Authors/Thomas Aquinas/metaphysics/liber9/lect10

Lecture 10

Latin	English
lib. 9 l. 10 n. 1 Postquam comparavit philosophus actum et potentiam secundum prius et posterius, hic comparat ea secundum bonum et malum; et circa hoc duo facit. Primo dicit quod in bonis, actus est melior potentia. Quod quidem manifestum est ex hoc, quod id quod est potentia, est idem in potentia existens ad contraria. Sicut quod potest convalescere, hoc potest infirmari, et simul est in potentia ad utrumque. Et hoc ideo quia eadem est potentia utriusque, convalescendi et laborandi, et quiescendi et movendi et aliorum huiusmodi oppositorum. Et ita patet quod aliquid simul potest contraria, licet contraria non possint simul esse actu. Contrariorum igitur utrumque seorsum, est hoc quidem bonum, ut sanum, aliud vero malum, ut infirmum. Nam semper in contrariis unum est ut deficiens, quod ad malum pertinet.	1883. Having compared actuality and potency from the viewpoint of priority and posteriority, the Philosopher now compares them from the viewpoint of good and evil; and in regard to this he does two things. First, he says that in the case of good things actuality is better than potency; and this was made clear from the fact that the potential is the same as what is capable of contrary determinations; for example, what can be well can also be ill and is in potency to both at the same time. The reason is that the potency for both is the same—for being well and ailing, and for being at rest and in motion, and for other opposites of this kind. Thus it is evident that a thing can be in potency to contrary determinations, although contrary determinations cannot be actual at the same time. Therefore, taking each contrary pair separately, one is good, as health, and the other evil, as illness. For in the case of contraries one of the two always has the character of something defective, and this pertains to evil.
lib. 9 l. 10 n. 2 Sic igitur quod est bonum in actu, est tantum bonum. Sed potentia se habet similiter ad utrumque, scilicet secundum quid; quod est esse in potentia. Habet autem neutrum simpliciter, quod est esse in actu. Relinquitur igitur quod actus est melior potentia; quia quod est simpliciter et pure bonum, est melius eo quod est secundum quid bonum, et coniunctum malo.	1884. Therefore what is actually good is good alone. But the potency may be related “to both” alike, i.e., in a qualified sense—as being in potency. But it is neither in an absolute sense—as being actual. It follows, then, that actuality is better than potency; because what is good in an absolute sense is better than what is good in a qualified sense and is connected with evil.
lib. 9 l. 10 n. 3 Secundo ibi, necesse autem ostendit quod e contrario in malis est actus peior potentia: et circa hoc tria facit. Primo ostendit propositum ex ratione supra inducta; quia id quod est simpliciter malum, et non secundum quid se habens ad malum, est peius eo quod est secundum quid malum, et quod se habet ad malum et ad bonum. Unde, cum potentia ad malum nondum habeat malum nisi secundum quid (et eadem est ad bonum, nam idem est potentia quod est ad contraria), relinquitur quod actus malus est peior potentia ad malum.	1885. And also (802). Second, he shows on the other hand that in the case of evil things the actuality is worse than the potency; and in regard to this he does three things. First, he proves his thesis by the argument introduced above; for what is evil in an absolute sense and is not disposed to evil in a qualified sense is worse than what is evil in a qualified sense and is disposed both to evil and to good. Hence, since the potency for evil is not yet evil, except in a qualified sense (and the same potency is disposed to good, since it is the same potency which is related to contrary determinations), it follows that actual evil is worse than the potency for evil.
lib. 9 l. 10 n. 4 Secundo ibi, palam ergo concludit ex dictis quod ipsum malum non est quaedam natura praeter res alias, quae secundum naturam sunt bonae. Nam ipsum malum secundum naturam est posterius quam potentia, quia est peius et magis elongatum a perfectione naturae. Unde, cum potentia non possit esse alia praeter res, multo minus ipsum malum.	1886. It is clear, then (803). Second, he concludes from what has been said that evil itself is not a nature distinct from other things which are good by nature; for evil itself is subsequent in nature to potency, because it is worse and is farther removed from perfection. Hence, since a potency cannot be something existing apart from a thing, much less can evil itself be something apart from a thing.
lib. 9 l. 10 n. 5 Tertio ibi, non ergo inducit aliam conclusionem. Si enim malum est peius potentia, potentia autem non invenitur in rebus sempiternis, ut supra ostensum est, non erit in eis aliquod malum, neque peccatum, neque alia corruptio. Nam corruptio quoddam malum est. Est hoc autem intelligendum inquantum sunt sempiterna et incorruptibilia. Nam secundum quid, nihil prohibet in eis esse corruptionem, ut secundum ubi, aut secundum aliquid huiusmodi.	1887. Hence in those (804). Third, he draws another conclusion. For if evil is worse than potency, and there is no potency in eternal things, as has been shown above (1867), then in eternal things there will be neither evil nor wrong nor any other corruption; for corruption is a kind of evil. But this must be understood insofar as they are eternal and incorruptible; for nothing prevents them from being corrupted as regards place or some other accident of this kind.
lib. 9 l. 10 n. 6 Deinde cum dicit inveniuntur autem postquam comparavit potentiam et actum secundum prius et posterius, et bonum et malum, hic comparat eadem secundum intelligentiam veri et falsi. Et circa hoc duo facit. Primo comparat ipsa secundum intelligere. Secundo vero secundum veritatem et falsitatem, ibi, quoniam vero ens. Dicit ergo primo, quod diagrammata, idest descriptiones geometriae inveniuntur, idest per inventionem cognoscuntur secundum dispositionem figurarum in actu. Geometrae enim inveniunt verum quod quaerunt, dividendo lineas et superficies. Divisio autem reducit in actum quod erat in potentia. Nam partes continui sunt potentia in toto ante divisionem. Si autem omnia essent divisa secundum quod requirit inventio veritatis, manifestae essent conclusiones quaesitae. Sed quia in prima protractione figurarum sunt in potentia huiusmodi divisiones, ideo non statim fit manifestum quod quaeritur.	1888. And it is (805). Having compared potency and actuality from the viewpoint of priority and posteriority and from that of good and evil, be now compares them with reference to the understanding of the true and the false. In regard to this he does two things. First (805:C 1888), he compares them with reference to the act of understanding; and second (806:C 1895), with reference to the true and the false (“Now the terms”). He accordingly says, first (805), that “geometrical constructions,” i.e., geometrical descriptions, “are discovered,” i.e., made known by discovery in the actual drawing of the figures. For geometers discover the truth which they seek by dividing lines and surfaces. And division brings into actual existence the things which exist potentially; for the parts of a continuous whole are in the whole potentially before division takes place. However, if all had been divided to the extent necessary for discovering the truth, the conclusions which are being sought would then be evident. But since divisions of this kind exist potentially in the first drawing of geometrical figures, the truth which is being sought does not therefore become evident immediately.
lib. 9 l. 10 n. 7 Hoc autem notificat per duo exempla: quorum primum est circa quaesitum: quare trigonum est duo recti, idest quare triangulus habet tres angulos aequales duobus rectis? Quod quidem sic demonstratur. (Figura). Sit triangulus abc, et protrahatur basis, ac in continuum et directum. Haec igitur basis protracta faciet cum latere trianguli bc, angulum in puncto c: qui quidem angulus extra existens aequalis est duobus angulis interioribus sibi oppositis, scilicet angulo abc, et angulo bac. Manifestum est autem quod duo anguli consistentes circa punctum c, quorum unus est extra triangulum, et alter intra, sunt aequales duobus rectis. Demonstratum enim est quod linea recta super aliam lineam cadens qualitercumque, faciet duos angulos rectos, aut aequales duobus rectis. Relinquitur ergo quod angulus interior in puncto c, constitutum cum aliis duobus qui sunt aequales angulo exteriori, omnes scilicet tres, sunt aequales duobus rectis.	1889. He explains this by means of two examples, and the first of these has to do with the question, “Why are the angles of a triangle equal to two right angles?” i.e., why does a triangle have three angles equal to two right angles? This is demonstrated as follows. Let ABC be a triangle having its base AC extended continuously and in a straight line. This extended base, then, together with the side BC of the triangle form an angle at point C, and this external angle is equal to the two interior angles opposite to it, i.e., angles ABC and BAC. Now it is evident that the two angles at point C, one exterior to the triangle and the other interior, are equal to two right angles; for it has been shown that, when one straight line falls upon another straight line, it makes two right angles or two angles equal to two right angles. Hence it follows that the interior angle at the point C together with the other two interior angles which are equal to the exterior angle, i.e., all three angles, are equal to two right angles.
lib. 9 l. 10 n. 8 Hoc est ergo quod philosophus dicit, quod probatur triangulum habere duos rectos, quia duo anguli qui sunt circa unum punctum, puta circa punctum c, quorum unus est interior et alius exterior, sunt aequales duobus rectis. Et ideo quando producitur angulus qui fit extra, producto uno latere trianguli, statim manifestum fit videnti dispositionem figurae, quod triangulus habet tres angulos aequales duobus rectis.	1890. This, then, is what the Philosopher means when he says that it may be demonstrated that a triangle has two right angles, because the two angles which meet at the point C, one of which is interior to the triangle and the other exterior, are equal to two right angles. Hence when an angle is constructed which falls outside of the triangle and is formed by one of its sides, it immediately becomes evident to one who sees the arrangement of the figure that a triangle has three angles equal to two right angles.
lib. 9 l. 10 n. 9 Secundum exemplum est circa hoc quaesitum: quare omnis angulus quod est in semicirculo descriptus est rectus. Quod quidem demonstratur sic. (Figura). Sit semicirculus abc, et in puncto b, qualitercumque cadat constituatur angulus: cui subtenditur basis ac quae est diameter circuli. Dico ergo quod angulus b, est rectus. Cuius probatio est, quia cum linea ac, sit diameter circuli, oportet quod transeat per centrum. Dividatur ergo per medium in puncto d, et producatur linea db. Sic igitur linea db, aequalis est lineae da, quia sunt protractae a centro usque ad circumferentiam; ergo in triangulo dba aequalis est angulus b, angulo a, quia omnis trianguli cuius duo latera sunt aequalia, anguli qui sunt supra bases, sunt aequales. Duo igitur anguli, a et b, sunt duplum solius anguli b. Sed angulus bdc cum sit exterior, est aequalis duobus angulis a et b partialibus: ergo angulus bdc est duplus anguli b partialis.	1891. The second example has to do with the question, “Why is every angle in a semicircle a right angle?” This is demonstrated as follows. Let ABC be a semicircle, and at any point B let there be an angle subtended by the base AC, which is the diameter of the circle. I say, then, that angle B is a right angle. This is proved as follows: since the line AC is the diameter of the circle, it must pass through the center. Hence it is divided in the middle at the point D, and this is done by the line DB. Therefore the line DB is equal to the line DA, because both are drawn from the center to the circumference. In the triangle DBA, then, angle B and angle A are equal, because in every triangle having two equal sides the angles above the base are equal. Thus the two angles A and B are double the angle B alone. But the angle BDC, since it is exterior to the triangle, is equal to the two separate angles A and B. Therefore angle BDC is double the angle B alone.
lib. 9 l. 10 n. 10 Et similiter probatur quod angulus c est aequalis angulo b trianguli bdc; eo quod duo latera db et dc sunt aequalia cum sint protracta a centro ad circumferentiam, et angulus exterior, scilicet adb, est aequalis utrique: ergo est duplus anguli b partialis. Sic ergo duo anguli adb et bdc sunt duplum totius anguli abc. Sed duo anguli adb et bdc sunt aut recti aut aequales duobus rectis, quia linea db cadit supra lineam ac: ergo angulus abc qui est in semicirculo, est rectus.	1892. And it is demonstrated in the same way that angle C is equal to angle B of the triangle BDC, because the two sides DB and DC are equal since they are drawn from the center to the circumference, and the exterior angle, ADB, is equal to both. Therefore it is double the angle B alone. Hence the two angles ADB and BDC are double the whole angle ABC. But the two angles ADB and BDC are either right angles or equal to two right angles, because the line DB falls on the line AC. Hence the angle ABC, which is in a semicircle, is a right angle.
lib. 9 l. 10 n. 11 Et hoc est quod philosophus dicit, quod ideo demonstratur esse rectus ille qui est in semicirculo, quia tres lineae sunt aequales: scilicet duae in quas dividitur basis, scilicet da et dc, et tertia quae ex media istarum duarum protracta superstat utrique, scilicet bd. Et hanc dispositionem videnti, statim manifestum est scienti principia geometriae, quod omnis angulus in semicirculo est rectus.	1893. This is what the Philosopher means when he says that the angle in a semicircle may be shown to be a right angle, because the three lines are equal, namely, the two into which the base is divided, i.e., DA and DC, and the third line, BD, which is drawn from the middle of these two lines and rests upon these. And it is immediately evident to one who sees this construction, and who knows the principles of geometry, that every angle in a semicircle is a right angle.
lib. 9 l. 10 n. 12 Sic igitur concludit philosophus manifestum esse, quod quando aliqua reducuntur de potentia in actum, tunc invenitur earum veritas. Et huius causa est, quia intellectus actus est. Et ideo ea quae intelliguntur, oportet esse actu. Propter quod, ex actu cognoscitur potentia. Unde facientes aliquid actu cognoscunt, sicut patet in praedictis descriptionibus. Oportet enim quod in eodem secundum numerum, posterius secundum ordinem generationis et temporis sit actus quam potentia, ut supra expositum est.	1894. Therefore the Philosopher concludes that it has been shown that, when some things are brought from potency to actuality, their truth is then discovered. The reason for this is that understanding is an actuality, and therefore those things which are understood must be actual. And for this reason potency is known by actuality. Hence it is by making something actual that men attain knowledge, as is evident in the constructions described above. For in numerically one and the same thing actuality must be subsequent to potency in generation and in time, as has been shown above.