Authors/Thomas Aquinas/metaphysics/liber10/lect7

Lecture 7

Latin	English
lib. 10 l. 7 n. 1 Postquam philosophus ostendit quid est contrarietas, hic determinat quasdam dubitationes circa praedeterminata; et circa hoc duo facit. Primo movet dubitationes. Secundo prosequitur eas, ibi, utrum enim semper in oppositione dicimus et cetera. Oriuntur autem dubitationes ex hoc quod supra dictum est, quod unum uni contrarium est. Quod quidem in duplici oppositione fallere videtur. Nam unum et multa opponuntur, cum tamen et multis opponantur pauca. Similiter autem et aequale videtur opponi duobus, scilicet magno et parvo. Unde relinquitur dubitatio quomodo praedicta opponuntur. Si enim opponantur secundum contrarietatem, videtur falsum esse quod dictum est, quod unum uni contrarium est.	2059. After having shown what contrariety is, here the Philosopher settles certain difficulties concerning the points established above. In regard to this he does two things. First (857)C 2059), he raises the difficulties; and second (858:C 2060), he solves them (“For we always”). Now the difficulties (857) stem from the statement that one thing has one contrary; and this appears to be wrong in the case of a twofold opposition. For while the many are opposed to the one the few are opposed to the many. And similarly the equal also seems to be opposed to two things, namely, to the large and to the small. Hence the difficulty arises as to how these things are opposed. For if they are opposed according to contrariety, then the statement which was made seems to be false, namely, that one thing has one contrary.
lib. 10 l. 7 n. 2 Deinde cum dicit utrum enim prosequitur praedictas dubitationes; et primo dubitationem aequalis ad magnum et parvum. Secundo prosequitur dubitationem de oppositione unius ad multa, ibi, similiter autem et de uno et de multis et cetera. Circa primum duo facit. Primo disputat quaestionem. Secundo veritatem determinat quaestionis, ibi, restat igitur aut ut negationem opponi. Et circa primum duo facit. Primo obiicit ad ostendendum aequale esse contrarium magno et parvo. Secundo obiicit ad oppositum, ibi, sed accidit unum et cetera. Circa primum tres ponit rationes. In prima quarum duo facit. Primo manifestat quoddam ex quo ratio procedit; dicens, quod hac dictione, utrum, semper utimur in oppositis. Ut cum quaerimus utrum aliquid sit album aut nigrum, quae sunt opposita secundum contrarietatem; et utrum sit album aut non album, quae sunt opposita secundum contradictionem. Sed utrum aliquid sit homo aut album non dicimus, nisi ex hac suppositione, quod non possit aliquid esse album et homo. Et sic quaerimus, utrum sit album vel homo, sicut quaerimus utrum veniat Cleon aut Socrates, supponentes quod non ambo simul veniant. Sed hic modus quaerendi in his quae non sunt opposita, in nullo genere est secundum necessitatem, sed solum secundum suppositionem. Et hoc ideo, quia hac dictione, utrum, utimur solum in oppositis ex necessitate; in aliis autem ex suppositione tantum, quia sola opposita ex natura non contingit simul existere. Et hoc, scilicet si non simul sit verum utrumque quo utitur qui quaerit, utrum veniat Socrates aut Cleon; quia si contingeret eos simul venire, derisoria esset interrogatio. Et si ita est quod simul non contingat eos venire, incidet praedicta quaestio in oppositione quae est inter unum et multa. Oportet enim quaerere de Socrate et Cleone, utrum ambo veniant, vel alter tantum. Quae quidem quaestio est secundum oppositionem unius ad multa. Et supposito quod alter veniat, tunc demum habet locum quaestio, utrum veniat Socrates aut Cleon.	2060. For we always (858). Then he deals with the foregoing difficulties; and, first, he examines the difficulty about the opposition between the equal and the large and the small. Second (868:C 2075), he discusses the difficulty about the opposition between the one and the many (“And one might”). In regard to the first he does two things. First, he argues the question dialectically. Second (864:C 2066), he establishes the truth about this question (“It follows”). In regard to the first he does two things. First, he argues on one side of the question in order to show that the equal is contrary to the large and to the small. Second (862:C 2064), he argues on the opposite side of the question (“But it follows”). In regard to the first he gives three arguments. In the first of these he does two things. First, he clarifies a presupposition of the argument by stating that we always use the term whether in reference to opposites; for example, when we ask whether a thing is white or black, which are opposed as contraries; and whether it is white or not white, which are opposed as contradictories. But we do not ask whether a thing is a man or white, unless we assume that something cannot be both a man and white. We then ask whether it is a man or white, just as we ask whether that is Cleon or Socrates coming, on the assumption that both are not coming at the same time. But this manner of asking about things which are not opposites does not pertain to any class of things by necessity but only by supposition. This is so because we use the term whether only of opposites by necessity, but of other things only by supposition; for only things which are opposed by nature are incapable of coexisting. And this is undoubtedly true if each part of the disjunction “whether Socrates or Cleon is coming” is not true at the same time, because, if it were possible that both of them might be coming at the same time, the above question would be absurd. And if it is true that both cannot be coming at the same time, then the above question involves the opposition between the one and the many. For it is necessary to ask whether Socrates and Cleon are both coming or only one of them. And this question involves the opposition between the one and the many. And if it is assumed that one of them is coming, then the question takes the form, whether Socrates or Cleon is coming.
lib. 10 l. 7 n. 3 Deinde cum dicit si itaque ex propositione iam manifesta argumentatur hoc modo. Hac particula, utrum, interrogantes, in oppositis semper utimur, ut supra dictum est. Sed utimur hac particula in aequali, magno et parvo. Quaerimus enim utrum hoc illo sit maius, aut minus, aut aequale. Est ergo aliqua oppositio aequalis ad magnum et parvum. Sed non potest dici, quod alterum horum sit contrarium magno vel parvo; quia nulla ratio est quare magis sit contrarium magno quam parvo. Nec iterum secundum praedicta videtur quod ambobus sit contrarium, quia unum uni est contrarium.	2061. If, then, the question (859). From the proposition which has now been made clear the argument proceeds as follows: those who ask questions concerning opposites use the term whether, as has been mentioned above. But we use this term in the case of the equal, the large and the small; for we ask whether one thing is more or less than or equal to another. Hence there is some kind of opposition between the equal and the large and the small. But it cannot. be said that the equal is contrary to either the large or the small, because there is no reason why it should be contrary to the large rather than to the small. And again, according to what has been said before, it does not seem that it is contrary to both, because one thing has one contrary.
lib. 10 l. 7 n. 4 Secundam rationem ponit ibi, amplius quae talis est. Aequale est contrarium inaequali. Sed inaequale significat aliquid inesse ambobus, scilicet magno et parvo; ergo aequale est contrarium ambobus.	2062. Again, the equal (860). He now gives the second argument, which runs thus: the equal is contrary to the unequal. But the unequal signifies something belonging to both the large and the small. Therefore the equal is contrary to both.
lib. 10 l. 7 n. 5 Tertiam rationem ponit ibi, et dubitatio quae procedit ex opinione Pythagorae, qui attribuebat inaequalitatem et alteritatem dualitatibus et numero pari, identitatem vero numero impari. Et est ratio talis. Aequale opponitur inaequali. Sed inaequale competit dualitatibus. Ergo aequale est contrarium duobus.	2063. And this difficulty (861). Then he gives the third argument, and this is based on the opinion of Pythagoras, who attributed inequality and otherness to the number two and to any even number, and identity to an odd number. And the reason is that the equal is opposed to the unequal; but the unequal is proper to the number two; therefore the equal is contrary to the number two.
lib. 10 l. 7 n. 6 Deinde cum dicit sed accidit obiicit in oppositum duabus rationibus: quarum prima talis est. Magnum et parvum sunt duo. Si igitur aequale est contrarium magno et parvo, unum est contrarium duobus. Quod quidem est impossibile, ut supra ostensum est.	2064. But it follows (862). Next, he gives two arguments for the opposite opinion. The first is as follows: the large and the small are two things. Therefore, if the equal is contrary to the large and to the small, one is contrary to two. This is impossible, as has been shown above (861:C 2o63).
lib. 10 l. 7 n. 7 Secundam rationem ponit ibi, amplius aequale quae talis est. Non est contrarietas medii ad extrema. Quod quidem et secundum sensum apparet, et ex definitione contrarietatis manifestatur, quia contrarietas perfecta est distantia. Quod autem est medium duorum aliquorum, non est perfecte distans ab altero eorum, quia extrema magis differunt ab invicem quam a medio. Et sic relinquitur quod contrarietas non est mediorum ad extrema; sed magis contrarietas est eorum quae habent inter se aliquod medium. Aequale autem videtur esse medium magni et parvi. Non igitur aequale est contrarium magno et parvo.	2065. Further, the equal (863). He now gives the second argument, which runs thus: there is no contrariety between an intermediate and its extremes. This is apparent to the senses, and it is also made clear from the definition of contrariety, because it is complete difference. But whatever is intermediate between any two things is not completely different from either of them, because extremes differ from each other more than from an intermediate. Thus it follows that there is no contrariety between an intermediate and its extremes. But contrariety pertains rather to things which have some intermediate between them. Now the equal seems to be the intermediate between the large and the small. Therefore the equal is not contrary to the large and to the small. Equal, large, small
lib. 10 l. 7 n. 8 Deinde cum dicit restat igitur determinat veritatem quaestionis. Et circa hoc tria facit. Primo ostendit aequale opponi magno et parvo, alio modo quam secundum contrarietatem, concludens hoc ex rationibus supra positis ad utramque partem. Nam primae rationes ostenderunt quod aequale opponitur magno et parvo. Secundae autem quod non est contrarium eis. Restat igitur quod opponatur eis alio modo oppositionis. Et remota ratione oppositionis secundum quam aequale dicitur ad inaequale, non ad magnum et parvum, restat quod aequale opponatur magno et parvo, aut sicut negatio eorum aut sicut privatio.	2066. It follows, then (864). Here he establishes the truth about this question; and in regard to this he does three things. First, he shows that the equal is opposed to the large and to the small in a way different from that of contrariety; and he draws this conclusion from the arguments given above on each side of the question. For the first set of arguments showed that the equal is opposed to the large and to the small, whereas the second showed that it is not contrary to them. It follows, then, that it is opposed to them by some other type of opposition. And after having rejected the type of opposition according to which the equal is referred to the unequal but not to the large and the small, it follows that the equal is opposed to the large and to the small either (1) as their negation or (2) as their privation.
lib. 10 l. 7 n. 9 Et quod altero istorum modorum opponatur utrique eorum, et non alteri tantum, ostendit dupliciter. Primo quidem, quia non est ratio quare aequale sit magis negatio aut privatio magni quam parvi, aut e converso. Unde oportet quod sit negatio aut privatio amborum.	2067. He shows in two ways that in the latter type of opposition the equal is opposed to both of the others (the large and the small) and not merely to one of them. First, he says that there is no reason why the equal should be the negation or the privation of the large rather than of the small, or vice versa. Hence it must be the negation or the privation of both.
lib. 10 l. 7 n. 10 Item ostendit hoc per signum. Quia enim aequale opponitur utrique, propter hoc utimur hac particula utrum, interrogantes de aequali per comparationem ad ambo, et non ad alterum tantum. Non enim quaerimus utrum hoc illo sit maius vel aequale, aut aequale vel minus. Sed semper ponimus tria; scilicet utrum sit maius aut minus aut aequale.	2068. He also makes this clear by an example, saying that, since the equal is opposed to both, then when we are making inquiries about the equal we use the term whether of both and not merely of one; for we do not ask whether one thing is more than or equal to another, or whether it is equal to or less than another. But we always give three alternatives, namely, whether it is more than or less than or equal to it.
lib. 10 l. 7 n. 11 Secundo ibi, non autem ostendit determinate, quo genere opponatur aequale magno et parvo; dicens, quod haec particula non, quae includitur in ratione aequalis, cum dicimus aequale esse quod nec est maius neque minus, non est negatio simpliciter, sed ex necessitate est privatio. Negatio enim absolute, de quolibet dicitur cui non inest sua opposita affirmatio. Quod non accidit in proposito. Non enim esse dicimus aequale omne id quod non est maius, aut minus; sed solum hoc dicimus in illis, in quibus aptum natum est esse maius aut minus.	2069. But it is not necessarily (865). Second, he indicates the type of opposition by which the equal is opposed to the large and to the small. He says that the particle not, which is contained in the notion of the equal when we say that the equal is what is neither more nor less, does not designate a (~) negation pure and simple but necessarily designates a (+) privation; for a negation pure and simple refers to anything to which its own opposite affirmation does not apply; and this does not occur in the case proposed. For we do not say that everything which is not more or less is equal, but we say this only of those things which are capable of being more or less.
lib. 10 l. 7 n. 12 Haec est igitur ratio aequalis, quod aequale est quod nec magnum nec parvum est, aptum tamen natum est esse aut magnum aut parvum, sicut aliae privationes definiuntur. Et ita manifestum est quod aequale opponitur ambobus, scilicet magno et parvo, ut negatio privativa.	2070. Hence the notion of equality amounts to this, that the equal is what is neither (~) large nor (~) small, but is (+) naturally capable of being either large or small, just as other privations are defined. Thus it is evident that the equal is opposed to both the large and the small as a privative negation.
lib. 10 l. 7 n. 13 Tertio concludendo ibi, quapropter et ostendit, quod aequale est medium magni et parvi. Et circa hoc duo facit. Primo concludit ex dictis propositum. Cum enim dictum sit, quod aequale est quod nec magnum nec parvum est, aptum tamen natum est esse aut hoc aut illud; quod autem hoc modo se habet ad contraria, medium est inter ea: sicut quod nec malum nec bonum est, opponitur ambobus, et est medium inter bonum et malum. Unde sequitur, quod aequale sit medium inter magnum et parvum. Sed haec est differentia inter utrumque: quia quod nec magnum nec parvum est, est nominatum. Dicitur enim aequale. Sed quod nec bonum nec malum est, innominatum est.	2071. Third, in concluding his discussion, he shows that the equal is intermediate between the large and the small. In regard to this he does two things. First, he draws his thesis as the conclusion of the foregoing argument. For since it has been said that the equal is what is neither large nor small but is naturally capable of being the one or the other, then anything that is related to contraries in this way is intermediate between them, just as what is neither good nor evil is opposed to both and is intermediate between them. Hence it follows that the equal is intermediate between the large and the small. But there is this difference between the two cases: what is neither large nor small has a name, for it is called the equal, whereas what is neither good nor evil does not have a name.
lib. 10 l. 7 n. 14 Et ratio huius est, quia quandoque ambae privationes duorum contrariorum cadunt super aliquid unum determinatum, et tunc est unum tantum medium, et potest de facili nominari sicut aequale. Ex eo enim est aliquid nec maius nec minus, quod habet unam et eamdem quantitatem. Sed quandoque illud super quod cadunt duae privationes contrariorum dicitur multipliciter, et non est unum tantum susceptivum utriusque privationis coniunctae; et tunc non habet unum nomen, sed vel omnino remanet innominatum, sicut quod nec bonum nec malum est, quod multipliciter contingit: vel habet diversa nomina. Sicut hoc quod dicimus quod neque album neque nigrum est. Hoc enim non est aliquid unum. Sed sunt quidam colores indeterminati, in quibus praedicta negatio privativa dicitur. Necesse est enim quod id quod neque est album nec nigrum, aut esse pallidum, aut croceum, aut aliquid tale.	2072. The reason for this is that sometimes both of the privations of two contraries coincide in some one definite term; and then there is only one intermediate, and it can easily be given a name, as the equal. For by the fact that a thing has one and the same quantity it is neither more nor less. But sometimes the term under which both of the privations of the contraries fall is used in several senses, and there is not merely one subject of both of the privations taken together; and then it does not have one name but either remains completely unnamed, like what is neither good nor evil, and this occurs in a number of ways; or it has various names, like what is neither white nor black; for this is not some one thing. But there are certain undetermined colors of which the aforesaid privative negation is used; for what is neither white nor black must be either gray or yellow or some such color.
lib. 10 l. 7 n. 15 Deinde cum dicit quare non excludit secundum praedicta quorumdam irrisionem de hoc, quod id, quod nec bonum nec malum est, ponitur medium inter bonum et malum. Dicebant enim, quod pari ratione posset assignari medium inter quaecumque. Dicit ergo quod, cum dictum sit, quod oportet esse aliquod susceptivum, quod natum est esse utrumlibet extremorum in his, in quibus medium praedicto modo assignatur per abnegationem utriusque, manifestum est quod non recte increpant in assignatione huiusmodi medii, illi qui opinantur sequi quod similiter posset dici in omnibus, puta: quod calcei et manus sit medium, quod nec calceus nec manus est, quia quod nec bonum nec malum est, medium est boni et mali: quod propter hunc modum quorumlibet sit futurum aliquod medium.	2073. Hence the criticism (867). Then he rejects the criticism which some men offered against the view that what is neither good nor evil is an intermediate between good and evil. For they said that it would be possible on the same grounds to posit an intermediate between any two things whatsoever. Hence he says that, in view of the explanation that things having an intermediate by the negation of both extremes as indicated require a subject capable of being either extreme, it is clear that the doctrine of such an intermediate is unjustly criticized by those who think that the same could therefore be said in all cases (say, that between a shoe and a hand there is something which is neither a shoe nor a hand) because what is neither good nor evil is intermediate between good and evil, since for this reason there would be an intermediate between all things.
lib. 10 l. 7 n. 16 Sed hoc non est necesse accidere: quia ista coniunctio negationum quae perficit medium, est oppositorum quae habent aliquod medium, et quae sunt in una distantia, quasi unius generis extrema et cetera. Sed aliorum de quibus ipsi inducunt, sicut calcei et manus, non est talis differentia quod sint in una distantia, quia sunt in alio genere, quorum negationes simul accipiuntur. Unde non est aliquid unum quod subiiciatur huiusmodi negationibus; et sic inter talia non est accipere medium.	2074. But this is not necessarily the case, because this combination of negations which constitute an intermediate belongs to opposites having some intermediate, between which, as the extremes of one genus, there is one distance. But the other things which they adduce, such as a shoe and a hand, do not have such a difference between them that they belong to one distance; because the things of which they are the combined negations belong to a different genus. Negations of this kind, then, do not have one subject; and it is not possible to posit an intermediate between such things.