the subject of the modal enunciation; the second part, the mode, is the predicate. In a modal enunciation, therefore, the composition of the dictum is subjected and modified; for when we say, "That Socrates be white is possible,” it does not signify the kind of conjunction of possibility there is with the dictum "That Socrates be white,” but it implies the kind of composition there is of the parts of the dictum among themselves, i.e., of white with Socrates, namely, that it is a possible composition. The modal enunciation, therefore, does not say that something is present in or not present in a subject, but rather, it enunciates a mode of the dictum. Nor properly speaking does it compose according to what is signified, since it is not a composition of the composition; rather, it adds a mode to the composition of the things. Hence the modal enunciation is simply an enunciation in which the dictum is modified.
Cajetanus lib. 2 l. 8 n. 5 Nec propterea censenda est enunciatio plures modalis, quia omnia duplicata habeat: quoniam unum modum de unica compositione enunciat, licet illius compositionis plures sint partes. Plura enim illa ad dicti compositionem concurrentia, veluti plura ex quibus fit unum subiectum concurrunt, de quibus dictum est supra quod enunciationis unitatem non impediunt. Sicut nec cum dicitur, domus est alba, est enunciatio multiplex, licet domus ex multis consurgat partibus.	5. Because the modal enunciation has everything duplicated, it must not on that account be thought to be many. It enunciates one mode of only one composition, although there are many parts of that composition. The many concurring for the composition of the dictum are like the many that concur to make one subject, of which it was said above that it does not impede the unity of the enunciation.” The enunciation, "The house is white,” is also a case in point, for it is not multiple, although a house is built of many parts.
Cajetanus lib. 2 l. 8 n. 6 Merito autem est, post enunciationes de inesse, de modalibus tractandum, quia partes naturaliter sunt toto priores, et cognitio totius ex partium cognitione dependet; et specialis sermo de his est habendus, quia proprias habet difficultates. Notavit quoque Aristoteles in textu multa. Horum ordinem scilicet, cum dixit: his vero determinatis etc.; modos qui et quot sunt, cum eos expressit et inseruit; variationem eiusdem modi, per affirmationem et negationem, cum dixit: possibile et non possibile, contingens et non contingens; necessitatem cum addidit: habent enim multas dubitationes proprias et cetera.	6. Modal enunciations are rightly treated after the absolute enunciation, for parts are naturally prior to the whole, and knowledge of the whole depends on knowledge of the parts. Moreover, a special discussion of them was necessary because the modal enunciation has its own peculiar difficulties. Aristotle indicates in his text many of the things we have taken up here: the order of modal enunciations, when he says, Having determined these things, etc.; what and how many modes there are when he expresses and lists them, the variation of the same mode by affirmation and negation when he says, the possible and not possible, contingent and not contingent; the necessity of treating them, when he adds, for they have many difficulties of their own.
Cajetanus lib. 2 l. 8 n. 7 Deinde cum dicit: nam si eorum etc., exequitur tractatum de oppositione modalium. Et circa hoc duo facit: primo, movendo quaestionem arguit ad partes; secundo, determinat veritatem; ibi: contingit autem et cetera. Est autem dubitatio: an in enunciationibus modalibus fiat contradictio negatione apposita ad verbum dicti, quod dicit rem; an non, sed potius negatione apposita ad modum qui qualificat. Et primo, arguit ad partem affirmativam, quod scilicet addenda sit negatio ad verbum; secundo, ad partem negativam, quod non apponenda sit negatio ipsi verbo; ibi: videtur autem et cetera.	7. Then he investigates the opposition of modal enunciations, where he says, Let us grant that of those things that are combined, contradictories are those opposed to each other by being related in a certain way according to "to be” and "not to be,” etc. First, he presents the question and in so doing gives arguments for the parts; secondly, he determines the truth, where he says, For it follows from what we have said, either that the same thing is asserted and denied at once of the same subject, etc. The question with respect to the opposition of modals is this: Is a contradiction made in modal enunciations by a negation added to the verb of the dictum, which expresses what is; or is it not, but rather by a negation added to the mode which qualifies? Aristotle first argues for the affirmative part, that the negation must be added to the verb; then he argues for the negative part, that the negation must not be added to the verb, where he says, However it seems that the same thing is possible to be and possible not to be, etc.
Cajetanus lib. 2 l. 8 n. 8 Intendit ergo primo tale argumentum; si complexorum contradictiones attenduntur penes esse et non esse (ut patet inductive in enunciationibus substantivis de secundo adiacente et de tertio, et in adiectivis), contradictionesque omnium hoc modo sumendae sunt, contradictoria huius, possibile esse, erit, possibile non esse, et non illa, non possibile esse. Et consequenter apponenda est negatio verbo, ad sumendam oppositionem in modalibus. Patet consequentia, quia cum dicitur, possibile esse, et, possibile non esse, negatio cadit supra esse. Unde dicit: nam si eorum, quae complectuntur, idest complexorum, illae sibi invicem sunt oppositae contradictiones, quae secundum esse vel non esse disponuntur, idest in quarum una affirmatur esse, et in altera negatur.	8. His first argument is this. If of combined things, contradictions are those related according to "to be” and "not to be” (as is clear inductively in substantive enunciations with a second determinant, in those with a third determinant, and in adjectival enunciations) and all contradictions must be obtained in this way, the contradictory of "possible to be” will be "possible not to be,” and not, "not possible to be.” Consequently, the negation must be added to the verb to get opposition in modal enunciations. The consequence is clear, for when we say "possible to be” and possible not to be” the negation falls on "to be.” Accordingly, he says, Let us grant that of those things that are combined, i.e., of complex things, contradictions are those opposed to each other which are disposed according to "to be” and "not to be,” i.e., in one of which "to be” is affirmed and in the other denied.
Cajetanus lib. 2 l. 8 n. 9 Et subdit inductionem, inchoans a secundo adiacente: ut, eius enunciationis quae est, esse hominem, idest, homo est, negatio est, non esse hominem, ubi verbum negatur, idest, homo non est; et non est eius negatio ea quae est, esse non hominem, idest, non homo est: haec enim non est negativa, sed affirmativa de subiecto infinito, quae simul est vera cum illa prima, scilicet, homo est.	9. He goes on to give an induction, beginning with an enunciation having a second determinant. The negation of "Man is,” is, "Man is not,” in which the verb is negated. The negation of "Man is,” is not, "Non-man is,” for this is not the negative but the affirmative of the infinite subject, which is true at the same time as the first enunciation, "Man is.”
Cajetanus lib. 2 l. 8 n. 10 Deinde prosequitur inductionem in substantivis de tertio adiacente: ut, eius quae est, esse album hominem idest, ut illius enunciationis, homo est albus, negatio est, non esse album hominem, ubi verbum negatur, idest, homo non est albus; et non est negatio illius ea, quae est, esse non album hominem, idest, homo est non albus. Haec enim non est negativa, sed affirmativa de praedicato infinito. Et quia istae duae affirmativae de praedicato finito et infinito non possunt de eodem verificari, propterea quia sunt de praedicatis oppositis, posset aliquis credere quod sint contradictoriae; et ideo ad hunc errorem tollendum interponit rationem probantem quod hae duae non sunt contradictoriae. Est autem ratio talis. Contradictoriorum talis est natura quod de omnibus aut dictio, idest affirmatio aut negatio verificatur. Inter contradictoria siquidem nullum potest inveniri medium; sed hae duae enunciationes, scilicet, est homo albus, et, est homo non albus, sunt contradictoriae per se; ergo sunt talis naturae quod de omnibus altera verificatur. Et sic, cum de ligno sit falsum dicere, est homo albus, erit verum dicere de eo, scilicet ligno, esse non album hominem, idest, lignum est homo non albus. Quod est manifeste falsum: lignum enim neque est homo albus, neque est homo non albus. Restat ergo ex quo utraque est simul falsa de eodem, quod non sit inter eas contradictio. Sed contradictio fit quando negatio apponitur verbo.	10. He continues the induction with substantive enunciations having a third determinant. The negation of the enunciation "Man is white” is "Man is not white,” in which the verb is negated. The negation is not "Man is nonwhite,” for this is not the negative, but the affirmative of the infinite predicate. Now it might be thought that the affirmatives of the finite and infinite predicates are contradictories since they cannot be verified of the same thing because of their opposed predicates. To obviate this error, Aristotle interposes an argument proving that these two are not contradictories. The nature of contradictories, he reasons, is such that either the assertion, i.e., the affirmation, or the negation, is verified of anything, for between contradictories no middle is possible. Now the two enunciations, that something "is white man” and "is nonwhite man” are per se contradictories. Therefore, they are of such a nature that one of them is verified of anything. For example, it is false to say "is white man” of wood; hence "is nonwhite man” will be true to say of it, namely of wood, i.e., "Wood is nonwhite man.” This is manifestly false, for wood is neither white man nor nonwhite man. Consequently, there is not a contradiction in the case in which each is at once false of the same subject. Therefore, contradiction is effected when the negation is added to the verb.
Cajetanus lib. 2 l. 8 n. 11 Deinde prosequitur inductionem in enunciationibus adiectivi verbi, dicens: quod si hoc modo, scilicet supradicto, accipitur contradictio, et in quantiscunque enunciationibus esse non ponitur explicite, idem faciet quoad oppositionem sumendam, id quod pro esse dicitur (idest verbum adiectivum, quod locum ipsius esse tenet, pro quanto, propter eius veritatem in se inclusam, copulae officium facit), ut eius enunciationis quae est, homo ambulat, negatio est, non ea quae dicit, non homo ambulat (haec enim est affirmativa de subiecto infinito), sed negatio illius est, homo non ambulat; sicut et in illis de verbo substantivo, negatio verbo addenda erat. Nihil enim differt dicere verbo adiectivo, homo ambulat, vel substantivo, homo est ambulans.	11. He continues his induction with enunciations having an adjective verb: Now if the case is as we have stated it, i.e., contradiction is taken as said above, then in enunciations in which "to be” is not the determining word added (explicitly), that which is said in place of "to be” will effect the same thing with respect to the opposition obtained (i.e., the adjective verb that occupies the place of "to be,” inasmuch as the truth of "to be” is included in it, effects the function of the copula). For example, the negation of the enunciation "Man walks” is not, "Non-man walks” (for this is the affirmative of the infinite subject) but "Man is not walking.” In this case, as in that of the substantive verb, the negation must be added to the verb, for there is no difference between using the adjective verb, as in "Man walks,” and using the substantive verb, as in "Man is walking.”
Cajetanus lib. 2 l. 8 n. 12 Deinde ponit secundam partem inductionis dicens: et si hoc modo in omnibus sumenda est contradictio, scilicet, apponendo negationem ad esse, concluditur quod et eius enunciationis, quae dicit, possibile esse, negatio est, possibile non esse, et non illa quae dicit, non possibile esse. Patet conclusionis sequela: quia in illa, possibile non esse, negatio apponitur verbo; in ista autem non. Dixit autem in principio huius rationis: eorum quae complectuntur, idest complexorum, contradictiones fiunt secundum esse et non esse, ad differentiam incomplexorum quorum oppositio non fit negatione dicente non esse, sed ipsi incomplexo apposita, ut, homo, et, non homo, legit, et non legit.	12. Then he posits the second part of the induction: And if this is always the case, i.e., that contradiction must be gotten by adding the negation to "to be,” we must conclude that the negation of the enunciation that asserts "Possible to be” is "possible not to be,” and not, "not possible to be.” The consequent of the conclusion is evident, for in "possible not to be” the negation is added to the verb, in "not possible to be,” it is not. At the beginning of this argument, Aristotle said, Of those things that are combined, i.e., complex things, the contradictions are effected according to "to be” and "not to be.” He said this in reference to the difference between complex and incomplex things, for opposition in the latter is not made by the negation expressing "not to be,” but by adding the negative to the incomplex thing itself, as in "man” and "non-man,” "reads” and "non-reads.”
Cajetanus lib. 2 l. 8 n. 13 Deinde cum dicit: videtur autem idem etc., arguit ad quaestionis partem negativam (scilicet quod ad sumendam contradictionem in modalibus non addenda est negatio verbo), tali ratione. Impossibile est duas contradictorias esse simul veras de eodem; sed supradictae, scilicet, possibile esse, et, possibile non esse, simul verificantur de eodem; ergo istae non sunt contradictoriae: igitur contradictio modalium non attenditur penes verbi negationem. Huius rationis primo ponitur in littera minor cum sua probatione; secundo maior; tertio conclusio. Minor quidem cum dicit: videtur autem idem possibile esse, et, non possibile esse. Sicut verbi gratia, omne quod est possibile dividi est etiam possibile non dividi, et quod est possibile ambulare est etiam possibile non ambulare. Ratio autem huius minoris est, quoniam omne quod sic possibile est (sicut, scilicet, est possibile ambulare et dividi), non semper actu est: non enim semper actualiter ambulat, qui ambulare potest; nec semper actu dividitur, quod dividi potest. Quare inerit etiam negatio possibilis, idest, ergo non solum possibilis est affirmatio, sed etiam negatio eiusdem. Adverte quod quia possibile est multiplex, ut infra dicetur, ideo notanter Aristoteles addidit ly sic, assumens, quod sic possibile est, non semper actu est. Non enim de omni possibili verum est dicere quod non semper actu est, sed de aliquo, eo scilicet quod est sic possibile, quemadmodum ambulare et dividi. Nota ulterius quod quia tale possibile habet duas conditiones, scilicet quod potest actu esse et quod non semper actu est, sequitur necessario quod de eo simul est verum dicere, possibile esse, et, non esse. Ex eo enim quod potest actu esse, sequitur quod sit possibile esse; ex eo vero quod non semper actu est, sequitur quod sit possibile non esse. Quod enim non semper est, potest non esse. Bene ergo intulit Aristoteles ex his duobus: quare inerit etiam negatio possibilis et non solum affirmatio; potest igitur et non ambulare, quod est ambulabile, et non videri, quod est visibile. Maior vero subiungitur, cum ait: at vero impossibile est de eodem veras esse contradictiones. Infertur quoque ultimo conclusio: non est igitur ista (scilicet, possibile non esse) negatio illius, quae dicit, possibile esse: quia sunt simul verae de eodem. Caveto autem ne ex isto textu putes possibile, ut est modus, debere semper accipi pro possibili ad utrumlibet: quoniam hoc infra declarabitur esse falsum; sed considera quod satis fuit intendenti declarare quod in modalibus non sumitur contradictio ex verbi negatione, afferre instantiam in una modali, quae continetur sub modalibus de possibili.	13. When he says, However, it seems that the same thing is possible to be and possible not to be, etc., he argues for the negative part of the question, namely, to get a contradiction in modals the negation should not be added to the verb. His reasoning is the following: It is impossible for two contradictories to be true at once of the same subject; but "possible to be” and "possible not to be” are verified at once of the same thing; therefore, these are not contradictories. Consequently, contradiction of the modals is not obtained by negation of the verb. In this reasoning, the minor is posited first, with its proof; secondly, the major; finally, the conclusion. The minor is: However, it seems that the same thing is possible to be and possible not to be. For instance, everything that has the possibility of being divided also has the possibility of not being divided, and that which has the possibility of walking also has the possibility of not walking. The proof of this minor is that everything that is possible in this way (as are possible to walk and to be divided) is not always in act; for he who is able to walk is not always actually walking, nor is that which can be divided always divided. And so the negation of the possible will also be inherent in it, i.e., therefore not only is the affirmation possible but also the negation. Notice that since the possible is manifold, as will be said further on, Aristotle explicitly adds "in this way” when he assumes here that that which is possible is not always in act. For it is not true to say of every possible that it is not always in act, but only of some, namely, those that are possible in the way in which to walk and to be divided are possible. Note also that "possible in this way” has two conditions: that it is able to be in act, and that it is not always in act. It follows necessarily, then, that it is true to say of it simultaneously that it is both possible to be and possible not to be. From the fact that it can be in act it follows that it is possible to be; from the fact that it is not always in act it follows that it is possible not to be, for that which not always is, is able not to be. Aristotle, then, rightly infers from these two: and so the negation of the possible will also be inherent in it; and not just the affirmation, for that which could walk could also not walk and that which could be seen not be seen. The major is: But it is impossible that contradictions in respect to the same thing be true. The final conclusion inferred is: Therefore, the negation of "possible to be” is not, "possible not to be” because they are true at once of the same thing. In relation to this part of the text, be careful not to suppose that possible as it is a mode, is always to be taken for possible to either of two alternatives, for this will be shown to be false later on. If you consider the matter carefully you will see that it was enough for his intention to give as an instance one modal contained under the modals of the possible in order to show that contradiction in modals is not obtained by negation of the verb.
Cajetanus lib. 2 l. 8 n. 14 Deinde cum dicit: contingit autem unum ex his etc., determinat veritatem huius dubitationis. Et quia duo petebat, scilicet, an contradictio modalium ex negatione verbi fiat an non, et, an potius ex negatione modi; ideo primo, determinat veritatem primae petitionis, quod scilicet contradictio harum non fit negatione verbi; secundo determinat veritatem secundae petitionis, quod scilicet fiat modalium contradictio ex negatione modi; ibi: est ergo negatio et cetera. Dicit ergo quod propter supradictas rationes evenit unum ex his duobus, quae conclusimus determinare, aut idem ipsum, idest, unum et idem dicere, idest affirmare et negare simul de eodem: idest, aut quod duo contradictoria simul verificantur de eodem, ut prima ratio conclusit; aut affirmationes vel negationes modalium, quae opponuntur contradictorie, fieri non secundum esse vel non esse, idest, aut contradictio modalium non fiat ex negatione verbi, ut secunda ratio conclusit. Si ergo illud est impossibile, scilicet quod duo contradictoria possunt simul esse vera de eodem, hoc, scilicet quod contradictio modalium non fiat secundum verbi negationem, erit magis eligendum. Impossibilia enim semper vitanda sunt. Ex ipso autem modo loquendi innuit quod utrique earum aliquid obstat. Sed quia primo obstat impossibilitas quae acceptari non potest, secundo autem nihil aliud obstat nisi quod negatio supra enunciationis copulam cadere debet, si negativa fieri debet enunciatio, et hoc aliter fieri potest quam negando dicti verbum, ut infra declarabitur; ideo hoc secundum, scilicet quod contradictio modalium non fiat secundum negationem verbi, eligendum est: primum vero est omnino abiiciendum.	14. Aristotle establishes the truth with respect to this difficulty where he says, For it follows from what we have said, either that the same thing is asserted and denied at once of the same subject, etc. Since he is investigating two things, i.e., whether contradiction of modals is made by the negation of the verb or not; and, whether it is not rather by negation of the mode, he first determines the truth in relation to the first question, namely, that contradiction of modals is not made by negation of the verb; then he determines the truth in relation to the second, namely, that contradiction of modals is made by negation of the mode, where he says, Therefore, the negation of "possible to be” is "not possible to be,” etc. Hence he says that because of the foresaid reasoning one of these two follows: first, that either the same thing, i.e., one and the same thing is said, i.e., is asserted and denied at once of the same subject, i.e., either two contradictories are verified at once of the same thing, as the first argument concluded; or secondly, that assertions and denials of modals, which are opposed contradictorily are not made by the addition of "to be” or "not to be,” i.e., contradiction of modals is not made by the negation of the verb, as the second argument concluded. If the former alternative is impossible, namely, that two contradictories can be true of the same thing at once, the latter, that contradiction of modals is not made according to negation of the verb, must obtain, for impossible things must always be avoided. His mode of speaking here indicates that there is some obstacle to each alternative. But since in the first the obstacle is an impossibility that cannot be accepted, while in the second the only obstacle is that the negation must fall upon the copula of the enunciation if a negative enunciation is to be formed, and this can be done otherwise than by denying the verb of the dictum, as will be shown later on, then the second alternative must be chosen, i.e., that the contradiction of modals is not made according to negation of the verb, and the first alternative is to be rejected.

LECTURE 9

Latin	English
Cajetanus lib. 2 l. 9 n. 1 Determinat ubi ponenda sit negatio ad assumendam modalium contradictionem. Et circa hoc quatuor facit: primo, determinat veritatem summarie; secundo, assignat determinatae veritatis rationem, quae dicitur rationi ad oppositum inductae; ibi: fiunt enim etc.; tertio, explanat eamdem veritatem in omnibus modalibus; ibi: eius vero etc.; quarto, universalem regulam concludit; ibi: universaliter vero et cetera. Quia igitur negatio aut verbo aut modo apponenda est, et quod verbo non addenda est, declaratum est per locum a divisione; concludendo determinat: est ergo negatio eius quae est possibile esse, ea quae est non possibile esse, in qua negatur modus. Et eadem est ratio in enunciationibus de contingenti. Huius enim, quae est, contingens esse, negatio est, non contingens esse. Et in aliis, scilicet de necesse et impossibile idem est iudicium.	1. Aristotle now determines where the negation must be placed in order to obtain contradiction in modals. He first determines the truth summarily; secondly, he presents the argument for the truth of the position, which is also the answer to the reasoning induced for the opposite position, where he says, For just as "to be” and "not to be” are the determining additions in the former, and the things subjected are "white” and "man,” etc.; thirdly, he makes this truth evident in all the modals, where he says, The negation, then, of "possible not to be” is "not possible not to be,” etc.; fourthly, he arrives at a universal rule where he says, And universally, as has been said, "to be” and "not to be must be posited as the subject, etc. Since the negation must be added either to the verb or to the mode and it was shown above in virtue of an argument from division that it is not to be added to the verb, he concludes: Therefore, the negation of "possible to be” is "not possible to be”, that is, the mode is negated. The reasoning is the same with respect to enunciations of the contingent, for the negation of "contingent to be” is "not contingent to be.” And the judgment is the same in the others, i.e., the necessary and the impossible.
Cajetanus lib. 2 l. 9 n. 2 Deinde cum dicit: fiunt enim in illis appositiones etc., subdit huius veritatis rationem talem. Ad sumendam contradictionem inter aliquas enunciationes oportet ponere negationem super appositione, idest coniunctione praedicati cum subiecto; sed in modalibus appositiones sunt modi; ergo in modalibus negatio apponenda est modo, ut fiat contradictio. Huius rationis, maiore subintellecta, minor ponitur in littera per secundam similitudinem ad illas de inesse. Et dicitur quod quemadmodum in illis enunciationibus de inesse appositiones, idest praedicationes, sunt esse et non esse, idest verba significativa esse vel non esse (verbum enim semper est nota eorum quae de altero praedicantur), subiective vero appositionibus res sunt, quibus esse vel non esse apponitur, ut album, cum dicitur, album est, vel homo, cum dicitur, homo est; eodem modo hoc in loco in modalibus accidit: esse quidem subiectum fit, idest dictum significans esse vel non esse subiecti locum tenet; contingere vero et posse oppositiones, idest modi, praedicationes sunt. Et quemadmodum in illis de inesse penes esse et non esse veritatem vel falsitatem determinavimus, ita in istis modalibus penes modos. Hoc est enim quod subdit, determinantes, scilicet, fiunt ipsi modi veritatem, quemadmodum in illis esse et non esse, eam determinat.	2. When he says, For just as "to be” and "not to be” are the determining additions in the former, and the things subjected are "white” and "man,” etc., he gives the argument for the truth of his position. To obtain contradiction among any enunciations the negation must be applied to the determining addition, i.e., to the word that joins the predicate with the subject; but in modals the determining additions are the modes; therefore, to get a contradiction in modals, the negation must be added to the mode. The major of the argument is subsumed; the minor is stated in Aristotle’s wording by a further similitude to absolute enunciations. In absolute enunciations the determining additions, i.e., the predications, are "to be” and "not to be,” i.e., the verb signifying "to be” or "not to be” (for the verb is always a sign of those things that are predicated of another). The things subjected to the determining additions, i.e., to which to be” and "not to be” are applied, are "white,” in "White is, "or man,” in "Man is.” This happens in modals in the same way but in a manner appropriate to them. "To be” is as the subject, i.e., the dictum signifying "to be” or "not to be” holds the place of the subject; "is possible” and "is contingent,” i.e., the modes, are the predicates. And just as in absolute enunciations we determine truth or falsity with "to be” and "not to be,” so in modals with the modes. He makes this point when he says, determining additions, i.e., these modes effect truth just as "to be” and "not to be” determine truth and falsity in the others.
Cajetanus lib. 2 l. 9 n. 3 Et sic patet responsio ad argumentum in oppositum primo adductum, concludens quod negatio verbo apponenda sit, sicut illis de inesse. Dicitur enim quod cum modalis enunciet modum de dicto sicut enunciatio de inesse, esse vel esse tale, puta esse album de subiecto, eumdem locum tenet modus hic, quem ibi verbum; et consequenter super idem proportionaliter cadit negatio hic et ibi. Eadem enim, ut dictum est, proportio est modi ad dictum, quae est verbi ad subiectum. Rursus cum veritas et falsitas affirmationem et negationem sequantur, penes idem attendenda est affirmatio vel negatio enunciationis, et veritas vel falsitas eiusdem; sicut autem in enunciationibus de inesse veritas vel falsitas esse vel non esse consequitur, ita in modalibus modum. Illa namque modalis est vera quae sic modificat dictum sicut dicti compositio patitur, sicut illa de inesse est vera, quae sic significat esse sicut est. Est ergo negatio modo hic apponenda, sicut ibi verbo, cum sit eadem utriusque vis quoad veritatem et falsitatem enunciationis. Adverte quod modos, appositiones, idest, praedicationes vocavit, sicut esse in illis de inesse, intelligens per modum totum praedicatum enunciationis modalis, puta, est possibile. In cuius signum modos ipsos verbaliter protulit dicens: contingere vero et posse appositiones sunt. Contingit enim et potest, totum praedicatum modalis continent.	3. Thus the response to the argument for the opposite position, which he gave first, is evident. That argument concluded that the negation should be added to the verb as it is in absolute enunciations. But since the modal enunciates a mode of a dictum—as the absolute enunciation enunciates "to be” or "not to be” such, for instance, "to be white” of a subject—the mode holds the same place here that the verb does there. Consequently, the negation falls upon the same thing proportionally here and there, for the proportion of mode to dictum is the same as the proportion of verb to subject. Again, since truth and falsity follow upon affirmation and negation, the affirmation and negation of an enunciation and its truth and falsity must be controlled by the same thing. In absolute enunciations truth and falsity follow upon "to be” or "not to be,” hence in the modals they follow upon the mode; for that modal is true which modifies the dictum as the composition of the dictum permits, just as that absolute enunciation is true which signifies that something is as it is. Therefore, negation is added here to the mode just as it is added there to the verb, since the power of each is the same with respect to the truth and falsity of an enunciation. Notice that he calls the modes "determining additions,” i.e., predications—as "to be” is in absolute enunciations—understanding by the mode the whole predicate of the modal enunciation, for example, "is possible.” As a sign of this he expresses the modes themselves verbally when he says, "is possible” and "is contingent” are determining additions. For "is contingent” and "is possible” comprise the whole predicate of the modal enunciation.
Cajetanus lib. 2 l. 9 n. 4 Deinde cum dicit: eius vero quod est possibile est non esse etc., explanat determinatam veritatem in omnibus modalibus, scilicet de possibili, et necessario, et impossibili. Contingens convertitur cum possibili. Et quia quilibet modus facit duas modales affirmativas, alteram habentem dictum affirmatum, et alteram habentem dictum negatum; ideo explanat in singulis modis quae cuiusque affirmationis negatio sit. Et primo in illis de possibili. Et quia primae affirmativae de possibili (quae scilicet habet dictum affirmatum) scilicet possibile esse, negatio assignata fuit, non possibile esse; ideo ad reliquam affirmativam de possibili transiens ait: eius vero, quae est possibile non esse (ubi dictum negatur) negatio est non possibile non esse. Et hoc consequenter probat per hoc quod contradictoria huius, possibile non esse, aut est, possibile esse, aut illa, quam diximus, scilicet, non possibile non esse. Sed illa, scilicet, possibile esse, non est eius contradictoria. Non enim sunt sibi invicem contradicentes, possibile esse, et, possibile non esse, quia possunt simul esse verae. Unde et sequi sese invicem putabuntur: quoniam, ut supra dictum fuit, idem est, possibile esse, et, non esse, et consequenter sicut ad, posse esse, sequitur, posse non esse, ita e contra ad, posse non esse, sequitur, posse esse; sed contradictoria illius, possibile esse, quae non potest simul esse vera est, non possibile esse: hae enim, ut dictum est, opponuntur. Remanet ergo quod huius negatio, possibile non esse, sit illa, non possibile non esse: hae namque simul nunquam sunt verae vel falsae. Dixit quod possibile esse et non esse sequi se invicem putabuntur, et non dixit quod se invicem consequuntur: quia secundum veritatem universaliter non sequuntur se, sed particulariter tantum, ut infra dicetur; propter quod putabitur quod simpliciter se invicem sequantur. Deinde declarat hoc idem in illis de necessario. Et primo, in affirmativa habente dictum affirmatum, dicens: similiter eius quae est, necessarium esse, negatio non est ea, quae dicit necessarium non esse, ubi modus non negatur, sed ea quae est, non necessarium esse. Deinde subdit de affirmativa de necessario habente dictum negatum, et ait: eius vero, quae est, necessarium non esse, negatio est ea, quae dicit, non necessarium non esse. Deinde transit ad illas de impossibili, eumdem ordinem servans, et inquit: et eius, quae dicit, impossibile esse, negatio non est ea quae dicit, impossibile non esse, sed, non impossibile esse: ubi iam modus negatur. Alterius vero affirmativae, quae est, impossibile non esse, negatio est ea quae dicit non impossibile non esse. Et sic semper modo negatio addenda est.	4. When he says, The negation, then, of "possible not to be” is [not, "not possible to be” but] "not possible not to be,” etc., he makes this truth evident in all the modals, i.e., the possible, the necessary, and the impossible (the contingent being convertible with the possible). And since any mode makes two modal affirmatives, one having an affirmed dictum and the other having a negated dictum, he shows what the negation of each affirmation is in each mode. First he takes those of the possible. The negation of the first affirmative of the possible (the one with an affirmed dictum), i.e., "possible to be,” was assigned as "not possible to be.” Hence, going on to the remaining affirmative of the possible he says, The negation, then, of "possible not to be” [wherein the dictum is negated] is, "not possible not to be.” Then he a proves this. The contradictory of "possible not to be” is either "Possible to be” or "not possible not to be.” But the former, i.e., "possible to be,” is not the contradictory of "possible not to be,” for they can be at once true. Hence they are also thought to follow upon each other, for, as was said above, the same thing is possible to be and not to be. Consequently, just as "possible not to be” follows upon "possible to be,” so conversely "possible to be” follows upon "possible not to be.” But the contradictory of "possible to be,” which cannot be true at the same time, is "not possible to be,” for these, as has been said, are opposed. Therefore, the negation of "possible not to be” is, "not possible not to be,” for these are never at once true or false. Note that he says, Wherefore "possible to be” and "possible not to be” would appear to be consequent to each other, and not that they do follow upon each other, for it is not true that they follow upon each other universally, but only particularly (as will be said later); this is the reason they appear to follow upon each other simply. Then he manifests the same thing in the modals of the necessary, and first in the affirmative with an affirmed dictum: The case is the same with respect to the necessary. The negation of "necessary to be” is not, "necessary not to be” (in which the mode is not negated) but, "not necessary to be.” Next he adds the affirmative of the necessary with a negated dictum: and the negation of "necessary not to be is "not necessary not to be.” Next, he takes up the impossible, keeping the same order. The negation of "impossible to be” is not, "impossible not to be” but, "not impossible to be,” in which the mode is negated. The negation of the other affirmative, "impossible not to be” is "not impossible not to be.” The negation, therefore, is always added to the mode.
Cajetanus lib. 2 l. 9 n. 5 Deinde cum dicit: universaliter vero etc., concludit regulam universalem dicens quod, quemadmodum dictum est, dicta importantia esse et non esse oportet ponere in modalibus ut subiecta, negationem vero et affirmationem hoc, idest contradictionis oppositionem, facientem, oportet apponere tantummodo ad suum eumdem modum, non ad diversos modos. Debet namque illemet modus negari, qui prius affirmabatur, si contradictio esse debet. Et exemplariter explanans quomodo hoc fiat, subdit: et oportet putare has esse oppositas dictiones, idest affirmationes et negationes in modalibus, possibile et non possibile, contingens et non contingens. Item cum dixit negationem alio tantum modo ad modum apponi debere, non exclusit modi copulam, sed dictum. Hoc enim est singulare in modalibus quod eamdem oppositionem facit, negatio modo addita, et eius verbo. Contradictorie enim opponitur huic, possibile est esse, non solum illa, non possibile est esse, sed ista, possibile non est esse; meminit autem modi potius, et propter hoc quod nunc diximus, ut scilicet insinuaret quod negatio verbo modi postposita, modo autem praeposita, idem facit ac si modali verbo praeponeretur, et quia, cum modo numquam caret modalis enunciatio, semper negatio supra modum poni potest. Non autem sic de eius verbo: verbo enim modi carere contingit modalem, ut cum dicitur, Socrates currit necessario; et ideo semper verbo negatio aptari potest. Quod autem in fine addidit, verum et non verum, insinuat, praeter quatuor praedictos modos, alios inveniri, qui etiam compositionem enunciationis determinant, puta, verum et non verum, falsum et non falsum: quos tamen inter modos supra non posuit, quia, ut declaratum fuit, non proprie modificant.	5. Then he says, And universally, as has been said, "to be”and "not to be” must be posited as the subject, and those that produce affirmation and negation must be joined to "to be” and "not to be,” etc. Here he concludes with the universal rule. As has been said, the dictums denoting "to be” and "not to be” must be posited in the modals as subjects, and the one making this an affirmation and negation, i.e., the opposition of contradiction, must be added only to the selfsame mode, not to diverse modes, for the selfsame mode which was previously affirmed must be denied if there is to be a contradiction. He gives examples of how this is to be done when he adds, And these are the words that are to be considered opposed, i.e., affirmations and negations in modals, possible–not possible, contingent–not contingent. Moreover, when he said elsewhere but in another way that the negation must be applied only to the mode, he did not exclude the copula of the mode, but the copula of the dictum. For it is unique to modals that the same opposition is made by adding a negation to the mode and to its verb. The contradictory of "is possible to be,” for instance, is not only "is not possible to be,” but also "not is possible to be.” There are two reasons, however, for his mentioning the mode rather than the verb: first, for the reason we have just given, namely, so as to imply that the negation placed after the verb of the mode, the mode having been put first, accomplishes the same thing as if it were placed before the modal verb; and secondly, because the modal enunciation is never without a mode; hence the negation can always be put on the mode. However, it cannot always be put on the verb of a mode, for the modal enunciation may lack the verb of a mode as for example in "Socrates runs necessarily,” in which case the negation can always be adapted to the verb. In adding "true” and "not true” at the end he implies that besides the four modes mentioned previously there are others that also determine the composition of the enunciation, for example, "true” and "not true,” "false” and "not false”; nevertheless he did not posit these among the modes first given because, as was shown, they do not properly modify.

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.

LECTURE 11

Latin	English
Cajetanus lib. 2 l. 11 n. 1 Postquam Aristoteles declaravit modalium consequentias, hic movet quandam dubitationem circa unum eorum quae determinata sunt, scilicet quod possibile sequitur ad necesse. Et duo facit: quia primo dubitationem absolvit; secundo, ex determinata quaestione alium ordinem earumdem consequentiarum modalibus statuit; ibi: et est fortasse et cetera. Circa primum duo facit: primo, movet quaestionem; secundo, determinat eam; ibi: manifestum est et cetera. Movet ergo quaestionem: primo dicens: dubitabit autem aliquis si ad id quod est necesse esse sequatur possibile esse; et secundo, arguit ad partem affirmativam subdens: nam si non sequatur, contradictoria eius sequetur, scilicet non possibile esse, ut supra deductum est: quia de quolibet est affirmatio vel negatio vera. Et si quis dicat hanc, scilicet, non possibile esse, non esse contradictoriam illius, scilicet, possibile esse, et propterea subterfugiendum velit argumentum, et dicere quod neutra harum sequitur ad necesse esse; talis licet falsum dicat, tamen concedatur sibi, quoniam necesse erit ipsum dicere illius contradictoriam fore, possibile non esse. Oportet namque aut non possibile esse aut possibile non esse, esse contradictoriam, possibile esse; et tunc in eumdem redibit errorem, quoniam utraeque, scilicet, non possibile esse et possibile non esse, falsae sunt de eo quod est, necesse esse. Et consequenter ad ipsum neutra sequi potest. Nulla enim enunciatio sequitur ad illam, cuius veritatem destruit. Relinquitur ergo quod, ad necesse esse sequitur possibile esse.	1. Now that he has explained the consequents of modals, Aristotle raises a question about one of the points that has already been determined, namely, that the possible follows upon the necessary. He first raises the question and then settles it where he says, It is evident by now that not every possibility of being or walking is one that admits of opposites, etc. Secondly, he establishes another order of the same consequents from the determination of the present question, where he says Indeed the necessary and not necessary may well be the principle of all that is or is not, etc. First, then, he raises the question: But it may be questioned whether "Possible to be follows upon "necessary to be.” Secondly, he argues to the affirmative part: Yet if not, the contradictory, "not possible to be,” would have to follow, as was deduced earlier, for either the affirmation or the negation is true of anything. And if someone should say "not possible to be” is not the contradictory of "possible to be,” because he wants to avoid the conclusion by saying that neither of these follows upon "necessary to be,” this may be conceded, although what he says is false. But then he will have to say that the contradictory of "possible to be” is "possible not to be,” for the contradictory of "possible to be” has to be either "not possible to be” or "possible not to be.” But if he says this, he will fall into another error, for it is false to say it is not possible to be of that which is necessary to be, and it is false to say it is possible not to be. Consequently, neither follows upon it, for no enunciation follows upon an enunciation whose truth it destroys. Therefore, "possible to be” follows upon "necessary to be.”
Cajetanus lib. 2 l. 11 n. 2 Tertio, arguit ad partem negativam cum subdit: at vero rursus etc., et intendit talem rationem. Si ad necesse esse sequitur possibile esse, cum ad possibile sequatur possibile non esse (per conversionem in oppositam qualitatem, ut dicitur in I priorum, quia idem est possibile esse et non esse), sequetur de primo ad ultimum quod necesse est possibile non esse: quod est falsum manifeste. Unde oppositionis hypothesim subdit: at vero rursus videtur idem possibile esse et non esse, ut domus, et possibile incidi et non incidi, ut vestis. Quare de primo ad ultimum necesse esse, erit contingens non esse. Hoc autem est falsum. Ergo hypothesis illa, scilicet, quod possibile sequatur ad necesse, est falsa.	2. Thirdly, he argues to the negative part where he says, On the other hand, it seems possible for the same thing to be cut and not to be cut, etc. His argument is as follows: If "possible to be” follows upon "necessary to be,” then, since "possible not to be” follows upon the possible (through conversion to the opposite quality, as is said in I Priorum [13: 32a 31], for the same thing is possible to be and not to be), from first to last it will follow that the necessary is possible not to be, which is clearly false. In this argument, Aristotle supplies a hypothesis opposed to the position that possible to be follows upon necessary to be: On the other hand, it seems possible for the same thing to be cut and not to be cut, for instance a garment, and to be and not to be, for instance a house. Therefore, from first to last, necessary to be will be possible not to be. But this is false. Therefore, the hypothesis that the possible follows upon the necessary is false.
Cajetanus lib. 2 l. 11 n. 3 Deinde cum dicit: manifestum est autem etc., respondet dubitationi. Et primo, declarat veritatem simpliciter; secundo, applicat ad propositum; ibi: hoc igitur possibile et cetera. Proponit ergo primo ipsam veritatem declarandam, dicens: manifestum est autem, ex dicendis, quod non omne possibile esse vel ambulare, idest operari: idest, non omne possibile secundum actum primum vel secundum ad opposita valet, idest ad opposita viam habet, sed est invenire aliqua possibilia, in quibus non sit verum dicere quod possunt in opposita. Deinde, quia possibile a potentia nascitur, manifestat qualiter se habeat potentia ipsa ad opposita: ex hoc enim clarum erit quomodo possibile se habeat ad opposita. Et circa hoc duo facit: primo manifestat hoc in potentiis eiusdem rationis; secundo, in his quae aequivoce dicuntur potentiae; ibi: quaedam vero potentiae et cetera. Circa primum tria facit: quia primo manifestat qualiter potentia irrationalis se habeat ad opposita; et ait quod potentia irrationalis non potest in opposita.	3. When he says, It is evident by now that not every possibility of being or walking, etc., he answers the question he proposed. First, he manifests the truth simply, then applies it to the question where he says, So it is not true to say the latter possible of what is necessary simply, etc. First, then, he proposes the truth he is going to explain: It is evident by now that not every possibility of being or walking, i.e., of operating; that is, not everything possible according to first or second act admits of opposites, i.e., has access to opposites; there are some possibles of which it is not true to say that they are capable of opposites. Then, since the possible arises from potency, he manifests how potency is related to opposites; for it will be clear from this bow the possible is related to opposites. First he manifests this in potencies having the same notion; secondly, in those that are called potencies equivocally where he says, But some are called potentialities equivocally, etc. With respect to the way in which potencies of the same specific notion are related to opposites, he does three things. First of all he manifests how an irrational potency is related to opposites; an irrational potency, he says, is not a potency that is capable of opposites.
Cajetanus lib. 2 l. 11 n. 4 Ubi notandum est quod, sicut dicitur IX Metaphys., potentia activa, cum nihil aliud sit quam principium quo in aliud agimus, dividitur in potentiam rationalem et irrationalem. Potentia rationalis est, quae cum ratione et electione operatur; sicut ars medicinae, qua medicus cognoscens quid sanando expediat infirmo, et volens applicat remedia. Potentia autem irrationalis vocatur illa, quae non ex ratione et libertate operatur, sed ex naturali sua dispositione; sicut calor ignis potentia irrationalis est, quia calefacit, non ut cognoscit et vult, sed ut natura sua exigit. Assignatur autem ibidem duplex differentia proposito deserviens inter istas potentias. Prima est quod activa potentia irrationalis non potest duo opposita, sed est determinata ad unum oppositorum, sive sumatur oppositum contradictorie sive contrarie. Verbi gratia: calor non potest calefacere et non calefacere, quae sunt contradictorie opposita, neque potest calefacere et frigefacere, quae sunt contraria, sed ad calefactionem determinatus est. Et hoc intellige per se, quia per accidens calor frigefacere potest, vel resolvendo materiam caloris, humidum scilicet, vel per antiperistasin contrarii. Et similiter potest non calefacere per accidens, scilicet si calefactibile deest. Potentia autem rationalis potest in opposita et contradictorie et contrarie. Arte siquidem medicinae potest medicus adhibere remedia et non adhibere, quae sunt contradictoria; et adhibere remedia sana et nociva, quae sunt contraria. Secunda differentia est quod potentia activa irrationalis, praesente passo, necessario operatur, deductis impedimentis: calor enim calefactibile sibi praesens calefacit necessario, si nihil impediat; potentia autem rationalis, passo praesente, non necessario operatur: praesente siquidem infirmo, non cogitur medicus remedia adhibere.	4. It must be noted in this connection that active potency, since it is the principle by which we act on something else, is divided into rational and irrational potency, as is said in IX Metaphysicae [2: 1046a 36]. Rational potency operates in connection with reason and choice; for example, the art of medicine by which the physician, knowing and willing what is expedient in healing an illness, applies a remedy. Irrational potency operates according to its own natural disposition, not according to reason and liberty; for example, the heat of fire is an irrational potency, because it heats, not as it knows and wills, but as its nature requires. In the Metaphysics, a twofold difference between these potencies is assigned which is relevant here. The first is that an irrational active potency is not capable of two opposites, but is determined to one opposite, whether "opposite” is taken contradictorily or contrarily; e.g., heat cannot heat and not heat, which are opposed contradictorily; nor can it heat and cool, which are contraries, but is deter mined to heating. Understand this per se, for heat can cool accidentally, either by destroying the matter of heat, namely, the humid, or through alternation of the contrary. It also has the potentiality not to heat accidentally, if that which can be heated is lacking. A rational potency, on the other hand, is capable of opposites, both contradictorily and contrarily; for by the art of medicine the physician can employ a remedy and not employ it, which are contradictories, and employ healing and harmful remedies, which are contraries. The second difference is that an irrational active potency necessarily operates when a subject is present and impediments are with drawn; for heat necessarily heats when a subject that can be heated is present, and nothing impedes it. A rational potency, however, does not necessarily operate when a subject is present; e.g., when a sick man is present the physician is not forced to employ a remedy.
Cajetanus lib. 2 l. 11 n. 5 Dimittantur autem metaphysico harum differentiarum rationes et ad textum redeamus. Ubi narrans quomodo se habeat potentia irrationalis ad oppositum, ait: et primum quidem, scilicet, non est verum dicere quod sit potentia ad opposita in his quae possunt non secundum rationem, idest, in his quorum posse est per potentias irrationales; ut ignis calefactivus est, idest, potens calefacere, et habet vim, idest, potentiam istam irrationalem. Ignis siquidem non potest frigefacere; neque in eius potestate est calefacere et non calefacere. Quod autem dixit primum ordinem, nota, ad secundum genus possibilis infra dicendum, in quo etiam non invenitur potentia ad opposita.	5. The reasons for these differences are given in the Metaphysics, but let us return to the text. Explaining bow an irrational potency is related to opposites, he says, First of all, this is not true, i.e., it is not true to say that there is a potency to opposites in those which are not according to reason, i.e., whose power is through irrational potencies; as fire which is calefactive, i.e., capable of heating, has this power, i.e., this irrational potentiality, since it is not able to cool, nor is it in its power 4 to heat and not to heat. Note that he speaks here of a first kind. This is in relation to a second genus of the possible which he will speak of later, in which there is not a potency to opposites either.
Cajetanus lib. 2 l. 11 n. 6 Secundo, manifestat quomodo potentia rationalis se habeat ad opposita, intendens quod potentia rationalis potest in opposita. Unde subdit: ergo potestates secundum rationem, idest rationales, ipsae eaedem sunt contrariorum, non solum duorum, sed etiam plurimorum, ut arte medicinae medicus plurima iuga contrariorum adhibere potest, et a multarum operationum contradictionibus abstinere potest. Praeposuit autem ly ergo, ut hoc consequi ex dictis insinuaret: cum enim oppositorum oppositae sint proprietates, et potentia irrationalis ex eo quod irrationalis ad opposita non se extendat; oportet potentiam rationalem ad opposita viam habere, eo quod rationalis sit.	6. Secondly, he shows how a rational potency is related to opposites, i.e., it is capable of opposites: Therefore potentialities that are in conjunction with reason, i.e., rational potencies, are capable of contraries, not only of two, but even of many; for example, a physician by the art of medicine can employ many pairs of contraries and he can abstain from doing or not doing many things. He begins with "therefore” so as to imply that this follows from what has been said.”’ The argument would be: properties of opposites are opposites; an irrational potency, because it is irrational, does not extend itself to opposites; therefore a rational potency, because it is rational, has access to opposites.
Cajetanus lib. 2 l. 11 n. 7 Tertio, explanat id quod dixit de potentiis irrationalibus, propter causam infra assignandam ab ipso; et intendit quod illud quod dixit de potentia irrationali, scilicet quod non potest in opposita, non est verum universaliter, sed particulariter. Ubi nota quod potentia irrationalis dividitur in potentiam activam, quae est principium faciendi, et potentiam passivam, quae est principium patiendi: verbi gratia, potentia ad calorem dividitur in posse calefacere, et in posse calefieri. In potentiis activis irrationalibus verum est quod non possunt in opposita, ut declaratum est; in potentiis autem passivis non est verum. Illud enim quod potest calefieri, potest etiam frigefieri, quia eadem est materia, seu potentia passiva contrariorum, ut dicitur in II de caelo et mundo, et potest non calefieri, quia idem est subiectum privationis et formae, ut dicitur in I Physic. Et propter hoc ergo explanando, ait: irrationales vero potentiae non omnes a posse in opposita excludi intelligendae sunt, sed illae quae sunt quemadmodum potentia ignis calefactiva (ignem enim non posse non calefacere manifestum est), et universaliter, quaecunque alia sunt talis potentiae, quod semper agunt, idest quod quantum est ex se non possunt non agere, sed ad semper agendum ex sua forma necessitantur. Huiusmodi autem sunt, ut declaravimus, omnes potentiae activae irrationales. Alia vero sunt talis conditionis quod etiam secundum irrationales potentias, scilicet passivas, simul possunt in quaedam opposita, ut aer potest calefieri et frigefieri. Quod vero ait, simul, cadit supra ly possunt, et non supra ly opposita; et est sensus, quod simul aliquid habet potentiam passivam ad utrunque oppositorum, et non quod habeat potentiam passivam ad utrunque oppositorum simul habendum. Opposita namque impossibile est haberi simul. Unde et dici solet et bene, quod in huiusmodi est simultas potentiae, non potentia simultatis. Irrationalis igitur potentia non secundum totum suum ambitum a posse in opposita excluditur, sed secundum partem eius, secundum potentias scilicet activas.	7. Thirdly, he explains what he has said about irrational potencies. He will assign the reason for doing this later. He makes the point that what he has said about irrational potentiality, i.e., that it is not capable of opposites, is not true universally, but particularly. It should be noted here that irrational potency is divided into active potency, which is the principle of acting, and passive potency, which is the principle of being acted upon; e.g., potency to heat is divided into potentiality to heat and potentiality to be heated. Now it is true that active irrational potencies are not capable of opposites, as was explained. This is not true, however, of passive potencies, for what can be heated can also be cooled, because the mat ter is the same, i.e., the passive potency of contraries, as is said in II De caelo et mundo [7: 286a 23]. It can also not be heated, since the subject of privation and of form is the same, as is said in I Physic [7: 189b 32]. Therefore, in explaining about irrational potencies, he says, But not all irrational potentialities should be understood to be excluded from the capacity of opposites. Those like the potentiality of fire to heat are to be excluded (for it is evident that fire cannot not heat) I and universally, whatever others are potencies of such a kind that they always act, i.e., the ones that of themselves cannot not act, but are necessitated by their form always to act. All active irrational potencies are of this kind, as we have explained. There are others, however, of such a condition that even though they are irrational potencies (i.e., passive) are simultaneously capable of certain opposites; for example, air can be heated and cooled. "Simultaneously” modifies "are capable” and not "opposites.” What he means is that the thing simultaneously has a passive potency to each opposite, and not that it has a passive potency to have both opposites simultaneously, for it is impossible to have opposites at one and the same time. Hence it is customary and correct to say that in these there is simultaneity of potency, not potency of simultaneity. Therefore, irrational potency is excluded from the capacity of opposites, not completely, but according to its part, namely, according to active potencies.
Cajetanus lib. 2 l. 11 n. 8 Quia autem videbatur superflue addidisse differentias inter activas et passivas irrationales, quia sat erat proposito ostendisse quod non omnis potentia oppositorum est; ideo subdit quod hoc idcirco dictum est, ut notum fiat quoniam nedum non omnis potestas oppositorum est, loquendo de potentia communissime, sed neque quaecunque potentiae dicuntur secundum eamdem speciem ad opposita possunt. Potentiae siquidem irrationales omnes sub una specie irrationalis potentiae concluduntur, et tamen non omnes in opposita possunt, sed passive tantum. Non supervacanea ergo fuit differentia inter passivas et activas irrationales, sed necessaria ad declarandum quod non omnes potentiae eiusdem speciei possunt in opposita. Potest et ly hoc demonstrare utranque differentiam, scilicet, inter rationales et irrationales, et inter irrationales activas et passivas inter se; et tunc est sensus, quod hoc ideo fecimus, ut ostenderemus quod non omnis potestas, quae scilicet secundum eamdem rationem potentiae physicae dicitur, quia scilicet potest in aliquid ut rationalis et irrationalis, neque etiam omnis potestas, quae sub eadem specie continetur, ut irrationalis activa et passiva sub specie irrationalis, ad opposita potest.	8. Because it might seem superfluous to have added the differences between active and passive irrational potencies, since enough had already been said to show that not every potency is of opposites, Aristotle gives the reason for this. It was not only to make it known that not every potency is of opposites, speaking of potency most commonly, but also that not all that are called potencies according to the same species are capable of opposites. For all irrational potencies are included under one species of irrational potency, and yet not all are capable of opposites, but only the passive potencies. It was not superfluous, therefore, to point out the difference between passive and active irrational potencies, since this was necessary in order to show that not all potencies of the same species are capable of opposites. " This” in the phrase "this has been said” could designate each difference, the one between rational and irrational potencies, and the one between active and passive irrational potencies. The meaning is, then, that we have said this to show that not every potentiality which is said according to the same notion of physical power—namely, because it can be in something as rational and irrational—not even every potentiality which is contained under the same species, as active and passive under the species irrational, is capable of opposites.

LECTURE 12

Latin	English
Cajetanus lib. 2 l. 12 n. 1 Intendit declarare quomodo illae quae aequivocae dicuntur potentiae, se habeant ad opposita. Et circa hoc duo facit: primo, declarat naturam talis potentiae; secundo, ponit differentiam et convenientiam inter ipsas et supradictas, ibi: et haec quidem et cetera. Ad evidentiam primi advertendum est quod V et IX Metaphys., Aristoteles dividit potentiam in potentias, quae eadem ratione potentiae dicuntur, et in potentias, quae non ea ratione qua praedictae potentiae nomen habent, sed alia. Et has appellat aequivoce potentias. Sub primo membro comprehenduntur omnes potentiae activae, et passivae, et rationales, et irrationales. Quaecunque enim posse dicuntur per potentiam activam vel passivam quam habeant, eadem ratione potentiae sunt, quia scilicet est in eis vis principiata alicuius activae vel passivae. Sub secundo autem membro comprehenduntur potentiae mathematicales et logicales. Mathematica potentia est, qua lineam posse dicimus in quadratum, et eo quod in semetipsam ducta quadratum constituit. Logica potentia est, qua duo termini coniungi absque contradictione in enunciatione possunt. Sub logica quoque potentia continetur quae ea ratione potentia dicitur, quia est. Hae vero merito aequivoce a primis potentiae dicuntur, eo quod istae nullam virtutem activam vel passivam praedicant; et quod possibile istis modis dicitur, non ea ratione possibile appellatur quia aliquis habeat virtutem ad hoc agendum vel patiendum, sicut in primis. Unde cum potentiae habentes se ad opposita sint activae vel passivae, istae quae aequivocae potestates dicuntur ad opposita non se habent. De his ergo loquens ait: quaedam vero potestates aequivocae sunt, et ideo ad opposita non se habent.	1. Aristotle now proposes to show in what way potencies that are called equivocal are related to opposites. He first explains the nature of this kind of potency, and then gives the difference and agreement all between these and the foresaid, where he says, This latter potentiality is only in that which is movable, but the former is also in the immovable, etc. In V and IX Metaphysicae [V, 12: 1019a 15; 12, 1: 1046a 4], Aristotle divides potency into those that are called potencies for the same reason, and those that have the name potency for another reason than the aforesaid potencies. The latter are named "potencies” equivocally. Under the first member are included all active and passive, rational and irrational potencies, for whatever are said to be possible through the active or passive potency they have, are potencies for the same reason, i.e., because there is in them the originative force of something active or passive. Mathematical and logical potencies are included under the second member of this division. That by which a line can lead to a square we call a mathematical potency, for a line constitutes a square when protracted back to itself. That by which two terms can be joined in an enunciation without contradiction is a logical potency. Logical potency also comprises that which is called "potency” because it is. The latter [mathematical and logical potencies] are named from the former equivocally because they predicate no active or passive capacity; and what is said to be possible in these ways is not termed possible in virtue of having the capacity to do or undergo as in the first case. Hence, since the potencies related to opposites are active or passive, the ones that are called potentialities equivocally are not related to opposites. These, then, are the potencies he speaks of when he says But some are called potentialities equivocally, and therefore they are not related to opposites.
Cajetanus lib. 2 l. 12 n. 2 Deinde declarans qualis sit ista potestas aequivoce dicta, subdit divisionem usitatam possibilis per quam hoc scitur, dicens: possibile enim non uno modo dicitur, sed duobus. Et uno quidem modo dicitur possibile eo quod verum est ut in actu, idest ut actualiter est; ut, possibile est ambulare, quando ambulat iam: et omnino, idest universaliter possibile est esse, quoniam est actu iam quod possibile dicitur. Secundo modo autem possibile dicitur aliquid non ea ratione quia est actualiter, sed quia forsitan aget, idest quia potest agere; ut possibile est ambulare, quoniam ambulabit. Ubi advertendum est quod ex divisione bimembri possibilis divisionem supra positam potentiae declaravit a posteriori. Possibile enim a potentia dicitur: sub primo siquidem membro possibilis innuit potentias aequivoce; sub secundo autem potentias univoce, activas scilicet et passivas. Intendebat ergo quod quia possibile dupliciter dicitur, quod etiam potestas duplex est. Declaravit autem potestates aequivocas ex uno earum membro tantum, scilicet ex his quae dicuntur possibilia quia sunt, quia hoc sat erat suo proposito.	2. To clarify the kind of potency that is called equivocal, he gives the usual division of the possible through which this is known. "Possible,” he says, is not said in one way, but in two. Something is said to be possible because it is true as in act, i.e., inasmuch as it actually is; for example, it is possible to walk when one is already walking, and in gene eral, i.e., universally, that is said to be possible which is possible to be because it is already in act. Something is said to be possible in the second way, not because it actually is, but because it is about to act, i.e., because it can act; for instance, it is possible for someone to walk because be is about to walk. Notice here that by this two-membered division of the possible he makes the division of potency posited above evident a posteriori, for the possible is named from potency. Under the first member of the possible he signifies potencies equivocally; under the second, potencies univocally, i.e., active and passive potencies. He means to show, then, that since possible is said in two ways, potentiality is also twofold. He explains equivocal potentialities in terms of only one member, namely, those that are called possible because they are, since this was sufficient for his purpose.
Cajetanus lib. 2 l. 12 n. 3 Deinde cum dicit: et haec quidem etc., assignat differentiam inter utranque potentiam, et ait quod potentia haec ultimo dicta physica, est in solis illis rebus, quae sunt mobiles; illa autem est et in rebus mobilibus et immobilibus. Possibile siquidem a potentia dictum eo quod possit agere, non tamen agit, inveniri non potest absque mutabilitate eius, quod sic posse dicitur. Si enim nunc potest agere et non agit, si agere debet, oportet quod mutetur de otio ad operationem. Id autem quod possibile dicitur eo quod est, nullam mutabilitatem exigit in eo quod sic possibile dicitur. Esse namque in actu, quod talem possibilitatem fundat, invenitur et in rebus necessariis, et in immutabilibus, et in rebus mobilibus. Possibile ergo hoc, quod logicum vocatur, communius est illo quod physicum appellari solet.	3. When he says, This latter potentiality is only in that which is movable, but the former is also in the immovable, etc., he specifies the difference between each potency. This last potency, he says, [possible because it can be] which is called physical potency, is only in things that are movable; but the former is in movable and immovable things. The possible that is named from the potency which can act, but is not yet acting, cannot be found without the mutability of that which is said to be possible in this way. For if that which can act now and is not acting, should act, it is necessary that it be changed from rest to operation. On the other hand, that which is called possible because it is, requires no mutability in that which is said to be possible in this way, for to be in act, which is the basis of such a possibility, is found in necessary things, in immutable things, and in mobile things. Therefore, the possible which is called logical, is more common than the one we customarily call physical.
Cajetanus lib. 2 l. 12 n. 4 Deinde subdit convenientiam inter utrunque possibile, dicens quod in utrisque potestatibus et possibilibus verum est non impossibile esse, scilicet, ipsum ambulare, quod iam actu ambulat seu agit, et quod iam ambulabile est; idest, in hoc conveniunt quod, sive dicatur possibile ex eo quod actu est, sive ex eo quod potest esse, de utroque verificatur non impossibile; et consequenter necessario verificatur possibile, quoniam ad non impossibile sequitur possibile. Hoc est secundum genus possibilis, respectu cuius Aristoteles supra dixit: et primum quidem etc., in quo non invenitur via ad utrunque oppositorum, hoc, inquam, est possibile quod iam actu est. Quod enim tali ratione possibile dicitur, iam determinatum est ex eo quod actu esse suppositum est. Non ergo possibile omne ad utrunque possibile est, sive loquamur de possibili physice, sive logice.	4. Then he shows that there is a correspondence between these possibles when he adds that not impossible to be is true of both of these potentialities and possibles, e.g., to walk is not impossible for that which is already walking in act, i.e., acting, and it is not impossible for that which could now walk; that is, they agree in that not impossible is verified of both—of either what is said to be possible from the fact that it is in act or of what is said to be possible from the fact that it could be. Consequently, the necessary is verified as possible, for possible follows upon not impossible. The possible that is already in act is the second genus of the possible in which access is not found to both opposites, of which Aristotle spoke when he said, First of all this is not true of the potentialities which are not according to reason, etc. For that which is said to be possible because it is already in act is already determined, since it is supposed as being in act. Therefore, not every possible is the possible of alternatives, whether we speak of the physical possible or the logical.
Cajetanus lib. 2 l. 12 n. 5 Deinde cum dicit: sic igitur possibile etc., applicat determinatam veritatem ad propositum. Et primo, concludendo ex dictis, declarat habitudinem utriusque possibilis ad necessarium, dicens quod hoc ergo possibile, scilicet physicum quod est in solis mobilibus, non est verum dicere et praedicare de necessario simpliciter: quia quod simpliciter necessarium est, non potest aliter esse. Possibile autem physicum potest sic et aliter esse, ut dictum est. Addit autem ly simpliciter, quoniam necessarium est multiplex. Quoddam enim est ad bene esse, quoddam ex suppositione: de quibus non est nostrum tractare, sed solummodo id insinuare. Quod ut praeservaret se ab illis modis necessarii qui non perfecte et omnino habent necessarii rationem, apposuit ly simpliciter. De tali enim necessario possibile physicum non verificatur. Alterum autem possibile logicum, quod in rebus immobilibus invenitur, verum est de illo enunciare, quoniam nihil necessitatis adimit. Et per hoc solvitur ratio inducta ad partem negativam quaestionis. Peccabat siquidem in hoc, quod ex necessario inferebat possibile ad utrunque quod convertitur in oppositam qualitatem.	5. When he says, So it is not true to say the latter possible of what is necessary simply, etc., he applies the truth he has determined to what has been proposed. First, by way of a conclusion from what has been said, he shows the relationship of each possible to the necessary. So, he says, it is not true to say and predicate this possible, namely physical, which is only in mobile things, of the necessary simply, because what is necessary simply cannot be otherwise. The physical possible, however, can be thus and otherwise, as has been said. He adds "simply” because the necessary is manifold. There is the necessary for well-being and there is also the necessary from supposition, but it is not our business to treat these, only to indicate them. In order, then, to avoid the modes of the necessary that do not have the notion of the necessary perfectly and in every way, he adds "simply.” Now the physical possible is not verified of this kind of necessary [i.e., of the necessary simply], but it is true to enunciate the logical possible, the one found in immovable things, of the necessary, since it takes away nothing of the necessity. The argument introduced for the negative part of this question”’ is destroyed by this. The error in that argument was the inference—by way of conversion into the opposite quality—of the possible to both alternatives from the necessary.
Cajetanus lib. 2 l. 12 n. 6 Deinde respondet quaestioni formaliter intendens quod affirmativa pars quaestionis tenenda sit, quod scilicet ad necessarium sequitur possibile; et assignat causam. Quia ad partem subiectivam sequitur constructive suum totum universale; sed necessarium est pars subiectiva possibilis: quia possibile dividitur in logicum et physicum, et sub logico comprehenditur necessarium; ergo ad necessarium sequitur possibile. Unde dicit: quare, quoniam partem, scilicet subiectivam, suum totum universale sequitur, illud quod ex necessitate est, idest necessarium, tamquam partem subiectivam, consequitur posse esse, idest possibile, tamquam totum universale. Sed non omnino, idest sed non ita quod omnis species possibilis sequatur; sicut ad hominem sequitur animal, sed non omnino, idest non secundum omnes suas partes subiectivas sequitur ad hominem: non enim valet: est homo, ergo est animal irrationale. Et per hoc confirmata ratione adducta ad partem affirmativam, expressius solvit rationem adductam ad partem negativam, quae peccabat secundum fallaciam consequentis, inferens ex necessario possibile, descendendo ad unam possibilis speciem, ut de se patet.	6. Then he replies to the question formally. He states that the affirmative part of the question must be held, namely, that the possible follows upon the necessary. Next, he assigns the cause. The whole universal follows constructively upon its subjective part; but the necessary is a subjective part of the possible, because the possible is divided into logical and physical and under the logical is comprehended the necessary; therefore, the possible follows upon the necessary. Hence he says, Therefore, since the universal follows upon the part, i.e., since the whole universal follows upon its subjective part, to be possible to be, i.e., possible, as the whole universal, follows upon that which necessarily is, i.e., necessary, as a subjective part. He adds: though not every kind of possible does, i.e., not every species of the possible follows; just as animal follows upon man, but not in every way, i.e., it does not follow upon man according to all its subjective parts, for it is not valid to say, "He is a man, therefore he is an irrational animal.” By this proof of the validity of the affirmative part, Aristotle has explicitly destroyed the reasoning adduced for the negative part, which, as is evident, erred according to the fallacy of the consequent in inferring the possible from the necessary by descending to one species of the possible.
Cajetanus lib. 2 l. 12 n. 7 Deinde cum dicit: et est fortasse quidem etc., ordinat easdem modalium consequentias alio situ, praeponendo necessarium omnibus aliis modis. Et circa hoc duo facit: primo, proponit quod intendit; secundo, assignat causam dicti ordinis; ibi: manifestum est autem et cetera. Dicit ergo: et est fortasse principium omnium enunciationum modalium vel esse vel non esse, idest, affirmativarum vel negativarum, necessarium et non necessarium. Et oportet considerare alia, scilicet, possibile contingere et impossibile esse, sicut horum, scilicet, necessarii et non necessarii, consequentia, hoc modo: consequentiae enunciationum modalium secundum quatuor ordines alio convenienti situ ab Aristotele positae et ordinatae: (Figura). Vides autem hic nihil immutatum, nisi quod necessariae quae ultimum locum tenebant, primum sortitae sunt. Quod vero dixit fortasse, non dubitantis, sed absque determinata ratione rem proponentis est.	7. When he says, Indeed the necessary and not necessary may well be the principle of all that is or is not, etc., he disposes the same consequences of modals in another arrangement, placing the necessary before all the other modes. First he proposes the order of modals and then assigns the cause of the order where he says, It is evident, then, from what has been said that that which necessarily is, actually is, etc. Indeed, he says, the necessary and not necessary may well be the principle of the "to be” or "not to be” of all modal enunciations, i.e., the necessary and not necessary is the principle of affirmatives or negatives. And the others, i.e., the possible, contingent, and impossible to be must be considered as consequent to these, i.e., to the necessary and not necessary. THE CONSEQUENTS OF MODAL ENUNCIATIONS ACCORDING TO THE FOUR ORDERS, POSITED AND DISPOSED BY ARISTOTLE IN ANOTHER APPROPRIATE ARRANGEMENT FIRST ORDER It is necessary to be It is not possible not to be It is not contingent not to be It is impossible not to be SECOND ORDER It is necessary not to be It is not possible to be It is not contingent to be It is impossible to be It is not necessary to be It is possible not to be It is contingent not to be It is not impossible not to be FOURTH ORDER It is not necessary not to be It is possible to be It is contingent to be It is not impossible to be Nothing is changed here except the enunciations predicating necessity. They have been allotted the first place, whereas in the former table they were placed last. When he says "may well be,” it is not because he is in any doubt, but because he is proposing this here without a determinate proof.
Cajetanus lib. 2 l. 12 n. 8 Deinde cum dicit: manifestum est autem etc., intendit assignare causam dicti ordinis. Et primo, assignat causam, quare praeposuerit necessarium possibili tali ratione. Sempiternum est prius temporali; sed necessarium dicit sempiternitatem (quia dicit esse in actu, excludendo omnem mutabilitatem, et consequenter temporalitatem, quae sine motu non est imaginabilis), possibile autem dicit temporalitatem (quia non excludit quin possit esse et non esse); ergo necesse merito prius ponitur quam possibile. Unde dicit, proponendo minorem: manifestum est autem ex his quae dicta sunt etc., tractando de necessario: quoniam id quod ex necessitate est, secundum actum est totaliter, scilicet quia omnem excludit mutabilitatem et potentiam ad oppositum: si enim mutari posset in oppositum aliquo modo, iam non esset necessarium. Deinde subdit maiorem per modum antecedentis conditionalis: quare si priora sunt sempiterna temporalibus et cetera. Ultimo ponit conclusionem: et quae actu sunt omnino, scilicet necessaria, priora sunt potestate, idest possibilibus, quae omnino actu esse non possunt, licet compatiantur.	8. When he says, It is evident, then, from what has been said that that which necessarily is, actually is, etc., he gives the cause of this order. First he gives the reason for placing the necessary before the possible: the sempiternal is prior to the temporal; but "necessary” signifies sempiternal (because it signifies "to be in act,” excluding all mutability and consequently temporality, which is not imaginable without movement) and the possible signifies temporality (since it does not exclude the possibility of being and not being); therefore, the necessary is rightly placed before the possible. He proposes the minor of this argument when he says, It is evident, then, from what has been said in treating the necessary, that that which necessarily is, is totally in act, since it excludes all mutability and potency to the opposite—for if it could be changed into the opposite in any way, then it would not be necessary. Next he gives the major, which is in the mode of an antecedent conditional: and if eternal things are prior to temporal, etc. Finally, he posits the conclusion: those that are wholly in act in every way, namely necessary, are prior to the potential, i.e., to possibles, which do not have being in act wholly although they are compatible with it.
Cajetanus lib. 2 l. 12 n. 9 Deinde cum dicit: et hae quidem etc., assignat causam totius ordinis a se inter modales statuti, tali ratione. Universi triplex est gradus. Quaedam sunt actu sine potestate, idest sine admixta potentia, ut primae substantiae, non illae quas in praesenti diximus primas, eo quod principaliter et maxime substent, sed illae quae sunt primae, quia omnium rerum sunt causae, intelligentiae scilicet. Alia sunt actu cum possibilitate, ut omnia mobilia, quae secundum id quod habent de actu sunt priora natura seipsis secundum id quod habent de potentia, licet e contra sit, aspiciendo ordinem temporis. Sunt enim secundum id quod habent de potentia priora tempore seipsis secundum id quod habent de actu. Verbi gratia, Socrates prius secundum tempus poterat esse philosophus, deinde fuit actualiter philosophus. Potentia ergo praecedit actum secundum ordinem temporis in Socrate, ordine autem naturae, perfectionis et dignitatis e converso contingit. Prior enim secundum dignitatem, idest dignior et perfectior habebatur Socrates cum philosophus actualiter erat, quam cum philosophus esse poterat. Praeposterus est igitur ordo potentiae et actus in unomet, utroque ordine, scilicet, naturae et temporis attento. Alia vero nunquam sunt actu sed potestate tantum, ut motus, tempus, infinita divisio magnitudinis, et infinita augmentatio numeri. Haec enim, ut IX Metaphys. dicitur, nunquam exeunt in actum, quoniam eorum rationi repugnat. Nunquam enim aliquid horum ita est quin aliquid eius expectetur, et consequenter nunquam esse potest nisi in potentia. Sed de his alio tractandum est loco.	9. Then he says, Some things are actualities without potentiality, namely, the primary substances, etc. Here he assigns the cause of the whole order established among modals. The grades of the universe are threefold. Some things are in act without potentiality, i.e., not combined with potency. These are the primary substances—not those we have called "first” in the present work because they principally and especially sustain—but those that are first because they are the causes of all things, namely, the Intelligences. In others, act is accompanied with possibility, as is the case with all mobile things, which, according to what they have of act, are prior in nature to themselves according to what they have of potency, although the contrary is the case in regard to the order of time. According to what they have of potency they are prior in time to themselves according to what they have of act. For example, according to time, Socrates first was able to be a philosopher, then he actually was a philosopher. In Socrates therefore, potency precedes act according to the order of time. The converse is the case, however, in the order of nature, perfection, and dignity, for when he actually was a philosopher, Socrates was regarded as prior according to dignity, i.e., more worthy and more perfect than when he was potentially a philosopher. Hence, when we consider each order, i.e., nature and time, in one and the same thing, the order of potency and act is reversed. Others never are in act but are only in potency, e.g., motion, time, the infinite division of magnitude, and the infinite augmentation of number. These, as is said in IX Metaphysicae [6: 1048b 9-17], never terminate in act, for it is repugnant to their nature. None of them is ever such that something of it is not expected, and consequently they can only be in potency. These, however, must be treated in another place.
Cajetanus lib. 2 l. 12 n. 10 Nunc haec ideo dicta sint ut, inspecto ordine universi, appareat quod illum imitati sumus in nostro ordine. Posuimus siquidem primo necessarium, quod sonat actu esse sine potestate seu mutabilitate, imitando primum gradum universi. Locavimus secundo loco possibile et contingens, quorum utrunque sonat actum cum possibilitate, et sic servatur conformitas ad secundum gradum universi. Praeposuimus autem possibile et non contingens, quia possibile respicit actum, contingens autem secundum vim nominis respicit defectum causae, qui ad potentiam pertinet: defectus enim potentiam sequitur; et ex hoc conforme est secundae parti universi, in qua actus est prior potentia secundum naturam, licet non secundum tempus. Ultimum autem locum impossibili reservavimus, eo quod sonat nunquam fore, sicut et ultima universi pars dicta est illa, quae nunquam actu est. Pulcherrimus igitur ordo statutus est, quando divinus est observatus.	10. This has been said so that once the order of the universe has been seen it should appear that we were imitating it in our present ordering. The necessary, which signifies "to be in act” without potentiality or mutability, has been placed first, in imitation of the first grade of the universe. We have put the possible and contingent, both of which signify act with possibility, in second place in conformity with the second grade of the universe. The possible has been Placed before the contingent because the possible relates to act whereas the contingent, as the force of the name suggests, relates to the defect of a cause-which pertains to potency, for defect follows upon potency. The order of these is similar to the order in the second part of the universe, where act is prior to potency according to nature, though not according to time. We have reserved the last place for the impossible because it signifies what never will be, just as the last part of the universe is said to be that which is never in act. Thus, a beautifully proportioned order is established when the divine is observed.
Cajetanus lib. 2 l. 12 n. 11 Quia autem suppositae modalium consequentiae nil aliud sunt quam aequipollentiae earum, quae ob varium negationis situm, qualitatem, vel quantitatem, vel utranque mutantis, fiunt; ideo ad completam notitiam consequentium se modalium, de earum qualitate et quantitate pauca admodum necessaria dicenda sunt. Quoniam igitur natura totius ex partium naturis consurgit, sciendum est quod subiectum enunciationis modalis et dicit esse vel non esse, et est dictum unicum, et continet in se subiectum dicti; praedicatum autem modalis enunciationis, modus scilicet, et totale praedicatum est (quia explicite vel implicite verbum continet, quod est semper nota eorum quae de altero praedicantur: propter quod Aristoteles dixit quod modus est ipsa appositio), et continet in se vim distributivam secundum partes temporis. Necessarium enim et impossibile distribuunt in omne tempus vel simpliciter vel tale; possibile autem et contingens pro aliquo tempore in communi.	11. Since the consequents of modals, i.e., those placed under each other, are their equivalents in meaning, and these are produced by the varying position of the negation changing the quality or quantity or both, a few things must be said about their quality and quantity to complete our knowledge of them. The nature of the whole arises from the parts, and therefore we should note the following things about the parts of the modal enunciation. The subject of the modal enunciation asserts to be or not to be, and is a singular dictum, and contains in itself the subject of the dictum. The predicate of a modal enunciation, namely, the mode, is the total predicate (since it explicitly or implicitly contains the verb, which is always a sign of something predicated of another, for which reason Aristotle says that the mode is a determining addition) and contains in itself distributive force according to the parts of time. The necessary and impossible distribute in all time either simply or in a limited way; the possible and contingent distribute according to some time commonly.
Cajetanus lib. 2 l. 12 n. 12 Nascitur autem ex his quinque conditionibus duplex in qualibet modali qualitas, et triplex quantitas. Ex eo enim quod tam subiectum quam praedicatum modalis verbum in se habet, duplex qualitas fit, quarum altera vocatur qualitas dicti, altera qualitas modi. Unde et supra dictum est aliquam esse affirmativam de modo et non de dicto, et e converso. Ex eo vero quod subiectum modalis continet in se subiectum dicti, una quantitas consurgit, quae vocatur quantitas subiecti dicti: et haec distinguitur in universalem, particularem et singularem, sicut et quantitas illarum de inesse. Possumus enim dicere, Socratem, quemdam hominem, vel omnem hominem, vel nullum hominem, possibile est currere. Ex eo autem quod subiectum unius modalis dictum unum est, consurgit alia quantitas, vocata quantitas dicti; et haec unica est singularitas: secundum omne enim dictum cuiusque modalis singulare est istius universalis, scilicet dictum. Quod ex eo liquet quod cum dicimus, hominem esse album est possibile, exponitur sic, hoc dictum, hominem esse album, est possibile. Hoc dictum autem singulare est, sicut et, hic homo. Propterea et dicitur quod omnis modalis est singularis quoad dictum, licet quoad subiectum dicti sit universalis vel particularis. Ex eo autem quod praedicatum modalis, modus scilicet, vim distributivam habet, alia quantitas consurgit vocata quantitas modi seu modalis; et haec distinguitur in universalem et particularem.	12. As a consequence of these five conditions there is a twofold quality and a threefold quantity in any modal. The twofold quality results from the fact that both the subject and the predicate of a modal have a verb in them. One of these is called the quality of the dictum, the other the quality of the mode. This is why it was said above that there is an enunciation which is affirmative of mode and not of dictum, and conversely. Of the threefold quantity of a modal enunciation, one arises from the fact that the subject of the modal contains in it the subject of the dictum. This is called the quantity of the subject of the dictum, and is distinguished into universal, particular, and singular, as in the case of the quantity of an absolute enunciation. For we can say: "That ‘Socrates,’ ‘some man,’ ‘every man,”’ or "‘no man,’ run is possible’ " The second quantity is that of the dictum, which arises from the fact that the subject of one modal is one dictum. This is a unique singularity, for every dictum of a modal is the singular of that universal, i.e.,dictum. "That man be white is possible” means "This dictum, ‘that man be white,’ is possible.” "This dictum” is singular in quantity, just as "this man” is. Hence, every modal is singular with respect to dictum, although with respect to the subject of the dictum it is universal or particular. The third quantity is that of the mode, or modal quantity, which arises from the fact that the predicate of the modal, i.e., the mode, has distributive force. This is distinguished into universal and particular.
Cajetanus lib. 2 l. 12 n. 13 Ubi diligenter duo attendenda sunt. Primum est quod hoc est singulare in modalibus, quod praedicatum simpliciter quantificat propositionem modalem, sicut et simpliciter qualificat. Sicut enim illa est simpliciter affirmativa, in qua modus affirmatur, et illa negativa, in qua modus negatur; ita illa est simpliciter universalis cuius modus est universalis, et illa particularis cuius modus est particularis. Et hoc quia modalis modi naturam sequitur. Secundum attendendum (quod est causa istius primi) est, quod praedicatum modalis, scilicet modus, non habet solam habitudinem praedicati respectu sui subiecti, scilicet esse et non esse, sed habitudinem syncategorematis distributivi, sed non secundum quantitatem partium subiectivarum ipsius subiecti, sed secundum quantitatem partium temporis eiusdem. Et merito. Sicut enim quia subiecti enunciationis de inesse propria quantitas est penes divisionem vel indivisionem ipsius subiecti (quia est nomen quod significat per modum substantiae, cuius quantitas est per divisionem continui: ideo signum quantificans in illis distribuit secundum partes subiectivas), ita quia subiecti enunciationis modalis propria quantitas est tempus (quia est verbum quod significat per modum motus, cuius propria quantitas est tempus), ideo modus quantificans distribuit ipsum suum subiectum, scilicet, esse vel non esse, secundum partes temporis. Unde subtiliter inspicienti apparebit quod quantitas ista modalis proprii subiecti modalis enunciationis quantitas est, scilicet, ipsius esse vel non esse. Ita quod illa modalis est simpliciter universalis, cuius proprium subiectum distribuitur pro omni tempore: vel simpliciter, ut, hominem esse animal est necessarium vel impossibile; vel accepto, ut, hominem currere hodie, vel, dum currit, est necessarium vel impossibile. Illa vero est particularis, in qua non pro omni, sed aliquo tempore distributio fit in communi tantum; ut, hominem esse animal, est possibile vel contingens. Est ergo et ista modalis quantitas subiecti sui passio (sicut et universaliter quantitas se tenet ex parte materiae), sed derivatur a modo, non in quantum praedicatum est (quod, ut sic, tenetur formaliter), sed in quantum syncategorematis officio fungitur, quod habet ex eo quod proprie modus est.	13. Now, there are two things about modal enunciations that must be carefully noted. The first—which is peculiar to modals—is that the predicate quantifies the modal proposition simply, as it also qualifies it simply. For just as the modal enunciation in which the mode is affirmed is affirmative simply, and negative when the mode is negated, so the modal enunciation in which the mode is universal is universal simply and particular in which the mode is particular. The reason for this is that the modal follows the nature of the mode. The second thing to be noted (which is the cause of the first) is that the predicate of a modal, i.e., the mode, not only has the relationship of a predicate to its subject (i.e., to "to be” and "not to be”), but also has the relationship to the subject, of a distributive syncategorematic term, which has the effect of distributing the subject, not according to the quantity of its subjective parts, but according to the quantity of the parts of its time. And rightly so, for just as the proper quantity of the subject of an absolute enunciation varies according to the division or lack of division of its subject (since the subject is a name which signifies in the mode of substance, whose quantity is from the division of the continuous, and therefore the quantifying sign distributes according to the subjective parts), so, because the proper quantity of the subject of a modal enunciation is time (since the subject is a verb, which signifies in the mode of movement, whose proper quantity is time), the quantifying mode distributes the subject, i.e., "to be” or "not to be” according to the parts of time. Hence, we arrive at the subtle point that the quantity of the modal is the quantity of the proper subject of the modal enunciation, namely, of "to be” or "not to be.” Therefore, a modal enunciation is universal simply when the proper subject is distributed throughout all time, either simply, as in "That man is an animal is necessary or impossible,” or taken in a limited way, as in "That man is running today,” or "while he is running, is necessary or impossible.” A modal enunciation is particular in which "to be” or "not to be” is distributed, not throughout all time, but commonly throughout some time, as in "That man is an animal is possible or contingent.” This modal quantity is therefore also a property of its subject (in that, universally, quantity comes from the matter) but is derived from the mode, not insofar as it is a predicate (because, as such, it is understood formally), but insofar as it performs a syncategorematic function, which it has in virtue of the fact that it is properly a mode.
Cajetanus lib. 2 l. 12 n. 14 Sunt igitur modalium (de propria earum quantitate loquendo) aliae universales affirmativae, ut illae de necessario, quia distribuunt ad semper esse; aliae universales negativae, ut illae de impossibili, quia distribuunt ad nunquam esse; aliae particulares affirmativae, ut illae de possibili et contingenti, quia distribuunt utrunque ad aliquando esse; aliae particulares negativae, ut illae de non necesse et non impossibili, quia distribuunt ad aliquando non esse: sicut in illis de inesse, omnis, nullus, quidam, non omnis, non nullus, similem faciunt diversitatem. Et quia, ut dictum est, haec quantitas modalium est inquantum modales sunt, et de his, inquantum huiusmodi, praesens tractatus fit ab Aristotele; idcirco aequipollentiae, seu consequentiae earum, ordinatae sunt negationis vario situ, quemadmodum aequipollentiae illarum de inesse: ut scilicet, negatio praeposita modo faciat aequipollere suae contradictoriae; negatio autem modo postposita, posita autem dicti verbo, suae aequipollere contrariae facit; praeposita vero et postposita suae subalternae, ut videre potes in consequentiarum figura ultimo ab Aristotele formata. In qua, tali praeformata oppositionum figura, clare videbis omnes se mutuo consequentes, secundum alteram trium regularum aequipollere, et consequenter, totum primum ordinem secundo contrarium, tertio contradictorium, quarto vero subalternum. (Figura).	14. Therefore, with respect to their proper quantity, some modals are universal affirmatives, i.e., those of the necessary because they distribute "to be” to all time. Others are universal negatives, i.e., those of the impossible because they distribute "to be” to no time. Still others are particular affirmatives, i.e., those signifying the possible and contingent, for both of these distribute "to be” to some time. Finally, there are particular negatives, i.e., those of the not necessary and not impossible, for they distribute "not to be” to some time. This is similar to the diversity in absolute enunciations from the use of "every,” "no” "some,” not all,” and "not none.” Now, since this quantity belongs to modals insofar as they are modals, as has been said, and since Aristotle is now considering them in this particular respect, the modal enunciations that are equivalent, i.e., their consequents, are ordered by the different location of the negation, as is the case with absolute enunciations that are equivalent. A negative placed before the mode makes an enunciation equivalent to its contradictory; placed after the mode, i.e., with the verb of the dictum, makes it equivalent to its contrary; placed before and after the mode makes it equivalent to its subaltern, as you can see in the last table of consequents given by Aristotle. In that table of oppositions, you see all the mutual consequents, according to one of the three rules for making enunciations equivalent. Consequently, the whole first order of equivalent enunciations is contrary to the second, contradictory to the third, and the fourth is subalternated to it. Necessary to be - contraries - Impossible to be subalterns subalterns Possible to be - subcontraries - Contingent not to be TABLE OF OPPOSITION OF EQUIPOLLENT MODALS This table is not Cajetan’s but is a full arrangement of the orders of modal enunciations asdeveloped in this lesson. Close I Universal Affirmatives It is necessary to be It is not possible not to be It is not contingent not to be It is impossible not to be contraries II Universal Negatives It is necessary not to be It is not possible to be It is not contingent to be It is impossible to be subalterns subalterns IV Particular Affirmatives It is not necessary not to be It is possible to be It is contingent to be It is not impossible to be subcontraries III Particular Negatives It is not necessary to be It is possible not to be It is contingent not to be It is not impossible not to be

LECTURE 13

Latin	English
Cajetanus lib. 2 l. 13 n. 1 Postquam determinatum est de enunciatione secundum quod diversificatur tam ex additione facta ad terminos, quam ad compositionem eius, hic secundum divisionem a s. Thoma in principio huius secundi factam, intendit Aristoteles tractare quandam quaestionem circa oppositiones enunciationum provenientes ex eo quod additur aliquid simplici enunciationi. Et circa hoc quatuor facit: primo, movet quaestionem secundo, declarat quod haec quaestio dependet ab una alia quaestione praetractanda; ibi: nam si ea, quae sunt in voce etc.; tertio, determinat illam aliam quaestionem; ibi: nam arbitrari etc.; quarto, redit ad respondendum quaestioni primo motae; ibi: quare si in opinione et cetera. Quaestio quam movere intendit est: utrum affirmativae enunciationi contraria sit negatio eiusdem praedicati, an affirmatio de praedicato contrario seu privativo? Unde dicit: utrum contraria est affirmatio negationi contradictoriae, scilicet, et universaliter oratio affirmativa orationi negativae; ut, affirmativa oratio quae dicit, omnis homo est iustus, illi contraria sit orationi negativae, nullus homo est iustus, aut illi, omnis homo est iniustus, quae est affirmativa de praedicato privativo? Et similiter ista affirmatio, Callias est iustus, est ne contraria illi contradictoriae negationi, Callias non est iustus, aut illi, Callias est iniustus, quae est affirmativa de praedicato privativo?	1. Now that he has treated the enunciation as it is diversified by an addition made to the terms and by an addition made to its composition (which is the division of the text made by St. Thomas at the beginning of the second book), Aristotle takes up another question about oppositions of enunciations. This question concerns the oppositions that result from something added to the simple enunciation. First he asks the question; secondly, he shows that this question depends upon another, which must be treated first, where he says, For if those things that are in vocal sound are determined by those in the intellect, etc.; third, he settles the latter question where he says, It is false, course, to suppose that opinions are to be defined as contrary because they are about contraries, etc.; finally, he replies to the first question where he says, If, therefore, this is the case with respect to opinion, and affirmations and negations in vocal sound are signs of those in the soul, etc. The first question he raises is this: is the contrary of an affirmative enunciation the negation of the same predicate or the affirmation of a contrary or privative predicate? Hence he says, There is a question as to whether the contrary of an affirmation is the contradictory negation, and universally, whether affirmative speech is contrary to negative speech. For instance, is affirmative speech which says "Every man is just,” contrary to negative speech which says "No man is just,” or to the affirmative of the privative predicate, "Every man is unjust”? And similarly, is the affirmation "Callias is just” contrary to the contradictory negation, "Callias is not just” or is it contrary to "Callias is unjust,” the affirmative of the privative predicate?
Cajetanus lib. 2 l. 13 n. 2 Ad evidentiam tituli huius quaestionis, quia hactenus indiscusse ab aliis est relictus, considerare oportet quod cum in enunciatione sint duo, scilicet ipsa enunciatio seu significatio et modus enunciandi seu significandi, duplex inter enunciationes fieri potest oppositio, una ratione ipsius enunciationis, altera ratione modi enunciandi. Si modos enunciandi attendimus, duas species oppositionis in latitudine enunciationum inveniemus, contrarietatem scilicet et contradictionem. Divisae enim superius sunt enunciationes oppositae in contrarias et contradictorias. Contradictio inter enunciationes ratione modi enunciandi est quando idem praedicatur de eodem subiecto contradictorio modo enunciandi; ut sicut unum contradictorium nil ponit, sed alterum tantum destruit, ita una enunciatio nil asserit, sed id tantum quod altera enunciabat destruit. Huiusmodi autem sunt omnes quae contradictoriae vocantur, scilicet, omnis homo est iustus, non omnis homo est iustus, Socrates est iustus, Socrates non est iustus, ut de se patet. Et ex hoc provenit quod non possunt simul verae aut falsae esse, sicut nec duo contradictoria. Contrarietas vero inter enunciationes ratione modi enunciandi est quando idem praedicatur de eodem subiecto contrario modo enunciandi; ut sicut unum contrariorum ponit materiam sibi et reliquo communem in extrema distantia sub illo genere, ut patet de albo et nigro, ita una enunciatio ponit subiectum commune sibi et suae oppositae in extrema distantia sub illo praedicato. Huiusmodi quoque sunt omnes illae quae contrariae in figura appellantur, scilicet, omnis homo est iustus, omnis homo non est iustus. Hae enim faciunt subiectum, scilicet hominem, maxime distare sub iustitia, dum illa enunciat iustitiam inesse homini, non quocunque modo, sed universaliter; ista autem enunciat iustitiam abesse homini, non qualitercunque, sed universaliter. Maior enim distantia esse non potest quam ea, quae est inter totam universitatem habere aliquid et nullum de universitate habere illud. Et ex hoc provenit quod non possunt esse simul verae, sicut nec contraria possunt eidem simul inesse; et quod possunt esse simul falsae, sicut et contraria simul non inesse eidem possunt. Si vero ipsam enunciationem sive eius significationem attendamus secundum unam tantum oppositionis speciem, in tota latitudine enunciationum reperiemus contrarietatem, scilicet secundum veritatem et falsitatem: quia duarum enunciationum significationes entia positiva sunt, ac per hoc neque contradictorie neque privative opponi possunt, quia utriusque oppositionis alterum extremum est formaliter non ens. Et cum nec relative opponantur, ut clarum est, restat ut nonnisi contrarie opponi possunt.	2. Since this question has not been discussed by others, we must begin by noting that there are two things in an enunciation, namely, the enunciation itself, i.e., the signification, and the mode of enunciating or signifying. Hence, a twofold opposition can be made between enunciations, one by reason of the enunciation itself, the other by reason of the mode of enunciating. If we consider the modes of enunciating, we find two species of opposition among enunciations, namely, contrariety and contradiction. This point was made earlier when opposed enunciations were divided into contraries and contradictories. There is contradiction by reason of mode of enunciating when the same thing is predicated of the same subject in a contradictory mode; so that just as one of a pair of contradictories posits nothing but only destroys the other, so one enunciation 4 asserts nothing, but only destroys what the other was enunciating. All enunciations that are called contradictories are of this kind; e.g., "Every man is just,” "Not every man is just”; "Socrates is just,” "Socrates is not just.” It follows from this that they cannot be at once true or false, just as two contradictories cannot be at once. There is contrariety between enunciations by reason of mode of enunciating when the same thing is predicated of the same subject in a contrary mode of enunciating; so that just as one of a pair of contraries posits matter common to itself and to the other which is at the extreme distance under that genus—as is evident for instance in white and black—so one enunciation posits a subject common to itself and its opposite at the extreme distance under that predicate. All the enunciations in the diagram that are called contrary are of this kind, for example, "Every man is just,” "No man is just.” These make the subject "man” distant to the greatest degree possible under justice, one enunciating justice to be in man, not in any way, but universally, the other enunciating justice to be absent from man, not in any way, but universally. For no distance can be greater than the distance between the total number of things having something and none of the total number of things having that thing. It follows that contrary enunciations cannot be at once true, just as contraries cannot be in the same thing at once. They can, however, be false at the same time, just as it is possible that contraries not be in the same thing at the same time. If we consider the enunciation itself (viz., its signification) according to only one species of opposition, we will find in the whole range of enunciations an opposition of contrariety, i.e., an opposition according to truth and falsity. The reason for this is that the significations of two enunciations are positive, and accordingly cannot be opposed either contradictorily or privatively because the other extreme of both of these oppositions is formally non-being. And since significations are not opposed relatively, as is evident, the only way they can be opposed is contrarily.
Cajetanus lib. 2 l. 13 n. 3 Consistit autem ista contrarietas in hoc quod duarum enunciationum altera alteram non compatitur vel in veritate vel in falsitate, praesuppositis semper conditionibus contrariorum, scilicet quod fiant circa idem et in eodem tempore. Patere quoque potest talem oppositionem esse contrarietatem ex natura conceptionum animae componentis et dividentis, quarum singulae sunt enunciationes. Conceptiones siquidem animae adaequatae nullo alio modo opponuntur conceptionibus inadaequatis nisi contrarie, et ipsae conceptiones inadaequatae, si se mutuo expellunt, contrariae quoque dicuntur. Unde verum et falsum, contrarie opponi probatur a s. Thoma in I parte, qu. 17. Sicut ergo hic, ita et in enunciationibus ipsae significationes adaequatae contrarie opponuntur inadaequatis, idest verae falsis; et ipsae inadaequatae, idest falsae, contrarie quoque opponuntur inter se, si contingat quod se non compatiantur, salvis semper contrariorum conditionibus. Est igitur in enunciationibus duplex contrarietas, una ratione modi, altera ratione significationis, et unica contradictio, scilicet ratione modi. Et, ut confusio vitetur, prima contrarietas vocetur contrarietas modalis, secunda contrarietas formalis. Contradictio autem non ad confusionis vitationem quia unica est, sed ad proprietatis expressionem contradictio modalis vocari potest. Invenitur autem contrarietas formalis enunciationum inter omnes contradictorias, quia contradictoriarum altera alteram semper excludit; et inter omnes contrarias modaliter quoad veritatem, quia non possunt esse simul verae, licet non inveniatur inter omnes quoad falsitatem, quia possunt esse simul falsae.	3. The contrariety spoken of here consists in this: of two enunciations one is not compatible with the other either in truth or falsity—presupposing always the conditions for contraries, that they are about the same thing and at once. It can be shown that such opposition is contrariety from the nature of the conceptions of the soul when composing and dividing, each of which is an enunciation. Adequate conceptions of the soul are opposed to inadequate conceptions only contrarily, and inadequate conceptions, if each cancels the other, are also called contraries. It is from this that St. Thomas proves, in [Summa theologiae] part I, question 17, that the true and false are contrarily opposed. Therefore, as in the conceptions of the soul, so in enunciations, adequate significations are contrarily opposed to inadequate, i.e., true to false; and the inadequate, i.e., the false, are also contrarily opposed among themselves if it happens that they are not compatible, supposing always the conditions for contraries. There is, therefore, in enunciations a twofold contrariety, one by reason of mode, the other by reason of signification, and only one contradiction, that by reason of mode. To avoid confusion, let us call the first contrariety modal and the second formal. We may call contradiction modal—not to avoid confusion since it is unique—but for propriety of expression. Formal contrariety is found between all contradictory enunciations, since one contradictory always excludes the other. It is also found between all modally contrary enunciations in regard to truth, since they cannot be at once true. However it is not found between the latter in regard to falsity, since they can be at once false.
Cajetanus lib. 2 l. 13 n. 4 Quia igitur Aristoteles in hac quaestione loquitur de contrarietate enunciationum quae se extendit ad contrarias modaliter, et contradictorias, ut patet in principio et in fine quaestionis (in principio quidem, quia proponit utrasque contradictorias dicens: affirmatio negationi etc.; et contrarias modaliter dicens: et oratio orationi etc., unde et exempla utrarunque statim subdit, ut patet in littera. In fine vero, quia ibi expresse quam conclusit esse contrariam affirmativae universali verae dividit, in contrariam modaliter universalem negativam, scilicet, et contradictoriam: quae divisio falsitate non careret, nisi conclusisset contrariam formaliter, ut de se patet), quia, inquam, sic accipit contrarietatem, ideo de contrarietate formali enunciationum quaestio intelligenda est. Et est quaestio valde subtilis, necessaria et adhuc nullo modo superius tacta. Est igitur titulus quaestionis; utrum affirmativae verae contraria formaliter sit negativa falsa eiusdem praedicati, aut affirmativa falsa de praedicato, vel contrario? Et sic patet quis sit sensus tituli, et quare non movet quaestionem de quacunque alia oppositione enunciationum (quia scilicet nulla alia in eis formaliter invenitur), et quod accipit contrarietatem proprie et strictissime, licet talis contrarietas inveniatur inter contradictorias modaliter et contrarias modaliter. Dictum vero fuit a s. Thoma provenire hanc dubitationem ex eo quod additur aliquid simplici enunciationi, quia si tantum simplices, idest, de secundo adiacente enunciationes attendantur, non habet haec quaestio radicem. Quia autem simplici enunciationi, idest subiecto et verbo substantivo, additur aliquid, scilicet praedicatum, nascitur dubitatio circa oppositionem, an illud additum in contrariis debeat esse illudmet praedicatum, negatione apposita verbo, an debeat esse praedicatum contrarium seu privativum, absque negatione praeposita verbo.	4. Aristotle in this question is speaking of the contrariety of enunciations that extends to contraries modally and to contradictories. This is evident from what he says in the beginning and at the end of the question. In the beginning, he proposes both contradictories when he says, an affirmation... to a negation, etc.; and contraries modally, when he says, and in the case of speech whether the one saying... is opposed to the one saying... etc. It is evident, too, from the examples immediately added. At the end, he explicitly divides what he has concluded to be contrary to a true universal affirmative, into the modally contrary universal negative and the contradictory. It is clear at once that this division would be false unless it comprised the contrary formally. Since he takes contrariety in this way the question must be understood with respect to formal contrariety of enunciations. This is a very subtle question and one that has to be treated and has not been thus far. The question, therefore, is this: whether the formal contrary of the true affirmative is the false negative of the same predicate or the false affirmative of the privative predicate, i.e., of the contrary. The meaning of the question is now clear, and it is evident why he does not ask about any other oppositions of enunciations-no other opposition is found in them formally. It is also evident that he is taking contrariety properly and strictly, notwithstanding the fact that such contrariety is found among contradictories modally and contraries modally. St. Thomas has already pointed out that this question arises from the fact that something is added to the simple enunciation, for as it far as simple enunciations are concerned, i.e., those with only a second determinant, there is no occasion for the question. When, however, something is added, namely a predicate, to the simple enunciation, i.e., to the subject and the substantive verb, the question arises as to whether what ought to be added in contrary enunciations is the selfsame predicate with a negation added to the verb or a contrary, i.e., privative, predicate without a negation added to the verb.
Cajetanus lib. 2 l. 13 n. 5 Deinde cum dicit: nam si ea etc., declarat unde sumenda sit decisio huius quaestionis. Et duo facit: quia primo declarat quod haec quaestio dependet ex una alia quaestione, ex illa scilicet: utrum opinio, idest conceptio animae, in secunda operatione intellectus, vera, contraria sit opinioni falsae negativae eiusdem praedicati, an falsae affirmativae contrarii sive privativi. Et assignat causam, quare illa quaestio dependet ex ista, quia scilicet enunciationes vocales sequuntur mentales, ut effectus adaequati causas proprias, et ut significata signa adaequata, et consequenter similis est in hoc utraque natura. Unde inchoans ab hac causa ait: nam si ea quae sunt in voce sequuntur ea, quae sunt in anima, ut dictum est in principio I libri, et illic, idest in anima, opinio contrarii praedicati circa idem subiectum est contraria illi alteri, quae affirmat reliquum contrarium de eodem (cuiusmodi sunt istae mentales enunciationes, omnis homo est iustus, omnis homo est iniustus); si ita inquam est, etiam et in his affirmationibus quae sunt in voce, idest vocaliter sumptis, necesse est similiter se habere, ut scilicet sint contrariae duae affirmativae de eodem subiecto et praedicatis contrariis. Quod si neque illic, idest in anima, opinatio contrarii praedicati, contrarietatem inter mentales enunciationes constituit, nec affirmatio vocalis affirmationi vocali contraria erit de contrario praedicato, sed magis affirmationi contraria erit negatio eiusdem praedicati.	5. When Aristotle says, For if those things that are in vocal sound are determined by those in the intellect, etc.; he shows where we have to begin in order to settle this question. First he shows that the question depends on another question, namely, whether a true opinion (i.e., a conception of the soul in the second operation of the intellect) is contrary to a false negative opinion of the same predicate, or to a false affirmative of the contrary, i.e., privative, predicate. Then he gives the reason why the former question depends on this. Vocal enunciations follow upon mental as adequate effects upon proper causes and as the signified upon adequate signs. So, in this the nature of each is similar. He begins, then, with the reason for this dependence: For if those things that are in vocal sound are determined by those in the intellect (as was said in the beginning of the first book) and if in the soul, those opinions are contrary which affirm contrary predicates about the same subject, (for example, the mental enunciations, "Every man is just, "Every man is unjust”), then in affirmations that are in vocal sound, the case must be the same. The contraries will be two affirmatives about the same subject with contrary predicates. But if in the soul this is not the case, i.e., that opinions with contrary predicates constitute contrariety in mental enunciations, then the contrary of a vocal affirmation will not be a vocal affirmation with a contrary predicate. Rather, the contrary of an affirmation will be the negation of the same predicate.
Cajetanus lib. 2 l. 13 n. 6 Dependet ergo mota quaestio ex ista alia sicut effectus ex causa. Propterea et concludendo addit secundum, quod scilicet de hac quaestione prius tractandum est, ut ex causa cognita effectus innotescat dicens: quare considerandum est, opinio vera cui opinioni falsae contraria est: utrum negationi falsae an certe ei affirmationi falsae, quae contrarium esse opinatur. Et ut exemplariter proponatur, dico hoc modo: sunt tres opiniones de bono, puta vita: quaedam enim est ipsius boni opinio vera, quoniam bonum est, puta, quod vita sit bona; alia vero falsa negativa, scilicet, quoniam bonum non est, puta, quod vita non sit bona; alia item falsa affirmativa contrarii, scilicet, quoniam malum est, puta, quod vita sit mala. Quaeritur ergo quae harum falsarum contraria est verae?	6. The first question, then, depends on this question as an effect upon its cause. For this reason, and by way of a conclusion to what he has just been saying, he adds the second question, which must be treated first so that once the cause is known the effect will be known: We must therefore consider to which false opinion the true opinion is contrary, whether it is to the false negation or to the false affirmation that it is to be judged contrary. Then in order to propose the question by examples he says: what I mean is this; there are three opinions of a good, for instance, of life. One is a true opinion, that it is good, for instance, that life is good. The other is a false negative, that it is not good, for instance, that life is not good. Still another, likewise false, is the affirmative of the contrary, that it is evil, for instance, that life is evil. The question is, then, which of these false opinions is contrary to the true one.
Cajetanus lib. 2 l. 13 n. 7 Quod autem subdidit: et si est una, secundum quam contraria est, tripliciter legi potest. Primo, dubitative, ut sit pars quaestionis; et tunc est sensus: quaeritur quae harum falsarum contraria est verae: et simul quaeritur, si est tantum una harum falsarum secundum quam fiat contraria ipsi verae: quia cum unum uni sit contrarium, ut dicitur in X metaphysicae, quaerendo quae harum sit contraria, quaeremus etiam an una earum sit contraria. Alio modo, potest legi adversative, ut sit sensus: quaeritur quae harum sit contraria; quamquam sciamus quod non utraque sed una earum est secundum quam fit contrarietas. Tertio modo, potest legi dividendo hanc particulam, et si est una, ab illa sequenti, secundum quam contraria est; et tunc prima pars expressive, secunda vero dubitative legitur; et est sensus: quaeritur quae harum falsarum contraria est verae, non solum si istae duae falsae inter se differunt in consequendo, sed etiam si utraque est una, idest alteri indivisibiliter unita, quaeritur secundum quam fit contrarietas. Et hoc modo exponit Boethius, dicens quod Aristoteles apposuit haec verba propter contraria immediata, in quibus non differt contrarium a privativo. Inter contraria enim mediata et immediata haec est differentia, quod in immediatis a privativo contrarium non infertur. Non enim valet, corpus colorabile est non album, ergo est nigrum: potest enim esse rubrum. In immediatis autem valet; verbi gratia: animal est non sanum, ergo infirmum; numerus est non par, ergo impar. Voluit ergo Aristoteles exprimere quod nunc, cum quaerimus quae harum falsarum, scilicet negativae et affirmativae contrarii, sit contraria affirmativae verae, quaerimus universaliter sive illae duae falsae indivisibiliter se sequantur, sive non.	7. Then he adds, the question, and if there is one, is either one the contrary. This passage can be read in three ways. It can be read inquiringly so that it is a part of the question, and then the meaning is: which of these false opinions is contrary to the true opinion, and, is there one of these by which the contrary to the true one is effected? For since one is contrary to one other, as is said in X Metaphysicae [1: 1055a 19], in asking which of these is the contrary we are also asking whether one of them is the contrary. This can also be read adversatively, and then the meaning is: which of these is the contrary, given that we know it is not both but one by which the contrariety is effected? This can be read in a third way by dividing the first clause, "and if it is one” from the second clause, "is either one the contrary.” The first part is then read assertively, the second inquiringly, and the meaning is: which of these two false opinions is contrary to the true opinion if the two false opinions differ as to consequence, and also if both are one, i.e., united to each other indivisibly? Boethius explains this passage in the last way. He says that Aristotle adds these words because of immediate contraries in which the contrary does not differ from the privative. For the difference between mediate and immediate contraries is that in the former the contrary is not inferred from the privative. For example, this is not valid: "A colored body is not white, therefore it is black”—for it could be red. In immediate contraries, on the other hand, it is valid to infer the contrary from the privative; e.g., "An animal is not healthy, therefore it is number is not even, therefore it is odd.” Therefore, Aristotle intends to show here that when we ask which of these false opinions, i.e., negative and affirmative contraries, is contrary to the true affirmative, we are asking universally whether these two false opinions follow each other indivisibly or not.
Cajetanus lib. 2 l. 13 n. 8 Deinde cum dicit: nam arbitrari, prosequitur hanc secundam quaestionem. Et circa hoc quatuor facit. Primo, declarat quod contrarietas opinionum non attenditur penes contrarietatem materiae, circa quam versantur, sed potius penes oppositionem veri vel falsi; secundo, declarat quod non penes quaecunque opposita secundum veritatem et falsitatem est contrarietas opinionum; ibi: si ergo boni etc.; tertio, determinat quod contrarietas opinionum attenditur penes per se primo opposita secundum veritatem et falsitatem tribus rationibus; ibi: sed in quibus primo fallacia etc.; quarto declarat hanc determinationem inveniri in omnibus veram; ibi: manifestum est igitur et cetera. Dicit ergo proponens intentam conclusionem, quod falsum est arbitrari opiniones definiri seu determinari debere contrarias ex eo quod contrariorum obiectorum sunt. Et adducit ad hoc duplicem rationem. Prima est: opiniones contrariae non sunt eadem opinio; sed contrariorum eadem est fortasse opinio; ergo opiniones non sunt contrariae ex hoc quod contrariorum sunt. Secunda est: opiniones contrariae non sunt simul verae; sed opiniones contrariorum, sive plures, sive una, sunt simul verae quandoque; ergo opiniones non sunt contrariae ex hoc quod contrariorum sunt. Harum rationum, suppositis maioribus, ponit utriusque minoris declarationem simul, dicens: boni enim, quoniam bonum est, et mali, quoniam malum est, eadem fortasse opinio est, quoad primam. Et subdit esse vera, sive plures sive una sit, quoad secundam. Utitur autem dubitativo adverbio et disiunctione, quia non est determinandi locus an contrariorum eadem sit opinio, et quia aliquo modo est eadem et aliquo modo non. Si enim loquamur de habituali opinione, sic eadem est; si autem de actuali, sic non eadem est. Alia siquidem mentalis compositio actualiter fit, concipiendo bonum esse bonum, et alia concipiendo malum esse malum, licet eodem habitu utrunque cognoscamus, illud per se primo, et hoc secundario, ut dicitur IX metaphysicae. Deinde subdit quod ista quae ad declarationem minorum sumpta sunt, scilicet bonum et malum, contraria sunt etiam contrarietate sumpta stricte in moralibus, ac per hoc congrua usi sumus declaratione. Ultimo inducit conclusionem. Sed non in eo quod contrariorum opiniones sunt, contrariae sunt, sed magis in eo quod contrariae, idest, sed potius censendae sunt opiniones contrariae ex eo quod contrariae adverbialiter, scilicet contrario modo, idest vere et false enunciant. Et sic patet primum.	8. When he says, It is false, of course, to suppose that opinions are to be defined as contrary because they are about contraries, etc., he proceeds with the second question. First he shows that contrariety of opinions is not determined by the contrariety of the matter involved, but rather by the opposition of true and false; secondly, he shows that there is not contrariety of opinions in just any opposites according to truth and falsity, where he says, Now if there is the opinion of that which is good, that it is good, and the opinion that it is not good, etc.; third, he determines that contrariety of opinions is concerned with the per se first opposites; according to truth and falsity, for three reasons, where he says, Rather, those opinions in which there is fallacy must be posited as contrary to true opinions, etc.; finally, he shows that this determination is true of all, where he says, It is evident that it will make no difference if we posit the affirmation universally, for the universal negation will be the contrary, etc. Aristotle says, then, proposing the conclusion he intends to prove, that it is false to suppose that opinions are to be defined or determined as contrary because they are about contrary objects. He gives two arguments for this. Contrary opinions are not the same opinion; but opinions about contraries are probably the same opinion; therefore, opinions are not contrary from the fact that they are about contraries. And, contrary opinions are not simultaneously true; but opinions about contraries, whether many or one, are sometimes true simultaneously; therefore, opinions are not contraries because they are about contraries. Having supposed the majors of these arguments, he posits a manifestation of each minor at the same time. In relation to the first argument, he says, for the opinion of that which is good, that it is good, and of that which is evil, that it is evil are probably the same. In relation to the second argument he adds: and, whether many or one, are true. He uses "probably,” an adverb expressing doubt and disjunction, because this is not the place to determine whether the opinion of contraries is the same opinion, and, because in some way the opinion is the same and in some way not. In the case of habitual opinion, the opinion of contraries is the same, but in the case of an actual opinion it is not. One mental composition is actually made in conceiving that a good is good and another in conceiving that an evil is evil, although we know both by the same habit, the former per se and first, the latter secondarily, as is said in IX Metaphysicae [4: 1051a 4]. Then he adds that good and evil—which are used for the manifestation of the minor—are contraries even when the contrariety is taken strictly in moral matters; and so in using this our exposition is apposite. Finally, he draws the conclusion: however, opinions are not contraries because they are about contraries, but rather because they are contraries, i.e., opinions are to be considered as contrary from the fact that they enunciate contrarily, adverbially, i.e., in a contrary mode, i.e., they enunciate truly and falsely. Thus the first argument is clear.
Cajetanus lib. 2 l. 13 n. 9 Si ergo boni et cetera. Quia dixerat quod contrarietas opinionum accipitur secundum oppositionem veritatis et falsitatis earum, declarat modo quod non quaecunque secundum veritatem et falsitatem oppositae opiniones sunt contrariae, tali ratione. De bono, puta, de iustitia, quatuor possunt opiniones haberi, scilicet quod iustitia est bona, et quod non est bona, et quod est fugibilis, et quod est non appetibilis. Quarum prima est vera, reliquae sunt falsae. Inter quas haec est diversitas quod, prima negat idem praedicatum quod vera affirmabat; secunda affirmat aliquid aliud quod bono non inest; tertia negat id quod bono inest, non tamen illud quod vera affirmabat. Tunc sic. Si omnes opiniones secundum veritatem et falsitatem sunt contrariae, tunc uni, scilicet verae opinioni non solum multa sunt contraria, sed etiam infinita: quod est impossibile, quia unum uni est contrarium. Tenet consequentia, quia possunt infinitae imaginari opiniones falsae de una re similes ultimis falsis opinionibus adductis, affirmantes, scilicet ea quae non insunt illi, et negantes ea quae illi quocunque modo coniuncta sunt: utraque namque indeterminata esse et absque numero constat. Possumus enim opinari quod iustitia est quantitas, quod est relatio, quod est hoc et illud; et similiter opinari quod iustitia non sit qualitas, non sit appetibilis, non sit habitus. Unde ex supradictis in propositione quaestionis, inferens pluralitatem falsarum contra unam veram, ait: si ergo est opinatio vera boni, puta iustitiae, quoniam est bonum; et si est etiam falsa opinatio negans idem, scilicet, quoniam non est quid bonum; est vero et tertia opinatio falsa quoque, affirmans aliquid aliud inesse illi, quod non inest nec inesse potest, puta, quod iustitia sit fugibilis, quod sit illicita; et hinc intelligitur quarta falsa quoque, quae scilicet negat aliquid aliud ab eo quod vera opinio affirmat inesse iustitiae, quod tamen inest, ut puta quod non sit qualitas, quod non sit virtus; si ita inquam est, nulla aliarum falsarum ponenda est contraria opinioni verae. Et exponens quid demonstret per ly aliarum, subdit: neque quaecunque opinio opinatur esse quod non est, ut tertii ordinis opiniones faciunt: neque quaecunque opinio opinatur non esse quod est, ut quarti ordinis opiniones significant. Et causam subdit: infinitae enim utraeque sunt, et quae esse opinantur quod non est, et quae non esse quod est, ut supra declaratum fuit. Non ergo quaecunque opiniones oppositae secundum veritatem et falsitatem contrariae sunt. Et sic patet secundum.	9. When he says, Now, if there is the opinion of that which is good, that it is good, and the opinion that it is not good, etc., he takes up the second point. Since he has just said that contrariety of opinions is taken according to their opposition of truth and falsity, he goes on to show that not just any opposites according to truth and falsity are contraries. This is his argument. Four opinions can be held about a good, for instance justice: that justice is good, that it is not good, that it is avoidable, that it is not desirable. Of these, the first is true, the rest false. The three false ones are diverse. The first denies the same predicate the true one affirmed; the second affirms something which does not belong to the good; the third denies what belongs to the good, but something other than the true one affirmed. Now if all opinions opposed as to truth and falsity are contraries, then not only are there many contraries to one true opinion, but an infinite number. But this is impossible, for one is contrary to one other. The consequence holds because infinite false opinions about one thing, similar to those cited, can be imagined; such opinions would affirm of it what does not belong to it and deny what is joined to it in some way. Both kinds are indeterminate and without number. We can think, for instance, that justice is a quantity, that it is a relation, that it is this and that; and likewise we can think that it is not a quality, is not desirable, is not a habit. Hence, from what was said above in proposing the question, Aristotle infers a plurality of false opinions opposed to one true opinion: Now if there is the opinion of that which is good, for instance justice, that it is good, and there is a false opinion denying the same thing, namely, that it is not good, and besides these a third opinion, false also, affirming that some other thing belongs to justice that does not belong and cannot belong to it (for instance, that justice is avoidable, that it is illicit) and a fourth opinion, also false, that denies something other than the true opinion affirms, something, however, which does belong to justice (for instance, that it is not a quality, that it is not a virtue), none of these other false enunciations are to be posited as the contrary of the true opinion. To explain what he is designating by "of these others,” he adds, neither those purporting that what is not, is, as opinions of the third order do, nor those purporting that what is, is not, as opinions of the fourth order signify. Then he adds the reason these cannot be posited as the contrary of the true opinion: for both the opinions that that is which is not, and that which is not, is, are infinite, as was shown above. Therefore, not just any opinions opposed according to truth and falsity are contraries. Thus the second argument is clear.

LECTURE 14

Latin	English
Cajetanus lib. 2 l. 14 n. 1 Quia subtili indagatione ostendit quod nec materiae contrarietas, nec veri falsique qualiscunque oppositio contrarietatem opinionum constituit, sed quod aliqua veri falsique oppositio id facit, ideo nunc determinare intendit qualis sit illa veri falsique oppositio, quae opinionum contrarietatem constituit. Ex hoc enim directe quaestioni satisfit. Et intendit quod sola oppositio opinionum secundum affirmationem et negationem eiusdem de eodem etc. constituit contrarietatem earum. Unde intendit probare istam conclusionem per quam ad quaesitum respondet: opiniones oppositae secundum affirmationem et negationem eiusdem de eodem sunt contrariae; et consequenter illae, quae sunt oppositae secundum affirmationem contrariorum praedicatorum de eodem, non sunt contrariae, quia sic affirmativa vera haberet duas contrarias, quod est impossibile. Unum enim uni est contrarium.	1. Aristotle has just completed a subtle investigation in which he has shown that contrariety of matter does not constitute contrariety of opinion, nor does just any kind of opposition of true and false, but some opposition of true and false does. Now he intends to determine what kind of opposition of true and false it is that constitutes contrariety of opinions, for this will answer the question directly. He maintains that only opposition of opinions according to affirmation and negation of the same thing of the same thing, etc., constitutes their contrariety. Accordingly, as the response to the question, he intends to prove the following conclusion: opinions opposed according to affirmation and negation of the same thing of the same thing are contraries; and consequently, opinions opposed according to affirmation of contrary predicates of the same subject are not contraries, for if these were contraries, the true affirmative would have two contraries, which is impossible, since one is contrary to one other.
Cajetanus lib. 2 l. 14 n. 2 Probat autem istam conclusionem tribus rationibus. Prima est: opiniones in quibus primo est fallacia sunt contrariae; opiniones oppositae secundum affirmationem et negationem eiusdem de eodem sunt in quibus primo est fallacia; ergo opiniones oppositae secundum affirmationem et negationem eiusdem de eodem sunt contrariae. Sensus maioris est: opiniones quae primo ordine naturae sunt termini fallaciae, idest deceptionis seu erroris, sunt contrariae: sunt enim, cum quis fallitur seu errat, duo termini, scilicet a quo declinat, et ad quem labitur. Huius rationis in littera primo ponitur maior, cum dicitur: sed in quibus primo fallacia est; adversative enim continuans sermonem supradictis, insinuavit non tot enumeratas opiniones esse contrarias, sed eas in quibus primo fallacia est modo exposito. Deinde subdit probationem minoris talem: eadem proportionaliter sunt, ex quibus sunt generationes et ex quibus sunt fallaciae; sed generationes sunt ex oppositis secundum affirmationem et negationem; ergo et fallaciae sunt ex oppositis secundum affirmationem et negationem. Quod erat assumptum in minore. Unde ponens maiorem huius prosyllogismi, ait: haec autem, scilicet fallacia, est ex his, scilicet terminis, proportionaliter tamen, ex quibus sunt et generationes. Et subsumit minorem: ex oppositis vero, scilicet secundum affirmationem et negationem, et generationes fiunt. Et demum concludit: quare etiam fallacia, scilicet, est ex oppositis secundum affirmationem et negationem eiusdem de eodem.	2. Aristotle uses three arguments to prove this conclusion. The first one is as follows: Those opinions in which there is fallacy first are contraries. Opinions opposed according to affirmation and negation of the same predicate of the same subject are those in which there is fallacy first. Therefore, these are contraries. The sense of the major is this: Opinions which first in the order of nature are the limits of fallacy, i.e., of deception or error, are contraries; for when someone is deceived or errs, there are two limits, the one from which he turns away and the one toward which he turns. In the text the major of the argument is posited first: Rather, those opinions in which there is fallacy must be posited as contrary to true opinions. By uniting this part of the text adversatively with what was said previously, Aristotle implies that not just any of the number of opinions enumerated are contraries, but those in which there is fallacy first in the manner we have explained. Then he gives this proof of the minor: those things from which generations are and from which fallacies are, are the same proportionally; generations are from opposites according to affirmation and negation; therefore fallacies, too, are from opposites according to affirmation and negation (which was assumed in the minor). Hence he posits the major of this prosyllogism: Now the things from which fallacies arise, namely, limits, are the things from which generations arise—proportionally however. Under it he posits the minor: but generations are from opposites, i.e., according to affirmation and negation. Finally, he concludes, therefore also fallacies, i.e., they are from opposites according to affirmation and negation of the same thing of the same thing.
Cajetanus lib. 2 l. 14 n. 3 Ad evidentiam huius probationis scito quod idem faciunt in processu intellectus cognitio et fallacia seu error, quod in processu naturae generatio et corruptio. Sicut namque perfectiones naturales generationibus acquiruntur, corruptionibus desinunt; ita cognitione perfectiones intellectuales acquiruntur, erroribus autem seu deceptionibus amittuntur. Et ideo, sicut tam generatio quam corruptio est inter affirmationem et negationem, ut proprios terminos, ut dicit V Physic.; ita tam cognoscere aliquid, quam falli circa illud, est inter affirmationem et negationem, ut proprios terminos: ita quod id ad quod primo attingit cognoscens aliquid in secunda operatione intellectus est veritatis affirmatio, et quod per se primo abiicitur est illius negatio. Et similiter quod per se primo perdit qui fallitur est veritatis affirmatio, et quod primo incurrit est veritatis negatio. Recte ergo dixit quod iidem sunt termini inter quos primo est generatio, et illi inter quos est primo fallacia, quia utrobique termini sunt affirmatio et negatio.	3. This proof will be more evident from the following: Knowledge and fallacy, or error, bring about the same thing in the intellect’s progression as generation and corruption do in nature’s progression. For just as natural perfections are acquired by generations and perish by corruptions, so intellectual perfections are acquired by knowledge and lost by errors or deceptions. Accordingly, just as generation and corruption are between affirmation and negation as proper terms, as is said in V Physicae [1:224b 35] so both to know something and to be deceived about it is between affirmation and negation as proper terms. Consequently, what one who knows attains first in the second operation of the intellect is affirmation of the truth, and what he rejects per se and first is the negation of it. In like manner, what he who is deceived loses per se and first is affirmation of the truth, and acquires first is negation of the truth. Therefore Aristotle is correct in maintaining that the terms between which there is generation first and between which there is fallacy first are the same, because with respect to both, the terms are affirmation and negation.
Cajetanus lib. 2 l. 14 n. 4 Deinde cum dicit: si ergo quod bonum est etc., intendit probare maiorem principalis rationis. Et quia iam declaravit quod ea, in quibus primo est fallacia, sunt affirmatio et negatio, ideo utitur, loco maioris probandae, scilicet, opiniones in quibus primo est fallacia, sunt contrariae, sua conclusione, scilicet, opiniones oppositae secundum affirmationem et negationem eiusdem sunt contrariae. Aequivalere enim iam declaratum est. Fecit autem hoc consuetae brevitati studens, quoniam sic procedendo, et probat maiorem, et respondet directe quaestioni, et applicat ad propositum simul. Probat ergo loco maioris conclusionem principaliter intentam quaestionis, hanc, scilicet: opiniones oppositae secundum affirmationem et negationem eiusdem sunt contrariae; et non illae, quae sunt oppositae secundum contrariorum affirmationem de eodem. Et intendit talem rationem. Opinio vera et eius magis falsa sunt contrariae opiniones; oppositae secundum affirmationem et negationem sunt vera et eius magis falsa; ergo opiniones oppositae secundum affirmationem et negationem sunt contrariae. Maior probatur ex eo quod, quae plurimum distant circa idem sunt contraria; vera autem et eius magis falsa plurimum distant circa idem, ut patet. Minor vero probatur ex eo quod opposita secundum negationem eiusdem de eodem est per se falsa respectu suae affirmationis verae. Opinio autem per se falsa magis falsa est quacunque alia. Unumquodque enim quod est per se tale, magis tale est quolibet quod est per aliud tale.	4. When he says, Now, if that which is good is both good and not evil, the former per se, the latter accidentally, etc., he intends to prove the major of the principal argument. He has already shown that the opinions in which there is fallacy first are affirmation and negation, and therefore in place of the major to be proved (i.e., opinions in which it there is fallacy first are contraries) he uses his conclusion—which has already been shown to be equivalent—that opinions opposed according to affirmation and negation of the same thing are contraries. Thus with his customary brevity he at once proves the major, responds directly to the question, and applies it to what he has proposed. In place of the major, then, he proves the conclusion principally intended, i.e., that opinions opposed according to affirmation and negation of the same thing are contraries, and not those opposed according to affirmation of contraries about the same thing. His argument is as follows: A true opinion and the opinion that is more false in respect to it are contrary opinions, but opinions opposed according to affirmation and negation are the true opinion and the opinion that is more false in respect to it; therefore, opinions opposed according to affirmation and negation are contraries. The major is proved thus: those things that are most distant in respect to the same thing are contraries; but the true and the more false are most distant in respect to the same thing, as is clear. The proof of the minor is that the opposite according to negation of the same thing of the same thing is per se false in relation to the true affirmation of it. But a per se false opinion is more false than any other, since each thing that is per se such is more such than anything that is such by reason of something else.
Cajetanus lib. 2 l. 14 n. 5 Unde ad suprapositas opiniones in propositione quaestionis rediens, ut ex illis exemplariter clarius intentum ostendat, a probatione minoris inchoat tali modo. Sint quatuor opiniones, duae verae, scilicet, bonum est bonum, bonum non est malum, et duae falsae, scilicet, bonum non est bonum, et, bonum est malum. Clarum est autem quod prima vera est ratione sui, secunda autem est vera secundum accidens, idest, ratione alterius, quia scilicet non esse malum est coniunctum ipsi bono: ideo enim ista est vera, bonum non est malum, quia bonum est bonum, et non e contra; ergo prima quae est secundum se vera, est magis vera quam secunda: quia in unoquoque genere quae secundum se est vera est magis vera. Illae autem duae falsae eodem modo censendae sunt, quod scilicet magis falsa est, quae secundum se est falsa. Unde quia prima earum, scilicet, bonum non est bonum, quae est negativa, est per se et non ratione alterius falsa, relata ad illam affirmativam, bonum est bonum; et secunda, scilicet, bonum est malum, quae est affirmativa contrarii, ad eamdem relata est falsa per accidens, idest ratione alterius (ista enim, scilicet, bonum est malum, non immediate falsificatur ab illa vera, scilicet bonum est bonum, sed mediante illa alia falsa, scilicet, bonum non est bonum); idcirco magis falsa respectu affirmationis verae est negatio eiusdem quam affirmatio contrarii. Quod erat assumptum in minore.	5. Accordingly, returning to the opinions already given in proposing the question so as to show his intention more clearly by example, he begins with the proof of the minor. There are four opinions, of which two are true, "A good is good,” "A good is not evil”; two are false, "A good is not good” and "A good is evil.” It is evident that the first is true by reason of itself, the second accidentally, i.e., by reason of another, for not to be evil is added to that which is good. Hence, "A good is not evil” is true because a good is good, and not contrarily. Therefore, the first of these opinions, which is per se true, is more true than the second, for in each genus that which per se is true is more true. The two false opinions are to be judged in the same way. The more false is the one that is per se false. The first of them, the negative, "A good is not good,” in relation to the affirmative, "A good is good,” is per se false, not false by reason of another. The second, the affirmative of the contrary, "A good is evil,” in relation to the same opinion, is false accidentally, i.e., by reason of another (for "A good is evil” is not immediately falsified by the true opinion, "A good is good,” but mediately through the other false opinion "A good is not good”). Therefore, the negation of the same thing is more false in respect to a trite affirmation than the affirmation of a contrary. This was assumed in the minor.
Cajetanus lib. 2 l. 14 n. 6 Unde rediens ad supra positas (ut dictum est) opiniones, infert primas duas veras opiniones dicens: si ergo quod bonum est et bonum est et non est malum, et hoc quidem, scilicet quod dicit prima opinio, est verum secundum se, idest ratione sui; illud vero, scilicet quod dicit secunda opinio, est verum secundum accidens, quia accidit, idest, coniunctum est ei, scilicet bono, malum non esse. In unoquoque autem ordine magis vera est illa quae secundum se est vera. Etiam igitur falsa magis est quae secundum se falsa est: siquidem et vera huius est naturae, ut declaratum est, quod scilicet magis vera est, quae secundum se est vera. Ergo illarum duarum opinionum falsarum in quaestione propositarum, scilicet, bonum non est bonum, et, bonum est malum, ea quae est dicens, quoniam non est bonum quod bonum est, idest negativa; scilicet, bonum non est bonum, est consistens falsa secundum se, idest, ratione sui continet in seipsa falsitatem; illa vero reliqua falsa opinio, quae est dicens, quoniam malum est, idest, affirmativa contraria, scilicet, bonum est malum, eius, quae est, idest, illius affirmationis dicentis, bonum est bonum, secundum accidens, idest, ratione alterius falsa est. Deinde subdit ipsam minorem: quare erit magis falsa de bono, opinio negationis, quam contrarii. Deinde ponit maiorem dicens quod, semper magis falsus circa singula est ille qui habet contrariam opinionem, ac si dixisset, verae opinioni magis falsa est contraria. Quod assumptum erat in maiore. Et eius probationem subdit, quia contrarium est de numero eorum quae circa idem plurimum differunt. Nihil enim plus differt a vera opinione quam magis falsa circa illam.	6. As was pointed out above, Aristotle returns to the opinions already posited, and infers the first two true opinions: Now if that which is good is both good and not evil, and if what the first opinion says is true per se, i.e., by reason of itself, and what the second opinion says is trite accidentally (since it is accidental to it, i.e., added to it, that is, to the good, not to be evil) and if in each order that which is per se true is more true, then that which is per se false is more false, since, as has been shown, the true also is of this nature, namely, that the more true is that which per se is true. Therefore, of the two false opinions proposed in the question, namely, "A good is not good,” and "A good is evil,” the one saying that what is good is not good, namely, the negative, is an opinion positing what is per se false, i.e., by reason of itself it contains falsity in it. The other false opinion, the one saying it is evil, namely, the affirmative contrary in respect to it, i.e., in respect to the affirmation saying that a good is good, is false accidentally, i.e., by reason of another. Then he gives the minor: Therefore, the opinion of the negation of the good will be more false than the opinion affirming a contrary. Next, he posits the major, the one who holds the contrary judgment about each thing is most mistaken, i.e., in relation to the true judgment the contrary is more false. This was assumed in the major. He gives as the proof of this, for contraries are those that differ most with respect to the same thing, for nothing differs more from a true opinion than the more false opinion in respect to it.
Cajetanus lib. 2 l. 14 n. 7 Ultimo directe applicat ad quaestionem dicens: quod si (pro, quia) harum falsarum, scilicet, negationis eiusdem et affirmationis contrarii, altera est contraria verae affirmationi, opinio vero contradictionis, idest, negationis eiusdem de eodem, magis est contraria secundum falsitatem, idest, magis est falsa, manifestum est quoniam haec, scilicet opinio falsa negationis, erit contraria affirmationi verae, et e contra. Illa vero opinio quae est dicens, quoniam malum est quod bonum est, idest, affirmatio contrarii, non contraria sed implicita est, idest, sed implicans in se verae contrariam, scilicet, bonum non est bonum. Etenim necesse est ipsum opinantem affirmationem contrarii opinari, quoniam idem de quo affirmat contrarium non est bonum. Oportet siquidem si quis opinatur quod vita est mala, quod opinetur quod vita non sit bona. Hoc enim necessario sequitur ad illud, et non e converso; et ideo affirmatio contrarii implicita dicitur. Negatio autem eiusdem de eodem implicita non est. Et sic finitur prima ratio.	7. Finally, he directly approaches the question. If (for "since”), then, of two opinions (namely, false opinions—the negation of the same thing and the affirmation of a contrary), one is the contrary of the true affirmation, and, the contradictory opinion, i.e., the negation of the same thing of the same thing, is more contrary according to falsity, i.e., is more false, it is evident that the false opinion of negation will be contrary to the true affirmation, and conversely. The opinion saying that what is good is evil, i.e., the affirmation of a contrary, is not the contrary but implies it, i.e., it implies in itself the opinion contrary to the true opinion, i.e., "A good is not good.” The reason for this is that the one conceiving the affirmation of a contrary must conceive that the same thing of which he affirms the contrary, is not good. If, for example, someone conceives that life is evil, he must conceive that life is not good, for the former necessarily follows upon the latter and not conversely. Hence, affirmation of a contrary is said to be implicative, but negation of the same thing of the same thing is not implicative. This concludes the first argument.
Cajetanus lib. 2 l. 14 n. 8 Notandum est hic primo quod ista regula generalis tradita hic ab Aristotele de contrarietate opinionum, quod scilicet contrariae opiniones sunt quae opponuntur secundum affirmationem et negationem eiusdem de eodem, et in se et in assumptis ad eius probationem propositionibus scrupulosa est. Unde multa hic insurgunt dubia. Primum est quia cum oppositio secundum affirmationem et negationem non constituat contrarietatem sed contradictionem apud omnes philosophos, quomodo Aristoteles opiniones oppositas secundum affirmationem et negationem ex hoc contrarias ponat. Augetur et dubitatio quia dixit quod ea in quibus primo est fallacia sunt contraria, et tamen subdit quod sunt oppositae sicut termini generationis, quos constat contradictorie opponi. Nec dubitatione caret quomodo sit verum id quod supra diximus ex intentione s. Thomae, quod nullae duae opiniones opponantur contradictorie, cum hic expresse dicitur aliquas opponi secundum affirmationem et negationem. Dubium secundo insurgit circa id quod assumpsit, quod contraria cuiusque verae est per se falsa. Hoc enim non videtur verum. Nam contraria istius verae, Socrates est albus, est ista, Socrates non est albus, secundum determinata; et tamen non est per se falsa. Sicut namque sua opposita affirmatio est per accidens vera, ita ista est per accidens falsa. Accidit enim isti enunciationi falsitas. Potest enim mutari in veram, quia est in materia contingenti. Dubium est tertio circa id quod dixit: magis vero contradictionis est contraria. Ex hoc enim videtur velle quod utraque, scilicet, opinio negationis et contrarii, sit contraria verae affirmationi; et consequenter vel uni duo ponit contraria, vel non loquitur de contrarietate proprie sumpta: cuius oppositum supra ostendimus.	8. The general rule about the contrariety of opinions that Aristotle has given here (namely, that contrary opinions are those opposed according to affirmation and negation of the same thing of the same thing) is accurate both in itself and in the propositions assumed for its proof. Many questions may arise, however, as a consequence of this doctrine and its proof. First of all, all philosophers hold that opposition according to affirmation and negation constitutes contradiction, not contrariety. How, then, can Aristotle maintain that opinions opposed in this way are contraries? The difficulty is augmented by the fact that he has said that those opinions in which there is fallacy first are contraries, yet he adds that they are opposed as the terms of generation are, which he establishes to be opposed contradictorily. In addition, there is a difficulty as to the way in which the assertion of St. Thomas, which we used above, is true, namely, that no two opinions are opposed contradictorily, since here it is explicitly said that some are opposed according to affirmation and negation. The second uestion involves his assumption that the contrary of each true opinion is per se false. This does not seem to be true, for according to what was determined previously, the contrary of the true opinion "Socrates is white” is "Socrates is not white.” But this is not per se false, for the opposed affirmation is true accidentally, and hence its negation is false accidentally. Falsity is accidental to such an enunciation because, being in contingent matter, it can be changed into a true one. A third difficulty arises from the fact that Aristotle says the contradictory opinion is nwre contrary. He seems to be proposing, according to this, that both the opinion of the negation and of a contrary are contrary to a true affirmation. Consequently, he is either positing two opinions contrary to one or he is not taking contrariety strictly, although we showed above that he was taking contrariety properly and strictly.
Cajetanus lib. 2 l. 14 n. 9 Ad evidentiam omnium, quae primo loco adducuntur, sciendum quod opiniones seu conceptiones intellectuales, in secunda operatione de quibus loquimur, possunt tripliciter accipi: uno modo, secundum id quod sunt absolute; alio modo, secundum ea quae repraesentant absolute; tertio, secundum ea quae repraesentant, ut sunt in ipsis opinionibus. Primo membro omisso, quia non est praesentis speculationis, scito quod si accipiantur secundo modo secundum repraesentata, sic invenitur inter eas et contradictionis, et privationis, et contrarietatis oppositio. Ista siquidem mentalis enunciatio, Socrates est videns, secundum id quod repraesentat opponitur illi, Socrates non est videns, contradictorie; privative autem illi, Socrates est caecus; contrarie autem illi, Socrates est luscus; si accipiantur secundum repraesentata. Ut enim dicitur in postpraedicamentis, non solum caecitas est privatio visus, sed etiam caecum esse est privatio huius quod est esse videntem, et sic de aliis. Si vero accipiantur opiniones tertio modo, scilicet, prout repraesentata per eas sunt in ipsis, sic nulla oppositio inter eas invenitur nisi contrarietas: quoniam sive opposita contradictorie sive privative sive contrarie repraesententur, ut sunt in opinionibus, illius tantum oppositionis capaces sunt, quae inter duo entia realia inveniri potest. Opiniones namque realia entia sunt. Regulare enim est quod quidquid convenit alicui secundum esse quod habet in alio, secundum modum et naturam illius in quo est sibi convenit, et non secundum quod exigeret natura propria. Inter entia autem realia contrarietas sola formaliter reperitur. Taceo nunc de oppositione relativa. Opiniones ergo hoc modo sumptae, si oppositae sunt, contrarietatem sapiunt, sed non omnes proprie contrariae sunt, sed illae quae plurimum differunt circa idem veritate et falsitate. Has autem probavit Aristoteles esse opiniones affirmationis et negationis eiusdem de eodem. Istae igitur verae contrariae sunt. Reliquae vero per reductionem ad has contrariae dicuntur.	9. In order to answer all of the difficulties in regard to the first argument it must be noted that opinions, or intellectual conceptions in the second operation, can be taken in three ways: (1) according to what they are absolutely; (2) according to the things they represent absolutely, (3) according to the things they represent, as they are in opinions. We will omit the first since it does not belong to the present consideration. If they are taken in the second way, i.e., according to the things represented, there can be opposition of contradiction, of privation, and of contrariety among them. The mental enunciation "Socrates sees,” according to what it represents, is opposed contradictorily to. Socrates does not see”; privatively to "Socrates is blind”; contrarily to "Socrates is purblind.” Aristotle points out the reason for this in the Postpredicamenta [Categ. 10: 12a 35]: not only is blindness privation of sight but to be blind is also a privation of to be seeing, and so of others. Opinions taken in the third way, i.e., as the things represented through opinions are in the opinions, have no opposition except contrariety; for opposites as they are in opinions, whether represented contradictorily or privatively or contrarily, only admit of the opposition that can be found between two real beings, for opinions are real beings. The rule is that whatever belongs to something according to the being which it has in another, belongs to it according to the mode and nature of that in which it is, and not according to what its own nature would require. Now, between real beings only contrariety is found formally. (I am omitting here the consideration of relative opposition.) Therefore, opinions taken in this mode, if they are opposed, represent contrariety, although not all are contraries properly. Only those differing most in respect to truth and falsity about the same thing are contraries properly. Now Aristotle proved that these are - judgments affirming and denying the same thing of the same thing. Therefore, these are the true contraries. The rest are called contraries by reduction to these.
Cajetanus lib. 2 l. 14 n. 10 Ex his patet quid ad obiecta dicendum sit. Fatemur enim quod affirmatio et negatio in seipsis contradictionem constituunt; in opinionibus vero existentes contrarietatem inter illas causant propter extremam distantiam, quam ponunt inter entia realia, opinionem scilicet veram et opinionem falsam circa idem. Stantque ista duo simul quod ea, in quibus primo est fallacia, sint opposita ut termini generationis, et tamen sint contraria utendo supradicta distinctione: sunt enim opposita contradictorie ut termini generationis secundum repraesentata; sunt autem contraria, secundum quod habent in seipsis illa contradictoria. Unde plurimum differunt. Liquet quoque ex hoc quod nulla est dissentio inter dicta Aristotelis et s. Thomae, quia opiniones aliquas opponi secundum affirmationem et negationem verum esse confitemur, si ad repraesentata nos convertimus, ut hic dicitur.	10. From this the answer to the objections is clear. We grant that affirmation and negation in themselves constitute contradiction. In actual judgments,”’ affirmation and negation cause contrariety between opinions because of the extreme distance they posit between real beings, namely, true opinion and false opinion in respect to the same thing. And these two stand at the same time: those in which there is fallacy first are opposed as the terms of generation are and yet they are contraries by the use of the foresaid distinction—for they are opposed contradictorily as terms of generation according to the things represented, but they are contraries insofar as they have in themselves those contradictories and hence differ most. It is also evident that there is no disagreement between Aristotle and St. Thomas, for we have shown that it is true that some opinions are opposed according to affirmation and negation if we consider the things represented, as is said here.
Cajetanus lib. 2 l. 14 n. 11 Tu autem qui perspicacioris ac provectioris ingenii es compos, hinc habeto quod inter ipsas opiniones oppositas quidam tantum motus est, eo quod de affirmato in affirmatum mutatio fit: inter ipsas vero secundum repraesentata, similitudo quaedam generationis et corruptionis invenitur, dum inter affirmationem et negationem mutatio clauditur. Unde et fallacia sive error quandoque et motus et mutationis rationem habet diversa respiciendo, quando scilicet ex vera in per se falsam, vel e converso, quis mutat opinionem; quandoque autem solam mutationem imitatur, quando scilicet absque praeopinata veritate ipsam falsam offendit quis opinionem; quandoque vero motus undique rationem possidet, quando scilicet ex vera affirmatione in falsam circa idem contrarii affirmationem transit. Quia tamen prima ut quis fallatur radix est oppositio affirmationis et negationis, merito ea in quibus primo est fallacia, sicut generationis terminos opponi dixit.	11. It will be noted, however, by those of you who are more penetrating and advanced in your thinking, that between opposite opinions there is something of true motion when a change is made from the affirmed to the affirmed; but according to the order of representation there is a certain similitude to generation and corruption so long as the change is bounded by affirmation and negation. Consequently, fallacy or error may be regarded in different ways. Sometimes it has the aspect of both movement and change. This is the case when someone changes his opinion from a true one to one that is per se false, or conversely. Sometimes change alone is imitated. This happens when someone arrives at a false opinion apart from a former true opinion. Sometimes, however, there is movement in every respect. This is the case when reason passes from the true affirmation to the false affirmation of a contrary about the same thing. However, since the first root of being in error is the opposition of affirmation and negation, Aristotle is correct in saying that those in which there is fallacy first are opposed as are the terms of generation.
Cajetanus lib. 2 l. 14 n. 12 Ad dubium secundo loco adductum dico quod peccatur ibi secundum aequivocationem illius termini per se falsa, seu per se vera. Opinio enim et similiter enunciatio potest dici dupliciter per se vera seu falsa. Uno modo, in seipsa, sicut sunt omnes verae secundum illos modos perseitatis qui enumerantur I posteriorum, et similiter falsae secundum illosmet modos, ut, homo non est animal. Et hoc modo non accipitur in hac regula de contrarietate opinionum et enunciationum opinio per se vera aut falsa, ut efficaciter obiectio adducta concludit. Si enim ad contrarietatem opinionum hoc exigeretur non possent esse opiniones contrariae in materia contingenti: quod est falsissimum. Alio modo potest dici opinio sive enunciatio per se vera aut falsa respectu suae oppositae. Per se vera quidem respectu suae falsae, et per se falsa respectu suae verae. Et tunc nihil aliud est dicere, est per se vera respectu illius, nisi quod ratione sui et non alterius verificatur ex falsitate illius. Et similiter cum dicitur, est per se falsa respectu illius, intenditur quod ratione sui et non alterius falsificatur ex illius veritate. Verbi gratia; istius verae, Socrates currit, non est per se falsa, Socrates sedet, quia falsitas eius non immediate sequitur ex illa, sed mediante ista alia falsa, Socrates non currit, quae est per se illius falsa, quia ratione sui et non per aliquod medium ex illius veritate falsificatur, ut patet. Et similiter istius falsae, Socrates est quadrupes, non est per se vera ista, Socrates est bipes, quia non per seipsam veritas istius illam falsificat, sed mediante ista, Socrates non est quadrupes, quae est per se vera respectu illius: propter seipsam enim falsitate istius verificatur, ut de se patet. Et hoc secundo modo utimur istis terminis tradentes regulam de contrarietate opinionum et enunciationum. Invenitur siquidem sic universaliter vera in omni materia regula dicens quod, vera et eius per se falsa, et falsa et eius per se vera, sunt contrariae. Unde patet responsio ad obiectionem, quia procedit accipiendo ly per se vera, et per se falsa primo modo.	12. With respect to the second question, I say that there is an equivocation of the term "per se false” and "per se true” in the objection. Opinion, as well as enunciation, can be called per se true or false in two ways. It can be called per se true in itself. This is the case in respect to all opinions and enunciations that are in accordance with the modes of perseity enumerated in I Posteriorum [4: 73a; 34–73b 15]. Similarly, they can be said to be per se false according to the same modes. An example of this would be "Man is not an animal.” Per se true or false is not taken in this mode in the rule about contrariety of opinions and enunciations, as the objection concludes. For if this were needed for contrariety of opinions there could not be contrary opinions in contingent matter, which is false. Secondly, an opinion or enunciation can be said to be per se true or false in respect to its opposite: per se true with respect to its opposite false opinion, and per se false with respect to its opposite true opinion. Accordingly, to say that an opinion is per se true in respect to its opposite is to say that on its own account and not on account of another it is verified by the falsity of its opposite. Similarly, to say that an opinion is per se false in respect to its opposite means that on its own account and not on account of another it is falsified by the truth of the opposite. For example, the opinion that is per se false in respect to the true opinion "Socrates is running "is not, "Socrates is sitting,” since the falsity of the latter does not immediately follow from the former, but mediately from the false opinion, "Socrates is not running.” It is the latter opinion that is per se false in relation to "Socrates is running,” since it is falsified on its own account by the truth of the opinion "Socrates is running,” and not through an intermediary. Similarly, the per se true opinion in respect to the false opinion "Socrates is four-footed” is not, "Socrates is two-footed,” for the truth of the latter does not by itself make the former false; rather, it is through "Socrates is not four-footed” as a medium, which is per se true in respect to "Socrates is four-footed”; for "Socrates is not four-footed” is verified on its own account by the falsity of "Socrates is four-footed,” as is evident. We are using "per se true” and "per se false” in this second mode in propounding the rule concerning contrariety of opinions and enunciations. Thus the rule that the true opinion and the per se false opinion in relation to it and the false opinion and the per se true in relation to it are contraries, is universally true in all matter. Consequently, the response to the objection is clear, for it results from taking "per se true” and "per se false” in the first mode.
Cajetanus lib. 2 l. 14 n. 13 Ad ultimum dubium dicitur quod, quia inter opiniones ad se invicem pertinentes nulla alia est oppositio nisi contrarietas, coactus fuit Aristoteles (volens terminis specialibus uti) dicere quod una est magis contraria quam altera, insinuans quidem quod utraque contrarietatis oppositionem habet respectu illius verae. Determinat tamen immediate quod tantum una earum, scilicet negationis opinio, contraria est affirmationi verae. Subdit enim: manifestum est quoniam haec contraria erit. Duo ergo dixit, et quod utraque, tam scilicet negatio eiusdem quam affirmatio contrarii, contrariatur affirmationi verae, et quod una tantum earum, negatio scilicet, est contraria. Et utrunque est verum. Illud quidem, quia, ut dictum est, ambae contrarietates oppositione contra affirmationem moliuntur; sed difformiter, quia opinio negationis primo et per se contrariatur, affirmationis vero contrarii opinio secundario et per accidens, idest per aliud, ratione scilicet negativae opinionis, ut declaratum est: sicut etiam in naturalibus albo contrariantur et nigrum et rubrum, sed illud primo, hoc reductive, ut reducitur scilicet ad nigrum illud inducendo, ut dicitur V Physic. Secundum autem dictum simpliciter verum est, quoniam simpliciter contraria non sunt nisi extrema unius latitudinis, quae maxime distant; extrema autem unius distantiae non sunt nisi duo. Et ideo cum inter pertinentes ad se invicem opiniones unum extremum teneat affirmatio vera, reliquum uni tantum falsae dandum est, illi scilicet quae maxime a vera distat. Hanc autem negativam opinionem esse probatum est. Haec igitur una tantum contraria est illi, simpliciter loquendo. Caeterae enim oppositae ratione istius contrariantur, ut de mediis dictum est. Non ergo uni plura contraria posuit, nec de contrarietate large loquutus est, ut obiiciendo dicebatur.	13. The answer to the third difficulty is the following. Since there is no other opposition but contrariety between opinions pertaining to each other, Aristotle (since he chose to use limited terms) has been forced to say that one is more contrary than another, which implies that both have opposition of contrariety in respect to a true opinion. However, he determines immediately that only one of them, the negative opinion, is contrary to a true affirmation, when he adds, it is evident that it must be the contrary. What he says, then, is that each, i.e., both negation of the same thing and affirmation of a contrary, is contrary to a true affirmation, and that only one of them, i.e., the negation, is contrary. Both of these statements are true, for both contrarieties are caused by an opposition contrary to the affirmation, as was said, but not uniformly. The opinion of negation is contrary first and per se, the opinion of affirmation of a contrary, secondarily and accidentally, i.e., through another, namely, by reason of the negative opinion, as has already been shown. There is a parallel to this in natural things: both black and red are contrary to white, the former first, the latter reductively, i.e., inasmuch as red is reduced to black in a motion from white to red, as is said in V Physicorum [5: 229b 15]. However, the second statement, i.e., that only one of them, the negation, is contrary, is true simply, for the most distant extremes of one extent are contraries absolutely. Nov,, there are only two extremes of one distance and since between opinions pertaining to each other true affirmation is at one extreme, the remaining extreme must be granted to only one false opinion, i.e., to the one that is most distant from the true opinion. This has been proved to be the negative opinion. Only this one, then, is contrary to that absolutely speaking. Other opposites are contrary by reason of this one, as was said of those in between. Therefore, Aristotle has not posited many opinions contrary to one, nor used contrariety in a broad sense, both of which were maintained by the objector.
Cajetanus lib. 2 l. 14 n. 14 Deinde cum dicit: amplius si etiam etc., probat idem, scilicet quod affirmationi contraria est negatio eiusdem, et non affirmatio contrarii secunda ratione, dicens: si in aliis materiis oportet opiniones se habere similiter, idest, eodem modo, ita quod contrariae in aliis materiis sunt affirmatio et negatio eiusdem; et hoc, scilicet quod diximus de boni et mali opinionibus, videtur esse bene dictum, quod scilicet contraria affirmationi boni non est affirmatio mali, sed negatio boni. Et probat hanc consequentiam subdens: aut enim ubique, idest, in omni materia, ea quae est contradictionis altera pars censenda est contraria suae affirmationi, aut nusquam, idest, aut in nulla materia. Si enim est una ars generalis accipiendi contrariam opinionem, oportet quod ubique et in omni materia uno et eodem modo accipiatur contraria opinio. Et consequenter, si in aliqua materia negatio eiusdem de eodem affirmationi est contraria, in omni materia negatio eiusdem de eodem contraria erit affirmationi. Deinde intendens concludere a positione antecedentis, affirmat antecedens ex sua causa, dicens quod illae materiae quibus non inest contrarium, ut substantia et quantitas, quibus, ut in praedicamentis dicitur, nihil est contrarium. De his quidem est per se falsa ea, quae est opinioni verae opposita contradictorie, ut qui putat hominem, puta Socratem non esse hominem, per se falsus est respectu putantis, Socratem esse hominem. Deinde affirmando ipsum antecedens formaliter, directe concludit intentum a positione antecedentis ad positionem consequentis dicens: si ergo hae, scilicet, affirmatio et negatio in materia carente contrario, sunt contrariae, et omnes aliae contradictiones contrariae censendae sunt.	14. When Aristotle says, Further, if this necessarily holds in a similar way in till other cases it would seen that what we have said is correct, etc., he gives the second argument to prove that the negation of the same thing is contrary to the affirmation, and not the affirmation of a contrary. If opinions are necessarily related in a similar way, i.e., in the same way, in other matter, that is, in such a way that affirmation and negation of the same thing are contraries in other matter, it would seem that what we have said about the opinions of that which is good and that which is evil is correct, i.e., that the contrary of the affirmation of that which is good is not the affirmation of evil but the negation of good. He proves this consequence when he adds: for the opposition of contradiction either holds everywhere or nowhere, i.e., in every matter one part of a contradiction must be judged contrary to its affirmation—or never, i.e., in no matter. For if there is a general art which deals with contrary opinions, contrary Opinions must be taken everywhere and in every matter in one and the same mode. Consequently, if in any matter, negation of the same thing of the same thin- is the contrary of the affirmation, then in all matter negation of the same thing of the same thing will be the contrary of the affirmation. Since he intends in his proof to conclude from the position of the antecedent, Aristotle affirms the antecedent through its cause: in matter in which there is not a contrary, such as substance and quantity, which have no contraries, as is said in the Predicamcnta [Categ. 5: 3b 24; 6: 5b 10], the one contradictorily opposed to the true opinion is per se false. For example, he who thinks that man, for instance Socrates, is not man, is per se mistaken with regard to one who thinks that Socrates is man. Then he affirms the antecedent formally and concludes directly from the position of the antecedent to the position of the consequent. If then these, namely, affirmation and negation in matter which lacks a contrary, are contraries, all other contradictions must be judged to be contraries.
Cajetanus lib. 2 l. 14 n. 15 Deinde cum dicit: amplius similiter etc., probat idem tertia ratione, quae talis est: sic se habent istae duae opiniones de bono, scilicet, bonum est bonum, et, bonum non est bonum, sicut se habent istae duae de non bono, scilicet, non bonum non est bonum, et, non bonum est bonum. Utrobique enim salvatur oppositio contradictionis. Et primae utriusque combinationis sunt verae, secundae autem falsae. Unde proponens hanc maiorem quoad primas veras utriusque combinationis ait: similiter se habet opinio boni, quoniam bonum est, et non boni quoniam non est bonum. Et subdit quoad secundas utriusque falsas: et super has opinio boni quoniam non est bonum, et non boni quoniam est bonum. Haec est maior. Sed illi verae opinioni de non bono, scilicet, non bonum non est bonum, contraria non est, non bonum est malum, nec bonum non est malum, quae sunt de praedicato contrario, sed illa, non bonum est bonum, quae est eius contradictoria; ergo et illi verae opinioni de bono, scilicet, bonum est bonum, contraria erit sua contradictoria, scilicet, bonum non est bonum, et non affirmatio contrarii, scilicet, bonum est malum. Unde subdit minorem supradictam dicens: illi ergo verae opinioni non boni, quae est dicens quoniam scilicet non bonum non est bonum, quae est contraria. Non enim est sibi contraria ea opinio, quae dicit affirmativae praedicatum contrarium, scilicet, quod non bonum est malum: quia istae duae aliquando erunt simul verae. Nunquam autem vera opinio verae contraria est. Quod autem istae duae aliquando simul sint verae, patet ex hoc quod quoddam non bonum malum est: iniustitia enim quoddam non bonum est, et malum. Quare contingeret contrarias esse simul veras: quod est impossibile. At vero nec supradictae verae opinioni contraria est illa opinio, quae est dicens praedicatum contrarium negativae, scilicet, non bonum non est malum, eadem ratione, quia simul et hae erunt verae. Chimaera enim est quoddam non bonum, de qua verum est simul dicere quod non est bona, et quod non est mala. Relinquitur ergo tertia pars minoris quod ei opinioni verae quae, est dicens quoniam non bonum non est bonum, contraria est ea opinio non boni, quae est dicens quod est bonum, quae est contradictoria illius. Deinde subdit conclusionem intentam: quare et ei opinioni boni, quae dicit bonum est bonum, contraria est ea boni opinio, quae dicit quod bonum non est bonum, idest, sua contradictoria. Contradictiones ergo contrariae in omni materia censendae sunt.	15. Then he says, Again, the opinions of that which is good, that it is good and of that which is not good, that it is not good, are parallel. This begins the third argument to prove the same thing. The two opinions of that which is good, that it is good, and that it is not good, are related in the same way as the two opinions of that which is not good, that it is not good and that it is good; i.e., the opposition of contradiction is kept in both. The first opinion of each combination is true, the second false. Hence with respect to the first true opinions of each combination he proposes this major: Again, the opinions of that which is good, that it is good, and of that which is not good, that it is not good, are parallel. With respect to the second false judgment of each combination he adds: so also are the opinions of that which is good, that it is not good, and of that which is not good, that it is good. This is the major. But the contrary of the true opinion of that which is not good, namely, the true opinion "That which is not good is not good,” is not, "That which is not good is evil,” nor "That which is not good is not evil,” which have a contrary predicate, but the opinion that that which is not good is good, which is its contradictory. Therefore, the contrary of the true opinion of that which is good, namely, the true opinion "That which is good is good,” will also be its contradictory, "That which is good is not good,” and not the affirmation of the contrary "That which is good is evil.” Hence he adds the minor which we have already stated: What, then, would be the contrary of the true opinion asserting that that which is not good is not good? The contrary of it is not the opinion which asserts the contrary predicate affirmatively, "That which is not good is evil,” because these two are sometimes at once true. But a true opinion is never contrary to a true opinion. That these two are sometimes at once true is evident from the fact that some things that are not good are evil. Take injustice; it is something not good, and it is evil. Therefore, contraries would be true at one and the same time, which is impossible. But neither is the contrary of the above true opinion the one asserting the contrary predicate negatively, "That which is not good is not evil,” and for the same reason. These will also be true at the same time. For example, a chimera is something not good, and it is true to say of it simultaneously that it is not good and that it is not evil. There remains the third part of the minor: the contrary of the true opinion that that which is not good is not good is the opinion that it is good, which is the contradictory of it. Then he concludes as he intended: the opinion that a good is not good is contrary to the opinion that a good is good, i.e., its contradictory. Therefore, it must be judged that contradictions are contraries in every matter.
Cajetanus lib. 2 l. 14 n. 16 Deinde cum dicit: manifestum est igitur etc., declarat determinatam veritatem extendi ad cuiusque quantitatis opiniones. Et quia de indefinitis, et particularibus, et singularibus iam dictum est, eo quod idem evidenter apparet de eis in hac re iudicium (indefinitae enim et particulares nisi pro eisdem supponant sicut singulares, per modum affirmationis et negationis non opponuntur, quia simul verae sunt); ideo ad eas, quae universalis quantitatis sunt se transfert, dicens, manifestum esse quod nihil interest quoad propositam quaestionem, si universaliter ponamus affirmationes. Huic enim, scilicet, universali affirmationi, contraria est universalis negatio, et non universalis affirmatio de contrario; ut opinioni quae opinatur, quoniam omne bonum est bonum, contraria est, nihil horum, quae bona sunt, idest, nullum bonum est bonum. Et declarat hoc ex quid nominis universalis affirmativae, dicens: nam eius quae est boni, quoniam bonum est, si universaliter sit bonum: idest, istius opinionis universalis, omne bonum est bonum, eadem est, idest, aequivalens, illa quae opinatur, quidquid est bonum est bonum; et consequenter sua negatio contraria est illa quam dixi, nihil horum quae bona sunt bonum est, idest, nullum bonum est bonum. Similiter autem se habet in non bono: quia affirmationi universali de non bono reddenda est negatio universalis eiusdem, sicut de bono dictum est.	16. He then says, It is evident that it will make no difference if we posit the affirmation universally, etc. Here he shows that the truth he has determined is extended to opinions of every quantity. The case has already been stated in respect to indefinites, particulars, and singulars. On this point their status is alike, for indefinites and particulars, unless they stand for the same thing, as is the case in singulars, are not opposed by way of affirmation and negation, since they are at once true. Therefore he turns his attention to those of universal quantity. It is evident, he says, that it will make no difference with respect to the proposed question if we posit the affirmations universally, for the contrary of the universal affirmative is the universal negative, and not the universal affirmation of a contrary. For example, the contrary of the opinion that everything that is good is good is the opinion that nothing that is good (i.e., no good) is good. He manifests this by the nominal definition of universal affirmative: for the opinion that that which is good is good, if the good is universal, i.e., the universal opinion "Every good is good,” is the same, i.e., is equivalent to the opinion that whatever is good is good. Consequently, its negation is the contrary I have stated, "Nothing which is good is good,” i.e., "No good is good.” The case is similar with respect to the not good. The universal negation of the not good is opposed to the universal affirmation of the not good, as we have stated with respect to the good.
Cajetanus lib. 2 l. 14 n. 17 Deinde cum dicit: quare si in opinione sic se habet etc., revertitur ad respondendum quaestioni primo motae, terminata iam secunda, ex qua illa dependet. Et circa hoc duo facit: quia primo respondet quaestioni; secundo, declarat quoddam dictum in praecedenti solutione; ibi: manifestum est autem quoniam et cetera. Circa primum duo facit. Primo, directe respondet quaestioni, dicens: quare si in opinione sic se habet contrarietas, ut dictum est; et affirmationes et negationes quae sunt in voce, notae sunt eorum, idest, affirmationum et negationum quae sunt in anima; manifestum est quoniam affirmationi, idest, enunciationi affirmativae, contraria erit negatio circa idem, idest, enunciatio negativa eiusdem de eodem, et non enunciatio affirmativa contrarii. Et sic patet responsio ad primam quaestionem, qua quaerebatur, an enunciationi affirmativae contraria sit sua negativa, an affirmativa contraria. Responsum est enim quod negativa est contraria. Secundo, dividit negationem contrariam affirmationi, idest, negationem universalem et contradictoriam, dicens: universalis, scilicet, negatio, affirmationi contraria est et cetera. Ut exemplariter dicatur, ei enunciationi universali affirmativae quae est, omne bonum est bonum, vel, omnis homo est bonus, contraria est universalis negativa, ea scilicet, nullum bonum est bonum, vel, nullus homo est bonus: singula singulis referendo. Contradictoria autem negatio, contraria illi universali affirmationi est, aut, non omnis homo est bonus, aut, non omne bonum est bonum, singulis singula similiter referendo. Et sic posuit utrunque divisionis membrum, et declaravit.	17. Then he says, If, therefore, this is the case with respect to opinion, and. affirmations and negations in vocal sound are signs of those in the soul, etc. With this he returns to the question first advanced, to reply to it, for he has now completed the second on which the first depends. He first replies to the question, then manifests a point in the solution of a preceding difficulty where he says, It is evident, too, that true cannot be contrary to true, either in opinion or in contradiction, etc. First, then, he replies directly to the question: If, therefore, contrariety is such in the case of opinions, and affirmations and negations in vocal sound are signs of affirmations and negations in the soul, it is evident that the contrary of the affirmation, i.e., of the affirmative, enunciation, is the negation of the same subject. In other words, the negative enunciation of the same predicate of the same subject will be the contrary, and not the affirmative enunciation of a contrary. Thus the response to the first question—whether the contrary of the affirmative enunciation is its negative or the contrary affirmative—is clear. The answer is that the negative is the contrary. Next, he divides negation as it is contrary to affirmation, i.e., into the universal negation, and the contradictory: The universal, i.e., negation, is contrary to the affirmation, etc. In order to state this division by way of example he relates one enunciation to one enunciation: the contrary of the universal affirmative enunciation "Every good is’ good” or "Every man is good,” is the universal negative "No good is good” or "No man is good.” Again, relating one to one, he says that the contradictory negation contrary to the universal affirmation is "Not every man is good” or "Not everything good is good.” Thus he posits both members of the division and makes the division evident.
Cajetanus lib. 2 l. 14 n. 18 Sed est hic dubitatio non dissimulanda. Si enim affirmationi universali contraria est duplex negatio, universalis scilicet et contradictoria, vel uni duo sunt contraria, vel contrarietate large utitur Aristoteles: cuius oppositum supra declaravimus. Augetur et dubitatio: quia in praecedenti textu dixit Aristoteles quod, nihil interest si universalem negationem faciamus ita contrariam universali affirmationi, sicut singularem singulari. Et ita declinari non potest quin affirmationi universali duae sint negationes contrariae, eo modo quo hic loquitur de contrarietate Aristoteles.	18. A difficulty arises at this point which we cannot disregard. If the contrary of the universal affirmative is a twofold negation, namely, the universal and the contradictory, either there are two contraries to one affirmation or Aristotle is using contrariety in a broad sense, although we showed that this was not the case apropos of an earlier passage of the text. The difficulty is augmented by the fact that Aristotle said in the passage immediately preceding that it makes no difference if we take the universal negation as contrary to the universal affirmation, i.e., as one of its negations. Hence, the conclusion cannot be avoided that in the mode in which Aristotle speaks of contrariety here, there are two contrary negations to the universal affirmative.
Cajetanus lib. 2 l. 14 n. 19 Ad huius evidentiam notandum est quod, aliud est loqui de contrarietate quae est inter negationem alicuius universalis affirmativae in ordine ad affirmationem contrarii de eodem, et aliud est loqui de illamet universali negativa in ordine ad negationem eiusdem affirmativae contradictoriam. Verbi gratia: sint quatuor enunciationes, quarum nunc meminimus, scilicet, universalis affirmativa, contradictoria, universalis negativa, et universalis affirmatio contrarii, sic dispositae in eadem linea recta: omnis homo est iustus, non omnis homo est iustus, omnis homo non est iustus, omnis homo est iniustus: et intuere quod licet primae omnes reliquae aliquo modo contrarientur, magna tamen differentia est inter primae et cuiusque earum contrarietatem. Ultima enim, scilicet affirmatio contrarii, primae contrariatur ratione universalis negationis, quae ante ipsam sita est: quia non per se sed ratione illius falsa est, ut probavit Aristoteles, quia implicita est. Tertia autem, idest universalis negatio, non per se sed ratione secundae, scilicet negationis contradictoriae, contrariatur primae eadem ratione, quia, scilicet, non est per se falsa illius affirmationis veritate, sed implicita: continet enim negationem contradictoriam, scilicet, non omnis homo est iustus, mediante qua falsificatur ab affirmationis veritate, quia simpliciter et prior est falsitas negationis contradictoriae falsitate negationis universalis: totum namque compositius et posterius est partibus. Est ergo inter has tres falsas ordo, ita quod affirmationi verae contradictoria negatio simpliciter sola est contraria, quia est simpliciter respectu illius per se falsa; affirmativa autem contrarii est per accidens contraria, quia est per accidens falsa; universalis vero negatio, tamquam medium sapiens utriusque extremi naturam, relata ad contrarii affirmationem est per se contraria et per se falsa, relata autem ad negationem contradictoriam est per accidens falsa et contraria. Sicut rubrum ad nigrum est album, et ad album est nigrum, ut dicitur in V physicorum. Aliud igitur est loqui de negatione universali in ordine ad affirmationem contrarii, et aliud in ordine ad negationem contradictoriam. Si enim primo modo loquamur, sic negatio universalis per se contraria et per se falsa est; si autem secundo modo, non est per se falsa, nec contraria affirmationi.	19. To clear up this difficulty we must note that it is one thing to speak of the contrariety there is between the negation of some universal affirmative in relation to the affirmation of a contrary, and another to speak of that same universal negative in relation to the negation contradictory to the same affirmative. For example, the four enunciations of which we are now speaking are the universal affirmative, the contradictory, the universal negative, and the universal affirmation of a contrary: "Every man is just,” "Not every man is just,” "No man is just,” "Every man is unjust.” Notice that although all the rest are contrary to the first in some way, there is a great difference between the contrariety of each to the first. The last one, the affirmation of a contrary, is contrary to the first by reason of the preceding universal negation, for it is false, not per se but by reason of that negation, i.e., it is implicative, as Aristotle has already proved. The third, the universal negation, is not per se contrary to the first either. It is contrary by reason of the second, the contradictory negation, and for the same reason, i.e., it is not per se false in respect to the truth of the affirmation but is implicative, for it contains the contradictory negation "Not every man is just,” by means of which it is made false in respect to the truth of the affirmation. The reason for this is that the falsity of the contradictory negation is prior absolutely to the falsity of the universal negation, for the whole is more composite and posterior as compared to its parts. There is, therefore, an order among these three false enunciations. Only the contradictory negation is simply contrary to the true affirmation, for it is per se false simply in respect to the affirmation; the affirmative of the contrary is per accidens contrary, since it is per accidens false; the universal negation, which is a medium partaking of the nature of each extreme, is per se contrary and per se false as related to the affirmation of a contrary, but is per accidens false and per accidens contrary as related to the contradictory negation; just as red in a motion from red to black takes the place of white, and in a motion from red to white takes the place of black, as is said in V Physicorum [5: 229b 15]. Therefore, it is one thing to speak of the universal negation in relation to affirmation of a contrary and another to speak of it in relation to the contradictory negation. If we are speaking of it in the first way, the universal negation is per se contrary and per se false; if in the second, it is not per se false or contrary to the affirmation.
Cajetanus lib. 2 l. 14 n. 20 Quia ergo agitur ab Aristotele nunc quaestio, inter affirmationem contrarii et negationem quae earum contraria sit affirmationi verae, et non agitur quaestio ipsarum negationum inter se, quae, scilicet, earum contraria sit illi affirmationi, ut patet in toto processu quaestionis; ideo Aristoteles indistincte dixit quod utraque negatio est contraria affirmationi verae, et non affirmatio contrarii. Intendens per hoc declarare diversitatem quae est inter affirmationem contrarii et negationem in hoc quod verae affirmationi contrariantur, et non intendens dicere quod utraque negatio est simpliciter contraria. Hoc enim in dubitatione non est quaesitum, sed illud tantum. Et similiter dixit quod nihil interest si quis ponat negationem universalem: nihil enim interest quoad hoc, quod affirmatio contrarii ostendatur non contraria affirmationi verae, quod inquirimus. Plurimum autem interesset, si negationes ipsas inter se discutere vellemus quae earum esset affirmationi contraria. Sic ergo patet quod subtilissime Aristoteles locutus de vera contrarietate enunciationum, unam uni contrariam posuit in omni materia et quantitate, dum simpliciter contrarias contradictiones asseruit.	20. Since Aristotle is now treating the question as to which is the contrary of a true affirmation, affirmation of a contrary or the negation, and not the question as to which of the negations is contrary to a true affirmation—as is clear in the whole progression of the question—bis answer is that both negations are contrary to the true affirmation without distinction, and that affirmation of a contrary is not. His intention is to manifest the diversity between the negation, and the affirmation of a contrary, inasmuch as they are contrary to a true affirmation. He does not intend to say that both negations are contrary simply, for this is not the difficulty in question here, but the former is. With respect to his saying that it makes no difference if we posit the universal negation, the same point applies, for in regard to showing that affirmation of a contrary is not contrary to a true affirmation, which is the question at issue here, it makes no difference which negation is posited. It would make a great deal of difference, however, if we wished to discuss which negation was contrary to a true affirmation. It is evident, then, that Aristotle’s discussion of the true contrariety of enunciations is very subtle, for he has posited one to one contraries in every matter and quantity, and affirmed that contradictions are contraries simply.
Cajetanus lib. 2 l. 14 n. 21 Deinde cum dicit: manifestum est autem etc., resumit quoddam dictum ut probet illud, dicens manifestum est autem ex dicendis quod non contingit veram verae contrariam esse, nec in opinione mentali, nec in contradictione, idest, vocali enunciatione. Et causam subdit: quia contraria sunt quae circa idem opposita sunt; et consequenter enunciationes et opiniones verae circa diversa contrariae esse non possunt. Circa idem autem contingit simul omnes veras enunciationes et opiniones verificari, sicut et significata vel repraesentata earum simul illi insunt: aliter verae tunc non sunt. Et consequenter omnes verae enunciationes et opiniones circa idem contrariae non sunt, quia contraria non contingit eidem simul inesse. Nullum ergo verum sive sit circa idem, sive sit circa aliud, est alteri vero contrarium. Et sic finitur expositio huius libri perihermenias.	21. When he says, It is evident, too, that true cannot be contrary to true, either in opinion or in contradiction, etc., he returns to a statement he has already made in order to prove it. It is evident, too, from what has been said, that true cannot be contrary to true, either in opinion or in contradiction, i.e., in vocal enunciation. He gives as the cause of this that contraries are opposites about the same thing; consequently, true enunciations and opinions about diverse things cannot be contraries. However, it is possible for all true enunciations and opinions about the same thing to be verified at the same time, inasmuch as the things signified or represented by them belong to the same thing at the same time; otherwise they are not true. Consequently, not all true enunciations and opinions about the same thing are contraries, for it is not possible for contraries to be in the same thing at the same time. Therefore, no true opinion or enunciation, whether it is about the same thing or is about another is contrary to another.