Works › On Interpretation, Books I–II
Volume 1 · pp. 431–432
Chapter III. On Those Enunciations In Which This Verb Is Is Not Placed, But Another.
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CAPUT III. De his enuntiationibus in quibus hoc verbum est, non ponitur, sed aliud.
In his autem enuntiationibus in quibus hoc verbum est non ponitur, sed aliud quodcumque verbum, ut currit, vel legit, vel ambulat, tot quoad oppositionem et consequentiam faciunt enuntiationes secundum quod dictum est (si sicut dictum est ponantur) ac si hoc verbum est adderetur, sicut est videre exemplariter, si dicatur, currit omnis homo, non currit omnis homo: quae sic sunt ordinandae, omnis homo currit, omnis homo non currit: et sic cum subjecto infinito, currit omnis non homo, non currit omnis non homo: et sic ordinentur, omnis non homo currit, omnis non homo non currit. Variatio tamen ista non debet fieri nisi ponendo negationem infinitantem ad universale quod sit in subjecto: quia cum hoc formae sit finitae et determinatae, potest infinitari: sed negatio infinitans non debet poni ad signum universale distributivum vel etiam particulare: quia illa non dicunt qualitates et formas determinatas et finitas, sed cuilibet applicabiles: et ideo quia sunt non finitae, infinitari non possunt.
Si autem quis objiciat, quod verbum in oratione non potest esse infinitum, ut dicit Boetius, et sic ista variatio non potest esse ex parte praedicati finiti, vel infiniti, Dicendum quod nec hoc dictum est, quod tanta fiat variatio sicut in praehabitis, sed quia ex parte subjecti finiti et infiniti simile est in istis et in illis. Dicunt aliqui quod si verbum resolvatur in hoc verbum est et in suum participium, tunc per omnia idem faciunt istae cum illis. Est enim idem, homo currit, et quod homo est currens. Sic ergo dicendum quod in his fit variatio ut non negatio non ad signum, sed ad universale referatur, quando est infinitans: eo quod signum distributivum non significat universale quod est formae circumscriptae et finitae, sed significat quoniam universaliter, et distribuitur universale cui adjungitur, et ideo est infinitae et circumscriptae formae, quae infinitari non potest.
Sic ergo pluralitas enuntiationum de inesse in quibus hoc verbum est est secundum vel tertium adjacens, crescit in quadraginta octo enuntiationes, quarum sedecim sunt quando hoc verbum est secundum adjacens est, et triginta duo quando est tertium adjacens: quae inter se habent oppositionem per affirmationem et negationem: et quaedam consequuntur ad quasdam, propter multiplicationem negationis et situm, diversas facientes aequipollentias, sicut cuilibet consideranti facile est videre, si in figura disponat oppositam contra oppositam, et postea oppositam uni reducat ad aequipollentiam oppositae alterius. Et ex hoc quod aliud verbum in enuntiatione ponitur, quam hoc verbum est, non surgit novus numerus enuntiationum, vel nova oppositio, vel nova consequentia, quae ex praedictis facile haberi non possit: propositiones enim facile est describere contra se invicem, et oppositas contrarie vel subcontrarie vel contradictorie sibi invicem opponere, et aequipollentes ad consequentiam adaptare per lineas ab una ad aliam tractas, in dispositione sive figura in qua describuntur.
Et sciendum quod ex situ negationis infinitantis ad signum distributivum non potest fieri enuntiationum variatio, eo quod signum infinitari non potest. Sic manifestum est cum dicitur, currit homo, non currit homo: quae subcontrariae sunt. Et similiter cum eaedem ponantur cum subjecto infinito sic, currit non homo, non currit non homo: quae etiam sunt subcontrariae. Istae ergo quatuor indefinitae ab illis quae sunt universales et contrariae non differunt, nisi quod illae universaliter sunt distributivae, et istae non sunt universaliter distributae: et non differunt ab invicem in hoc, quod istae de universali subjecto sunt, et illae non: quia tam illae quam istae conveniunt in hoc quod sunt de subjecto quod est universale.
CHAPTER III. On those enunciations in which this verb "is" is not placed, but another.
But in those enunciations in which this verb "is" is not placed, but some other verb, as "runs," or "reads," or "walks," they make as many enunciations with respect to opposition and consequence, according to what has been said, if they are posited as was said, as if this verb "is" were added. This can be seen by example, if it is said, "every man runs," "not every man runs," which are to be ordered thus: "every man runs," "every man does not run"; and so with an infinite subject, "every non-man runs," "not every non-man runs"; and so they should be ordered, "every non-man runs," "every non-man does not run." Yet this variation ought not to be made except by placing an infinitizing negation with the universal which is in the subject; because, since it is of a finite and determinate form, it can be infinitized. But an infinitizing negation ought not to be placed with a universal distributive sign, or even with a particular sign, because those do not say determinate and finite qualities and forms, but things applicable to anything; and therefore, because they are not finite, they cannot be infinitized.
But if someone objects that a verb in speech cannot be infinite, as Boethius says, and thus that this variation cannot be on the part of the finite or infinite predicate, it must be said that this was not said, that so great a variation is made as in the things treated before, but that on the part of the finite and infinite subject it is similar in these and in those. Some say that if the verb is resolved into this verb "is" and into its participle, then these do the same in all respects as those. For "man runs" and that man is running are the same. Therefore it must be said that in these a variation is made so that negation, when it is infinitizing, is not referred to the sign but to the universal, because the distributive sign does not signify the universal which belongs to a circumscribed and finite form, but signifies universally, and the universal to which it is joined is distributed; and therefore it belongs to an infinite and circumscribed form, which cannot be infinitized.
Therefore in this way the plurality of enunciations about being-in, in which this verb "is" is adjacent as second or third, grows into forty-eight enunciations, of which sixteen are when this verb "is" is adjacent as second, and thirty-two when it is adjacent as third. These have opposition among themselves through affirmation and negation; and some follow upon others, because of the multiplication and position of negation, making diverse equivalences, as it is easy for anyone considering to see, if in the figure he sets opposite against opposite, and afterwards reduces what is opposed to one to the equivalence of the opposite of another. And from the fact that another verb is placed in the enunciation than this verb "is," there does not arise a new number of enunciations, or a new opposition, or a new consequence, which cannot easily be had from the foregoing. For propositions are easy to describe against one another, and to oppose the opposed ones to one another contrarily or subcontrarily or contradictorily, and to adapt equivalents to consequence by lines drawn from one to another in the arrangement or figure in which they are described.
And it must be known that from the position of an infinitizing negation with a distributive sign no variation of enunciations can be made, since the sign cannot be infinitized. Thus it is manifest when it is said, "man runs," "man does not run": these are subcontrary. And similarly when the same are posited with an infinite subject thus, "non-man runs," "non-man does not run": these also are subcontrary. Therefore these four indefinites do not differ from those which are universal and contrary except that those are distributive universally, and these are not universally distributed; and they do not differ from each other in this, that these are about a universal subject and those are not, because both those and these agree in this, that they are about a subject which is universal.
Ex quo sequitur quod ista signa omnis, nullus, et quaecumque alia talia fuerint, non significant universale determinatae et communis formae, sed significant quoniam universaliter, et similiter particularia signa significant quoniam particulariter. In his enuntiationibus quae supra inductae sunt, signum distributivum nihil aliud significat, nisi quoniam universaliter de homine vel non homine, vel affirmat vel negat, ille qui enuntiat.
Ex quo sequitur etiam quod caetera illa quae enuntiationem variant, vel oppositionem, vel consequentiam, oportet apponi istis in quibus est aliud verbum quam hoc verbum est, quaecumque apponuntur illis in quibus hoc verbum est tertium adjacens cum subjecto et praedicato ponitur. Omnia ergo quaecumque apponuntur circa oppositiones et consequentias illarum quae sunt cum verbo est, quod est tertium adjacens, sunt etiam in his in quibus aliud verbum ponitur quam hoc verbum est.
Hoc autem adhuc probatur per hoc quod consequentiae sunt eaedem in illis in quibus est aliud verbum, et in illis in quibus ponitur hoc verbum est. Patet quod affirmatio universalis contraria est negationi universali, ut haec quae dicit quoniam omne animal est justum, contraria est isti quae dicit quoniam nullum animal est justum. De his manifestum est quod consequuntur legem contrariorum: quoniam nunquam simul erunt verae, nec possunt esse simul in eodem tempore, hoc est, ita quod simul sint in eodem tempore: illae autem quae opposita sunt, sunt ambae particulares, et ideo aliquando in contingenti materia possunt esse simul verae, ut quidam homo est justus, quidam homo non est justus: vel quoddam animal est justum, et non omne animal est justum: quia haec, non omne animal est justum, valet istam, quoddam animal non est justum. Et in talibus eam quidem quae est, nullus homo justus est, sequitur illa quae est, homo est non justus, et istam quae est, omnis homo est non justus: quia negativa et affirmativa de praedicato opposito aequipollent. Illam vero quae est, aliquis homo justus est, sequitur illa quae est opposita praecedenti, haec scilicet, non omnis homo est non justus: haec enim aequipollet illi, quidam homo est justus. Ista tamen consequentia est in his quae fiunt cum constantia subjecti, scilicet quod aliquis homo sit vel aliquod animal1. Eadem autem penitus opposita et contraria sunt et in his in quibus aliud verbum ponitur quam hoc verbum est.
### Marginal Labels - 431: Objectio. - 431: Solutio. - 431: Aliter.
From this it follows that those signs "every," "none," and whatever other such signs there are, do not signify a universal of a determinate and common form, but signify universally; and similarly particular signs signify particularly. In these enunciations which were introduced above, the distributive sign signifies nothing other than that universally about man or non-man, the one who enunciates either affirms or denies.
From this it also follows that the remaining things which vary enunciation, or opposition, or consequence, must be applied to those in which there is another verb than this verb "is," whatever are applied to those in which this verb "is" is placed as adjacent as third with subject and predicate. Therefore all things whatever which are applied around the oppositions and consequences of those which are with the verb "is," which is adjacent as third, are also in these in which another verb is placed than this verb "is."
But this is further proved by this, that the consequences are the same in those in which there is another verb and in those in which this verb "is" is placed. It is clear that a universal affirmation is contrary to a universal negation, as this which says that every animal is just is contrary to that which says that no animal is just. Concerning these it is manifest that they follow the law of contraries, because they will never be true at the same time, nor can they be together at the same time, that is, so that they are simultaneously in the same time. But those which are opposed are both particular, and therefore sometimes in contingent matter they can be true at the same time, as "some man is just," "some man is not just"; or "some animal is just," and "not every animal is just," because this, "not every animal is just," is equivalent to that, "some animal is not just." And in such things that which is "no man is just" follows that which is "man is non-just," and that which is "every man is non-just," because the negative and the affirmative about an opposite predicate are equivalent. But that which is "some man is just" follows that which is opposed to the preceding, namely this, "not every man is non-just"; for this is equivalent to that, "some man is just." Yet this consequence is in those things which are made with constancy of subject, namely that some man be or some animal1. But altogether the same opposites and contraries are also in those in which another verb is placed than this verb "is."
### Marginal Labels - 431: Objection. - 431: Solution. - 431: Otherwise.
Notes
- Note this limitation, because it is also of service to the rules placed in the preceding chapter. (Nota hanc limitationem, quia deservit etiam regulis positis in praecedenti capitulo.) ↩
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