Authors/Thomas Aquinas/metaphysics/liber10/lect8

Lecture 8

Latin	English
lib. 10 l. 8 n. 1 Postquam prosecutus est philosophus quaestionem, quae mota fuerat de oppositione aequalis ad magnum et parvum, hic prosequitur quaestionem motam de oppositione unius ad multa. Et circa hoc duo facit. Primo obiicit ad quaestionem. Secundo determinat veritatem, ibi, sed forsan multa dicuntur et cetera. Circa primum tria facit. Primo assignat rationem dubitationis; dicens, quod sicut dubitabile est de oppositione aequalis ad magnum et parvum, similiter quidem potest dubitari de uno et multis, utrum opponantur adinvicem. Et ratio dubitationis est, quia si multa absque distinctione opponantur uni, sequuntur quaedam impossibilia, nisi distinguatur de multo, sicut ipse post distinguit.	2075. Having treated the question which he had raised regarding the opposition of the equal to the large and to the small, here the Philosopher deals with the question ‘concerning the opposition of the one to the many. In regard to this he does two things. First (868)C 2075), he debates the question. Second (871:C 2080), he establishes the truth (“But perhaps”). In regard to the first he does three things. First, he gives the reason for the difficulty. He says that, just as there is a difficulty about the opposition of the equal to the large and to the small, so too the difficulty can arise whether the one and the many are opposed to each other. The reason for the difficulty is that, if the many without distinction are opposed to the one, certain impossible conclusions will follow unless one distinguishes the various senses in which the term many is used, as he does later on (871:C 2080).
lib. 10 l. 8 n. 2 Deinde cum dicit nam unum probat quod dixerat. Probat enim, quod si unum opponitur multis, quod unum sit paucum vel pauca. Et hoc duabus rationibus: quarum prima talis est. Multa opponuntur paucis. Si igitur multa opponuntur uni simpliciter sine distinctione; cum unum uni sit contrarium, sequitur quod unum sit paucum vel pauca.	2076. For one will (869). He then proves what he had said; for he shows that, if the one is opposed to the many, the one is few or a few. He does this by two arguments, of which the first is as follows. The many are opposed to the few. Now if the many are opposed to the one in an unqualified sense and without distinction, then, since one thing has one contrary, it follows that the one is few or a few.
lib. 10 l. 8 n. 3 Secunda ratio talis est. Duo sunt multa. Quod probatur ex hoc quod duplex est multiplex. Sed multa opponuntur paucis. Ergo duo opponuntur aliquibus paucis. Sed duo non possunt esse multa ad aliquid paucum, nisi ad unum. Nihil enim minus est duobus nisi unum. Sequitur igitur quod unum sit paucum.	2077. The second argument runs thus. Two things are many. This is proved by the fact that the double is multiple. But the many are opposed to the few. Therefore two are opposed to few. But two cannot be many in relation to a few except to one; for nothing is less than two except one. It follows, then, that one is a few.
lib. 10 l. 8 n. 4 Deinde cum dicit amplius si ostendit hoc esse impossibile, scilicet quod unum sit paucum. Ita enim se habent unum et paucum ad pluralitatem, sicut productum et breve ad longitudinem. Utraque enim utriusque, proprie passiones sunt. Sed omne breve est longitudo quaedam. Ergo omne paucum est pluralitas quaedam. Si ergo unum est paucum, quod necesse videtur dicere si duo sunt multa, sequitur quod unum sit quaedam pluralitas.	2078. Further, if much (870). Then he shows that this—one is a few—is impossible; for one and a few are related to plurality as the long and the short are to length; for each one of these is a property of its respective class. But any short thing is a certain length. Hence every few is a certain plurality. Therefore if one is a few, which it seems necessary to say if two are many, it follows that one is a plurality.
lib. 10 l. 8 n. 5 Et ita unum erit non solum multum, sed etiam multa. Nam omne multum est etiam multa; nisi forte hoc differat in humidis facile divisibilibus, ut sunt aqua, oleum, aer et huiusmodi, quae nominat hic continua bene terminabilia. Nam humidum est, quod bene terminatur termino alieno. In talibus enim etiam aliquid continuum dicitur multum, sicut multa aqua vel multus aer, quia propter facilitatem divisionis sunt propinqua multitudini. Sed cum horum aliquid est continuum, ita dicitur esse multum singulariter, quod non dicitur esse multa pluraliter. Sed in aliis non dicimus multum, nisi quando sunt divisa actu. Non enim si lignum sit continuum, dicimus quod sit multum, sed magnum. Divisione autem actu adveniente, non solum dicimus quod sit multum, sed quod etiam sit multa. In aliis igitur non differt dicere multum et multa, sed solum in continuo bene terminabili. Si igitur unum sit multum, sequitur quod sit multa; quod est impossibile.	2079. The one, then, will not only be much but also many; for every much is also many, unless perhaps this differs in the case of fluid things, which are easily divided, as water, oil, air and the like which he calls here an easily-bounded continuum; for fluid things are easily limited by a foreign boundary. For in such cases the continuous is also called much, as much water or much air, since they are close to plurality by reason of the ease with which they are divided. But since any part of these is continuous, that is said to be much (in the singular) which is not said to be many (in the plural). But in other cases we use the term many only when the things are actually divided; for if wood is continuous we do not say that it is many but much; but when it becomes actually divided we not only say that it is much but also many. Therefore in other cases there is no difference between saying much and many, but only in the case of an easily-bounded continuum. Hence, if one is much, it follows that it is many. This is impossible.
lib. 10 l. 8 n. 6 Deinde cum dicit sed forsan solvit propositam dubitationem. Et circa hoc duo facit. Primo ostendit quod multum non eodem modo opponitur uni et pauco. Secundo ostendit qualiter multum opponitur uni, ibi, opponitur itaque unum multis et cetera. Circa primum duo facit. Primo solvit propositam dubitationem. Secundo ex dictis excludit quemdam errorem, ibi, quapropter nec recte et cetera. Duo autem superius in obiiciendo tetigerat, ex quibus impossibile hoc sequi videbatur: scilicet quod multum sit multa, et quod multa opponantur paucis. Primo ergo manifestat primum; dicens, quod forsan in quibusdam multa dicuntur indifferenter sicut multum. Sed in quibusdam multum et multa accipiuntur ut aliquid differens; scilicet in continuo bene terminabili; sicut de una aqua continua dicimus quod est aqua multa, et non quod sunt aquae multae. Sed in his quae sunt divisa actu, quaecumque sint illa, in his indifferenter dicitur et multum et multa.	2080. But perhaps (871). Here he solves the difficulty which he had raised; and in regard to this he does two things. First, he shows that much is not opposed to one and to a few in the same way. Second (874:C 2087), he shows how the many and the one are opposed (“The one”). In regard to the first he does two things. First, he solves the proposed difficulty; and second (873:C 2084),in the light of what has been said he rejects an error (“For this reason”). And since he had touched on two points above, in the objection which he had raised, from which it would seem to follow that it is impossible for much to be many and for many to be opposed to a few, he therefore first of all makes the first point clear. He says that perhaps in some cases the term many is used with no difference from the term much. But in some cases, namely, in that of an easily-bounded continuum, much and many are taken in a different way, for example, we say of one continuous volume of water that there is much water, not many waters. And in the case of things which are actually divided, no matter what they may be, much and many are both used indifferently.
lib. 10 l. 8 n. 7 Deinde cum dicit uno quidem manifestat secundum, scilicet qualiter multa opponantur paucis; dicens, quod multa dicuntur dupliciter. Uno enim modo significant pluralitatem excedentem, vel simpliciter, vel per respectum ad aliquid. Simpliciter quidem, sicut dicimus aliqua esse multa, eo quod excedunt pluralitatem, quae solet communiter in rebus sui generis reperiri, ut si dicamus multam pluviam, quando ultra communem cursum pluit. Per respectum autem ad aliquid, ut si dicamus decem homines multos in comparatione ad tres. Et similiter paucum dicitur pluralitas habens defectum, idest deficiens a pluralitate excedente.	2081. In one sense (872). Then he explains the second point: how the many and the few are opposed. He says that the term many is used in two senses. First, it is used in the sense of a plurality of things which is excessive, either (1) in an absolute sense or in comparison with something. (a) It is used in an absolute sense when we say that some things are many because they are excessive, which is the common practice with things that belong to the same class; for example, we say much rain when the rainfall is above average. It is used in comparison with something when we say that ten men are many compared with three. And in a similar way a few means “a plurality which is deficient,” i.e., one which falls short of an excessive plurality.
lib. 10 l. 8 n. 8 Alio modo dicitur multum absolute, sicut numerus dicitur quaedam multitudo. Et sic multum opponitur tantum uni, non autem pauco. Nam multa secundum hanc significationem sunt quasi plurale eius quod dicitur unum; ut ita dicamus unum et multa, ac si diceremus unum et una pluraliter, sicut dicimus album et alba, et sicut mensurata dicuntur ad mensurabile. Nam multa mensurantur per unum, ut infra dicetur. Et secundum hanc significationem, a multis dicuntur multiplicia. Manifestum est enim quod secundum quemlibet numerum dicitur aliquid multipliciter; sicut a binario, duplum, et ternario triplum, et sic de aliis. Unusquisque enim numerus est multa hoc modo, quia refertur ad unum, et quia quodlibet mensurabile est uno. Et hoc, secundum quod multa opponuntur uni, non autem secundum quod opponuntur pauco.	2082. (b) The term much is used in an absolute sense in a second way when a number is said to be a plurality; and in this way many is opposed only (+) to one, but not (~) to a few. For many in this sense is the plural of the word one; and so we say one and many, the equivalent of saying one and ones, as we say white and whites, and as things measured are referred to what is able to measure. For the many are measured by one, as is said below (2087). And in this sense multiples are derived from many. For it is evident that a thing is said to be multiple in terms of any number; for example, in terms of the number two it is double, and in terms of the number three it is triple, and so on. For any number is many in this way, because It is referred to one, and because anything is measurable by one. This happens insofar as many is opposed to one, but not insofar as it is opposed to few.
lib. 10 l. 8 n. 9 Unde et ipsa duo quae sunt numerus quidam, sunt multa secundum quod multa opponuntur uni. Sed secundum quod multa significant pluralitatem excedentem, duo non sunt multa, sed sunt pauca. Nihil enim est paucius duobus, quia unum non est paucum, ut supra probatum est. Paucitas enim est pluralitas habens defectum. Prima vero pluralitas habens defectum est dualitas. Unde dualitas est prima paucitas.	2083. Hence two things, which are a number, are many insofar as many is opposed to one; but insofar as many signifies an excessive plurality, two things are not many but few; for nothing is fewer than two, because one is not few, as has been shown above (2078). For few is a plurality which has some deficiency. But the primary plurality which is deficient is two. Hence two is the first few.
lib. 10 l. 8 n. 10 Deinde cum dicit quapropter non excludit, secundum praedicta, quemdam errorem. Sciendum est enim, quod Anaxagoras posuit generationem rerum fieri per extractionem. Unde posuit a principio omnia existere simul in quodam mixto, sed intellectus incepit segregare ab illo mixto singulas res, et haec est rerum generatio. Et quia generatio, secundum eum, est in infinitum, ideo posuit quod res in illo mixto existentes infinitatem habeant. Dixit igitur quod ante distinctionem rerum omnes res essent simul, infinitae quidem et pluralitate et parvitate.	2084. For this reason (873). In the light of what has been said he now rejects an error. For it should be noted that Anaxagoras claimed that the generation of things is a result of separation. Hence he posited that in the beginning all things were together in a kind of mixture, but that mind began to separate individual things from that mixture, and that this constitutes the generation of things. And since, according to him, the process of generation is infinite, he therefore claimed that there are an infinite number of things in that mixture. Hence he said that before all things were differentiated they were together, unlimited both in plurality and in smallness.
lib. 10 l. 8 n. 11 Et quod quidem infinitum in parvitate et pluralitate posuit, recte dictum est; quia in quantitatibus continuis invenitur infinitum per divisionem; quam quidem infinitatem significavit per parvitatem. In quantitatibus autem discretis invenitur infinitum per additionem, quam quidem significavit per pluralitatem.	2085. And the claims which he made about the infinite in respect to its plurality and smallness are true, because the infinite is found in continuous quantities by way of division, and this infinity he signified by the phrase in smallness. But the infinite is found in discrete quantities by way of addition, which he signified by the phrase in plurality.
lib. 10 l. 8 n. 12 Cum igitur hic recte dixisset, destitit ab hoc suo dicto non recte. Visum enim fuit ei postmodum quod loco eius quod dixit parvitatem, debuit dicere et paucitatem. Quae quidem correptio, ideo non recta fuit, quia res non sunt infinitae paucitate. Est enim invenire paucum primum, scilicet duo, non autem unum, ut quidam dicunt. Ubi enim est invenire aliquid primum, non proceditur in infinitum. Si autem unum esset paucum, oporteret in infinitum procedere. Sequeretur enim, quod unum esset multa, quia omne paucum est multum, vel multa, ut supra dictum est. Si autem unum esset multa, oporteret esse aliquid minus eo, quod esset paucum, et illud iterum oporteret esse multum, et sic in infinitum abiretur.	2086. Therefore, although Anaxagoras had been right here, he mistakenly abandoned what he had said. For it seemed to him later on that in place of the phrase in smallness he ought to have said in fewness; and this correction was not a true one, because things are not unlimited in fewness. For it is possible to find a first few, namely, two, but not one as some say. For wherever it is possible to find some first thing there is no infinite regress. However, if one were a few, there would necessarily be an infinite regress; for it would follow that one would be many, because every few is much or many, as has been stated above (870:C 2078). But if one were many, something would have to be less than one, and this would be few, and that again would be much; and in this way there would be an infinite regress.
lib. 10 l. 8 n. 13 Deinde cum dicit opponitur itaque ostendit quomodo unum et multa opponantur. Et circa hoc duo facit. Primo ostendit quod unum opponitur multis relative. Secundo ostendit, quod multitudo absoluta non opponitur pauco, ibi, pluralitas autem. Circa primum tria facit. Primo ostendit quod unum opponitur multis relative; dicens quod unum opponitur multis, sicut mensura mensurabili; quae quidem opponuntur ut ad aliquid. Non tamen ita quod sit de numero eorum quae sunt ad aliquid secundum seipsa. Supra enim in quinto dictum est, quod dupliciter dicuntur aliqua esse ad aliquid. Quaedam namque referuntur adinvicem ex aequo, sicut dominus et servus, pater et filius, magnum et parvum; et haec dicit esse ad aliquid ut contraria; et sunt ad aliquid secundum seipsa; quia utrumque eorum hoc ipsum quid est, ad alterum dicitur.	2087. The one (874). Next, he shows how the one and the many are opposed; and in regard to this he does two things. First, he shows that the one is opposed to the many in a relative sense. Second (2096), he shows that an absolute plurality is not opposed to few. In regard to the first he does three things. First, he shows that the one is opposed to the many relatively. He says that the one is opposed to the many as a measure to what is measurable, and these are opposed relatively, but not in such a way that they are to be counted among the things which are relative of themselves. For it was said above in Book V (1026) that things are said to be relative in two ways: for some things are relative to each other on an equal basis, as master and servant, father and son, great and small; and he says that these are relative as contraries; and they are relative of themselves, because each of these things taken in its quiddity is said to be relative to something else.
lib. 10 l. 8 n. 14 Alia vero sunt ad aliquid non ex aequo; sed unum eorum dicitur ad aliquid, non quod ipsum referatur, sed quia aliquid refertur ad ipsum, sicut in scientia et scibili contingit. Scibile enim dicitur relative, non quia ipsum refertur ad scientiam, sed quia scientia refertur ad ipsum. Et sic patet quod huiusmodi non sunt relativa secundum se, quia scibile non hoc ipsum quod est, ad alterum dicitur, sed magis aliud dicitur ad ipsum.	2088. But other things are not relative on an equal basis, but one of them is said to be relative, not because it itself is referred to something else, but because something else is referred to it, as happens, for example, in the case of knowledge and the knowable object. For what is knowable is called such relatively, not because it is referred to knowledge, but because knowledge is referred to it. Thus it is evident that things of this kind are not relative of themselves, because the knowable is not said to be relative of itself, but rather something else is said to be relative to it.
lib. 10 l. 8 n. 15 Deinde cum dicit unum vero manifestat qualiter unum opponitur multis ut mensurabili. Et quia de ratione mensurae est quod sit minimum aliquo modo, ideo primo dicitur, quod unum est minus multis, et etiam duobus, licet non sit paucum. Non enim sequitur, si aliquid sit minus, quod sit paucum; licet de ratione pauci sit quod sit minus, quia omnis paucitas pluralitas quaedam est.	2089. But nothing prevents (875). Then he shows how the one is opposed to the many as to something measurable. And because it belongs to the notion of a measure to be a minimum in some way, he therefore says, first, that one is fewer than many and also fewer than two, even though it is not a few. For if a thing is fewer, it does not follow that it is few, even though the notion of few involves being less, because every few is a certain plurality.
lib. 10 l. 8 n. 16 Sciendum vero est, quod pluralitas sive multitudo absoluta, quae opponitur uni quod convertitur cum ente, est quasi genus numeri; quia numerus nihil aliud est quam pluralitas et multitudo mensurabilis uno. Sic igitur unum, secundum quod simpliciter dicitur ens indivisibile, convertitur cum ente. Secundum autem quod accipit rationem mensurae, sic determinatur ad aliquod genus quantitatis, in quo proprie invenitur ratio mensurae.	2090. Now it must be noted that plurality or multitude taken absolutely, which is opposed to the one which is interchangeable with being, is in a sense the genus of number; for a number is nothing else than a plurality or multitude of things measured by one. Hence one, (1) insofar as it means an indivisible being absolutely, is interchangeable with being; but (2) insofar as it has the character of a measure, in this respect it is limited to some particular category, that of quantity, in which the character of a measure is properly found.
lib. 10 l. 8 n. 17 Et similiter pluralitas vel multitudo, secundum quod significat entia divisa, non determinatur ad aliquod genus. Secundum autem quod significat aliquid mensuratum, determinatur ad genus quantitatis, cuius species est numerus. Et ideo dicit quod numerus est pluralitas mensurata uno, et quod pluralitas est quasi genus numeri.	2091. And in a similar way (1) insofar as plurality or multitude signifies beings which are divided, it is not limited to any particular genus. But (2) insofar as it signifies something measured, it is limited to the genus of quantity, of which number is a species. Hence he says that number is plurality measured by one, and that plurality is in a sense the genus of number.
lib. 10 l. 8 n. 18 Et non dicit quod sit simpliciter genus; quia sicut ens genus non est, proprie loquendo, ita nec unum quod convertitur cum ente, nec pluralitas ei opposita. Sed est quasi genus, quia habet aliquid de ratione generis, inquantum est communis.	2092. He does not say that it is a genus in an (~) unqualified sense, because, just as being is not a genus properly speaking, neither is the one which is interchangeable with being nor the plurality which is opposed to it. But it is (+) in some sense a genus, because it contains something belonging to the notion of a genus inasmuch as it is common.
lib. 10 l. 8 n. 19 Sic igitur accipiendo unum quod est principium numeri et habet rationem mensurae, et numerum qui est species quantitatis et est multitudo mensurata uno, opponuntur unum et multa, non ut contraria, ut supra dictum est de uno quod convertitur cum ente, et de pluralitate sibi opposita; sed opponuntur sicut aliqua eorum quae sunt ad aliquid, quorum scilicet unum dicitur relative, quia alterum refertur ad ipsum. Sic igitur opponitur unum et numerus, inquantum unum est mensura et numerus est mensurabilis.	2093. Therefore, when we take the one which is the principle of number and has the character of a measure, and number, which is a species of quantity and is the plurality measured by one, the one and the many are not opposed as contraries, as has already been stated above (1997) of the one which is interchangeable with being and of the plurality which is opposed to it; but they are opposed in the same way as things which are relative, i.e., those of which the term one is used relatively. Hence the one and number are opposed inasmuch as the one is a measure and number is something measurable.
lib. 10 l. 8 n. 20 Et quia talis est natura horum relativorum quod unum potest esse sine altero, sed non e converso, ideo hoc invenitur in uno et numero, quia si est numerus, oportet quod sit unum. Sed non oportet quod ubicumque est unum, quod sit numerus. Quia si est aliquid indivisibile ut punctus, ibi est unum, et non numerus. In aliis vero relativis quorum utrumque secundum se dicitur ad aliquid, neutrum est sine reliquo. Non enim est sine servo dominus, nec servus sine domino.	2094. And because the nature of these relative things is such that one of them can exist without the other, but not the other way around, this is therefore found to apply in the case of the one and number. For wherever there is a number the one must also exist; but wherever there is a one there is not necessarily a number. For if something is indivisible, as a point, we find the one there, but not number. But in the case of other relative things, each of which is said to be relative of role of something measured; for in a itself, one of these does not exist without the other; for there is no master without a servant, and no servant without a master.
lib. 10 l. 8 n. 21 Deinde cum dicit similiter autem manifestat similitudinem relationis scibilis ad scientiam et unius ad multa; dicens, quod cum scientia similiter secundum rei veritatem dicatur ad scibile sicut numerus ad unum, non similiter assignatur a quibusdam; quia videtur quibusdam, sicut Pythagoricis, sicut supra dictum est, quod scientia sit mensura et scibile mensuratum. Sed contrarium apparet. Dictum est enim quod, si est unum quod est mensura, non est necesse numerum esse qui est mensuratum, sed e converso. Videmus enim quod si est scientia, oportet scibile esse. Non autem oportet, si est aliquid scibile, quod sit eius scientia. Unde apparet quod magis scibile est sicut mensura et scientia sicut mensuratum. Quodam enim modo mensuratur scibili scientia, sicut numerus uno. Ex hoc enim vera scientia rei habetur, quod intellectus apprehendit rem sicuti est.	2095. But while (876). Here he explains the similarity between the relation of the knowable object to knowledge and that of the one to the many. He says that, although knowledge is truly referred to the knowable object in the same way that number is referred to the one, or the unit, it is not considered to be similar by some thinkers; for to some, the Protagoreans, as has been said above (1800), it seemed that knowledge is a measure, and that the knowable object is the thing measured. But just the opposite of this is true; for it has been pointed out that, if the one, or unit, which is a measure, exists, it is not necessary that there should be a number which is measured, although the opposite of this is true. And if there is knowledge, obviously there must be a knowable object; but if there is some knowable object it is not necessary that there should be knowledge of it. Hence it appears rather that the knowable object has the role of a measure, and knowledge the sense knowledge is measured by the knowable object, just as a number is measured by one; for true knowledge results from the intellect apprehending a thing as it is.
lib. 10 l. 8 n. 22 Deinde cum dicit pluralitas autem ostendit quod pluralitas vel multitudo absoluta non opponitur pauco, dicens: dictum est quod pluralitas secundum quod est mensurata, opponitur uni ut mensurae, sed non est contraria pauco. Sed pauco, quod significat pluralitatem excessam, opponitur multum, quod significat pluralitatem excedentem. Similiter etiam pluralitas non uno modo opponitur uni, sed dupliciter. Uno modo, sicut supra dictum est, opponitur ei ut divisibile indivisibili. Et hoc si accipiatur communiter unum quod convertitur cum ente, et pluralitas ei correspondens. Alio modo opponitur pluralitas uni ut ad aliquid, sicut scientia ad scibile. Et hoc dico si accipiatur pluralitas quae est numerus, et unum quod habet rationem mensurae, et est principium numeri.	2096. And plurality (877). Then he shows that an absolute plurality or multitude is not opposed to a few. He says that it has been stated before that insofar as a plurality is measured it is opposed to the one as to a measure, but it (~) is not opposed to a few. However, much, in the sense of a plurality which is excessive, (+) is opposed to a few in the sense of a plurality which is exceeded. Similarly a plurality is not opposed to one in a single way but in two. (1) First, it is opposed to it in the way mentioned above (2081), as the divisible is opposed to the indivisible; and this is the case if the one which is interchangeable with being and the plurality which is opposed to it are understood universally. (2)Second, plurality is opposed to the one as something relative, just as knowledge is opposed to its object. And this is the case, I say, if one understands the plurality which is number, and the one which has the character of a measure and is the basis of number.