Authors/Thomas Aquinas/metaphysics/liber10

Aquinas: Commentary on the Metaphysics Book 10 With English translation by John P. Rowan, Chicago, 1961

Lecture 1

Latin	English
lib. 10 l. 1 n. 1 Superius in quarto huius philosophus ostendit quod ista scientia habet pro subiecto ens, et unum, quod cum ente convertitur. Et ideo, postquam determinavit de ente per accidens, et de ente quod significat veritatem propositionis, in sexto; et de ente per se secundum quod dividitur per decem praedicamenta, in septimo et in octavo; et secundum quod dividitur per potentiam et actum, in nono: nunc in hoc decimo intendit determinare de uno, et de his quae consequuntur ad unum: et dividitur in duas partes. In prima determinat de uno secundum se. In secunda per comparationem ad multa, ibi, opponuntur autem unum et multa. Prima dividitur in duas. In prima ostendit quot modis unum dicitur. In secunda determinat quamdam proprietatem eius, ibi, maxime vero in eo quod est metrum esse. Prima in tres. In prima determinat quot modis dicitur unum. In secunda reducit omnes illos ad rationem unam, ibi, dicitur quidem igitur unum. In tertia ostendit quot modis unum praedicatur de his de quibus dicitur, ibi, oportet enim intelligere. Circa primum tria facit. Primo ponit duos modos unius. Secundo ostendit rationem unitatis in his duobus modis, ibi, tale vero. Tertio ponit alios duos modos unius, ibi, haec autem.	1920. Above in Book IV of this work the Philosopher showed (548)</a></a> that this science has for its subject being and the kind of unity which is interchangeable with being. Therefore, having drawn his conclusions about accidental being (1172) and about the kind of being which signifies the truth of a proposition, which he does in Book VI (1223), and about essential being as divided into the ten categories, which he does in Books VII (1245) and VIII (1681), and as divided into potency and actuality, which he does in Book IX (1768), his aim in this tenth book is to settle the issue about unity or oneness and the attributes which naturally accompany it. This is divided into two parts. In the first (1920) he establishes what is true of unity in itself; and in the second (1983) he considers unity in relation to plurality. The first part is divided into two members. In the first he explains the different senses in which the term one is used. In the second (1937) he establishes a property of unity or oneness. The first part is divided into three members. In the first he establishes the different senses in which the term one is used. In the second (1932) he reduces all these to one common meaning. In the third (1933) he explains the different ways in which the term one is used of the things of which it is predicated. In regard to the first he does three things. First, he gives two senses in which the term one is used. Second (1927), he exposes the notion of unity contained in these two senses. Third (1929), he gives two other senses of the term one.
lib. 10 l. 1 n. 2 Circa primum primo ponit primum modum dicendi unum; dicens, quod in quinto libro ostensum est, quoties dicantur nomina quae pertinent ad considerationem huius scientiae. Dictum est enim quod unum dicitur multis modis. Sed cum multipliciter dicatur unum, principales modi sunt quatuor: ita tamen quod dicamus modos unius, secundum quos unum dicitur primo et per se, et non per accidens. Nam unum per accidens habet alios suos modos.	1921. In treating the first member of this division he gives, first, the primary senses in which the term one is used. He says that he has explained in Book V (749) the different meanings of the terms which pertain to the study of this science; for it was pointed out there (842) that the term one is used in many senses. And while this is true, there are four principal senses in which it is employed. But let us speak of those senses in which the term one is used primarily and essentially and not accidentally; for what is accidentally one has different modes of its own.
lib. 10 l. 1 n. 3 Et inter modos unius dicti per se, unus modus est secundum quod continuum dicitur unum. Quod quidem accipi potest dupliciter: aut universaliter, scilicet quocumque modo sit aliquid continuum dicatur unum: aut unum continuitate solum quod secundum naturam est continuum, quod maxime continuum est, et non est continuum per violentiam, aut per artem, neque per alium modum contactus, sicut patet in castraturis lignorum, neque per aliquam continuitatem, sicut in his quae continuantur vel ligantur clavo vel quocumque vinculo.	1922. (1) Now one of the senses in which things are said to be essentially one is that in which the continuous is said to be one; and this can be taken in two ways: either (a) the continuous in general (i.e., anything continuous in any way at all) is called one; or only the continuous (b) by nature is called one by continuity. And this latter is what is continuous in the fullest sense of the term, and not that which is continuous by force or by art or by any kind of contact (as is evident in the case of pieces of wood), or by any kind of continuity (as is evident in the case of things which are continuous or held together by a nail or by any other bond).
lib. 10 l. 1 n. 4 Continuum autem secundum naturam dicitur dupliciter: scilicet, quod est totum uniforme, ut linea recta, aut etiam circularis: et quod non est totum uniforme, sicut duae lineae constituentes angulum in quo continuantur. Maxime autem horum est unum et per prius unum, quod dicitur linea recta vel circularis, quam lineae angulum constituentes. Nam linea recta oportet quod habeat unum motum. Non enim potest esse quod una pars eius moveatur et alia quiescat, nec una sic moveatur, alia vero aliter; sed tota simul et uno motu movetur. Et similiter etiam in circulari est.	1923. And the phrase continuous by nature designates two things: what is a (+) uniform whole, as a straight line or even a circular one, and what is not a (~) uniform whole, as two lines which constitute the angle in which they are connected. And of these, lines which are said to be straight and those which are said to be circular are one to a greater degree than those which form an angle, and they are one anteriorly. For a straight line must have one motion, since one part cannot be moved and another at rest, or one be moved in this way and another in that; but the whole must be moved simultaneously and by one motion. The same holds true of a circular line.
lib. 10 l. 1 n. 5 Sed in duobus continuis constituentibus angulum, hoc non convenit. Possumus enim imaginari quod una linea quiescat, et altera moveatur ei appropinquans, et minorem angulum constituat; aut ab ea elongata, et constituens angulum maiorem. Vel etiam quod utraque moveatur in diversas partes. Et ideo dicit quod illud continuum est magis unum, cuius motus est indivisibilior, et magis simplex.	1924. But this does not apply to two continuous quantities which form an angle; for we can imagine either that one line is at rest and the other is moved closer to it so as to form a smaller angle, or that it is moved away from it so as to form a larger angle, or even that both lines are moved in opposite directions. Hence he says that a continuous quantity whose motion is more indivisible and simpler is one to a greater degree.
lib. 10 l. 1 n. 6 Secundo cum dicit amplius tale ponit secundum modum: in quo quidem consideratur non solum quod id quod dicitur unum, sit tale, idest continuum; sed et quod plus habeat, scilicet quod sit quoddam totum habens aliquam formam aut speciem; sicut animal est unum, et superficies triangularis est una. Hoc igitur unum supra unitatem continuitatis addit unitatem quae est ex forma, secundum quam aliquid est totum, et speciem habens.	1925. And not only (815). (2) Then he gives a second sense in which things are said to be essentially one; and here we must consider that what “is such,” i.e., continuous, is not only said to be one but also has something more; i.e., it is a whole having some form or specifying principle, just as an animal is one, and a triangular surface is one. Hence this sense of one adds to the oneness of continuity the kind of unity which comes from the form by which a thing is a whole and has a species.
lib. 10 l. 1 n. 7 Et quia aliquid est totum per naturam, aliquid vero per artem, addidit, quod maxime est unum, siquidem est unum per naturam, et non per violentiam. Sicut per violentiam ad aliquod totum constituendum coniunguntur quaecumque uniuntur aut visco aut aliqua tali coniunctione. Sed id quod est coniunctum per naturam est magis unum, quia scilicet est sibiipsi causa quod sit continuum, quia per suam naturam est tale.	1926. And since one thing is a whole by nature and another by art, he added that “a thing is one to the greatest degree” if it is such by nature and not by force. For example, all those things which are united by glue or by some such bond so as to become a whole are joined by force. But whatever is joined by nature is one to the greatest degree, because it is clearly the cause of its own continuity; for it is such by its very nature.
lib. 10 l. 1 n. 8 Deinde cum dicit tale vero ostendit rationem unitatis in istis duobus modis; dicens, quod aliquid est tale et continuum et unum, eo quod motus eius est et unus et indivisibilis, loco et tempore. Loco quidem, quia versus quamcumque partem loci movetur una pars continui et alia. Tempore vero, quia quando movetur una, et alia.	1927. And a thing is such (816). Then be clarifies the meaning of unity contained in these two senses of the term one. He says that a thing is such, i.e., continuous and one, because its motion is one and indivisible both as to place and to time; as to place, because whithersoever one part of a continuous thing is moved another part is also moved; and as to time, because when one part is moved another is also moved.
lib. 10 l. 1 n. 9 Unde si aliquod continuum et totum per naturam dicitur unum quia motus eius est unus, manifestum est quod si aliquod continuum et totum habet in se principium primi motus, hoc erit primum unum in magnitudine. Sicut inter motus, primus motus est localis; et inter motus locales, primus est circularis, ut probatur in octavo physicorum. Et inter corpora, quae moventur motu circulari, aliquod est quod habet principium talis motus, scilicet corpus quod revolvitur et revolvit alia corpora motu diurno. Unde manifestum est, quod haec est prima magnitudo una, quia habet primum principium motus primi. Sic igitur apparent duo modi unitatis: aut sicut continuum dicitur unum, aut sicut totum dicitur unum.	1928. Hence, if a thing that is continuous and whole by nature is said to be one because its motion is one, then it is evident that, if anything continuous and whole has within itself a principle of the primary kind of motion, this will be the primary kind of one in the realm of continuous quantity; for example, of all motions the primary kind is local motion, and of local motions the primary kind is circular motion, as is proved in Book VIII of the Physics. And of bodies which are moved by circular motion there is one which contains the principle of such motion, i.e., the body which is moved circularly and causes the circular motion of other bodies by a daily motion. It is evident, then, that this is, the one primary continuous quantity which contains the first principle of the primary kind of motion. Hence two senses of the term one are evident, namely, that in which the continuous is called one, and that in which a whole is called one.
lib. 10 l. 1 n. 10 Deinde cum dicit haec autem ponit alios modos unius; dicens, quod quaedam alia dicuntur unum non propter motum unum, sed propter rationem unam. Huiusmodi autem sunt quorum intelligentia est una, quae una apprehensione apprehenduntur ab anima. Et dicuntur una apprehensione apprehendi talia, quorum est una apprehensio indivisibilis.	1929. And other things (817). Then he gives the other ways in which things are said to be one. He says that certain other things are said to be one, not because their motion is one, but because their intelligible structure is one. And things of this kind whose concept is one are those which are apprehended by a single intellectual act. And such things as are said to be apprehended by a single intellectual act are those of which there is a single apprehension of an undivided object.
lib. 10 l. 1 n. 11 Quod quidem contingit dupliciter. Aut quia apprehensio indivisibilis est eius quod est unum specie, aut eius quod est unum numero. Numero quidem indivisibile est ipsum singulare, quod non potest praedicari de multis. Specie autem unum, est indivisibile, quod est unum secundum scientiam et notitiam. Non enim in diversis singularibus est aliqua natura una numero, quae possit dici species. Sed intellectus apprehendit ut unum id in quo omnia inferiora conveniunt. Et sic in apprehensione intellectus, species fit indivisibilis, quae realiter est diversa in diversis individuis.	1930. This can be so for two reasons: either (3) because the undivided, object apprehended is specifically one, or (4) because it is numerically one. Now what is numerically undivided is the singular thing itself, which cannot be predicated of many things; and what is specifically one is undivided because it is a single object of knowledge and acquaintance. For in distinct singular things there is no nature numerically one which can be called a species, but the intellect apprehends as one that attribute in which all singulars agree. Hence the species, which is distinct in distinct individuals in reality, becomes undivided when apprehended by the intellect.
lib. 10 l. 1 n. 12 Et quia substantia prior est ratione omnibus aliis generibus, cum unum dicatur his modis propter rationem unam, sequitur quod primum unum secundum hos modos, sit unum substantia; quod scilicet est substantiis causa unius; sicut secundum primos duos modos, primum unum erat magnitudo circulariter mota.	1931. And since substance is prior in intelligibility to all the other genera, and the term one is used in these senses because it has one meaning, then it follows that the primary sort of one in these senses is what is one in substance, i.e., what causes substance to be one, just as in the first two senses the primary sort of one was the continuous quantity which is moved circularly.
lib. 10 l. 1 n. 13 Deinde cum dicit dicitur quidem reducit modos unius supra positos ad unam rationem, colligendo quae supra dixerat. Dicit ergo quod unum dicitur quatuor modis. Primo quidem continuum secundum naturam. Secundo totum. Tertio singulare. Quarto, universale ut species. Et omnia haec dicuntur unum per rationem unam, scilicet per hoc quod est esse indivisibile. Nam proprie unum est ens indivisibile. Sed in primis duobus dicitur unum, quia est motus indivisibilis; in aliis autem duobus, quia est intelligentia, aut ratio indivisibilis; ut sub hoc etiam comprehendatur apprehensio rei particularis.	1932. The term one (818). Here he reduces the senses of one given above to a single meaning by summarizing what he had said above. He says that the term one is used of four things: first, (1) of what is continuous by nature; (2) second, of a whole; (3) third, of a singular thing; and (4) fourth, of the universal, for example, a species. And all of these are said to be one because of one common aspect, namely, being indivisible; for properly speaking, a one is an undivided being. But the term one is used in the first two senses because a motion is undivided, and in the latter two senses because an intelligible structure or concept is undivided, inasmuch as the apprehension of a particular thing is also included under this.
lib. 10 l. 1 n. 14 Deinde cum dicit oportet enim ostendit quo modo unum praedicetur de his quae dicuntur unum; dicens, quod oportet intelligere quod non similiter sumendum est unum, cum aliqua res dicitur una, et cum dicitur quod quid est unum, quod est ratio unitatis. Sicut etiam non hoc modo dicitur lignum esse album, quia lignum sit hoc ipsum quod est album; sed quia album accidit ei.	1933. Here he shows how the term one is predicated of things which are said to be one. He says that it must be borne in mind that the term one should not be taken to mean the same thing when a thing is said to be one and when someone expresses the essence of oneness, which is its intelligible structure; just as wood too is not said to be white in the sense that whiteness is the essence of wood, but in the sense that it is an accident of it.
lib. 10 l. 1 n. 15 Hoc autem quod dixerat sic manifestat. Quia unum dicitur multis modis, ut dictum est, quaelibet res dicitur esse una ex eo, quod inest ei aliquis istorum modorum; puta vel continuum, vel totum, vel species, vel singulare. Sed hoc ipsum quod est unum, quandoque quidem accipitur secundum quod inest alicui dictorum modorum, puta ut dicam quod unum secundum quod est continuum, unum est. Et similiter de aliis. Quandoque autem hoc ipsum quod est unum, attribuitur ei quod est magis propinquum naturae unius, sicut indivisibili, quod tamen secundum se potestate continet praedictos modos: quia indivisibile secundum motum, est continuum et totum. Indivisibile autem secundum rationem, est singulare et universale.	1934. Then he gives the following explanation of a statement which he had made, saying that, since the term one is used in many senses (as has been stated), a thing is said to be one because some one of these senses applies to it, i.e., continuous, whole, species, or singular thing. But the essence of oneness sometimes applies to something that is one in some one of the foregoing senses, as when I say that what is one in continuity is one (and the same holds true of the others); and sometimes it is attributed to something which is nearer to the nature of one, for example, what is undivided but contains within itself potentially the senses of one given above; because what is undivided as regards motion is continuous and whole, and what is undivided in meaning is singular or universal.
lib. 10 l. 1 n. 16 Et ad hoc subdit exemplum de elemento et causa, quae quidem accipiuntur secundum determinationes ad res, prout dicimus rem talem esse elementum vel causam, assignando definitionem nominis, prout dicimus causam hoc ipsum quod est esse causam. Quo modo dicimus quod ignis est elementum, aut etiam infinitum secundum se, idest hoc ipsum quod est infinitum, quod Pythagorici ponebant separatum, et elementum omnium, vel aliquid aliud tale, propter quod potest dici elementum esse. Sed quodammodo ignis non est elementum neque infinitum. Non enim ignis est hoc ipsum quod est elementum, quia non est eadem ratio ignis et elementi; sed quantum in re est et in natura, ignis est elementum. Sed nomen elementi cum de igne praedicatur, significat aliquid accidisse igni, scilicet quod ignis sit ex quo aliquid est, ut ex primo interius existente, quod est ratio elementi. Dicit autem inexistente, ad removendum privationes.	1935. He adds to this the example of elements and causes, viewed in the problem of identifying them in things, as when we say that such and such a thing is an element or cause by defining the term; for example, we say that that is a cause which has the essence of a cause. And in this way we say that fire is an element or “the indeterminate itself,” i.e., what is unlimited in itself (which the Pythagoreans posited as a separate entity and the element of all things), or anything else of this sort for whatever reason it can be called an element. But in a sense fire is not an element, and neither is the indeterminate; for fire does not constitute the essence of an element, because the notion of fire is not the same as that of an element. It is an element, however, as existing in reality or in the natural world. But when the term element is predicated of fire, it signifies that something “has become accidental to fire,” i.e., that fire is that of which something is composed as a primary constituent, and this is the formal note of an element. He says “constituent” in order to exclude privations.
lib. 10 l. 1 n. 17 Sicut autem dictum est de elemento, sic est in causa, et uno et omnibus talibus; quia res de quibus dicuntur non sunt hoc ipsum quod significant nomina: sicut homo albus, non est hoc ipsum quod significat hoc nomen album. Album enim significat qualitatem. Propter quod et hoc unum esse est indivisibile esse. Quod quidem competit enti, quod est inseparabile loco et specie, vel quocumque alio modo.	1936. What has been said about an element also applies to cause and to one and to all such terms; because the things of which they are predicated are not the very things which the terms signify; for example, white man is not the very thing which the term white signifies, for white signifies a quality. Hence the essence of oneness consists in being undivided, i.e., in being an individual thing; and this is proper to a thing which is inseparable as to place or to form or in whatever other way it is inseparable.

Lecture 2

Latin	English
lib. 10 l. 2 n. 1 Postquam ostendit philosophus quot modis unum dicitur, et quae sit ratio unius, ad quam omnes modi reducuntur, scilicet esse indivisibile; hic ex hac ratione unius ostendit quamdam eius proprietatem, scilicet esse mensuram: et dividitur in partes duas. In prima ostendit, quomodo uni competit ratio mensurae, et aliis generibus accidentium. In secunda vero ostendit quomodo unum habens rationem mensurae inveniatur in substantia, ibi, secundum substantiam vero et naturam. Circa primum duo facit. Primo ostendit in quo genere primo inveniatur unum habens rationem mensurae; et quomodo exinde ad alia derivetur secundum propriam rationem mensurae. Secundo ponit quomodo derivetur ad alia secundum quamdam similitudinem, ibi, et scientiam autem rerum metrum. Circa primum duo facit. Primo ostendit ubi primo sit unum rationem mensurae habens, et quomodo exinde ad alia fiat derivatio. Secundo ponit quaedam consideranda circa mensuras, ibi, non semper autem numero unum. Circa primum tria facit. Primo ostendit quomodo unum quod est mensura inveniatur in quantitate, et exinde ad alia genera derivetur. Secundo in qua specie quantitatis est primo, ibi, et quo primo cognoscitur. Tertio quomodo derivetur in alias species quantitatis, ibi, hinc autem et in aliis.	1937. Having explained the various senses in which unity is predicated of things, and having stated what its essential note is, to which all its usages are reduced, i.e., being indivisible, here the Philosopher infers a property of unity from its essential note, namely, that it is a measure. This is divided into two parts. In the first he shows how the notion of a measure belongs to unity and to the various classes of accidents. In the second (1961) he shows how unity in the sense of a measure is found in substances (“It is necessary”). In regard to the first part of this division he does two things. First, he indicates the class of things in which unity in the sense of a measure is primarily found, and how it is transferred from this class to the others with the proper notion of a measure. Second (1956), he explains how it is transferred figuratively to the other classes (“And for the same reason”). In treating the first part he does two things. First, he indicates the class of things in which unity in the sense of a measure is first found, and how it is transferred from this class to the others. Second (1950), he makes a study of measures (“However, a measure”). In regard to the first he does three things. First, he shows how unity as a measure is found in quantity, and how it is transferred from this category to the others. Second (1939), he indicates the species of quantity in which it is first found (“And that by which”). Third (1940), he shows how it is transferred to other species of quantity (“And the measure”).
lib. 10 l. 2 n. 2 Dicit ergo primo, quod cum ratio unius sit indivisibile esse; id autem quod est aliquo modo indivisibile in quolibet genere sit mensura; maxime dicetur in hoc quod est esse primam mensuram cuiuslibet generis. Et hoc maxime proprie dicitur in quantitate, et inde derivatur ad alia genera ratio mensurae. Mensura autem nihil aliud est quam id quo quantitas rei cognoscitur. Quantitas vero rei cognoscitur per unum aut numerum. Per unum quidem, sicut cum dicimus, unum stadium, vel unum pedem. Per numerum autem, sicut dicimus tria stadia, vel tres pedes. Ulterius autem omnis numerus cognoscitur per unum, eo quod unitas aliquoties sumpta quemlibet numerum reddit. Unde relinquitur quod omnis quantitas cognoscatur per unum. Addit autem inquantum quantitas, ut hoc referatur ad mensuram quantitatis. Nam proprietates et alia accidentia quantitatis alio modo cognoscuntur.	1938. He accordingly says, first, that, since the essential note of unity consists in being indivisible, and what is indivisible in each genus is somehow the measure of that genus, unity must be said to be in the highest degree the first measure of each genus. This is said to apply most properly to quantity, and it is from this class that the notion of a measure is transferred to other classes of things. Now a measure is nothing else than that by which a thing’s quantity is known, and this is known by the unit or by a number: by a unit, as when we say one furlong or one foot; and by a number, as when we say three furlongs or three feet. Again, every number is known by the unit because the unit taken a certain number of times gives a number. It follows, then, that every quantity is known by unity. To “quantity” he adds “as quantity,” intending that this be referred to the measure of quantity; for the properties and other accidents of quantity are known in a different way.
lib. 10 l. 2 n. 3 Deinde cum dicit et quo primo dicit in qua specie quantitatis primo sit unum et mensura. Et circa hoc duo facit. Primo ostendit quod ratio mensurae primo invenitur in discreta quantitate, quae est numerus; dicens, quod id quo primo cognoscitur quantitas est ipsum unum, idest unitas, quae est principium numeri. Nam unum in aliis speciebus quantitatis non est ipsum unum, sed aliquid cui accidit unum; sicut dicimus unam manum, aut unam magnitudinem. Unde sequitur, quod ipsum unum, quod est prima mensura, sit principium numeri secundum quod est numerus.	1939. And that by which (821). Then he indicates in what species of quantity unity or measure is primarily found. First, he makes it clear that the notion of a measure is primarily found in discrete quantity, which is number. He says that that by which quantity is first known is “unity itself,” i.e., the unit which is the principle of number. For in other species of quantity the unit is not unity itself but something of which unity is an attribute, as when we speak of one hand or of one continuous quantity. Hence it follows that unity itself, which is the first measure, is the principle of number as number.
lib. 10 l. 2 n. 4 Secundo cum dicit hinc autem ostendit quomodo derivetur in alias species quantitatis. Et circa hoc duo facit. Primo ostendit ad quas species quantitatis derivetur; dicens, quod hinc, scilicet ex numero et uno quod est principium numeri, dicitur mensura in aliis quantitatibus, id scilicet quo primo cognoscitur unumquodque eorum. Et id quod est mensura cuiuslibet generis quantitatis, dicitur unum in illo genere.	1940. And the measure (822). Second, he shows how unity is transferred to other species of quantity; and in regard to this he does two things. First, he indicates the species of quantity to which it is transferred. He says that it is from this class, i.e., from number and from the unit, which is the principle of number, that the notion of a measure is transferred to other quantities as that by which each of them is first known. And whatever is the measure in each class of things is the unit in that class.
lib. 10 l. 2 n. 5 Et hoc exemplificat in tribus generibus; scilicet in dimensionibus quae sunt scilicet longitudo, et latitudo, et profunditas. Et in ponderibus, in hoc quod dicit, in gravitate. Et in motibus, in hoc, quod dicit, in velocitate, quod referatur ad mensuram temporis. Et de dimensionibus quidem nulli dubium erat, quin quantitates essent, et quod proprie eis primo competeret mensurari. Sed de gravitate et velocitate poterat esse dubium, eo quod magis videntur esse qualitates quam quantitates.	1941. He gives examples of this in three classes of things, i.e., in dimensions—length, breadth and width; in weight, or in what he calls heaviness; and in speed, or in what he calls rapidity, which refers to the measure of time. In the case of dimensions no one doubted that they were quantities and that they were properly susceptible to measurement, but in the case of weight and of speed there could be a difficulty because these seem to be qualities rather than quantities.
lib. 10 l. 2 n. 6 Et ideo dicit, quomodo pertinent ad genus quantitatis, et quomodo competit eis mensurari; dicens, quod gravitas et velocitas habent aliquid commune in contrariis, quia scilicet in uno contrariorum invenitur alterum: nam grave est aliquo modo leve, et e converso; et velox est aliquo modo tardum. Utrumque enim eorum est duplex. Sicut grave, uno modo dicitur absolute, scilicet quod habet inclinationem ut feratur ad medium, sine hoc quod consideretur quantum habeat de tali inclinatione: et sic non pertinet ad genus quantitatis, nec competit ei mensurari. Alio modo dicitur grave per comparationem ad aliud, scilicet quod excedit alterum in inclinatione praedicta; ut scilicet dicamus, quod terra est gravis in comparatione ad aquam, et plumbum in comparatione ad lignum. Sic igitur ratione huius excessus, invenitur aliqua ratio quantitatis et mensurae. Et similiter velox dicitur dupliciter. Uno modo absolute, scilicet quod habet motum quemcumque. Et alio modo quod habet excessum motus. Et uno modo competit sibi ratio quantitatis et mensurae. Alio modo non.	1942. He therefore explains how these pertain to the genus of quantity, and how they are susceptible to measurement. He says that heaviness and rapidity have something in common with their contraries because one contrary is found in the other; for what is heavy is in some sense light, and the reverse; and what is rapid is in some sense slow. For each of these terms is used in two senses. (1) In one sense the term heavy is used without qualification of anything that has an inclination to be borne towards the center of the earth, without taking into consideration how great its inclination is; and in this sense heavy does not refer to the category of quantity, and it is not susceptible to measurement. (2) In the other sense it is used of one thing in comparison with something else, namely, of what exceeds something else in terms of the abovementioned inclination; for example, we say that earth is heavy in comparison with water, and that lead is heavy in comparison with wood. Therefore it is by reason of this excess that some notion of quantity and measure is found. The term rapid is similarly used in two senses. In one sense it is used without qualification of anything that has any motion; and in a second sense it is used of anything that has an excessive motion. And in one respect the notions of quantity and measure properly apply to it, and in another respect they do not.
lib. 10 l. 2 n. 7 Et ut exponat quod dixerat de conditione gravitatis et velocitatis in contrariis, subdit quod in ipso tardo invenitur velocitas, inquantum id quod est simpliciter et absolute tardum, per excessum se habet ad tardiora. Et similiter gravitas invenitur in levi, sicut aer est levis ad terram, et gravis ad ignem comparatus.	1943. With a view to clarifying his statement about the condition of heaviness and rapidity in reference to contraries he adds that rapidity is found in something that is slow inasmuch as what is simply and unqualifiedly slow is more rapid in comparison with something that is slower than itself. And in a similar way heaviness is found in light things; for example, air is light in comparison with earth, and heavy in comparison with fire.
lib. 10 l. 2 n. 8 Deinde cum dicit in omnibus ostendit qualiter a numero derivetur ratio mensurae ad alia. Et primo hoc manifestat simul in dimensionibus et ponderibus. Secundo in velocitate motuum, ibi, et motum simplici motu. Dicit ergo primo, quod hoc modo derivatur ratio mensurae a numero ad alias quantitates, quod sicut unum quod est mensura numeri est indivisibile, ita in omnibus aliis generibus quantitatis aliquod unum indivisibile est mensura et principium. Sicut in mensuratione linearum utuntur homines quasi indivisibili, mensura pedali, idest unius pedis: ubique enim quaeritur pro mensura aliquid indivisibile, quod est aliquod simplex, vel secundum qualitatem, vel secundum quantitatem. Secundum qualitatem quidem, ut album in coloribus, quod quodammodo est mensura colorum, ut dicetur infra. Secundum quantitatem vero, ut unitas in numero, et mensura pedalis in lineis.	1944. And in all cases (823). Then he shows how the notion of a measure is transferred from number to other kinds of quantity. He immediately makes this clear, first, in the case of dimensions and in that of weights; and second (1947), in that of the rapidity of motions (“And they also measure”). He accordingly says, first, that the notion of a measure is transferred from number to the other kinds of quantity in this way that, just as the unit which is the measure of number is indivisible, so too all the other kinds of quantity have something that is one and indivisible as their measure and principle. For example, in measuring lines men use “the foot measure,” i.e., the measure of one foot, as something indivisible; for wherever something indivisible is sought as. a measure, there is something simple either in quality or in quantity; in quality, as whiteness in the case of colors, which is in a sense the measure of colors, as will be mentioned below (1968); and in quantity, as the unit in the case of numbers, and the foot measure in the case of lines.
lib. 10 l. 2 n. 9 Assignat autem rationem, quare mensuram oportet esse aliquid indivisibile; quia scilicet hoc est certa mensura, a qua non potest aliquid auferri vel addi. Et ideo unum est mensura certissima; quia unum quod est principium numeri, est omnino indivisibile, nullamque additionem aut subtractionem suscipiens manet unum. Sed mensurae aliorum generum quantitatis imitantur hoc unum, quod est indivisibile, accipiens aliquid minimum pro mensura secundum quod possibile est. Quia si acciperetur aliquid magnum, utpote stadium in longitudinibus, et talentum in ponderibus, lateret, si aliquod modicum subtraheretur vel adderetur; et semper in maiori mensura hoc magis lateret quam in minori.	1945. Further, he points out why a measure must be something indivisible. The reason is that an exact measure must be something which can be neither added to nor subtracted from. Thus the unit is the most exact or certain measure, because the unit which is the principle of number is altogether indivisible, and whatever unity is not susceptible either to addition or to subtraction remains one. The measures of the other classes of quantity resemble this unit which is indivisible inasmuch as men take some smallest thing as a measure to the extent that this is possible. For if anything large were taken, as the furlong among distances and the talent among weights, it would escape our notice if some small portion were subtracted from or added to it. And this would always be more true of a larger measure than of a smaller one.
lib. 10 l. 2 n. 10 Et ideo omnes accipiunt hoc pro mensura tam in humidis, ut est oleum et vinum, quam in siccis, ut est granum et hordeum, quam in ponderibus et dimensionibus, quae significantur per grave et magnitudinem; quod primo invenitur tale, ut ab eo non possit aliquid auferri sensibile vel addi quod lateat. Et tunc putant se cognoscere quantitatem rei certitudinaliter, quando cognoscunt per huiusmodi mensuram minimam.	1946. Hence all men take this as a measure both in the case of liquids, such as oil and wine, and in that of solids, such as grain and barley; and also in that of weights and dimensions, which are designated as heaviness and continuous quantity. And this is first found to be such that nothing perceptible can be subtracted from it or added to it that might escape our notice. And men think they know the quantity of a thing exactly when they know it by the smallest measure of this kind.
lib. 10 l. 2 n. 11 Deinde cum dicit et motum manifestat idem in velocitate motuum; dicens, quod etiam motum mensurant homines motu simplici, idest uniformi et velocissimo quod habet minimum de tempore. Et ideo in astrologia accipiunt tale principium ad mensurandum. Accipiunt enim motum primi caeli, scilicet motum diurnum, qui est regularis et velocissimus, ad quem iudicant et mensurant omnes alios motus.	1947. And they also (824). Then he makes the same thing clear with regard to the rapidity of motions. He says that men also measure motion “by that motion which is simple,” i.e., the motion which is uniform and quickest, because it takes the least time. Hence in astronomy they take such motion as the basis of measurement; for they take the motion of “the first heaven,” i.e., the daily motion, which is regular and quickest, and they judge and measure all other motions by this.
lib. 10 l. 2 n. 12 Et quia ex velocitate et tarditate motuum contingit gravitas et acuitas in sonis, ut determinatur in musica, subdit exemplum de mensuratione sonorum; dicens, quod in musica prima mensura diesis est, idest differentia duorum semitonorum. Tonus enim dividitur in duo semitona inaequalia, ut in musica probatur. Et similiter in voce, mensura est elementum, quia etiam brevitas et longitudo vocis velocitatem et tarditatem motus consequitur.	1948. And because the low and high pitch of sounds results from the quickness and slowness of motions, as is established in the science of music, he adds as an example the measurement of sounds. He says that in music the first measure is the “diesis,” i.e., the difference between two half tones; for a tone is divided into two unequal half tones, as is proved in the science of music. And similarly in speech the measure is the letter, because the shortness or length of a word is a natural consequence of the quickness or slowness of a motion.
lib. 10 l. 2 n. 13 Omnes autem istae mensurae sunt aliquid unum: non ita quod aliqua mensura sit communis omnibus; sed quia quaelibet mensura in se est aliquid unum, ut dictum est.	1949. Now all these something one, not in measures are the sense that some measure is common to all, but in the sense that any measure in itself is something one, as has been pointed out.
lib. 10 l. 2 n. 14 Deinde cum dicit non semper postquam ostendit philosophus ubi sit primo unum habens rationem mensurae, hic determinat quaedam circa mensuras consideranda. Et est primum, quod licet id quod est mensura habeat rationem unius, inquantum accedit ad indivisibilitatem, non tamen necessarium est unum numero esse quod mensurat. Sed aliquando plura sunt mensurantia, sicut in melodiis sunt duae dieses, idest duo semitona. Sed propter parvitatem non discernitur secundum auditum. Nam sensus non percipit differentiam valde parvorum, sed eorum differentia percipitur in rationibus, idest secundum diversas rationes proportionum, quia ex diversis proportionibus numeralibus causantur.	1950. However, a measure (825). After having shown in what class of things unity as a measure is primarily found, here the Philosopher clears up certain points that have to be investigated about measures. The first of these is that, although a measure is understood to be one thing inasmuch as it comes close to being indivisible, it is not necessary that a measure be something numerically one; but sometimes many things are measures; for example, in the case of musical sounds “there are two dieses,” i.e., two half tones. However, because of their smallness they are not distinguished by the sense of hearing, for the senses do not perceive the difference between two things that are very small; but their difference is perceived “in their ratios,” i.e., in the different ratios which comprise their proportions, because they are caused by different numerical proportions.
lib. 10 l. 2 n. 15 Similiter etiam voces quibus etiam mensuramus, plures sunt. Quantitas enim unius metri vel unius pedis, mensuratur ex diversis syllabis, quarum aliae sunt breves, et aliae longae. Similiter etiam est diameter circuli vel quadrati, et etiam latus quadrati: et quaelibet magnitudo mensuratur duobus: non enim invenitur quantitas ignota nisi per duas quantitates notas.	1951. Similarly the things by which we measure words are also many; for the quantity of one meter or of one foot is measured by different syllables, some of which are short and some long. The same thing is true of the diameter of a circle and of the diagonal of a square, and also of the side of a square. And any continuous quantity is measured by two things, for an unknown quantity is found only by means of two known quantities.
lib. 10 l. 2 n. 16 Hoc autem dicto, concludit epilogando quae supra dicta sunt, scilicet quod unum est mensura omnium. Cuius ratio est, quia unum est ad quod terminatur divisio. Ea vero, ex quibus est substantia uniuscuiusque, cognoscuntur per divisionem sive resolutionem totius in componentia; sive sint partes secundum quantitatem, sive sint partes secundum speciem, ut materia et forma, et elementa corporum mixtorum. Et ideo oportet id quod est per se unum, esse indivisibile, cum sit mensura qua cognoscitur res; quia quod in singulis est primum in compositione et ultimum in resolutione, est indivisibile, et per hoc cognoscitur res, ut dictum est.	1952. Having said this he brings this part of his discussion to a close by summarizing what has been said above, namely, that unity constitutes the measure of all things. The reason for this is that unity is the term of division. And those principles which constitute the substance of each thing are known by the division or dissolution of the whole into its component parts, whether they are quantitative parts or specific parts such as matter and form and the elements of compounds. Therefore what is one in itself must be indivisible since it is the measure by which a thing is known, because in the case of singular things whatever is first in the process of composition and last in the process of dissolution is indivisible, and it is by means of this that the thing is known, as has been explained.
lib. 10 l. 2 n. 17 Sed tamen non similiter in omnibus invenitur indivisibile; sed quaedam sunt omnino indivisibilia, sicut unitas quae est principium numeri. Quaedam vero non sunt omnino indivisibilia, sed indivisibilia secundum sensum, secundum quod voluit auctoritas instituentium tale aliquid pro mensura; sicut mensura pedalis, quae quidem indivisibilis est proportione, sed non natura. Nam omne continuum forsan divisibile est. Dicit autem forsan propter dubitationem quorumdam ponentium magnitudinem componi ex indivisibilibus; vel quia magnitudines naturales non dividuntur in infinitum, sed solae mathematicae. Est enim invenire minimam carnem, ut tangitur primo physicorum.	1953. Yet indivisibility is not found in all things in the same way. (1) Some things are altogether indivisible, such as the unit which is the basis of number, whereas (2) others are not altogether indivisible but only to the senses, according as the authority of those who instituted such a measure wished to consider something as a measure; for example, the foot measure, which is indivisible in proportion [to the things measured] but not by nature. “For perhaps everything continuous is divisible”; and he says “perhaps” because of the difficulty facing those men who claimed that continuous quantity is composed of indivisible elements, or that natural continuous quantities are not infinitely divisible, but only mathematical quantities. For it is possible to find the smallest amount of flesh, as is mentioned in Book I of the Physics.
lib. 10 l. 2 n. 18 Deinde cum dicit semper autem ponit secundum quod considerandum est circa mensuram; dicens, quod metrum, idest mensura, semper debet esse cognatum, scilicet eiusdem naturae vel mensurae, cum mensurato: sicut mensura magnitudinum debet esse magnitudo: et non sufficit quod conveniat in natura communi, sicut omnes magnitudines conveniunt: sed oportet esse convenientiam mensurae ad mensuratum in natura speciali secundum unumquodque, sic quod longitudinis sit longitudo mensura, latitudinis latitudo, vox vocis, et gravitas gravitatis, et unitatum unitas.	1954. And a measure (826). Then he gives the second point that has to be investigated about a measure. He says that “the meter,” i.e., the measure, should always be of the same kind as the thing measured, i.e., of the same nature or measure as the thing measured; for example, a continuous quantity should be the measure of continuous quantities; and it is not enough that they have a common nature, as all continuous quantities do, but there must be some agreement between the measure and the thing measured in the line of their special nature. Thus a length is the measure of lengths, a width of widths, a vocal sound of vocal sounds, a weight of weights, and a unit of units.
lib. 10 l. 2 n. 19 Sic enim oportet accipere ut absque calumnia loquamur; sed non quod numerorum mensura sit numerus. Numerus autem non habet rationem mensurae primae, sed unitas. Et si unitas mensura est, ad significandum convenientiam inter mensuram et mensuratum, oportet dicere, quod unitas sit mensura unitatum, et non numerorum. Et tamen si rei veritas attendatur, oportebit hoc etiam concedere, quod numerus esset mensura numerorum, aut etiam unitas numerorum similiter acciperetur. Sed non similiter dignum videtur dicere unitatem esse mensuram unitatum, et numerum numeri, vel unitatem numeri; propter differentiam, quae videtur esse inter unitatem et numerum. Sed istam differentiam observare, idem est, ac si quis dignum diceret quod unitates essent mensurae unitatum, sed non unitas; quia unitas differt ab unitatibus ut singulariter prolatum ab his quae pluraliter proferuntur. Et similis ratio est de numero ad unitatem; quia numerus nihil aliud est quam pluralitas unitatum. Unde nihil aliud est dicere unitatem esse mensuram numeri, quam unitatem esse mensuram unitatum.	1955. “For this is the view which must be taken” in order that we may speak without being criticized, “but not that number is the measure of numbers.” Now number does not have the notion of a first measure but unity does; and if unity is a measure, then in order to signify the agreement between the measure and the thing measured it will be necessary to say that unity is the measure of units and not of numbers. Yet if the truth of the matter be taken into consideration, it will be necessary to admit also that number is the measure of numbers or even that the unit may be taken in a similar way as the measure of numbers. But it does not seem equally fitting to say that the unit is the measure of units and number of number or unity of number, because of the difference which appears to exist between the unit and number. But to observe this difference is the same as if someone were to say that it is fitting for units to be the measure of units but not the unit, because the unit differs from units as things expressed in the singular differ from those expressed in the plural. And the same argument applies to number in relation to the unit, because a number is nothing else than a plurality of units. Hence to say that the unit is the measure of number is merely to say that the unit is the measure of units.
lib. 10 l. 2 n. 20 Deinde cum dicit et scientiam ostendit qualiter mensura transfertur ad quaedam secundum similitudinem; dicens, quod cum dictum sit quod mensura est, qua quantitas rei cognoscitur, dicemus scientiam esse mensuram rerum scibilium et sensum rerum sensibilium, quia ipsis aliquid cognoscimus, sensu scilicet sensibilia et scientia scibilia. Non tamen eodem modo sicut mensura. Nam per mensuram cognoscitur aliquid sicut per principium cognoscendi: per sensum autem et scientiam sicut per potentiam cognoscitivam, aut habitum cognoscitivum.	1956. And for the same reason (827). Then he shows how the term measure is transferred in a figurative way to another class of things. He says that, since it has been stated that a measure is that by which the quantity of a thing is known, we may say that intellectual knowledge is the measure of that which is knowable intellectually, and that sensory perception is the measure of that which is perceptible; because we know something by means of them, namely, sensible objects by means of perception and intelligible objects by means of intellectual knowledge; but we do not know them in the same was as we do by a measure. For something is known by a measure as a principle of knowledge, whereas in sensation and knowledge we are measured by things that are outside ourselves.
lib. 10 l. 2 n. 21 Sic igitur per hanc similitudinem dicuntur mensurae, quia secundum rei veritatem magis mensurantur quam mensurent. Non enim quia nos aliquid sentimus aut scimus, ideo sic est in rerum natura. Sed quia sic est in rerum natura, ideo vero aliquid scimus, aut sentimus, ut dicitur nono metaphysicorum. Et sic accidit nobis, quod in sentiendo et sciendo mensuramur per res quae extra nos sunt.	1957. Therefore they are called measures figuratively, because in reality they are measured rather than measure. For it is not because we perceive or know a thing that it is so in reality; but it is because it is so in reality that we have a true knowledge or perception of it, as is said in Book IX (807:C 1896). Thus it follows that in perceiving and knowing something we measure our knowledge by means of the things which exist outside the mind.
lib. 10 l. 2 n. 22 Nobis autem cognoscentibus et mensurantibus, sicut aliquo alio nos mensurante, cognoscimus quanti sumus in quantitate corporali per mensuram cubitalem applicatam nobis. Et sic sicut cubitus exterius appositus est mensura quantitatis corporalis nostrae, ita res scitae vel per sensum apprehensae, sunt mensurae per quas potest sciri utrum vere cognoscamus aliquid per sensum vel per intellectum.	1958. However, in knowing and measuring ourselves by some other measure we know how much bodily quantity we have by applying the cubit measure to ourselves. Hence, just as the external cubit is offered as a measure of our bodily quantity, in a similar way the things known or sensuously apprehended are the measures whereby we can know whether we truly apprehend something by our senses or by our intellect.
lib. 10 l. 2 n. 23 Si qua vero scientia est quae est causa rei scitae, oportebit quod sit eius mensura. Ut scientia artificis est mensura artificiatorum; quia unumquodque artificiatum secundum hoc perfectum est, quod attingit ad similitudinem artis. Et hoc modo se habet scientia Dei respectu omnium. Sed Protagoras dixit hominem esse mensuram omnium rerum inquantum est sciens aut sentiens, quia scientia et sensus sunt mensura substantiarum, scilicet sensibilium et scibilium. Dicebant enim Protagorici, ut in quarto habitum est, quod res sunt tales, quia sic sentimus eas, vel sic opinamur in eis. Cum igitur nihil superabundans vel magnum dicant, videntur tamen aliquid dicere, quia occulte insinuant quae dicere volunt.	1959. And if there is a science which is the cause of the. thing known, it must be this science which measures that thing, just as the science of the master planner is the measure of things made by art, because anything made by art is complete insofar as it attains a likeness to the art. It is in this way that the science of God is related to all things. But Protagoras said that man is the measure of all things inasmuch as he knows or perceives them, because knowledge and perception are the measure of substances, i.e., of things which are intelligible and perceptible. For the followers of Protagoras, as has been stated in Book IV (344:C 637), said that things are such because we so perceive them or judge about them. Therefore, although they say nothing extraordinary or important, they nevertheless seem to be saying something of consequence, because they covertly insinuate their doctrine.
lib. 10 l. 2 n. 24 Deinde cum dicit quod quidem epilogat quae dicta sunt; scilicet quod de ratione unius est, quod sit mensura. Et hoc maxime proprium est, prout est in quantitate; deinde in qualitate, et in aliis generibus; quia id quod est mensura, debet esse indivisibile, aut secundum quantitatem, aut secundum qualitatem. Et ita sequitur, quod unum sit indivisibile, aut simpliciter, sicut unitas, quae est principium numeri, aut secundum quid, idest inquantum est unum, ut dictum est in aliis mensuris.	1960. It is evident (828). Then he sums up the points discussed, namely, that the notion of unity involves being a measure; and this applies most properly to quantity, and then to quality and to the other genera, because anything that is a measure should be indivisible either in quantity or in quality. Thus it follows that unity is indivisible, “either in an unqualified sense” as the unit which is the basis of number, or “in a qualified sense,” i.e., to the extent that it is one, as was stated with regard to the other measures.

Lecture 3

Latin	English
lib. 10 l. 3 n. 1 Postquam ostendit philosophus, quomodo unum sit in quantitate primum secundum quamlibet rationem mensurae, et exinde ad alia genera derivetur, nunc determinat de uno qualiter se habeat ad substantiam; utrum scilicet unum sit ipsa substantia rei: et dividitur in tres partes. In prima movet quaestionem et ponit opiniones diversas. In secunda autem determinat veritatem, ostendendo quod unum et ens non sunt substantia eorum de quibus dicuntur, ibi, si itaque nullum. In tertia comparat unum ad ens, ibi, quia vero idem significant. Dicit ergo primo, quod quia iam manifestum est qualiter unum secundum quod habet rationem mensurae se habet in quantitate et in aliis generibus, quaerendum est de uno quomodo se habeat quantum pertinet ad substantias et naturas rerum. Quae quidem dubitatio est mota superius in tertio libro in quo motae sunt quaestiones diversae.	1961. After having shown how unity in the sense of a measure is found first in quantity and then is transferred to the other categories, here the Philosopher deals with the relationship of unity to substance, i.e., whether unity constitutes the very substance of a thing. This is divided into three parts. In the first (829)C ig6i) he raises the question and gives the different opinions regarding it. In the second (830:C 1963) he answers the question by showing that unity and being are not the substance of the things of which they are predicated (“If, then”). In the third (832:C 1974) he compares unity with being (“That unity and being”). He accordingly says, first (829), that, since it has already been shown how unity in the sense of a measure belongs to quantity and to the other classes of things, it is now necessary to ask how unity relates to the substances and natures of things. This question was asked above in Book III (266:C 488), in which different problems were raised.
lib. 10 l. 3 n. 2 Est autem dubitatio, utrum hoc ipsum quod dicitur unum, sit substantia aliqua et per se subsistens, ut dixerunt Pythagorici, et postea Platonici eos sequentes; aut magis ei quod est unum supponatur quaedam natura subsistens, secundum quam notius et magis debet dici quid est quod dicitur unum. Et hoc supposuerunt naturales: quorum unus dixit amorem esse aliquid quod est unum; sicut Empedocles qui ponebat quatuor principia materialia, scilicet quatuor elementa, quibus priora dicunt esse principia agentia, quae ipse ponebat, scilicet amorem et odium. Inter quae praecellit amor, inquantum perfectum et bonorum principium. Unde, si id quod est primum principium dicitur unum, consequitur secundum opinionem eius, quod amor sit illud quod est unum. Quod est conveniens, inquantum amor unionem quamdam indicat amantis et amati. Alius vero, scilicet Diogenes, ponens aerem principium omnium rerum, dixit aerem esse id quod est unum. Alius vero dixit infinitum esse id quod est unum, sicut Melissus, qui posuit esse unum ens infinitum et immobile, ut patet in primo physicorum.	1962. The question is whether the very thing which is called unity is a substance, i.e., something which subsists of itself, as the Pythagoreans first claimed, and as the Platonists, who followed them, later held; or rather whether there is some subsistent nature which underlies unity, in terms of which the quiddity of the thing designated as one should be more meaningfully and adequately expressed. The philosophers of nature presupposed this entity, one of them saying that unity is love, namely, Empedocles, who claimed that there are four material principles, the four elements, to which the active principles posited by him, love and hate, are said to be prior. And of these the most important is love, inasmuch as it is perfect and the principle of good things. Therefore, if the first principle is called unity, it follows according to him that unity is love. And this fits the case inasmuch as it indicates a certain union of the lover and the thing loved. Another philosopher, Diogenes, who claimed that air is the principle of all things (41:C 86), said that unity is air. And still another philosopher said that unity is the indeterminate, namely, Melissus, who claimed that there was one infinite and unchangeable being, as is clear in Book I of the Physics.
lib. 10 l. 3 n. 3 Deinde cum dicit si itaque determinat propositam quaestionem; dicens, quod unum non est substantia subsistens, de qua dicitur quod sit unum. Probat autem hoc dupliciter. Primo ratione. Secundo similitudine, ibi, adhuc autem similiter. Dicit ergo, quod probatum est superius, in septimo scilicet in quo agebat de ente et praecipue de substantia, quod nullum universalium esse potest substantia, quae scilicet per se sit subsistens; quia omne universale commune est multis. Nec possibile est universale esse substantiam subsistentem; quia sic oporteret quod esset unum praeter multa, et ita non esset commune, sed esset quoddam singulare in se.	1963. If, then (830). Here he answers the question which was raised. He says that unity is not a subsisting substance, of which one may predicate the term one. He proves this in two ways. First (830:C 1963), by an argument; and second (831:C 1967), by a comparison (“Further, the same”). He says, then, that it was proved above in Book VII (651:C 1572), where he treats of being, and especially of substance, that no universal can be a substance which subsists of itself because every universal is common to many. A universal also cannot be a subsisting substance because otherwise it would have to be one thing apart from the many, and then it could not be common but would be in itself a singular thing.
lib. 10 l. 3 n. 4 Nisi forte diceretur commune per modum causae. Sed alia est communitas universalis et causae. Nam causa non praedicatur de suis effectibus, quia non est idem causa suiipsius. Sed universale est commune, quasi aliquid praedicatum de multis; et sic oportet quod aliquo modo sit unum in multis, et non seorsum subsistens ab eis.	1964. Unity might, it is true, be said to be common as a cause is. But the common aspect of a universal differs from that of a cause; for a cause is not predicated of its effects, since the same thing is not the cause of itself. But a universal is common in the sense of something predicated of many things; and thus it must be in some way a one-in-many, and not something subsisting apart from them.
lib. 10 l. 3 n. 5 Sed oportet ens et unum magis universaliter et communiter de omnibus praedicari. Non ergo sunt ipsa substantia subsistens, quae dicitur ens vel unum, sicut Plato posuit.	1965. But being and unity must be predicated of all things in the most universal and common way. Hence those things which are called being and unity are not themselves subsisting substances, as Plato maintained.
lib. 10 l. 3 n. 6 Per hanc rationem concluditur, quod nulla genera sunt aliquae naturae et substantiae per se subsistentes, quasi separabiles ab aliis, de quibus dicuntur. Quod etiam superius inter quaestiones fuit dubitatum. Nec tamen hoc pro tanto dicitur, quod unum sit genus. Eadem enim ratione unum non potest esse genus, qua nec ens, quia nec univoce praedicatur, et propter alia quae superius in tertio tacta sunt. Et ex eadem ratione unum et ens non potest esse substantia subsistens.	1966. From this argument he concludes that no genera are natures and substances which subsist of themselves as though separable from the things of which they are predicated. This too was one of the questions debated above (229:C 432). Yet this is not said in the sense that unity is a genus; for unity cannot be a genus for the very same reason that being cannot, since it is not predicated univocally. This is also true in the light of the other reasons given in Book III (269-74:C 493-501). And for the same reason unity and being cannot be subsisting substances.
lib. 10 l. 3 n. 7 Deinde cum dicit adhuc autem ostendit idem ex similitudine; dicens, quod oportet quod unum similiter se habeat in omnibus generibus, quia ens et unum aequaliter de omnibus generibus praedicantur. In omnibus autem generibus quaeritur aliquid quod est unum, quasi ipsa unitas non sit ipsa natura quae dicitur una; sicut patet in qualitatibus et quantitatibus. Unde manifestum est, quod in omnibus generibus non est sufficiens dicere, quod hoc ipsum quod est unum, sit natura ipsius quod unum dicitur; sed oportet quaerere quid est quod est unum, et ens.	1967. Further, the same thing (831). Here he proves the same point by a comparison. He says that unity must be found in the same way in all categories of things, because being and unity are predicated in an equal number of ways of all genera. But in each genus of things we look for something that is one (implying that unity is not the very nature of what is said to be one), as is evident in the case of qualities and in that of quantities. It is clear, then, that in no genus is it sufficient to say that the nature of what is said to be one is just unity itself, but we must inquire what unity and being are.
lib. 10 l. 3 n. 8 Et quod in qualitatibus et in quantitatibus oporteat quaerere quid est quod dicitur unum, manifestat per exempla. Et primo in coloribus. Quaerimus enim aliquid quod est unum, sicut album quod est primum inter colores. Unde si in quolibet genere est unum id quod est primum, oportet quod album sit unum in genere colorum, et quasi mensura aliorum colorum; quia unusquisque color tanto perfectior est, quanto magis accedit ad album. Et quod album sit primum in coloribus, ostendit, quia colores medii generantur ex albo et nigro, et ita sunt posteriores. Nigrum etiam est posterius albo, quia est privatio albi, sicut tenebrae privatio lucis. Non autem sic est intelligendum, quod nigrum sit pura privatio, sicut tenebrae; cum nigrum sit species coloris, et per consequens natura coloris in eo servetur; sed quia in nigro est minimum de luce, quae facit colores. Et sic comparatur ad album, sicut defectus lucis ad lucem.	1968. That it is necessary to investigate what unity is in the category of qualities and in that of quantities he makes clear by examples. He does this first in the case of colors; for we look for something which is one, such as whiteness, which is the primary color. Hence, if what is primary in each class of things is its unity, whiteness must constitute the unity in the class of color; and it must be in a sense the measure of the other colors, because the more perfect a thing’s color the closer it comes to whiteness. He shows that whiteness is the primary color by reason of the fact that intermediate colors are produced from white and from black, and are therefore subsequent. Black is subsequent to white because it is the privation of white as darkness is of light. But this must not be understood to mean that black is pure privation in the same way that darkness is (for black is a species of color, and thus possesses the nature of color), but that blackness contains the least amount of light, which causes colors; and thus it is compared to white as the absence of light is compared to light.
lib. 10 l. 3 n. 9 Et quia in coloribus quaeritur aliquid quod possit dici primum et unum, scilicet album; manifestum est, quod si omnia entia colores essent, haberent quidem aliquem numerum. Non tamen ita quod numerus esset ipsae res subsistentes; sed esset numerus aliquarum rerum subsistentium, scilicet colorum. Et per consequens esset aliquid quod subiiceret ipsi uni, scilicet album.	1969. And because in colors we look for something that is first and one, namely white, it is clear that if all beings were colors, they would have some number, not in the sense, however, that number would constitute subsisting things themselves, but in the sense that there would be a number of subsisting things of a particular sort, i.e., colors. And then there would be something that is the subject of unity, namely, that which is white.
lib. 10 l. 3 n. 10 Et similiter esset si omnia essent melodia; quia entia haberent aliquem numerum, qui quidem esset numerus diesum sive tonorum. Sed tamen numerus non est ipsa substantia entium. Et per consequens oporteret quaerere aliquid quod esset unum, scilicet quod est diesis. Non tamen ita quod ipsum unum esset substantia.	1970. The same thing would be true if all things were tunes; because beings would be of a certain number, that is, a number of minor half tones or tones. Yet number is not the very substance of beings, and consequently it would be necessary to look for something which is one, namely, the minor half tone; but not in such a way that unity itself would be a substance. 1971, In a similar way too if all beings were sounds, they would be a number of beings, because there are a number of particular subjects of number, namely, “of elements,” or letters. Hence the vowel, which is the primary letter (since consonants cannot be pronounced without vowels) would constitute their unity. And in a similar way if all figures were rectilinear figures, there would be a number of subjects, namely, figures; and the triangle, which is the primary rectilinear figure, would constitute their unity; for all such figures are reducible to the triangle. The same reasoning applies to every category.
lib. 10 l. 3 n. 11 Et similiter si omnia entia essent toni, esset quidem numerus entium, quia aliquorum subiectorum ipsi numero, scilicet elementorum, idest literarum. Et per consequens litera vocalis quae est prima inter literas, cum sine ea consonantes sonum reddere non possint, essent unum: similiter si omnia essent figurae rectilineae, numerus esset aliquorum subiectorum, scilicet figurarum, et unum esset triangulus, quae est prima rectilinea figura. Omnes enim figurae rectilineae in triangulum resolvuntur. Et eadem ratio est in omnibus generibus.	1971, In a similar way too if all beings were sounds, they would be a number of beings, because there are a number of particular subjects of number, namely, “of elements,” or letters. Hence the vowel, which is the primary letter (since consonants cannot be pronounced without vowels) would constitute their unity. And in a similar way if all figures were rectilinear figures, there would be a number of subjects, namely, figures; and the triangle, which is the primary rectilinear figure, would constitute their unity; for all such figures are reducible to the triangle. The same reasoning applies to every category.
lib. 10 l. 3 n. 12 Si igitur ita est quod in omnibus aliis generibus, scilicet passionibus et qualitatibus et quantitatibus, et in motu, inveniatur numerus et unum, et numerus et unum non sunt substantia eorum de quibus dicuntur, sed numerus dicitur de quibusdam substantiis; et similiter unum requirat aliquod subiectum quod dicatur unum; necesse est quod similiter se habeat in substantiis, quia ens et unum similiter praedicantur de omnibus. Manifestum est igitur quod in quolibet genere est aliqua natura, de qua dicitur unum; non tamen ita quod ipsum unum sit ipsa natura; sed quia dicitur de ea.	1972. If it is in this way, then, that number and unity are found in all other categories: in affections, qualities, and quantities, and in motion; and if number and unity are not the substance of the things of which they are predicated, but number is predicated of certain substances, and if unity similarly requires some subject which is said to be one, the same thing must be true of substances, because being and unity are predicated in the same way of all things. It is evident, then, that in any category of things there is some nature of which the term one is predicated, not because unity itself is the nature of a thing, but because it is predicated of it.
lib. 10 l. 3 n. 13 Et sicut in coloribus cum dicimus unum, quaerimus aliquem colorem qui dicatur unum; sic in substantia cum dicimus unum, necesse est quaerere aliquam substantiam, de qua dicatur ipsum unum. Et hoc primo et principaliter dicitur de eo, quod est primum in substantiis (quod inquiret inferius); et per consequens de aliis generibus et cetera.	1973. And just as when we speak of unity in the case of colors we are looking for some color which is said to be one, so too when we speak of unity in the case of substances we are looking for some substance of which unity may be predicated. And this is predicated primarily and chiefly of what is first among substances (which he investigates below, 2553-66), and subsequently of the other classes of things.
lib. 10 l. 3 n. 14 Deinde cum dicit quia vero quia eamdem rationem dixerat de ente et de uno, ostendit quod ens et unum aliqualiter idem significant. Et dicit aliqualiter; quia ens et unum sunt idem subiecto, differunt tantum sola ratione. Unum enim addit indivisionem supra ens. Dicitur enim unum ens indivisibile vel indivisum. Ostendit autem quod significat idem, tribus rationibus.	1974. That unity and being (832). Since he had given the same argument for being and for unity, he now shows that unity and being somehow signify the same thing. He says “somehow” because unity and being are the same in their subject and differ only in meaning. For unity adds to being the note of undividedness, because what is one is said to be an indivisible or undivided being. He gives three reasons why unity signifies the same thing as being.
lib. 10 l. 3 n. 15 Quarum prima est, quod unum consequitur omnia alia praedicamenta, et non est in aliquo uno praedicamento tantum: neque in substantia, neque in quantitate, neque in aliquo alio: sicut se habet et de ente.	1975. (1) The first is that unity naturally belongs to all of the different categories and not just to one of them; that is, it does not pertain just to substance or to quantity or to any other category. The same thing is also true of being.
lib. 10 l. 3 n. 16 Secundo, quia cum dicitur unus homo, non aliquam naturam aliam ab homine praedicat, sicut nec ipsum quod est ens praedicat aliam naturam a decem praedicamentis; quia si praedicaret aliam naturam, oporteret abire in infinitum, quia etiam illa natura dicetur unum et ens. Et sic unum unicuique idem est. Et si ens de eis praedicaret aliam naturam, procederetur in infinitum. Si autem non, pari ratione standum fuit in primo.	1976. (2) The second reason is that, when a man is said to be one, the term one does not express a different nature from man, just as being does not express a different nature from the ten categories; for, if it did express a different nature, an infinite regress would necessarily result, since that nature too would be said to be one and a being. And if being were to express a nature different from these things, an infinite regress would also follow; but if not, then the conclusion of this argument must be the same as that of the first one.
lib. 10 l. 3 n. 17 Tertia ratio est, quia unumquodque dicitur unum inquantum est ens. Unde per dissolutionem, res ad non esse rediguntur.	1977. (3) The third reason is that everything is said to be one inasmuch as it is a being. Hence when a thing is dissolved it is reduced to non-being.
lib. 10 l. 3 n. 18 Videtur autem in hac determinatione philosophus sibi contrarius esse. Nam primo dixit, quod unum et ens non sunt substantia eorum de quibus dicuntur. Hic autem dicit, quod unum et ens non praedicant aliquam aliam naturam ab his de quibus dicuntur.	1978. [Objection] Now in this solution of the question the Philosopher seems to contradict himself; for he first said that unity and being are not the substance of the things of which they are predicated, but here he says that unity and being do not express a nature different from the things of which they are predicated.
lib. 10 l. 3 n. 19 Sciendum est igitur quod substantia dicitur dupliciter. Uno modo suppositum in genere substantiae, quod dicitur substantia prima et hypostasis, cuius proprie est subsistere. Alio modo quod quid est, quod etiam dicitur natura rei. Secundum ergo Platonis opinionem, cum universalia essent res subsistentes, significabant substantiam non solum secundo modo, sed primo. Aristoteles vero probat in septimo quod universalia non subsistunt. Unde sequitur quod universalia non sunt substantiae primo modo, sed secundo modo tantum. Propter quod dicitur in praedicamentis, quod secundae substantiae, quae sunt genera et species, non significant hoc aliquid quod est substantia subsistens, sed significant quale quid, idest naturam quamdam in genere substantiae.	1979. Hence it must be noted that the term substance is used in two senses. (1) In one sense it means a supposit in the genus of substance, which is called first substance and hypostasis, to which it properly belongs to subsist. (2) In a second sense it means a thing’s quiddity, which is also referred to as a thing’s nature. Therefore, since universals are subsistent things according to the opinion of Plato, they signify substance not only in the second sense but also in the first. But Aristotle proves in Book VII (1572) that universals are not subsistent things, and therefore it follows that universals are not substances in the first sense but only in the second. And for this reason it is said in the Categories that second substances, which are genera and species, do not signify particular things, which are subsisting substances, but “they signify the quiddity of a thing,” i.e., a nature in the genus of substance.
lib. 10 l. 3 n. 20 Sic igitur philosophus supra probavit, quod unum et ens non significant substantiam quae est hoc aliquid, sed oportet quaerere aliquid quod sit unum et ens. Sicut quaeritur aliquid quod sit homo vel animal, ut Socrates vel Plato. Postmodum vero ostendit quod significant naturam eorum de quibus dicuntur, et non aliquid additum sicut accidentia. In hoc enim differunt communia ab accidentibus, quamvis utrisque sit commune non esse hoc aliquid: quia communia significant ipsam naturam suppositorum, non autem accidentia, sed aliquam naturam additam.	1980. The Philosopher accordingly proved above that unity and being do not signify substance in the sense of this particular thing, but it is necessary to look for something that is one and a being, just as we look for something that is a man or an animal, as Socrates or Plato. Later he shows that these terms signify the natures of the things of which they are predicated and not something added, like accidents. For common attributes differ from accidents in this respect (although they agree in not being particular things), that common attributes signify the very nature of supposits, whereas accidents do not, but they signify some added nature.
lib. 10 l. 3 n. 21 Hoc autem non considerans Avicenna posuit quod unum et ens sunt praedicata accidentalia, et quod significant naturam additam supra ea de quibus dicuntur. Deceptus enim fuit ex aequivocatione unius. Quod quidem secundum quod est principium numeri habens rationem mensurae in genere quantitatis, significat quamdam naturam additam his de quibus dicitur, cum sit in genere accidentis. Sed unum quod convertitur cum ente circuit omnia entia. Unde non significat aliquam naturam determinatam ad aliquod genus.	1981. And Avicenna, who did not take this into account, claimed that unity and being are accidental predicates, and that they signify a nature added to the things of which they are predicated. For he was deceived by the equivocal use of the term one, because the unity which is the principle of number and has the role of a measure in the genus of quantity signifies a nature added to the things of which it is predicated, since it belongs to a class of accident. But the unity which is interchangeable with being extends to everything that is, and therefore it does not signify a nature which is limited to one category.
lib. 10 l. 3 n. 22 Similiter etiam deceptus est ex aequivocatione entis. Nam ens quod significat compositionem propositionis est praedicatum accidentale, quia compositio fit per intellectum secundum determinatum tempus. Esse autem in hoc tempore vel in illo, est accidentale praedicatum. Sed ens quod dividitur per decem praedicamenta, significat ipsas naturas decem generum secundum quod sunt actu vel potentia.	1982. He was also deceived by the equivocal use of the term being; for being as signifying the composition of a proposition is predicated accidentally, since composition is made by the intellect with regard to a definite time. Now to exist at this or at that particular time is to be an accidental predicate. But being as divided by the ten categories signifies the very nature of the ten categories insofar as they are actual or potential.

Lecture 4

Latin	English
lib. 10 l. 4 n. 1 Postquam philosophus determinavit de uno secundum se, hic determinat de uno per comparationem ad multitudinem; et dividitur in partes duas. In prima determinat de uno et multitudine, et de his quae ad ea consequuntur. In secunda determinat de contrarietate quae inter unum et multa invenitur, eo quod specialem difficultatem habeat consideratio eius, ibi, quoniam autem differre contingit abinvicem. Prima dividitur in duas. In prima ostendit quomodo unum opponitur multitudini. In secunda determinat de his quae consequuntur ad unum et multitudinem, ibi, est autem unius. Circa primum tria facit. Primo ostendit secundum quid accipienda sit oppositio quae est inter unum et multa; dicens, quod licet unum et multa multis modis opponantur, ut patet infra; eorum tamen unus et principalior est secundum quod unum et multitudo opponuntur ut divisibile et indivisibile; quia hic oppositionis modus attenditur secundum propriam rationem utriusque.	1983. After having treated of one considered in itself, here the Philosopher deals with one in comparison with many; and this is divided into two parts. In the first (1983) he treats one and many and their concomitant attributes. In the second (2023) he establishes what is true about the contrary character of one and many; for the investigation of this involves a special difficulty. The first member of this division is divided into two parts. In the first part he shows how one and many are opposed. In the second (1999) he considers their concomitant attributes. In regard to the first he does three things. First, he indicates how we should understand the opposition between one and many. He says that, although one and many are opposed in many ways, as will be made clear below, none the less one of these ways, and the most important one, concerns one and many insofar as they are opposed as something indivisible is opposed to something divisible, because this mode of opposition pertains to the proper notion of each.
lib. 10 l. 4 n. 2 Ratio enim multitudinis consistit in hoc quod est esse divisa abinvicem, aut divisibilia. Dicit autem divisa, propter ea quae actu a seinvicem separata sunt, et propter hoc multa dicuntur. Divisibilia autem, propter ea quae non sunt actu separata, sed appropinquant separationi, sicut humida, ut aer et aqua, et alia his similia, in quibus propter facilitatem divisionis, multitudinem dicimus. Dicitur enim multa aqua et multus aer. Ratio vero unius consistit in hoc, quod est esse indivisibile, aut non esse divisum. Dicitur enim et continuum unum, quia non et actu divisum, licet sit divisibile.	1984. For the essential note of plurality consists in things being divided from each other or in being divisible. He says “divided” because of the things which are actually separated from each other and which are for this reason said to be many. He says “divisible” because of the things which are not actually separated from each other but come close to being separated, for example, moist things such as air and water and the like, of which we use the term much because they are easily divided; thus we speak of much water and much air.1985. But the formal constituent of unity or oneness consists in being indivisible or in being undivided; for the continuous is said to be one because it is not actually divided, although it is divisible.
lib. 10 l. 4 n. 3 Secundo ibi, quoniam ergo ostendit ad quod genus oppositionis praedictus modus oppositionis reducatur; dicens, quod cum quatuor sint oppositionis genera, quorum unum est oppositio, quae dicitur secundum privationem; manifestum est quod unum et multa non opponuntur ut contradictio, neque ad aliquid, quae sunt duo genera oppositionis, sed opponuntur ut contraria.	1986. Hence, since (834). Second, he makes clear to what kind of opposition the aforesaid manner of being opposed is ultimately reduced. He says that, since there are four kinds of opposition, one of which is based on privation, it is evident that one and many are not opposed as contradictories or as relative terms, which are two kinds of opposition, but as contraries.
lib. 10 l. 4 n. 4 Et quidem quod non opponantur secundum contradictionem, manifestum est, quia neutrum eorum verificatur de non ente. Non ens enim neque unum neque multa est. Oporteret autem alteram partem contradictionis verificari tam de ente quam de non ente. Similiter etiam manifestum est, quod non opponuntur ut ad aliquid dicta. Nam unum et multitudo dicuntur absolute.	1987. That they are not opposed as (~) contradictories is evident because neither of them applies to non-being, for non-being is neither one nor many. But the second member of the contradiction would have to apply to being as well as to non-being. That they are not opposed as relative terms is likewise evident, for the terms one and many are used in an absolute sense.
lib. 10 l. 4 n. 5 Sed cum dixerit quod unum et multitudo opponuntur ut indivisibile et divisibile, quae videntur opponi secundum privationem et habitum, concludit tamen quod unum et multitudo opponuntur ut contraria. Oppositio enim quae est secundum privationem et habitum, est principium oppositionis quae est secundum contrarietatem, ut infra patebit. Alterum enim contrariorum semper est privatio, sed non privatio pura. Sic enim non participaret naturam generis, cum contraria sint in eodem genere. Oportet igitur quod utrumque contrariorum sit natura quaedam, licet alterum eorum participet naturam generis cum quodam defectu, sicut nigrum se habet ad album, ut supra dictum est. Quia igitur unum non significat privationem puram, non enim significat ipsam indivisionem, sed ipsum ens indivisum, manifestum est quod unum et multitudo non opponuntur secundum privationem puram et habitum, sed sicut contraria.	1988. And although he had said that one and many are opposed as what is indivisible and what is divisible, and these appear to be opposed as privation and possession, none the less he concludes that one and many are opposed as contraries; for the opposition between privation and possession is the basis of the opposition between contraries, as will be made clear below (2036). For one of the two contraries is always a privation, but not a pure privation; otherwise it would not share in the nature of the genus, since contraries belong to the same genus. Each of the two contraries, then, must be a positive reality, even though one of them shares in the nature of the genus with a certain deficiency, as black in relation to white, as has been stated above (1967). Therefore, since unity does not signify a pure privation, for it does not designate the mere lack of division but the very being which is undivided, it is evident that one and many are opposed not as pure privation and possession but as contraries.
lib. 10 l. 4 n. 6 Tertio ibi, dicitur autem. Respondet tacitae quaestioni. Quia enim dixerat quod unum se habet ad multitudinem ut divisibile ad indivisibile, indivisibile autem videtur privatio esse divisibilis, cum privatio sit posterior habitu et forma, videtur sequi, quod unum sit posterius multitudine: cum tamen supra dixerit, quod unum est principium multitudinis, ex quo cognoscitur.	1989. And what is one (835). [Objection] Third, he answers an implied question. Because he had said that one is related to many as what is indivisible to what is divisible, and what is indivisible seems to be the privation of what is divisible since privation is subsequent to possession or form, it seems to follow that one is subsequent to many, although he had said above (1939) that one is the principle of many, from which it becomes known.
lib. 10 l. 4 n. 7 Ad huius igitur obiectionis solutionem videndam, considerandum est, quod ea quae sunt priora secundum naturam et magis nota, sunt posteriora et minus nota quo ad nos, eo quod rerum notitiam per sensum accipimus. Composita autem et confusa prius cadunt in sensu, ut dicitur in primo physicorum. Et inde est, quod composita prius cadunt in nostram cognitionem. Simpliciora autem quae sunt priora et notiora secundum naturam, cadunt in cognitionem nostram per posterius. Inde est quod prima rerum principia non definimus nisi per negationes posteriorum; sicut dicimus quod punctum est, cuius pars non est; et Deum cognoscimus per negationes, inquantum dicimus Deum incorporeum esse, immobilem, infinitum.	1990. In order to see the solution of this difficulty, then, it must be borne in mind that things which are prior and better known by nature are subsequent and less well known to us, because we derive our knowledge of things from the senses. Now the first things to be perceived by us are composite and confused things, as is said in Book I of the Physics; and this is why the first things to be known by us are composite things. But simpler things, which are prior and more intelligible by nature, are known by us only derivatively; and this is why we define the first principles of things only by the negations of subsequent things; for example, we say that the point is what has no parts; and we know God by way of negations inasmuch as we say that God is incorporeal, unchangeable and infinite.
lib. 10 l. 4 n. 8 Sic igitur licet unum prius secundum naturam sit multitudine, tamen secundum cognitionem nostram definitur et nominatur ex privatione divisionis. Et propter hoc philosophus dicit quod ipsum unum dicitur, idest nominatur et ostenditur, idest cognoscitur ex suo contrario, sicut indivisibile ex divisibili: propter hoc quod multitudo est magis sensibilis quam unum, et divisibile magis quam indivisibile. Unde multitudo ratione prius est quam indivisibile, non quidem secundum ordinem naturae, sed propter sensum qui est principium nostrae cognitionis.	1991. Accordingly, even though what is one is prior by nature to what is many, yet in our knowledge it is defined and gets its name from the privation of division. This is why the Philosopher says that “what is one is described,” i.e., named, “and made known,” i.e., understood, “in reference to its contrary,” just as the indivisible is known from the divisible. And for this reason many things are able to be perceived more easily than one thing; and what is divisible is able to be perceived more easily than what is indivisible, not in the order of nature but because of sensory perception, which is the foundation of our knowledge.
lib. 10 l. 4 n. 9 Sed contra ea quae hic philosophus determinat, duplex dubitatio consurgit. Prima quidem circa hoc quod dicit, quod unum et multa opponuntur ut contraria. Hoc enim videtur impossibile, quia unum constituit multitudinem. Unum autem contrariorum non constituit aliud, sed magis destruit.	1992. [Objection] But a twofold difficulty arises with regard to those things which the Philosopher is expounding. The first concerns his statement that one and many are opposed as contraries. For this appears to be impossible, because unity is the basis of plurality, whereas one of two contraries does not ground the other but rather destroys it.
lib. 10 l. 4 n. 10 Sciendum igitur est, quod cum contraria differant secundum formam, ut infra dicetur, cum dicimus aliqua esse contraria, accipiendum est utrumque eorum secundum quod habet formam, non autem secundum quod est pars habentis formam. Corpus enim secundum quod absque anima accipitur ut formam habens, opponitur animali ut inanimatum animato. Secundum vero quod accipitur non quasi aliquod perfectum et formatum, non opponitur animali, sed est pars materialis ipsius. Et sic etiam videmus in numeris. Nam binarius secundum quod est quoddam totum, speciem et formam determinatam habens, est diversum specie a ternario; si vero consideretur absque hoc quod sit perfectum per formam, est pars ternarii.	1993. Hence it must be noted that, since contraries differ formally, as is said below (2120), when we say that things are contraries, each of them is to be taken (+) insofar as it has a form, but not (~) insofar as it is a part of something having a form. (+) For insofar as body is taken without the soul, as something having a form, it is opposed to animal as the non-living is opposed to the living. (~) But insofar as it is not taken as something complete and informed, it is not opposed to animal but is a material part of it. We see that this is likewise true of numbers; for insofar as the number two is a kind of whole having a determinate species and form, it differs specifically from the number three; but if it is taken insofar as it is not made complete by a form, it is a part of the number three.
lib. 10 l. 4 n. 11 Sic igitur et ipsum unum secundum quod consideratur ut in se perfectum et speciem quamdam habens, opponitur multitudini; quia quod est unum, non est multa neque e contra. Prout vero consideratur ut non completum secundum speciem et formam, sic non opponitur multitudini, sed est pars eius.	1994. Therefore insofar as unity itself is considered to be complete in itself and to have a certain species, it is opposed to plurality; because what is one is not many, nor is the reverse true. But insofar as it is considered to be incomplete as regards form and species, it is not opposed to plurality but is a part of it.
lib. 10 l. 4 n. 12 Secunda autem dubitatio oritur circa hoc quod dicit, quod multitudo est prior ratione quam unum. Cum enim unum sit de ratione multitudinis, eo quod multitudo non est aliud quam aggregatio unitatum, si ipsum unum est posterius ratione quam multitudo, sequitur quod in ratione unius et multitudinis, est quidam circulus; ita quod necesse sit per multitudinem intelligi unitatem, et e converso. Circulus autem in rationibus rerum non suscipitur, quia esset idem eodem notius et minus notum, quod est impossibile.	1995. [Objection] The second difficulty has to do with the statement that plurality is prior in intelligibility to unity; for, since the concept of plurality or multitude involves unity, because a plurality is nothing else than an aggregate of units, if unity is subsequent in intelligibility to plurality, it follows that the notions of unity and plurality involve circularity, i.e., in the sense that unity is intelligible in terms of plurality and vice versa. But circularity of definition is not admissible in designating the intelligible structures of things, because the same thing would then be known both to a greater and to a lesser degree. This is impossible.
lib. 10 l. 4 n. 13 Dicendum igitur quod nihil prohibet aliquid esse prius et posterius eodem secundum rationem, secundum diversa in eo considerata. In multitudine enim considerari potest, et quod multitudo est, et ipsa divisio. Ratione igitur divisionis prior est quam unum secundum rationem. Nam unum est quod non dividitur. Secundum autem quod est multitudo, posterius est uno secundum rationem, cum multitudo dicatur aggregatio unitatum.	1996. The answer to this difficulty, then, must be that nothing prevents one and the same thing from being prior and subsequent in intelligibility according to different traits which are considered in it. For in multitude it is possible to consider both multitude as such and division itself. Thus from the viewpoint of division multitude is prior in intelligibility to unity; for that is one which is undivided. But multitude as multitude is subsequent in intelligibility to unity, since a multitude means an aggregate of units or ones.
lib. 10 l. 4 n. 14 Divisio autem quae praesupponitur ad rationem unius, secundum quod convertitur cum ente, non est divisio quantitatis continuae, quae praeintelligitur uni quod est principium numeri. Sed est divisio quam causat contradictio, prout hoc ens et illud, dicuntur divisa, ex eo quod hoc non est illud.	1997. Now the division which is implied in the notion of that kind of unity which is interchangeable with being is not (~) the division of continuous quantity, which is understood prior to that kind of unity which is the basis of number, but is (+) the division which is caused by contradiction, inasmuch as two particular beings are said to be divided by reason of the fact that this being is not that being.
lib. 10 l. 4 n. 15 Sic ergo primo in intellectu nostro cadit ens, et deinde divisio; et post hoc unum quod divisionem privat, et ultimo multitudo quae ex unitatibus constituitur. Nam licet ea quae sunt divisa, multa sint, non habent tamen rationem multorum, nisi postquam huic et illi attribuitur quod sit unum. Quamvis etiam nihil prohiberet dici rationem multitudinis dependere ex uno, secundum quod est mensurata per unum, quod iam ad rationem numeri pertinet.	1998. Therefore what we first understand is being, and then division, and next unity, which is the privation of division, and lastly multitude, which is a composite of units. For even though things which are divided are many, they do not have the formal note of a many until the fact of being one is attributed to each of the particular things concerned. Yet nothing prevents us from also saying that the notion of multitude depends on that of unity insofar as multitude is measured by one; and this already involves the notion of number.
lib. 10 l. 4 n. 16 Deinde cum dicit est autem determinat de his quae causantur ex uno et multo; et circa hoc duo facit. Primo ponit ea quae consequuntur unum et multa; dicens, quod sicut superius in quinto dictum est, ubi divisit sive distinxit quot modis dicantur contraria, ad unum consequitur idem et simile et aequale. Nam idem est unum in substantia, simile unum in qualitate, aequale vero unum in quantitate.	1999. And as we have (836). Here he indicates the attributes which stem from unity and plurality; and in regard to this he does two things. First, he gives the attributes which naturally stem from unity and plurality. He says that sameness, likeness and equality flow from unity, as has been pointed out above in Book V (911), where he divided or distinguished the various senses in which things are said to be contrary; for those things are the same which are one in substance; those are like which are one in quality; and those are equal which are one in quantity.
lib. 10 l. 4 n. 17 Ad pluralitatem vero pertinent contraria horum, scilicet diversum et dissimile et inaequale. Nam diversa sunt quorum non est substantia una, et dissimilia quae non habent qualitatem unam, et inaequalia quae non habent unam quantitatem.	2000. And the contraries of these, diverse, unlike and unequal, pertain to plurality. For those things are diverse whose substance is not one; those are unlike whose quality is not one; and those are unequal whose quantity is not one.
lib. 10 l. 4 n. 18 Deinde cum dicit dicto vero ostendit quot modis dicantur praedicta; et circa hoc duo facit. Primo distinguit modos eorum, quae consequuntur ad unum. Secundo distinguit modos eorum quae consequuntur pluralitatem, ibi, quare palam quod diversum et dissimile. Circa primum duo facit. Primo ostendit quot modis dicitur idem. Secundo quot modis dicitur simile, ibi, similia vero, si non sunt et cetera. Aequale vero non distinguit, quia non dicitur multipliciter, nisi forte secundum diversas species quantitatis.	2001. Now things (837). He now explains the various senses in which these terms are used; and in regard to this he does two things. First, he shows how the modes of those attributes which accompany unity differ from each other. Second (2013) he does the same thing for those attributes which accompany plurality (“It is evident”). In regard to the first part he does two things. First, he explains the various ways in which things are said to be the same; and second (2006), those in which they are said to be like (“Things are like”). He does not make any distinctions as regards equality, however, because there are not many ways in which things are said to be equal, unless perhaps in reference to the various kinds of quantity.
lib. 10 l. 4 n. 19 Ponit ergo tres modos quibus dicitur idem. Cum enim idem sit unum in substantia, substantia autem dupliciter dicatur, scilicet ipsum suppositum, et natura sive species, tripliciter dicitur idem. Vel secundum suppositum solum, ut hoc album, hoc musicum, si Socrates sit albus vel musicus; vel solum per naturam suppositi sive rationem vel speciem eius, sicut Socrates et Plato sunt idem humanitate; vel secundum utrumque, sicut Socrates est idem Socrati.	2002. He accordingly gives three ways in which the term same is used. For since same means one in substance, and substance is used of two things, namely, of the supposit itself and of the nature or species of a thing, the term same is used of three things: either (1) of the supposit alone, as this white thing or this musical man, assuming that Socrates is white or musical; or (2) of the nature of the supposit alone, that is, its intelligible expression or species, as Socrates and Plato are the same in terms of humanity; or (3) of both together, as Socrates is the same as Socrates.
lib. 10 l. 4 n. 20 Hos igitur tres modos philosophus assignans dicit, quod cum idem multipliciter dicatur, uno modo dicitur idem secundum numerum, quod aliquando dicimus ipsum, sicut si dicamus, Socrates est homo, et ipsum est album. Cum enim hoc pronomen, ipsum, sit relativum, relativum autem idem suppositum referat, ubicumque ponitur hoc quod dico ipsum, designat quod sit idem suppositum numero.	2003. Hence, the Philosopher, in giving these three ways in which the term is used, says that the term same is used in many senses. (1) In one sense it means what is numerically the same, which we sometimes express by the term itself, as when we say that Socrates is a man and that he himself is white. For since the pronoun itself is reflexive, and a reflexive term brings back the same supposit, wherever the term itself is used it signifies that the supposit is numerically one and the same.
lib. 10 l. 4 n. 21 Alio modo dicitur idem si fuerit unum, non solum unitate suppositi, ut hoc lignum et hoc album, sed simul ratione et numero, ut tu tibiipsi es idem et specie et materia; ut materia referatur ad suppositum quae est individuationis principium, et species pro natura suppositi accipiatur.	2004. (2) A thing is said to be the same in another sense if it is one not only by the oneness of the supposit, as this wood and this white thing, but if it is the same both in its intelligible structure and in number, as you are the same as yourself both specifically and materially, inasmuch as matter, which is the principle of individuation is taken for the supposit, and species is taken for the nature of the supposit.
lib. 10 l. 4 n. 22 Tertio modo dicitur idem quando ratio primae substantiae, idest suppositi est una, licet suppositum non sit unum. Et hoc est idem specie vel genere, sed non numero. Ponit autem exemplum in quantitatibus, secundum opinionem eorum, qui ponebant quantitates esse substantias rerum: secundum quam quidem opinionem plures lineae rectae, sunt sicut plura supposita in genere substantiae: mensura autem lineae est sicut species eius. Unde multae lineae rectae aequales, sunt unum secundum hanc positionem, sicut diversa supposita sunt unum quae communicant in una ratione speciei. Et quia mathematici utuntur lineis in abstractione, apud eos plures lineae aequales rectae accipiuntur ut una. Et similiter plura tetragona, scilicet figurae quatuor angulorum quae sunt aequalia quantitate, et sunt isagona, idest aequalium angulorum, accipiuntur ut idem. Et aequalitas in eis est quasi unitas secundum rationem speciei.	2005. (3) Things are said to be the same in a third sense when “the intelligible structure of the primary substance,” i.e., of the supposit, is one, even though there is not one supposit. And these things are the same specifically or generically but not numerically. He gives an example of this in the case of quantity, according to the opinion of those who claimed that quantities are the substances of things; and according to this opinion many straight lines are regarded as many supposits in the genus of substance, and the measure of a line is considered to be its species. This opinion maintains, then, that many straight lines are one, just as distinct supposits are one which have one specific nature in common. And since mathematicians speak of lines in the abstract, for them many equal straight lines are considered as one. And in a similar fashion many “equal quadrangles,” i.e., figures which have four angles and are equal in size and “equiangular,” i.e., having equal angles, are considered to be the same. And in such things as these equality provides the unity of their specific nature.
lib. 10 l. 4 n. 26 Deinde cum dicit similia vero ostendit quot modis dicitur simile; et ponit quatuor modos; quorum primus respondet tertio modo eius, quod dicitur idem. Quia enim idem est unum in substantia, simile vero unum in qualitate, oportet illud, secundum quod dicitur simile, se habere ad id, secundum quod dicitur idem, sicut se habet qualitas ad substantiam. Et quia usus est aequalitate quasi unitate in substantia, utitur figura et proportione quasi qualitate.	2006. Things are “like” (838). Here he reveals the different ways in which things are said to be like, and there are four of these. (1) The first corresponds to the third way in which things are the same; for since that is the same which is one in substance, and that is like which is one in quality, the basis of likeness must be related to the basis of sameness as quality to substance. And since he has used equality to designate oneness of substance, he uses figure and proportion to designate quality.
lib. 10 l. 4 n. 27 Attendendum etiam est, quod cum qualitas et quantitas fundentur in substantia: ubi est unitas substantiae, sequitur quod sit unitas quantitatis et qualitatis, non tamen unitas nominatur a quantitate et qualitate, sed a principaliori, scilicet substantia. Et ideo ubi est unitas substantiae, non dicitur similitudo vel aequalitas, sed identitas tantum.	2007. It should also be noted that, since quality and quantity are rooted in substance, it follows that wherever there is oneness of substance there is oneness of quantity and quality, although this oneness or unity does not derive its name from quantity and quality but from something more basic, namely, substance. Hence, wherever there is oneness of substance we do not speak of likeness or of equality but only of identity.
lib. 10 l. 4 n. 28 Ad similitudinem ergo vel aequalitatem requiritur diversitas substantiae. Et propter hoc dicit quod similia dicuntur aliqua, licet non sint simpliciter eadem secundum speciem substantiae, et si non sint etiam indifferentia secundum substantiam subiectam quae dicitur suppositum, sed sunt eadem secundum speciem aliquo modo, sicut maius tetragonum dicitur esse simile minori tetragono, quando scilicet anguli unius sunt aequales angulis alterius, et latera aequales angulos continentia sunt proportionalia. Sic igitur patet quod haec similitudo attenditur secundum unitatem figurae et proportionis. Et similiter multae rectae lineae inaequales non sunt eaedem simpliciter, licet sint similes.	2008. Diversity of substance, then, is required for likeness or equality. This is why he says that some things are said to be like even though they are not absolutely the same as to the species of their substance (provided that they are also not without difference in their underlying subject, which is called the supposit) but are specifically the same in some way. Thus a larger quadrangle is said to be like a smaller one when the angles of one are equal to those of the other and the sides containing the angles are proportional. It is evident, then, that this likeness is viewed from the standpoint of oneness of figure and proportion. And in a similar way many unequal straight lines are not the same in an absolute sense even though they are like.
lib. 10 l. 4 n. 29 Potest autem et hic considerari quod quando est unitas secundum rationem perfectam speciei, dicitur identitas; quando autem est unitas non secundum totam rationem speciei, dicitur similitudo. Ut si quis dicat quod ea quae sunt unum genere, sunt similia; ea vero quae sunt unum specie, sunt eadem; ut videntur innuere exempla posita. Nam lineas rectas aequales et tetragona aequalia dixit habere identitatem adinvicem; tetragona autem inaequalia et rectas lineas inaequales habere similitudinem.	2009. It can also be noted here that, when there is unity in regard to the complete concept of the species, we speak of identity. But when there is no unity in regard to the whole concept of the species, we speak of likeness; so that if someone says that things which are generically one are like, then those which are specifically one are the same, as the examples given above would seem to indicate. For he said that equal straight lines and equal quadrangles are identical with each other, whereas unequal quadrangles and unequal straight lines are said to be like.
lib. 10 l. 4 n. 30 Secundus modus est si aliqua conveniunt in una forma quae nata sit suscipere magis et minus, et tamen participent illam formam sine magis et minus: sicut albedo recipit intensionem et remissionem; unde si aliqua sunt alba aequaliter sine magis et minus, dicuntur similia.	2010. (2) Things are said to be like in a second sense when they have in common one form which admits of difference in degree although they participate in that form without difference in degree; for example, whiteness admits of greater and lesser intensity, so that, if some things are equally white without any difference in degree, they are said to be like.
lib. 10 l. 4 n. 31 Tertius modus est quando aliqua conveniunt in una forma aut passione, etiam secundum magis et minus; sicut magis album et minus album dicuntur similia, quia est una species, idest qualitas ipsorum.	2011. (3) Things are said to be like in a third sense when they have in common one form or affection but to a greater or lesser degree; for example, a thing which is whiter and one which is less white are said to be like because they have “one form,” i.e., one quality.
lib. 10 l. 4 n. 32 Quartus modus est secundum quod aliqua dicuntur similia, non propter unam qualitatem tantum, sed consideratione multorum: ut dicantur illa esse similia quae in pluribus conveniunt quam differant, vel simpliciter, vel quantum ad ea quae in promptu apparent. Sicut stamnum argento dicitur simile, quia in multis convenit. Et similiter ignis auro, et crocus rubeo.	2012. (4) Things are said to be like in a fourth sense when they have in common not merely one quality but many, as those things which are said to be like because they agree in more respects than they differ, either in an absolute sense, or in regard to certain particular attributes; for example, tin is said to be like silver because it resembles it in many respects. And similarly fire is like gold, and saffron like red.
lib. 10 l. 4 n. 33 Deinde cum dicit quare palam prosequitur de illis quae consequuntur ad pluralitatem. Et primo de dissimili et de diverso. Secundo de differenti, ibi, differentia vero et diversitas et cetera. Dicit ergo primo, quod quia idem et diversum opponuntur, et simile et dissimile: idem autem et simile multipliciter dicuntur; manifestum est quod diversum et dissimile multipliciter dicentur, quia scilicet quando unum oppositorum dicitur multipliciter, et reliquum, ut dicitur in primo topicorum.	2013. It is evident (839). Here he treats the attributes which naturally accompany plurality. First, he considers unlikeness and diversity; and second (2017), he treats difference (“But different”). He accordingly says, first, that, since the terms same and diverse and like and unlike are opposed to each other, and since the terms same and like are used in many senses, it is evident that the terms diverse and unlike are used in many senses; for when, one of two opposites is used in many senses, the other is also used in many senses, as is said in the Topics, Book I.
lib. 10 l. 4 n. 34 Omissa autem multiplicitate dissimilis quia facile apparet qualiter modi eius accipiantur per oppositum ad modos similis, ponit tres modos eius quod est diversum. Quorum primus est quod diversum dicitur omne quod est aliud per oppositum ad idem. Sicut enim idem dicebatur omne quod est ipsum, quod est relativum identitatis, ita diversum dicitur esse quod est aliud, quod est relativum diversitatis. Et propter hoc, unumquodque ad aliud comparatum, aut est idem aut diversum. Alius modus est quando non est una materia et una ratio; sicut tu et propinquus tibi, diversi estis. Tertius autem modus est, sicut in mathematicis: ut si dicantur lineae inaequales diversae.	2014. But omitting the many senses in which the term unlike is used, since it is quite apparent how the senses of this term are taken in contrast to those of the term like, he gives three senses in which the term diverse, or other, is employed. (1) First, the term diverse refers to everything that is other in contrast to the same; for just as everything that is itself is said to be the same, and this is the relation of identity, in a similar fashion everything that is diverse is said to be other, and this is the relation of diversity. Hence everything is either the same as or other than everything else. (2) Second, the term diverse, or other, is used in another sense when the matter and intelligible structure of things are not one; and in this sense you and your neighbor are diverse. (3) The term is used in a third sense in mathematics, as when unequal straight lines are said to be diverse.
lib. 10 l. 4 n. 35 Et quia dixerat quod omne ad omne est idem aut diversum, ne quis crederet hoc esse verum, tam in entibus quam in non entibus, removet hoc dicens: diversum aut idem dicitur omne ad omne in his quae dicuntur unum et ens, non autem in non entibus. Idem enim et diversum non opponuntur ut contradictoria, quorum alterum necesse est verum esse de quolibet ente aut non ente; sed opponuntur ut contraria, quae non verificantur nisi de ente. Et ideo diversum non dicitur de non entibus. Sed non idem, quod contradictorie opponitur eidem, dicitur etiam de non entibus. Sed in omnibus entibus dicitur idem aut diversum. Omne enim quod est ens et unum in se, comparatum alteri, aut est unum ei, et sic est idem; aut non unum, aptum natum esse unum, et sic est diversum. Sic igitur diversum et idem opponuntur.	2015. [Objection] And since he had said that everything is either the same as or other than everything else, lest someone think that this is true not only of beings but also of non-beings, he rejects this by saying that everything is either the same as or other than everything else in the case of those things of which the terms being and unity are predicated, but not in the case of those things which are non-beings. For same and diverse are not opposed as contradictory terms, of which one or the other must be true of any being or non-being; but they are opposed as contraries, which are only verified of beings. Hence diversity is not predicated of non-beings. But the phrase not the same, which is the opposite of the same in a contradictory sense, is also used of non-beings. However, same or diverse is used of all beings; for everything that is a being and is one in itself, when compared with something else, is either one with it, and then it is the same, or it is capable of being one with it but is not, and then it is diverse. Diverse and same, then, are opposites.
lib. 10 l. 4 n. 36 Si quis autem obiiciat quod diversum et idem non sunt in omnibus entibus, cum idem sequatur unitatem substantiae, diversitas autem substantiae pluralitatem; dicendum est, quod quia substantia radix est aliorum generum, illud quod est substantiae, transfertur ad omnia alia genera, sicut de eo quod quid est philosophus dixit supra in septimo.	2016. But if someone were to raise the objection that diversity and sameness do not apply to all beings, since sameness is a natural consequence of oneness of substance, and diversity is a natural consequence of plurality of substance, we should have to answer that, since substance is the root of the other genera, whatever belongs to substance is transferred to all the other genera, as the Philosopher pointed out above regarding quiddity in Book VII (1334).
lib. 10 l. 4 n. 37 Deinde cum dicit differentia vero ostendit in quo differat differentia et diversitas; dicens, quod aliud est differentia, aliud diversitas. Duo enim quorum unum est diversum ab altero, non est necesse per aliquid esse diversa. Possunt enim esse diversa seipsis. Et hoc ex praedictis patet; quia quodcumque ens alteri comparatum, aut est diversum, aut est idem.	2017. But “different” (840). Then he shows how difference and diversity differ. He says that diverse and different mean different things; for any two things which are diverse need not be diverse in some particular respect, since they can be diverse in themselves. This is evident from what has been said above, because every being is either the same as or other than every other being.
lib. 10 l. 4 n. 38 Sed quod est differens ab aliquo, oportet quod per aliquid sit differens. Unde necesse est, ut id quo differentia differunt, sit aliquid idem in illis quae non sic differunt. Hoc autem quod est idem in pluribus, vel est genus, vel est species. Unde omne differens, differt aut genere, aut specie.	2018. But that which differs from something else must differ from it in some particular respect. Hence that by which different things differ must be something that is the same in things which do not differ in this way. Now that which is the same in many things is either a genus or a species. Therefore all things that differ must differ either generically or specifically.
lib. 10 l. 4 n. 39 Genere quidem differunt, quorum non est communis materia. Dictum est enim supra in octavo, quod licet materia non sit genus, tamen ab eo quod est materiale in re, sumitur ratio generis. Sicut natura sensibilis est materialis in homine respectu rationis. Et ideo illud quod non communicat in natura sensibili cum homine, est alterius generis.	2019. Those things differ generically which have no common matter; for it has been said above, in Book VIII (1697), that although matter is not a genus, still the essential note of a genus is taken from a thing’s material constituent; for example, sensory nature is material in relation to the intellectual nature of man. Hence anything that does not possess sensory nature in common with man belongs to a different genus.
lib. 10 l. 4 n. 40 Et quia ea quae non communicant in materia, non generantur adinvicem, sequitur ea genere esse diversa, quorum non est generatio adinvicem. Quod etiam necesse fuit addere propter ea quae non habent materiam, sicut accidentia sunt. Ut sint genere diversa quaecumque sunt in diversis praedicamentis, ut linea et albedo, quorum unum non fit ex alio.	2020. And since those things which do not have a common matter are not generated from each other, it follows that those things are generically diverse which are not generated from each other. It was also necessary to add this because of the things which do not have matter, such as accidents, so that those things which belong to different categories are generically diverse, for example, a line and whiteness, neither one of which is produced from the other.
lib. 10 l. 4 n. 41 Specie vero differentia dicuntur, quorum est idem genus, et secundum formam differunt. Dicitur autem genus quod praedicatur de duobus specie differentibus, sicut de homine et de equo. Contraria autem differunt, et contrarietas est differentia quaedam.	2021. Now those things are said to be specifically diverse which are the same generically and differ in form. And by genus we mean that attribute which is predicated of two things which differ specifically, as man and horse. Moreover, contraries differ, and contrariety is a type of difference.
lib. 10 l. 4 n. 42 Deinde cum dicit quod autem probat per inductionem quod dixerat de ratione differentiae; quia omnia differentia videntur esse talia, scilicet quod non solum sint diversa, sed aliquo modo diversa: sicut haec quidem diversa sunt genere; haec autem sunt in eodem praedicamento, et in eodem genere, sed differunt specie; et quaedam sunt eadem specie. Quae aut sunt genere eadem aut diversa, determinatum est in aliis, idest in quinto huius.	2022. That this assumption (841). Then he proves by an induction what he had said above about the formal note whereby things differ, because all things that are different seem to be such that they are not merely diverse but diverse in some particular respect. Some things, for instance, are diverse in genus; some belong to the same category and the same genus but differ in species, and some are the same in species. What things are the same or diverse in genus has been established elsewhere, namely, in Book V of this work (931).

Lecture 5

Latin	English
lib. 10 l. 5 n. 1 Postquam philosophus determinavit de uno et multo, et de his quae ad ea consequuntur, quorum unum est contrarietas, quae est differentia quaedam, ut dictum est, hic determinat de contrarietate, quia eius consideratio specialem habet difficultatem. Et dividitur in partes duas. In primo ostendit quod contrarietas est differentia maxima. In secunda inquirit, utrum contraria differant genere, aut specie, ibi, diversum autem specie ab aliquo et cetera. Prima dividitur in duas. In prima determinat de contrariis. In secunda de mediis, ibi, quoniam vero contrariorum contingit et cetera. Prima dividitur in duas. In prima ostendit naturam contrarietatis. In secunda movet quasdam dubitationes circa praedeterminata, ibi, quoniam autem unum uni contrarium est. Prima dividitur in duas partes. In prima ostendit quid sit contrarietas. In secunda determinat de contrarietate per comparationem ad alias species oppositionis, ibi, prima vero contrarietas et cetera. Circa primum duo facit. Primo ostendit definitionem contrarietatis. Secundo ad definitionem assignatam reducit omnes alias definitiones, quae de contrariis assignantur, ibi, necesse est alios terminos, et cetera. Circa primum duo facit. Primo ponit definitionem contrarietatis. Secundo ex definitione assignata quaedam corollaria concludit, ibi, at vero maximum in unoquoque genere et cetera. Circa primum duo facit. Primo ostendit aliquam esse differentiam maximam, hoc modo. In quibuscumque est invenire magis et minus, est invenire maximum, cum non sit procedere in infinitum: sed contingit differre aliquid ab altero magis et minus: ergo et contingit aliqua duo maxime differre. Et ita est aliqua differentia maxima.	2023. Having settled the issue about the one and the many, and about the attributes which naturally accompany them, of which one is contrariety, which is a kind of difference, as has been pointed out (840:C 2021), here the Philosopher explains contrariety, because the investigation of it involves a special difficulty. This is divided into two parts. In the first (842:C 2023) he shows that contrariety is the greatest difference. In the second (887:C 2112) he inquires whether contraries differ generically or specifically (“That which is “ ). The first part is divided into two. In the first he settles the issue about contraries. In the second (878:C 2097) he deals with their intermediates (“And since”). The first part is divided into two. In the first he settles the issue about the nature of contraries. In the second (857:C 2059) he raises certain difficulties about the points which have been established (“But since one thing”). The first part is divided into two. In the first he shows what contrariety is. In the second (848:C 2036) he establishes what is true of contrariety as compared with the other kinds of opposition (“The primary contrariety”). In treating the first part he does two things. First, he gives a definition of contrariety. Second (847:C 2032), he reduces all the other definitions which have been assigned to contraries to the one given (“And the other”). In regard to the first he does two things. First, he gives the definition of contrariety. Second (844:C 2027), he draws a corollary from this definition (“Now what is”). In regard to the first he does two things. First (842), he shows that there is a greatest difference, as follows: there is some maximum in all things which admit of difference in degree, since an infinite regress is impossible. But it is possible for one thing to differ from something else to a greater or lesser degree. Hence it is also possible for two things to differ from each other to the greatest degree; and therefore there is a greatest difference.
lib. 10 l. 5 n. 2 Secundo ibi, et hanc ostendit, quod contrarietas sit maxima differentia, per inductionem. Quaecumque enim differunt, aut differunt genere, aut differunt specie. Illa autem, quae differunt genere, non sunt comparabilia adinvicem, sed magis distant quam possit in eis accipi magis et minus differre. Hoc enim accipitur in illis quorum est transmutatio invicem. Intelligitur enim processus quidam et via transmutationis de uno in aliud per hoc, primo quod magis differunt, et postea minus, et sic quousque unum transmutatur in alterum. In illis autem quae differunt genere, non est accipere huiusmodi viam transmutationis unius in alterum. Unde in eis non est accipere magis et minus differre, et per consequens nec maxime differre: et sic in differentibus genere non est maxima differentia.	2024. And I call (843). Second, he shows by an induction that contrariety is the greatest difference; for all things which differ must differ either generically or specifically. Now those things which differ generically cannot be compared with each other, being too far apart to admit of any difference of degree between them. This is understood to apply to those things which are changed into each other, because a certain process or way of change of one thing into another is understood from the fact that at first they differ more and afterwards less, and so on until one is changed into the other. But in the case of things which differ generically we do not find any such passage of one thing into another. Hence such things cannot be considered to differ in degree, and so cannot differ in the highest degree. Thus in things which differ generically there is no greatest difference.
lib. 10 l. 5 n. 3 In illis vero quae differunt specie, oportet maximam differentiam esse inter contraria, quae generationes mutuae sunt ex contrariis sicut ex ultimis. Generatur quidem medium ex extremo aut e converso, aut etiam medium ex medio, ut pallidum ex nigro vel ex rubeo: non tamen huiusmodi generationes sunt ex duobus quasi ultimis. Cum enim in generatione, ex nigro procedit ad pallidum, adhuc ulterius potest procedere ad aliquid magis differens. Sed cum iam pervenerit ad album, non potest ulterius procedere ad aliquid magis differens a nigro. Et sic ibi est status sicut in ultimo. Et propter hoc dicit quod generationes fiunt ex contrariis sicut ex ultimis. Sed manifestum est, quod distantia ultimorum semper est maxima. Relinquitur ergo, quod inter ea quae differunt specie, maxime differunt contraria.	2025. However, in the case of things which differ specifically there must be a greatest difference between contraries, because:’reciprocal processes of generation arise from contraries as their extremes. And an intermediate arises from an extreme or vice versa, or an intermediate also arises from an intermediate, as gray is produced from black or from red. Yet generations of this kind do not arise from two things as extremes; for when something passes from black to gray in the process of generation, it can still pass farther to some color which differs to a greater degree. But when it has already become white, it cannot continue farther to any color which differs to a greater degree from black, and there it must stop as in its extreme state. This is why he says that processes of generation arise from contraries as extremes. But it is evident that the distance between extremes is always the greatest. Hence it follows that contraries have the greatest difference among things which differ specifically.
lib. 10 l. 5 n. 4 Cum autem ostenderimus quod ea quae differunt genere non dicuntur maxime differre, et tamen est aliqua maxima differentia, sequitur quod contrarietas non sit aliud quam maxima differentia.	2026. And since we have shown that things which differ generically are not said to have a greatest difference, although there is a greatest difference, it follows that contrariety is nothing else than the greatest difference.
lib. 10 l. 5 n. 5 Deinde cum dicit at vero inducit duo corollaria ex praemissis: quorum primum est quod contrarietas sit perfecta differentia. Quod sic probatur. Maximum in unoquoque genere est idem quod perfectum est. Quod patet ex hoc, quod maximum est quod non exceditur; et perfectum est, extra quod non potest aliquid sumi. Et sic eadem videtur esse differentia maximi et perfecti.	2027. Now what is greatest (844). He draws two corollaries from what has been said. The first is that contrariety is the perfect difference. This is proved as follows. What is greatest in any class is the same as what is perfect. This is clear from the fact that that is greatest which nothing exceeds; and that is perfect to which nothing can be added. Hence the difference of the greatest and that of the perfect [from a common referent] are seen to be the same.
lib. 10 l. 5 n. 6 Et quod perfectum sit extra quod non potest aliquid sumi, patet; quia omnia dicuntur perfecta, eo quod deveniunt ad finem. Extra finem autem nihil est: quia finis est id quod est ultimum in omni re, et quod continet rem. Unde nihil est extra finem. Nec id quod perfectum est, indiget aliquo exteriori; sed totum continetur sub sua perfectione. Et sic patet quod perfecta differentia est quae pervenit ad finem.	2028. That that is perfect to which nothing external can be added is evident, because all things are said to be perfect when they go up to the end. Now there is nothing beyond the end, because the end is what is ultimate in every case and contains the thing. Hence nothing lies beyond the end, nor does what is perfect need anything external, but the whole is contained under its own perfection. Thus it is evident that the perfect difference is one which goes up to the end.
lib. 10 l. 5 n. 7 Et sic, cum contrarietas sit maxima differentia, ut probatum est, sequitur quod sit differentia perfecta. Sed quia contraria dicuntur multipliciter, ut postmodum dicetur, non omnia contraria dicuntur perfecte differentia. Sed ita consequitur quaelibet contraria perfecte differre, sicut competit eis esse contraria; quibusdam scilicet primo, et quibusdam secundario.	2029. Therefore, since contrariety is the greatest difference, as has already been proved (843:C 2024), it follows that it is the perfect difference. But since things are said to be contrary in many ways, as will be stated later (849:C 2039), not all contraries are said to differ perfectly; but it follows that all contraries differ perfectly in the way in which contrariety belongs to them, i.e., to some primarily and to others secondarily.
lib. 10 l. 5 n. 8 His enim. Secundum corollarium ponit dicens, quod cum praedicta sint vera, manifestum est quod non convenit plura esse contraria uni. Quod quidem probat dupliciter. Primo, quia contrarietas est maxima et perfecta differentia quasi ultimorum. Unius autem distantiae non possunt esse plura ultima quam duo. Sicut videmus quod unius rectae lineae sunt duo puncta extrema. Nec iterum ultimo est aliquid ulterius. Unde impossibile est, si contrarietas est una distantia, quod uni contrariorum contrarientur aliqua duo ex aequo quasi ultima. Nec quod unum contrarietur magis, et alterum minus: quia id quod contrarietur minus, non esset ultimum, sed aliquid haberet ulterius.	2030. Since this is so (845). Here he gives the second corollary. He says that, since the foregoing remarks are true, it is evident that one thing cannot have many contraries. He proves this in two ways. He does this, first, on the grounds that contrariety is the greatest and perfect difference between extremes. But there can be no more than two extremes of one distance; for we see that one straight line has two end points. Further, there is nothing beyond the extreme. If, then, contrariety is one distance, it is impossible for two things to be equally opposed as extremes to one contrary, or for one to be more contrary and another less so, because whatever is less contrary will not be an extreme but will have something beyond it.
lib. 10 l. 5 n. 9 Deinde cum dicit totaliter autem probat idem alio modo; dicens, quod contrarietas est differentia quaedam. Omnis autem differentia est aliquorum duorum. Unde et perfecta differentia est duorum. Et sic unum uni tantum est contrarium.	2031. And in general (846). He now proves the same thing in another way. He says that since contrariety is a kind of difference, and every difference is a difference between two things, then the perfect difference must also be a difference between two things. Thus one thing has only one contrary.
lib. 10 l. 5 n. 10 Deinde cum dicit necesse autem ostendit, quod omnes definitiones de contrariis datae, secundum praedictam definitionem contrarietatis verificantur. Et ponit quatuor terminos, idest definitiones contrariorum ab aliis assignatas; quarum prima est, quod contraria sunt quae plurimum differunt. Hoc enim verificatur secundum praedicta, cum contrarietas sit perfecta differentia, quae facit plurimum differre. Manifestum est enim ex praedictis, quod in his quae differunt genere non est accipere quid magis differens his quae differunt specie: quia ad ea quae sunt extra genus, non est differentia, ut dictum est. Eorum vero, quae differunt specie, maxima differentia est contrariorum. Et sic sequitur quod contraria sunt quae plurimum differunt.	2032. And the other (847). Next he shows that all the definitions of contraries which have been given are seen to be true on the basis of the definition of contrariety posited above (842:C 2023). He gives “four formulations,” i.e., definitions, of contraries assigned by other thinkers. The first is that contraries are things which have the greatest difference. Now this is seen to be true on the basis of the foregoing definition, since contrariety is the perfect difference, and this causes things to differ most. For it is evident from what has been said that in the case of things which differ generically nothing can be found which differs more than things which differ specifically, because there is no difference as regards those things which lie outside the genus, as has been stated. And of things which differ specifically the greatest difference is between contraries. Hence it follows that contraries are things which differ most.
lib. 10 l. 5 n. 11 Secunda definitio est, quod contraria sunt quae plurimum differunt in eodem genere. Quae etiam verificatur secundum praedicta: quia contrarietas est perfecta differentia. Maxima autem differentia eorum quae sunt in eodem genere est perfecta differentia. Unde relinquitur quod contraria sunt quae plurimum differunt in eodem genere.	2033. The second definition is that contraries are attributes which differ to the greatest degree in the same genus. This is also seen to be true on the basis of the foregoing definition, because contrariety is the perfect difference. But the greatest difference between things which belong to the same genus is the perfect difference. Hence it follows that contraries are attributes which have the greatest difference in the same genus.
lib. 10 l. 5 n. 12 Tertia definitio est quod contraria sunt quae plurimum differunt in eodem susceptibili. Quod etiam verificatur ex praedictis; quia eadem est materia contrariorum, cum ex invicem generentur.	2034. The third definition is that contraries are attributes which have the greatest difference in the same subject. This is also seen to be true on the basis of the foregoing definition; for contraries have the same matter since they are generated from each other.
lib. 10 l. 5 n. 13 Quarta definitio est, quod contraria sunt, quae plurimum differunt sub eadem potentia, idest arte vel scientia. Nam scientia est potentia rationalis, ut in nono dictum est. Et haec etiam definitio ex praedictis verificatur; quia una scientia est circa unum genus. Cum igitur contraria sint in eodem genere, oportet quod sint sub eadem potentia sive scientia. Et quia contrarietas est perfecta differentia in eodem genere, oportet quod contraria plurimum differant eorum quae sunt sub eadem scientia.	2035. The fourth definition is that contraries are attributes which have the greatest difference “under the same potency,” i.e., the same art or science; for science is a rational potency, as has been stated in Book IX (746:C 1789). This definition is also seen to be true on the basis of the foregoing definition, because there is one science of one class of things. Therefore, since contraries belong to the same genus, they must come under the same potency or science. And since contrariety is the perfect difference in the same genus, contraries must have the greatest difference among those things which come under the same science.

Lecture 6

Latin	English
lib. 10 l. 6 n. 1 Postquam philosophus definivit contrarietatem, hic comparat ipsam ad alias species oppositionis; et circa hoc duo facit. Primo proponit quod intendit; scilicet quod contrarietatis principium est oppositio privationis et habitus. Secundo manifestat quod supposuerat, ibi, si ergo opponuntur et cetera. Circa primum duo facit. Primo enim proponit quod principium contrarietatis est privatio et habitus; dicens, quod prima contrarietas est privatio et habitus, quia scilicet in omni contrarietate privatio et habitus includitur.	2036. Having defined contrariety the Philosopher now compares it with the other kinds of opposition. In regard to this he does two things. First (848)C 2036), he states his thesis, namely, that the basis of contrariety is the opposition between privation and possession. Second (850:C 2040), he proves it (“If, then”). In regard to the first he does two he states that the basis of contrariety is privation and possession. He says that the primary contrariety is privation and possession because privation and possession are included in every contrariety.
lib. 10 l. 6 n. 2 Sed ne aliquis crederet quod idem esset opponi secundum privationem et habitum, et secundum contrarietatem, subiungitur quod non omnis privatio sit contrarium; quia privatio, sicut in superioribus habitum est, multipliciter dicitur. Aliquando enim quocumque modo, si non habeat quod natum est haberi, dicitur esse privatio. Sed talis privatio non est contrarium, quia talis privatio non ponit aliquam naturam oppositam habitui, licet supponat subiectum determinatum. Sed privatio dicitur esse contrarium, quaecumque fuerit perfecta privatio.	2037. But lest someone should think that the opposition between privation and possession and that between contraries are the same, he adds that not every privation is a contrary; for, as has been pointed out above, the term privation is used in several ways. Sometimes a thing is said to be deprived of something when it does not have in any way what it is naturally fitted to have. However, such privation is not a contrary, because it does not presuppose a positive reality which is opposed to possession, though it does presuppose a definite subject. But it is only that privation which is perfect that is said to be a contrary.
lib. 10 l. 6 n. 3 Cum autem privatio secundum id quod est, non recipiat magis et minus, non potest dici perfecta privatio nisi ratione alicuius naturae, quae perfectam distantiam habeat ad habitum. Sicut non omnis privatio albi est contraria albo; sed privatio magis distans ab albo, quam oportet fundari in aliqua natura eiusdem generis, maxime distante ab albo. Et secundum hoc dicimus quod nigrum est contrarium albo.	2038. And since privation by its very nature does not admit of difference in degree, a privation can be said to be perfect only by reason of some positive reality which is farther removed from possession. For example, not every privation of white is its contrary, but only that which is farthest removed from white, which must be rooted in some nature of the same genus and farthest removed from white. And according to this we say that black is the contrary of white.
lib. 10 l. 6 n. 4 Deinde cum dicit alia autem secundo ostendit qualiter ab ista prima contrarietate, alia contraria deriventur; dicens, quod alia contraria dicuntur secundum hoc, scilicet secundum privationem et habitum diversimode. Quaedam enim dicuntur contraria in eo quod habent in se inclusam privationem et habitum; sicut album et nigrum, et calidum et frigidum. Alia per hoc quod actu faciunt privationem et habitum, sicut sunt calefaciens et infrigidans. Aut per hoc quod sunt virtute activa privationis et habitus, sicut calefactivum et infrigidativum. Alia vero per hoc quod sunt acceptiones dictorum, sicut calefieri et infrigidari. Aut per hoc quod sunt abiectiones eorum, sicut corruptio caliditatis et frigiditatis. Et non solum aliqua dicuntur contraria per hoc, quod dicunt dictas habitudines ad prima contraria; sed etiam per hoc, quod habent habitudines easdem ad contraria sequentia. Sicut si dicamus quod ignis et aqua sunt contraria, quia habent calidum et frigidum, quae etiam dicebantur contraria per hoc quod includunt privationem et habitum.	2039. And the other contraries (849). Second, he explains how the other contraries are derived from this first contrariety. He says that other contraries “are referred to these,” namely, to privation and possession, in different ways. For some things are called contraries because they have in themselves privation and possession, for example, such things as white and black, hot and cold; others because they actually cause privation and possession, as things which cause heat and cold, or because they are virtually the active causes of privation and possession, as things capable of heating and cooling. And others are called contraries because they are acquisitions of the attributes mentioned, as the processes of becoming hot and becoming cold, or because they are the losses of these, as the destruction of heat and cold. And others again are called contraries not only because they express the aforesaid relationships to the primary contraries but also because they have the same relationships to subsequent contraries; for example, if we were to say that fire and water are contraries because they have heat and cold, which are called contraries themselves, as we have seen, because they include privation and possession. Other kinds of opposition
lib. 10 l. 6 n. 5 Deinde cum dicit si ergo manifestat quod supposuerat, scilicet quod prima contrarietas est privatio et habitus: et hoc dupliciter. Primo per syllogismum. Secundo per inductionem, ibi, palam autem et per inductionem et cetera. Circa primum duo facit. Primo ostendit quod contrarietas non est contradictio; dicens, quod cum quatuor modis aliqua alicui opponantur: uno modo ut contradictio, sicut sedens non sedenti; alio modo ut privatio, sicut caecus videnti: tertio modo ut contrarietas, sicut nigrum albo: quarto modo ad aliquid, sicut filius patri;- inter ista quatuor genera oppositionis primum est contradictio.	2040. If, then, the modes (850). Then he proves his thesis, namely, that the primary contrariety is privation and possession; and he does this in two ways: first, by a syllogism; second (2054), by an induction (“This also”). In regard to the first he does two things. First, he shows that contrariety is not contradiction. He says that among the four kinds of opposition between two things—(1) contradiction, as sitting is opposed to not-sitting; (2) privation, as blindness is opposed to sight; (3) contrariety, as black is opposed to white; and (4) relation, as a son is opposed to his father—the first is contradiction.
lib. 10 l. 6 n. 6 Cuius ratio est, quia contradictio includitur in omnibus aliis tamquam prius et simplicius. Opposita enim secundum quodcumque oppositionis genus impossibile est simul existere. Quod quidem contingit ex hoc, quod alterum oppositorum de sui ratione habet negationem alterius. Sicut de ratione caeci est quod sit non videns. Et de ratione nigri, quod non sit album. Et similiter de ratione filii est quod non sit pater eius cuius est filius.	2041. The reason is that contradiction is included in all the other kinds of opposition as something prior and simpler; for in any kind of opposition it is impossible that opposites should exist simultaneously. This follows from the fact that one of two opposites contains the negation of the other in its notion; for example, the notion of blind contains the fact of its not seeing, and the notion of black, of its not being white. And similarly the notion of son contains his not being the father of him of whom he is the son.
lib. 10 l. 6 n. 7 Manifestum est autem quod in contradictione non est aliquod medium. Necesse est enim aut affirmare aut negare, ut supra in quarto manifestum fuit. Contrariorum autem convenit esse medium. Et sic manifestum est quod contrarietas et contradictio non sunt idem.	2042. Moreover, it is evident that there is no intermediate in contradiction; for one must either affirm or deny, as has been shown in Book IV (725). However, it belongs to contraries to have an intermediate; and thus it is clear that contrariety and contradiction are not the same.
lib. 10 l. 6 n. 8 Deinde cum dicit privatio vero ostendit qualiter se habeat privatio ad contradictionem, manifestans qualiter conveniant et qualiter differant. Dicit ergo, quod privatio est quaedam contradictio. Dicitur enim privatio uno modo, quando aliquid non habet quod nullo modo natum est habere; ut si diceremus quod lapis non habet visum. Alio modo dicitur aliquid privari, si non habeat quod natum est habere; sicut animal si non habeat visum. Et hoc dupliciter: uno modo qualitercumque non habeat. Alio modo si non habeat cum aliqua determinatione, puta in tempore determinato, aut aliquo modo determinato; quia privatio multipliciter dicitur, sicut supra habitum est in quinto et nono.	2043. And privation (851). Then he shows how privation is related to contradiction by indicating the way in which they are alike and that in which they differ. He says that privation is a kind of contradiction; for the term privation is used in one sense when a thing does not have in any way some attribute which it is capable of having, for example, when an animal does not have sight. And this occurs in two ways: (a) first, if it does not have it in any way at all; and (b) second, if it does not have it in some definite respect, for example, at some definite time or in some definite manner, because privation is used in many senses, as has been stated in Books V (1070) and IX (1784).
lib. 10 l. 6 n. 9 Ex his ergo patet quod privatio est quaedam contradictio. Et quidem, quod sit contradictio patet ex hoc, quod aliquid dicitur privatum ex hoc quod non habet.	2044. It is evident from what has been said, then, that privation is a kind of contradiction; and this is shown from the fact that a thing is said to be deprived of something because it does not have it.
lib. 10 l. 6 n. 10 Sed quod non sit contradictio absoluta, sed contradictio quaedam, patet ex hoc quod contradictio de sui ratione non requirit neque aptitudinem, neque etiam existentiam alicuius subiecti. Verificatur enim de ente et de non ente quocumque. Dicimus enim quod animal non videt, et lignum non videt, et quod non ens non videt. Sed privatio de necessitate requirit aliquod subiectum, et quandoque etiam requirit aptitudinem in subiecto: quod enim est omnino non ens non dicitur privatum.	2045. That it is not a simple contradiction but one of a sort is evident from the fact that according to its meaning a contradiction requires neither (~) the aptitude nor the existence of any subject; for it may be truly affirmed of any being or non-being whatsoever. Thus we say that an animal does not see, and that wood does not see, and that a non-being does not see. A privation, however, necessarily (+) requires some subject, and sometimes it also requires aptitude in a subject; for that which is a non-being in every respect is not said to be deprived of anything.
lib. 10 l. 6 n. 11 Et ideo dicit quod privatio aut est in determinata potentia, scilicet cum aptitudine ad habitum, aut saltem concepta cum susceptivo, idest cum subiecto, licet non habente aptitudinem ad habitum. Sicut si dicamus vocem invisibilem, aut lapidem rem mortuam.	2046. He says, then, that privation “is found either in a determinate potency,” i.e., one with a capacity for possessing something, or at least “is conceived along with something that is susceptible of it,” i.e., along with a subject, even though it has no capacity for possessing something. This would be the case, for example, if we were to say that a word is invisible, or that a stone is dead.
lib. 10 l. 6 n. 12 Et ideo contradictio non potest habere medium: sed privatio aliquo modo medium habet. Necesse est enim omne aut aequale aut non aequale esse, sive sit ens sive non ens. Sed non necesse est dici de omni, quod sit aequale aut inaequale; sed solum hoc necesse est in susceptivo aequalitatis.	2047. (~) Contradiction, then, cannot have an intermediate, whereas in a sense (+) privation has an intermediate; for everything must be either equal or not equal, whether it is a being or a non-being. However, it is not necessary to say that everything is either equal or unequal, but this is necessary only in the case of something that is susceptible of equality.
lib. 10 l. 6 n. 13 Sic igitur oppositio contradictionis omnino est immediata: oppositio vero privationis est immediata in determinato susceptivo; non autem est immediata simpliciter. Ex quo patet quod contrarietas, quae nata est habere medium, propinquior est privationi quam contradictioni. Nondum tamen habetur, quod privatio sit contrarietas.	2048. Hence the opposition of contradiction has no intermediate whatsoever, whereas the opposition of privation has no intermediate in a determinate subject; but it is not without an intermediate in an absolute sense. And from this it is evident that contrariety, which is such as to have an intermediate, is closer to privation than to contradiction. Yet it still does not follow that privation is the same as contrariety.
lib. 10 l. 6 n. 14 Si itaque restat tertio ostendendum, quod contrarietas sit privatio; et circa hoc duo facit. Primo ostendit per syllogismum quod contrarietas sit privatio, hoc modo. Omne illud ex quo fit generatio, aut est species sive quicumque habitus speciei; aut est privatio speciei, sive cuiuscumque formae. Omne quidem dicit, quia est duplex generatio. Generatur enim aliquid simpliciter in genere substantiae, et secundum quid in genere accidentium. Generationes enim sunt ex contrariis in materia. Manifestum est ergo, quod omnis contrarietas est aliqua privatio. Si enim alterum extremorum in qualibet generatione est privatio, et utrumque contrariorum est extremum generationis, quia contraria generantur ex invicem, sicut album ex nigro, et nigrum ex albo; necesse est quod semper alterum contrariorum sit privatio.	2049. If, then, the processes (852). Third, it remains to be shown that contrariety is privation, and in regard to this he does two things. First, he shows by a syllogism that contrariety is privation. He argues as follows: everything from which a process of generation arises is either a form (i.e., the possession of some form) or the privation of some specifying principle (i.e., some form). He says “everything” because generation is twofold. For things are generated absolutely in the genus of substance, but in a qualified sense in the genus of accidents; for generations arise from contraries in matter. Hence it is evident that every contrariety is a privation; for if in any process of generation one of the two extremes is a privation, and each of the contraries is an extreme in the process of generation (because contraries are generated from each other, as white from black and black from white), then one of the two contraries must be a privation.
lib. 10 l. 6 n. 15 Deinde cum dicit privatio vero ostendit quod non omnis privatio est contrarietas, quod etiam supra dixerat, dicens: non omnis privatio est contrarietas. Et causa huius est, quia privatum contingit multipliciter privari. Quocumque enim modo id quod natum est habere aliquam formam, non habeat illam, dici potest esse privatum; sive sit in dispositione propinqua ad formam illam, sive remota. Sed contrarium est semper in dispositione remota: quia contraria sunt ex quibus fiunt permutationes sicut ex extremis. Unde supra dictum est, quod sunt maxime distantia. Aliquid enim privari dicitur albedine si non sit album, sive sit pallidum, sive quocumque alio colore coloratum. Sed non ideo dicitur esse contrarium nisi quando est maxime distans ab albo, scilicet quando est nigrum. Unde manifestum est quod non omnis privatio est contrarietas.	2050. But perhaps (853). Here he proves another assertion made above, that not every privation is a contrariety. He says that the reason for this is that there are many ways of being deprived; for a thing that is capable of having a form and does not have it in any way can be said to be deprived of it, and it makes no difference whether it is proximately or remotely disposed for that form. Now a contrary is always remotely disposed; for contraries are the sources, in the sense of extremes from which changes arise. Hence it was said above (2038) that they are farthest removed from each other. For whether a thing is yellowish or of some other color, it is said to be deprived of whiteness if it is not white. But it is not on that account called a contrary except when it is farthest removed from whiteness, namely, when it is black. Thus it is clear that not every privation is a contrariety.
lib. 10 l. 6 n. 16 Ex hoc etiam apparet quod, cum privatio nihil aliud requirat nisi absentiam formae, supposita tantum habitudine in subiecto, sine hoc quod determinet aliquam dispositionem in subiecto, per quam subiectum sit propinquum formae vel distans ab ea: quod privatio non significat aliquam naturam in subiecto, sed praesupponit subiectum cum aptitudine. Contrarium vero requirit determinatam dispositionem subiecti, secundum quam maxime distet a forma. Unde de necessitate aliquam naturam significat in subiecto, quae est eiusdem generis cum forma absente; sicut nigrum est in genere albi.	2051. And since privation requires nothing else than the absence of form (merely presupposing a disposition in a subject without conferring upon that subject any definite disposition through which the subject is close to a form or distant from it), it is evident that privation does not designate any positive reality in a subject, but presupposes a subject with an aptitude. But a contrary requires a definite disposition in a subject, by which it is farthest removed from a form. Therefore it necessarily designates in a subject some positive reality which belongs to the same class as the absent form, as black belongs to the same class as white.
lib. 10 l. 6 n. 17 Considerandum est etiam quod est duplex privatio. Quaedam quae habet immediatum ordinem ad subiectum formae, sicut tenebra habet immediatum ordinem ad diaphanum. Et inter huiusmodi privationem et formam oppositam est mutua transmutatio. Aer enim de lucido fit tenebrosus, et de tenebroso fit lucidus. Quaedam autem privatio est quae non comparatur ad subiectum formae nisi mediante forma, cum sit ut quaedam corruptio eius; sicut caecitas est corruptio visus, mors est corruptio vitae. Et in talibus non est mutua conversio, sicut supra in nono habitum est.	2052. It should also be noted that privation is of two kinds. (1) There is one which has an immediate relationship to the subject of the form (as darkness has an immediate relationship to the transparent medium), and between a privation of this kind and its opposite form there is (+) reciprocal change; for the atmosphere passes from a state of illumination to one of darkness, and from a state of darkness to one of illumination. (2) And there is another kind of privation which is related to the subject of the form only by means of the form, since it has the nature of a corruption of form; for example, blindness is the corruption of sight, and death the corruption of life. In such cases there is no (~) reciprocal change, as has been pointed out in Book IX (1785).
lib. 10 l. 6 n. 18 Cum igitur hic ostenditur contrarietatem esse privationem ex mutua transmutatione, quae est in contrariis et privatione et forma, manifestum est quod non dicitur ista esse contrarietas quae est corruptio formae, sed quae habet immediatum ordinem ad subiectum formae. Et sic cessat illa obiectio quae ponitur in praedicamentis, quod a privatione ad habitum non fit reversio. Contraria autem transmutantur invicem.	2053. Therefore, since it has been shown here that contrariety is the privation arising from reciprocal change which involves contraries and privation and form, it is clear that contrariety is not the type of privation which is the corruption of a form, but that which has an immediate relation to the subject of the form. Hence the objection raised in the Categories, that it is impossible to revert from privation to possession, does not apply here. But contraries are changed into each other.
lib. 10 l. 6 n. 19 Deinde cum dicit palam autem ostendit per inductionem quod contrarietas sit privatio; et hoc dupliciter. Primo inducendo in singulis contrariis. Secundo reducendo ad prima contraria, ibi, sufficit autem et si prima et cetera. Circa primum duo facit. Primo ostendit per inductionem quod contrarietas sit privatio; dicens, quod hoc quod supra ratione syllogistica ostensum est palam est etiam per inductionem. Quia omnis contrarietas invenitur habere privationem alterius contrariorum. Semper enim duorum contrariorum unum est defectivum respectu alterius. Sed tamen non in omnibus contrariis similiter invenitur unum privatio alterius, ut infra dicetur. Et quod unum contrariorum sit privatio alterius, ex hoc apparet, quia inaequalitas est privatio aequalitatis, et dissimilitudo similitudinis, et malitia virtutis.	2054. This also becomes (854). Then he shows by induction that contrariety is privation, and he does this in two ways. First, by making an induction from each type of contrary; and second (856:C 2058), by reducing them to a primary kind of contrary (“But it is”). In regard to the first (854) he does two things. First, he shows by an induction that contrariety is privation. He says that the point proved above by a syllogistic argument is also made clear by an induction; for every contrariety is found to include the privation of one of the two contraries, since one of the two is always lacking in the other. Yet one contrary is not found to be the privation of the other in the same way in all types of contraries, as will be stated below (855:C 2055). That one of two contraries is the privation of the other is evident from the fact that inequality is the privation of equality, and unlikeness the privation of likeness, and evil the privation of virtue.
lib. 10 l. 6 n. 20 Deinde cum dicit differt autem ostendit quod diversimode unum contrariorum est privatio alterius. Hoc enim contingit secundum diversam rationem privationis. Quae quidem diversitas attenditur dupliciter. Uno modo ex hoc quod privatio potest dici, vel quia solum aliquod privatum est modo quocumque. Vel quia est privatum in aliquo tempore determinato, vel in aliqua parte determinata. In tempore quidem determinato, sicut si sit privatum in aliqua aetate. In parte autem determinata, sicut si sit privatum in aliqua parte principali. Aut etiam in omni, idest in toto. Dicitur enim aliquis insensatus, si in aetate perfecta discretione careat, non autem in puerili aetate. Et similiter aliquis nudus, non si aliqua pars eius non sit tecta, sed si plures aut principales partes intectae remaneant.	2055. And privation differs (855). Then he shows that one contrary is the privation of the other in various ways; for this is relative to different types of privation. Now this difference may be considered from two points of view. First, privation can mean either that a thing has been deprived of something in any way at all; or, that it is deprived at some definite time or in some definite way. For example, it is deprived at some definite time if this occurs at some definite age; and it is deprived in some definite part if the privation is found in some important part. Or it may also be “entirely,” i.e., in the whole. For a man is said to be senseless if he lacks discretion at a mature age but not as a child. And similarly a person is said to be naked, not if any part of him is uncovered, but if many of his parts or the principal ones are left uncovered.
lib. 10 l. 6 n. 21 Et propter istam diversitatem privationis, quae in contrarietate includitur, contingit quod quorumdam contrariorum est medium, et quorumdam non. Inter bonum enim et malum, medium est. Est enim aliquis homo neque bonus neque malus. Dicitur enim bonus homo secundum virtutem. Nam virtus est quae bonum facit habentem. Non autem omnis qui caret virtute malus est. Nam puer caret virtute, et tamen non dicitur malus. Sed si in aetate, in qua debet habere virtutem, non habeat, malus dicitur. Vel etiam si aliquis virtute careat quantum ad aliquos actus minimos et quasi indifferentes ad vitam, non dicitur malus; sed solum si careat virtute quantum ad actus principales et necessarios ad vitam. Sed par et impar in numeris non habent medium: quia numerus dicitur impar ex hoc quod quocumque modo caret paritate.	2056. And because of the various kinds of privation which are included under contrariety it is possible for some contraries to have an intermediate and for some not. For there is an intermediate between good and evil, since a man may be neither good nor evil. For a man is said to be good by reason of virtue, because virtue is what causes its possessor to be good. However, not everyone who lacks virtue is evil; for a boy lacks virtue, yet he is not said to be evil. But if one does not have virtue at an age when he ought to have it, he is then said to be evil. Or if someone also lacks virtue as regards certain insignificant actions and those which, so to speak, make no difference to life, he is not said to be evil, but only if he lacks virtue as to the important and necessary acts of life. But the even and the odd in numbers do not have an intermediate; for a number is said to be odd in the sense that it lacks evenness in any way at all.
lib. 10 l. 6 n. 22 Alia vero diversitas privationis est, quod privatio quaedam determinat sibi subiectum, quaedam vero non. Dictum est enim supra, quod id quod caret aliquo, etiam si non natum sit habere, quandoque dicitur privatum. Ex hac autem diversitate privationis potest contingere in aliquibus contrariis, quod habeant medium vel non habeant: sicut si dicamus, quod cum homo dicatur bonus secundum virtutes politicas, si malum quod includit privationem boni requirat determinatum subiectum, rusticus qui non participat conversatione civili, nec bonus nec malus est bonitate vel malitia civili. Sic igitur patet ex praedictis, quod alterum contrariorum dicitur secundum privationem.	2057. The second way in which privations differ is this: one kind of privation has a definite subject of its own, and another kind has not. For it was said above that everything which lacks an attribute, even though it is not naturally such as to have it, is sometimes said to be deprived of it. And according to this difference between privations it is possible for some contraries to have an intermediate or not. For example, we might say that, since man is said to be good with respect to political virtue, if evil, which includes the privation of good, requires a determinate subject, then a rustic who does not participate in civic affairs is neither good nor evil with respect to civic goodness or evil. Hence it is evident from what has been said that one of two contraries is used in a privative sense.
lib. 10 l. 6 n. 23 Deinde cum dicit sufficit autem ostendit idem reducendo ad prima contraria; dicens quod sufficit ad ostendendum quod alterum contrariorum sit privatio, si hoc invenitur in primis contrariis, quae sunt genera aliorum contrariorum, sicut sunt unum et multa. Et quod ista sint prima contraria, patet ex hoc, quod omnia alia contraria reducuntur ad illa. Nam ad unum et multa reducuntur aequale et inaequale, simile et dissimile, idem et diversum. Differentia autem, diversitas quaedam est, et contrarietas differentia quaedam, ut supra habitum est. Et sic patet quod omnis contrarietas reducitur ad unum et multa. Unum autem et multa opponuntur ut divisibile et indivisibile, ut supra habitum est. Et ita relinquitur, quod omnia contraria privationem includant.	2058. But it is enough (856). He proves the same point by reducing the other contraries to the primary ones. He says that in order to show that one of two contraries is a privation it is enough if this is found to be true in the case of the primary contraries, which are the genera of the others, for example, one and many. That these are the primary contraries is evident from the fact that all other contraries are reduced to them; for equal and unequal, like and unlike, same and other, are reduced to one and many. Moreover, difference is a kind of diversity, and contrariety is a kind of difference, as has been said above (2017; 2023). Hence, it is evident that every contrariety is reducible to one and many. But one and many are opposed as the indivisible and the divisible, as has been pointed out above (1983). Therefore it follows that all contraries include privation.

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.

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.

Lecture 9

Latin	English
lib. 10 l. 9 n. 1 Postquam philosophus determinavit de contrariis, hic determinat de mediis contrariorum; et circa hoc duo facit. Primo proponit de quo est intentio; dicens: quia contrariorum contingit aliquid esse medium, ut supra dictum est, et quaedam contrariorum medium habent, ostendendum est quod necesse est media esse ex contrariis. Non autem hoc solum ostendit, sed etiam quaedam alia quae ad huius probationem sunt necessaria.	2097. Having expressed his views about contraries, the Philosopher now does the same thing with regard to the intermediates between contraries; and concerning this he does two things. First (878)C 2097), he indicates what his plan is. He says that, since there can be an intermediate between contraries, as has been shown above (850:C 2042), and some contraries have an intermediate, it is necessary to show that intermediates are composed of contraries. He not only does this but also proves certain points needed for this proof. Intermediaries of contraries
lib. 10 l. 9 n. 2 Deinde cum dicit omnia namque prosequitur suam intentionem; et circa hoc tria facit. Primo ostendit, quod media sunt in eodem genere cum contrariis. Secundo ostendit, quod media sunt inter contraria tantum, ibi, at vero media et cetera. Tertio vero ostendit, quod media componuntur ex contrariis, quod est principaliter intentum, ibi, si vero sunt in eodem genere. Dicit ergo primo, quod omnia media sunt in eodem genere cum his quorum sunt media. Quod sic probat. Quia haec est diffinitio mediorum, quod media sunt inter quae prius venit illud quod mutatur de uno extremorum, quam in alterum extremum.	2098. For all intermediates (879). Then he carries out his plan; and in regard to this he does three things. First, he shows that intermediates belong to the same genus as contraries. Second (2101), he shows that there are intermediates only between contraries (“But all intermediates”). Third (2098), he establishes his main thesis, that intermediates are composed of contraries (“Now if intermediates”). He accordingly says, first, that all intermediates belong to the same class as the things of which they are the intermediates. He proves this by pointing out that intermediates are defined as that into which a thing undergoing change from one extreme to another first passes.
lib. 10 l. 9 n. 3 Et hoc manifestat per duo exempla. Primo quidem in sonis. Sunt enim quidam soni graves, et quidam acuti, et quidam medii. Et secundum hanc distinctionem sonorum, distinguuntur chordae in musicis instrumentis. Illae enim chordae, quae reddunt graves sonos, dicuntur hypatae, quia principales. Illae vero quae reddunt acutos sonos, dicuntur netae. Si igitur musicus paulatim a gravibus ad acutos descendere velit, quod est transire per mediam rationem, necesse est quod prius veniat ad sonos medios. Secundo autem manifestat in coloribus. Si enim aliquid mutatur ex albo in nigrum, oportet quod primum veniat ad medios colores quam ad nigrum. Et similiter est in aliis mediis.	2099. He makes this clear by two examples. First, he uses the example of sounds; for some sounds are low and some are high and some are intermediate. And strings on musical instruments are distinguished by this distinction of sounds; for those strings which yield low pitched sounds are called “top-strings” because they are the basic ones, and those which yield high pitched sounds are called “bottom-strings.” Hence, if a musician wishes to proceed step by step from low sounds to high ones, and so to pass through an intermediate register, he must first come to the intermediate sounds. Second, he makes this clear by using colors. For if a thing is changed from white to black, it must first pass through the intermediate colors before it reaches black. The same thing is true of other intermediates.
lib. 10 l. 9 n. 4 Sic igitur patet quod de mediis fit transmutatio ad extrema, et e converso. Sed in his quae sunt in diversis generibus, non fit transmutatio in invicem nisi per accidens, sicut patet in colore et figura. Non enim mutatur aliquid de colore in figuram aut e converso; sed de colore in colorem, et de figura in figuram. Unde necesse est quod media et extrema sint in eodem genere.	2100. It is evident, then, that change passes from intermediates to extremes and the reverse. But things belonging to diverse genera are changed into each other only accidentally, as is clear with regard to color and figure; for a thing is not changed from color to figure or vice versa, but from color to color, and from figure to figure. Hence intermediates and extremes must belong to the same genus.
lib. 10 l. 9 n. 5 Deinde cum dicit at vero ostendit quod media sunt inter contraria; et circa hoc duo facit. Primo ostendit quod media necesse est esse inter opposita. Secundo inter quae opposita, quia inter contraria, ibi, oppositorum vero. Dicit ergo primo, quod omnia media necesse est esse inter opposita. Quod sic probat. Quia solum ex oppositis, per se loquendo, fiunt mutationes, ut probatur in primo physicorum. Ex nigro enim aliquid fit album per se loquendo. Dulce autem non fit ex nigro nisi per accidens, inquantum dulce convenit esse album. Sed media sunt inter illa ex quibus est mutua transmutatio, sicut per definitionem mediorum suprapositam patet. Impossibile est ergo quod media sint non oppositorum; quia sequeretur quod esset permutatio non ex oppositis.	2101. But all intermediates (880). Here he shows that intermediates stand between contraries; and in regard to this he does two things. First, he shows that intermediates must stand between opposites. Second (881:C 2102), he indicates the kind of opposites between which they stand, namely, contraries (“For the opposites”). He accordingly says, first (880), that all intermediates must stand between opposites. He proves this as follows: changes arise, properly speaking, only from opposites, as is proved in Book I of the Physics; for properly speaking a thing changes from black to white; and what is sweet comes from black only accidentally inasmuch as it is possible for something sweet to become white. But intermediates stand between things which are changed into each other, as is evident from the definition of intermediates given above (879:C 2098). Therefore it is impossible that intermediates should not stand between opposites; otherwise it would follow that change would not proceed from opposites.
lib. 10 l. 9 n. 6 Deinde cum dicit oppositorum enim manifestat inter quae opposita possint esse media; dicens, quod inter opposita in contradictione nullo modo potest esse medium. Contradictio enim est oppositio, cuius altera pars ex necessitate adest cuicumque subiecto, sive sit ens, sive non ens. De quolibet enim ente vel non ente necesse est dicere quod sedet, vel non sedet. Et sic patet, quod contradictio nullum habet medium.	2102. For the opposites (881). Then he indicates the kinds of opposites that can have intermediates. He says that there cannot be any intermediates whatsoever between the opposite terms of a contradiction; for contradictory opposition is such that one part of it must belong to any type of subject, whether it be a being or a non-being. For we must say that any being or non-being either is sitting or is not sitting. Thus it is evident that contradictories have no intermediate.
lib. 10 l. 9 n. 7 Sed aliorum oppositorum alia sunt ad aliquid, alia privatio et forma, alia ut contraria. Eorum autem, quae sunt ad aliquid, quaedam se habent ut contraria, quae ex aequo adinvicem referuntur; et ista habent medium. Quaedam vero non se habent ut contraria, quae non ex aequo adinvicem referuntur, sicut scientia et scibile; et ista non habent medium. Cuius causa est, quia media et extrema sunt in eodem genere. Haec autem non sunt in eodem genere, cum unum secundum se referatur, ut scientia, non autem aliud, ut scibile. Quomodo ergo scientiae et scibilis potest aliquid esse medium? Sed magni et parvi potest esse aliquid medium, idest aequale, ut supra dictum est. Et similiter eorum quae referuntur adinvicem, ut contraria. Quomodo autem ea quae opponuntur privative habeant media vel non habeant, et quomodo haec oppositio aliquo modo pertinet ad contrarietatem, hic tacet, quia supra exposuit.	2103. But in the case of other opposites some involve relations, some privation and form, and some contraries. Now of opposites which are relative, some are like contraries which are related to each other on an equal basis, and these have an intermediate. But some do not have the character of contraries, for example, those which are not related to each other on an equal basis, as knowledge and a knowable object; and these do not have an intermediate. And the reason is that intermediates and extremes belong to the same genus. But these things do not belong to the same genus, since the one is related in itself, as knowledge, but the other is not, as the knowable object. How, then, can there be an intermediate between knowledge and the knowable object? But there can be “an intermediate” between the large and the small, and this is the equal, as has been stated above (881)C 2102). The same thing is true of those things which are related to each other as contraries. He does not mention how things which are opposed privatively have an intermediate or how they do not, and how this opposition somehow pertains to contrariety, because he has explained these points above (851-3:C 2043-53).
lib. 10 l. 9 n. 8 Deinde cum dicit si vero ostendit tertium quod principaliter intendit, scilicet quod media sunt composita ex contrariis. Et circa hoc duo facit. Primo proponit quod intendit; dicens, quod si media in eodem genere sint cum extremis, sicut ostensum est, et si iterum media sint solum contrariorum, ut etiam ostensum est; necesse est media componi ex his contrariis inter quae sunt.	2104. Now if intermediates (882). Third, he proves the point that constitutes his main thesis. He says that, if intermediates belong to the same genus as extremes, as has been shown (879:C 2098), and if again there are intermediates only between contraries, as has also been shown (882:C 2104), then intermediates must be composed of the contraries between which they stand.
lib. 10 l. 9 n. 9 Deinde cum dicit nam erit probat propositum. Et circa hoc tria facit. Primo ostendit quod contrariae species habent priora contraria ex quibus constituuntur. Quod sic probat. Oportet enim quod contrariorum, aut sit aliquod genus, aut nullum. Si autem nullum genus esset contrariorum, non haberent medium; quia medium non est nisi eorum quae sunt unius generis, ut ex dictis patet. Sed si contrariorum, quorum ponitur medium, sit aliquod genus prius ipsis contrariis, necesse est etiam quod sint differentiae contrariae priores speciebus contrariis, quae faciant et constituant species contrarias ex ipso genere uno. Species enim ex genere et differentiis constituuntur.	2105. For there will (883). Then he proves his thesis; and in regard to this he does three things. First, he proves that contrary species have prior contraries of which they are composed. He proceeds as follows: there must either be a genus of contraries or not. But if there is no genus of contraries, contraries will not have an intermediate; for there 4 an intermediate only between those things which belong to one genus, as is evident from what has been said. But if those contraries which are assumed to have an intermediate have some genus which is prior to the contraries themselves, there must also be different contraries prior to contrary species, which make and constitute contrary species from this one genus. For species are constituted of genus and differences.
lib. 10 l. 9 n. 10 Et hoc manifestat per exemplum. Sicut si album et nigrum sint contrariae species, et habeant unum genus quod est color, necesse est quod habeant aliquas differentias constitutivas; ita quod album sit color disgregativus visus, nigrum vero color congregativus. Et sic hae differentiae congregativum et disgregativum sunt priores albo et nigro. Unde, cum utrobique sit contrarietas, manifestum est quod contraria sunt seinvicem priora. Contrariae enim differentiae sunt priores contrariis speciebus. Et sunt etiam magis contrariae, quia sunt causae contrarietatis ipsis speciebus.	2106. He makes this clear by an example. If white and black belong to contrary species and have one genus, color, they must have certain constitutive differences, so that white is a color capable of expanding vision, and black is a contracting color. Therefore the differences “contracting” and “expanding” are prior to white and to black. Hence, since in each case there is a contrariety, it is evident that some contraries are prior to others; for contrary differences are prior to contrary species; and they are also contrary to a greater degree because they are causes of the contrariety in these species.
lib. 10 l. 9 n. 11 Considerandum tamen quod disgregativum et congregativum visus, non sunt verae differentiae constitutivae albi et nigri, sed magis effectus eorum. Ponuntur tamen loco differentiarum, signa earum. Sicut interdum per accidentia, designantur differentiae et formae substantiales. Disgregatio enim visus provenit ex vehementia lucis, cuius plenitudo albedinem constituit. Et congregatio visus provenit ex causa contraria.	2107. However, it must be understood that, while “expanding” and “contracting” as referred to vision are not true differences which constitute white and black, but rather are their effects, still they are given in place of differences as signs of them, just as differences and substantial forms are sometimes designated by accidents. For the expansion of vision comes from the strength of the light, whose fullness constitutes whiteness. And the contraction of vision has as its cause the opposite of this.
lib. 10 l. 9 n. 12 Deinde cum dicit et reliqua ostendit quod etiam mediae species habent priora media, ex quibus constituuntur; dicens, quod cum media sint species eiusdem generis, et omnes species ex genere et differentia constituantur, necesse est quod media constituantur ex genere et differentiis. Sicut quicumque colores sunt medii inter album et nigrum, oportet hos definiri ex genere, quod est color, et ex quibusdam differentiis. Et hae differentiae, ex quibus constituuntur medii colores, non possunt esse immediate prima contraria, scilicet differentiae contrariae quae constituebant contrarias species albi et nigri. Aliter oportet quod quilibet color medius esset albus aut niger. Nam color congregativus est niger, et disgregativus est albus. Oportet igitur quod differentiae constitutivae mediorum colorum sint alterae a differentiis contrariis, quae sunt constitutivae contrariarum specierum. Et quia, sicut se habent species ad species, ita se habent differentiae ad differentias: oportet quod sicut medii colores sunt species mediae inter species contrarias, ita differentiae constitutivae earum sint mediae inter differentias contrarias quae dicuntur prima contraria.	2108. And the other (884). He shows too that intermediate species have prior intermediates of which they are composed. He says that, since intermediates are species of the same genus, and all species are constituted of genus and differences, intermediates must be constituted of genus and differences; for example, any colors that are intermediate between white and black must be defined by their genus, color’ and by certain differences; and these differences of which intermediate colors are composed cannot be the immediate “primary contraries,” i.e., the differences which constitute the contrary species of white and black. Again, any color must be intermediate between white and black; for black is a contracting color and white an expanding color. Hence the differences which constitute intermediate colors must differ according to the different contraries which are constitutive of contrary species. And since differences are related to differences as species are to species, then just as intermediate colors are intermediate species between contrary species, in a similar fashion the differences which constitute them must be intermediate between the contrary differences which are called primary contraries.
lib. 10 l. 9 n. 13 Deinde cum dicit primae autem ostendit, quod mediae differentiae ex differentiis contrariis componuntur; dicens, quod differentiae primae contrariae sunt disgregativum visus et congregativum. Unde istae differentiae sunt illud primum, ex quo componimus omnes species generis. Sed, si aliqua contraria non essent in eodem genere, quaerendum restaret ex quo eorum media constituerentur. Sed in his quae sunt in eodem genere, non est difficile hoc accipere; quia necesse est omnia quae sunt in eodem genere aut esse incomposita, idest simplicia, aut componi ex incompositis, idest simplicibus, quae sunt in genere illo. Contraria enim sunt incomposita ex invicem; quia nec album componitur ex nigro, neque nigrum ex albo, neque congregativum ex disgregativo, neque e converso. Quare oportet quod contraria sint principia, quia simplicia in quolibet genere sunt principia.	2109. And the primary (885). Then he shows that intermediate differences are composed of contrary differences. He says that primary contrary differences are those which can expand and contract sight, so that these differences constitute a primary type of which we compose every species of a genus. But if certain contraries did not belong to the same genus, we would still have to consider of which of these contraries the intermediates would be composed. This is not difficult to understand in the case of those things which belong to the same genus, because all things belonging to the same genus “must either be incomposite,” i.e., simple things, or they must be composed “of incomposites,” i.e., of simple things, which belong to the same genus. For contraries are not composed of each other, because white is not composed of black, nor black of white; nor is the contracting composed of the expanding or the reverse. Hence contraries must be principles, because the simple things in any genus are the principles of that genus.
lib. 10 l. 9 n. 14 Sed de mediis oportet dicere, quod aut omnia componantur ex simplicibus, idest ex contrariis, aut nullum; quia eadem ratio videtur de omnibus. Sed non potest dici, quod nullum: quia aliquod est medium quod componitur ex contrariis: ex quo contingit quod transmutatio primo pervenit ad media quam ad extrema. Hoc autem sic apparet: quia illud in quod primo pervenit transmutatio, est magis et minus respectu utriusque extremorum. Prius enim aliquid fit minus album et minus nigrum, quam totaliter album et totaliter nigrum: et hoc ipsum quod est minus album, quam album simpliciter, et minus nigrum quam nigrum simpliciter. Est etiam magis accedens ad album quam nigrum simpliciter; et magis accedens ad nigrum quam album simpliciter. Et sic patet, quod illud in quod primo venit transmutatio, est magis et minus respectu utriusque extremorum. Et propter hoc oportet quod sit medium contrariorum. Et sic sequitur quod omnia media sint composita ex contrariis. Nam idem medium quod est magis et minus respectu utriusque extremorum, oportet esse compositum ex extremis simplicibus, respectu quorum dicitur magis et minus. Et quia non sunt aliqua extrema priora contrariis in eodem genere, relinquitur quod duae differentiae contrariae constitutivae mediorum sint compositae ex contrariis differentiis. Et ita media erunt ex contrariis. Quod patet, quia omnia inferiora, idest omnes species generis, tam contraria quam media, sunt ex primis contrariis, scilicet differentiis.	2110. But it is necessary to say that all intermediates are composed either “of simple things,” i.e., of contraries, or they are not, because the same reasoning seems to apply to all. But it cannot be said that they are not, because there is an intermediate which is composed of contraries, and according to this it is possible for change to first affect intermediates before it affects extremes. This becomes evident as follows: that in which change first occurs admits of difference in degree in relation to the two extremes; for something becomes slightly white or slightly black before it becomes completely white or completely black; and it is what is less white that becomes plain white, and what is less black that becomes plain black. And it also comes closer to white than to plain black, and closer to black than to plain white. Thus it is evident that the thing which change first affects admits of difference in degree in relation to both extremes; and for this reason contraries must have an intermediate. It follows, then, that all intermediates are composed of contraries; for the same intermediate which is more and less in relation to both extremes must be composed of both unqualified extremes, in reference to which it is said to be more and less. And since there are no extremes which are prior to contraries in the same genus, it follows that the two contrary differences which constitute intermediates are composed of contrary differences. Thus intermediates must come from contraries. This is evident because “all inferiors,” i.e., all species of a genus, both contraries and intermediates, are composed of primary contraries, i.e., differences.
lib. 10 l. 9 n. 15 Deinde cum dicit quod quidem concludit epilogando quod supra de mediis dictum est. Et est litera plana.	2111. Hence it is evident (886). He brings his discussion to a close by summarizing what has been said above about intermediates. This part of the text is clear.

Lecture 10

Latin	English
lib. 10 l. 10 n. 1 Quia philosophus superius ostendit contrarietatem esse differentiam quamdam, differentia autem vel est secundum genus, vel secundum speciem; intendit hic Aristoteles ostendere quomodo contraria se habeant ad hoc, ut differant genere et specie. Et dividitur in partes duas. In prima ostendit quod differentia secundum speciem pertinet ad contrarietatem. In secunda ostendit quomodo de quibusdam contrariis aliter est, ibi, dubitabit autem aliquis quare femina et cetera. Circa primum tria facit. Primo ostendit quod differentia quae facit differre specie, est secundum se ipsius generis, quasi ipsam naturam generis in diversas species dividens. Secundo ostendit quod hoc convenit contrarietati, ibi, contrarietas igitur haec et cetera. Tertio concludit quoddam corollarium ex dictis, ibi, quare palam, quia ad id quod vocatur genus et cetera. Dicit ergo primo, quod in omni diversitate secundum speciem oportet duo accipere: scilicet ut hoc sit diversum ab aliquo, et ut sit aliquid diversificatum per haec duo. Et hoc quod est diversificatum per haec duo, oportet inesse ambobus. Sicut animal est quod est diversificatum in diversas species, scilicet in hominem et equum: et oportet quod ambo, scilicet homo et equus, sint animalia. Unde patet quod necesse est ea quae sunt diversa specie adinvicem, in eodem genere esse.	2112. Because the Philosopher has shown above (840:C 2107) that contrariety is a kind of difference, and difference is either generic or specific, his aim here is to show how contraries differ generically and specifically. This is divided into two parts. In the first (887:C 2112) he shows that difference in species is contrariety. In the second (891:C 2127) he shows how this does not apply in the case of some contraries (“But someone”). In regard to the first he does three things. First, he shows that the difference which causes difference in species belongs essentially to the same genus as the attribute which divided the nature itself of the genus into different species. Second (888:C 2120), he shows that this is proper to contrariety (“Therefore this will”). Third (890:C 2124), he draws a corollary from what has been said (“It is evident”). He accordingly says, first (887), that wherever there is difference in species two things must be considered, namely, that one thing differs from something else, and that there is something which is differentiated by these two. And that which is differentiated by these two must belong to both; for example, animal is something divided into various species, say, man and horse; and both of these, man and horse, must be animals. It is evident, then, that things which differ specifically from each other must belong to the same genus.
lib. 10 l. 10 n. 2 Id enim vocatur genus, quod est unum et idem ambobus, non secundum accidens de utroque praedicatum, neque secundum accidens diversificatum in utroque. Unde oportet, quod habeat differentiam non secundum accidens: sive genus ponatur ens quasi materia, sive qualitercumque aliter.	2113. For that which is one and the same for both and is not predicated of each accidentally or differentiated into each accidentally is called their genus. Hence it must have a difference which is not accidental whether the genus is assumed to have the nature of matter or is taken in some other way.
lib. 10 l. 10 n. 3 Hoc autem ideo dicit, quia aliter diversificatur materia per formas et aliter genus per differentias. Forma enim non est hoc ipsum quod est materia, sed facit compositionem cum ea. Unde materia non est ipsum compositum, sed aliquid eius. Differentia vero additur generi non quasi pars parti, sed quasi totum toti. Unde genus est hoc ipsum quod est species, et non solum aliquid eius. Si autem esset pars, non praedicaretur de ea.	2114. Now he says this because matter is differentiated in one way by form, and genus is differentiated in another way by differences; for form is not matter itself but enters into composition with it. Hence matter is not the composite itself but is something belonging to it. But a difference is added to a genus, not as part to part, but as whole to whole; so that the genus is the very thing which is the species, and is not merely something belonging to it. But if it were a part, it would not be predicated of it.
lib. 10 l. 10 n. 4 Sed tamen, quia totum potest denominari ab una sola parte sua, puta si homo denominetur habens caput, vel habens manus, contingit ipsum compositum ex materia et forma denominari. Et quidem nomen, quo aliquid totum denominatur ab eo quod est materiale in ipso, est nomen generis. Nomen autem, quo denominatur a principio formali, est nomen differentiae. Sicut homo nominatur animal a natura sensibili, rationale vero a natura intellectiva. Sicut igitur habens manum competit toti, licet manus sit pars, ita genus et differentia conveniunt toti, licet sumantur a partibus.	2115. Yet since a whole can be named from one of its own parts alone, for example, if a man is said to be headed or handed, it is possible for the composite itself to be named from its matter and form. And the name which any whole gets from its material principle is that of the genus. But the name which it gets from its formal principle is the name of the difference. For example, man is called an animal because of his sensory nature, and he is called rational because of his intellective nature. Therefore, just as “handed” belongs to the whole even though the hand is a part, in a similar way genus and difference refer to the whole even though they are derived from the parts of the thing.
lib. 10 l. 10 n. 5 Si ergo consideretur in genere et differentia id a quo utrumque sumitur, hoc modo genus se habet ad differentias, sicut materia ad formas. Si autem consideretur secundum quod nominant totum, sic aliter se habent. Hoc tamen commune est utrobique, quod sicut ipsa essentia materiae dividitur per formas, ita ipsa natura generis diversificatur per differentias. Sed hoc utrobique distat, quia materia est in utroque divisorum, non tamen est utrumque eorum; genus autem utrumque eorum est: quia materia nominat partem, genus autem totum.	2116. If in the case of genus and difference, then, one considers the principle from which each is derived, the genus is related to differences as matter is to forms. But if one considers them from the viewpoint of their designating the whole, then they are related in a different way. Yet this is common to both, namely, that just as the essence of matter is divided by forms, so too the nature of a genus is divided by differences. But both differ in this respect, that, while matter is contained in both of the things divided, it is not both of them. However, the genus is both of them; because matter designates a part, but the genus designates the whole.
lib. 10 l. 10 n. 6 Et ideo exponens quod dixerat, genus esse quo ambo specie differentia dicuntur unum et idem, subiungit quod non solum oportet genus esse commune duobus differentibus secundum speciem, sicut quod utrumque sit animal, sicut aliquid indivisum est commune diversis, ut eadem domus aut possessio; sed oportet hoc ipsum quod est animal esse alterum utrumque; ita quod hoc animal sit equus et hoc animal sit homo.	2117. Therefore in explaining his statement that a genus is that by which both of the things which differ specifically are said to be one and the same, he adds that, not only must the genus be common to both of the things which differ specifically (as, for instance, both are animals) as something which is undivided is common to different things, just as a house and a possession are the same, but the animal in both must differ, so that this animal is a horse and that animal is a man.
lib. 10 l. 10 n. 7 Et hoc dicit contra Platonicos, qui ponebant communia separata, quasi ipsamet natura communis non diversificaretur, si natura speciei esset aliquid aliud praeter naturam generis. Unde contra hoc concludit ex dictis, quod hoc ipsum quod est commune, diversificatur secundum speciem. Unde oportet quod commune, ut animal, ipsum secundum se sit hoc tale secundum unam differentiam, et illud tale secundum aliam differentiam, sicut quod hoc sit equus, et illud homo. Et ita sequitur, quod si animal sit secundum se hoc tale et hoc tale, quod differentia faciens differre specie, sit quaedam diversitas generis. Et exponit diversitatem generis, quae ipsam naturam generis diversificat.	2118. He says this against the Platonists, who claimed that there are common separate natures in the sense that the common nature would not be diversified if the nature of the species were something else besides the nature of the genus. Hence from what has been said he concludes against this position that whatever is common is differentiated specifically. lience the common nature in.itself, for example, animal, must be this sort of animal with one difference, and that sort of animal with another difference, so that the one is a horse and the other is a man. Thus if animal in itself is this and that sort of animal, it follows that the difference which causes difference in species is a certain difference of the genus. And he explains the diversification of a genus which makes a difference in the generic nature itself.
lib. 10 l. 10 n. 8 Per hoc autem quod hic philosophus dicit, non solum excluditur opinio Platonis ponentis commune unum et idem per se existere: sed etiam excluditur opinio eorum qui dicunt, quod illud quod pertinet ad naturam generis, non differt specie in speciebus diversis; sicut quod anima sensibilis non differt specie in homine et equo.	2119. Now what the Philosopher says here rules out not only the opinion of Plato, who claimed that one and the same common nature exists of itself, but also the opinion of those who say that whatever pertains to the nature of the genus does not differ specifically in different species, for example, the opinion that the sensory soul of a man does not differ specifically from that in a horse.
lib. 10 l. 10 n. 9 Deinde cum dicit contrarietas igitur ostendit quod differentia diversificans secundum se genus modo praedicto, est contrarietas; dicens: cum differentia secundum speciem sit secundum se diversificans genus, manifestum est quod haec differentia est contrarietas. Et hoc primo manifestat ex inductione. Videmus enim quod omnia genera dividuntur per opposita. Quod quidem necesse est. Nam ea quae non sunt opposita, possunt simul existere in eodem. Quae autem huiusmodi sunt, non possunt esse diversa, cum non ex necessitate sint in diversis. Unde oportet quod solum oppositis aliquid commune dividatur.	2120. Therefore this will (888). Then he shows that the difference which divides the genus essentially in the foregoing way is contrariety. He says that, since the specific difference divides the genus essentially, it is evident that this difference is contrariety. He makes this clear, first, by an induction; for we see that all genera are divided by opposites. And this must be so; for those things which are not opposites can coexist in the same subject; and things of this kind cannot be different, since they are not necessarily in different things. Hence anything common must be divided by opposites alone.
lib. 10 l. 10 n. 10 Non autem divisio generis in diversas species potest fieri per alia opposita. Nam contradictorie opposita non sunt in eodem genere, cum negatio nihil ponat. Et simile est de privative oppositis, cum privatio non sit nisi negatio in subiecto aliquo. Relativa etiam, ut supra habitum est, non sunt eiusdem generis, nisi quae secundum se adinvicem referuntur, quae quodammodo sunt contraria, ut supra dictum est. Et sic relinquitur quod sola contraria faciunt differre specie, ea quae sunt unius generis.	2121. But the division of a genus into different species cannot come about by way of the other kinds of opposites. For things which are opposed as contradictories do not belong to the same genus, since negation posits nothing. The same is true of privative opposites, for privation is nothing else than negation in a subject. And relative terms, as has been explained above (881:C 2103), belong to the same genus only if they are in themselves relative to each other and are in a sense contraries, as has been stated above (ibid.). It is evident, then, that only contraries cause things belonging to the same genus to differ specifically.
lib. 10 l. 10 n. 11 Deinde cum dicit et quod manifestat idem per rationem; dicens, quod contraria sunt in eodem genere, sicut ostensum est. Dictum est enim quod contrarietas est differentia perfecta. Et iterum dictum est quod differentia secundum speciem est aliquid alicuius, idest ab aliquo. Et quod praeter hoc, idem genus oportet esse in ambobus differentibus specie. Et ex his duobus sequitur, quod omnia contraria sint in eadem coelementatione categoriae, idest in eadem ordinatione praedicamentali. Ut hoc tamen intelligatur de contrariis, quaecumque sunt differentia specie, et non genere. Quod quidem dicit praeservando se a corruptibili et incorruptibili, de quibus post dicetur quod sunt diversa genere.	2122. And it has (889). Then he proves the same point by an argument. He says that contraries belong to the same genus, as has been shown (883:C 2105). For it has been pointed out (844:C 2027-29) that contrariety is the perfect difference; and it has also been stated (889) that difference in species is “something of something,” i.e., from something. And besides this it has been noted (887:C 2112) that the same genus must belong to both of the things which differ specifically. Now from these two considerations it follows that all contraries are contained in the same “order of the categories,” i.e., in the same classification of predicates, yet in such a way that this is understood of all contraries which differ specifically but not generically. He says this in order to preclude the corruptible and the incorruptible, which are later said to differ generically.
lib. 10 l. 10 n. 12 Et non solum contraria sunt in uno genere, sed sunt etiam diversa abinvicem. Quod patet: quia ea quae perfecte differunt, sicut contraria, non sunt invicem simul. Unde, cum ad differentiam secundum speciem requiratur identitas generis, et diversificatio generis per diversas species, et cum utrumque in contrarietate reperiatur, sequitur quod differentia secundum speciem sit contrarietas. Quod manifestum est; quia hoc est aliqua esse diversa secundum speciem existentia in eodem genere, habere contrarietatem differentiarum, cum sint individua, idest non ulterius divisa in species, sicut sunt species specialissimae. Quae quidem dicuntur individua, inquantum ulterius non dividuntur formaliter. Particularia vero dicuntur individua, inquantum nec materialiter nec formaliter ulterius dividuntur. Et sicut diversa specie sunt quae contrarietatem habent, ita eadem specie sunt, quae non habent contrarietatem, cum sint individua secundum formalem differentiam. Contrarietates enim fiunt in divisione, non solum in supremis generibus, sed etiam in mediis, prius quam veniatur ad individua, idest ad ultimas species. Sic igitur manifestum est, quod licet non in omni genere sit contrarietas specierum, in omni tamen genere est contrarietas differentiarum.	2123. And contraries not only belong to one genus but they also differ from each other. This is evident, for things which differ perfectly as contraries are not generated from each other at the same time. Therefore, since difference in species requires identity of genus and the division of the genus into different species, and since both of these are found in contrariety, it follows that difference in species is contrariety. This is evident because in order for things in the same genus to differ specifically they must have contrariety of differences “while being undivided,” i.e., when they are not further divided into species, as the lowest species. And these are said to be undivided inasmuch as they are not further divided formally. But particular things are said to be undivided inasmuch as they are not further divided either formally or materially. And just as those things are specifically different which have contrariety, so too those things are specifically the same which do not have contrariety, since they are not divided by any formal difference. For contrarieties arise in the process of division not only in the highest genera but also in the intermediate ones, “before one reaches the things which are undivided,” i.e., the lowest species. It is accordingly evident that, even though there is not contrariety of species in every genus, there is contrariety of differences in every genus.
lib. 10 l. 10 n. 13 Deinde cum dicit quare palam concludit quoddam corollarium ex dictis; scilicet quod nihil eorum quae conveniunt in genere, sicut sunt species generis, dicitur idem specie, nec diversum specie ad genus; quia id ad quod aliquid dicitur specie idem, habet unam et eamdem differentiam; illud autem ad quod aliquid dicitur diversum specie, habet oppositam differentiam. Si igitur aliqua specierum diceretur idem specie vel diversum ad genus, sequeretur quod genus haberet in sui ratione aliquam differentiam. Sed hoc falsum est.	2124. It is evident (890). Here he draws a corollary from what has been said, namely, that none of the things which agree in being species of the same genus are said to be either specifically the same as the genus or specifically different from it; for things which are said to be specifically the same have one and the same difference, whereas things which are said to be specifically different have opposite differences. Hence, if any species is said to be specifically the same as the genus or specifically different from it, it follows that the genus will contain some difference in its definition. But this is false.
lib. 10 l. 10 n. 14 Quod sic patet. Materia enim ostenditur negatione, idest natura materiae intelligitur per negationem omnium formarum. Genus autem est quodammodo materia, sicut expositum est. Et loquimur nunc de genere quod invenitur in naturis rerum, non de genere quod in hominibus dicitur, sicut genus Romanorum vel Heraclidarum. Unde patet quod etiam genus in sua ratione non habet differentiam aliquam.	2125. This is made evident as follows: matter “is made known by negation, i.e., the nature of matter is understood by negating all forms. And in a sense genus is matter, as has been explained (887:C 2113-15); and we are now speaking of genus in the sense that it is found in the natures of things, and not in the sense that it applies to men, as the genus (or race) of the Romans or of the Heraclidae. Hence it is clear that a genus does not have a difference in its definition.
lib. 10 l. 10 n. 15 Et sic patet, quod nulla species a suo genere differt specie, nec est cum eo idem specie: et similiter non differunt aliqua specie ab illis quae non sunt in eodem genere, proprie loquendo, sed differunt genere ab eis. Specie vero differunt ab his quae sunt in eodem genere: quia contrarietas est differentia qua aliqua differunt specie, ut ostensum est: non quia ipsa contrarietas differentiarum differat specie, licet contraria differant specie; sed contrarietas est solum in his quae sunt eiusdem generis. Unde relinquitur quod differre specie non sit proprie in his quae sunt alterius generis.	2126. Thus it is evident that no species is specifically different from its genus, nor is it specifically the same as its genus. And similarly things that do not belong to the same genus do not differ specifically from each other, properly speaking, but they do differ generically. And things that differ specifically differ from those that belong to the same genus; for a contrariety is the difference by which things differ specifically, as has been explained (888:C 2120)—not that the contrariety itself of the differences need differ specifically, even though contraries differ specifically; but contrariety is found only in those things that belong to the same genus. It follows, then, that to differ specifically does not properly pertain to things that belong to different genera.

Lecture 11

Latin	English
lib. 10 l. 11 n. 1 Quia philosophus iam ostendit quod differentia secundum speciem est contrarietas, hic ostendit in quibus contrarietas non sit differentia secundum speciem; et dividitur in partes duas. In prima ostendit quod sunt contraria, quae non faciunt differre secundum speciem, sed sunt in eadem specie. In secunda ostendit quae sunt contraria quae faciunt genere differre, non solum specie, ibi, quoniam vero contraria diversa et cetera. Circa primum duo facit. Primo movet dubitationem. Secundo solvit, ibi, aut quia hoc quidem dicit et cetera. Dicit ergo primo, quod dubitatio est quare femina non differt specie a viro, cum femininum et masculinum sint contraria, et differentia secundum speciem causetur ex contrarietate, ut supra ostensum est.	2127. Since the Philosopher has already shown that contrariety constitutes difference in species, here he indicates the kinds of things in which contrariety does not constitute difference in species; and this is divided into two parts. In the first (891)C 2127), he shows that there are contraries which do not cause difference in species but belong to the same species. In the second (895:C 2136), he indicates what the contraries are which cause things to differ in genus and not merely in species (“But since contraries”). In regard to the first he does two things. First, he raises a question. Second (892:C 2131), he answers it (“And the reason”). He accordingly says, first (891), that the question arises why woman does not differ specifically from man, since female and male are contraries, and difference in species is caused by contrariety, as has been established (887:C 2112).
lib. 10 l. 11 n. 2 Et iterum cum ostensum sit, quod ipsa natura generis diversificetur in diversas species per differentias, quae sunt per se differentiae generis, quare animal masculinum et animal femininum non sunt diversa secundum speciem, cum masculinum et femininum sint per se differentiae animalis, et non se habeant per accidens ad animal, sicut albedo et nigredo, sed masculinum et femininum praedicentur de animali inquantum est animal, sicut par et impar de numero, in quorum definitione ponitur numerus, sicut in definitione masculini et feminini animal.	2128. Again, since it has been shown that the nature of a genus is divided into different species by those differences which are essential to the genus, the question also arises why a male and a female animal do not differ spegifically, since male and female are essential differences of animal and are not accidental to animal as whiteness and blackness are; but male and female are predicated of animal as animal just as the even and the odd, whose definition contains number, are predicated of number; so that animal is given in the definition of male and female.
lib. 10 l. 11 n. 3 Ex duplici ergo ratione quaestio dubitabilis redditur: tum quia contrarietas facit differre specie: tum quia differentiae dividentes genus in diversas species sunt per se differentiae generis: quorum utrumque supra ostensum est.	2129. Hence the first question presents a difficulty for two reasons: both because contrariety causes difference in species, and because the differences that divide a genus into different species are essential differences of the genus. Both of these points have been proved above (887:C 2112).
lib. 10 l. 11 n. 4 Et quia hanc dubitationem in specialibus terminis moverat, reducit eam ad generaliorem formam; et dicit quod haec dubitatio fere est eadem, sicut si quaeratur, quare quaedam contrarietas facit differre specie, et quaedam non: sicut ambulativum et volativum, sive gressibile et volatile, faciunt differre specie animalia, sed albedo et nigredo non.	2130. And since he had raised this question in certain special terms, he reduces it to a more general form. He says that this question is almost the same as asking why one kind of contrariety causes things to differ in species and another does noi; for capabilities of walking and of flying, i.e., having the power to move about and to fly, cause animals to differ specifically, but whiteness and blackness do not.
lib. 10 l. 11 n. 5 Deinde cum dicit aut quia solvit propositam quaestionem. Et circa hoc duo facit. Primo solvit eam in generali, ad quod quaestionem reduxerat. Secundo adaptat generalem solutionem ad speciales terminos, in quibus primo moverat quaestionem, ibi, masculus vero et femina. Dicit ergo, quod ideo contingit quod quaedam contrarietas facit differre specie et quaedam non, quia quaedam contraria sunt propriae passiones generis, et quaedam sunt minus propriae. Quia enim genus a materia sumitur, materia autem per se habet ordinem ad formam; illae propriae sunt differentiae generis, quae sumuntur a diversis formis perficientibus materiam. Sed quia forma speciei iterum multiplicatur in diversa secundum materiam signatam, quae est subiecta individualibus proprietatibus, contrarietas accidentium individualium minus proprie se habet ad genus, quam contrarietas differentiarum formalium. Et ideo subiungit, quod quia in composito est materia et forma, haec quidem est ratio, idest forma quae constituit speciem, haec autem est materia quae est individuationis principium: quaecumque contrarietates sunt in ratione, idest ex parte formae, faciunt differre secundum speciem. Illae vero quae sunt ex parte materiae, quae sunt propriae individui, quod est acceptum cum materia, non faciunt differre secundum speciem.	2131. And the reason (892). Here he answers the question that was raised, and in regard to this he does two things. First, he answers the question in a general way with reference to the issue to which he had reduced the question. Second (893:C 2134), he adapts the general answer to the special terms in which he had first asked the question (“However, male and female”). He accordingly says (892) that one kind of contrariety can cause difference in species and another cannot, because some contraries are the proper affections of a genus, and others are less proper. For, since genus is taken from matter, and matter in itself has a relation to form, those differences which are taken from the different forms perfecting matter are the proper differences of a genus. But since the form of the species may be further multiplied to become distinct things by reason of designated matter, which is the subject of individual properties, the contrariety of individual accidents is related to a genus in a less proper way than the contrariety of formal differences. Hence he adds that, since the composite contains matter and form, and the one “is the intelligible structure,” i.e., the form, which constitutes the species, and the other is matter, which is the principle’ of individuation, all those “contraries in the intelligible structure,” i.e., all which have to do with the form, cause difference in species, whereas those contrarieties which have to do with matter and are proper to the individual thing, which is taken with matter, do not cause difference in species.
lib. 10 l. 11 n. 6 Et propter hoc albedo et nigredo non faciunt homines differre secundum speciem. Non enim homo albus et homo niger differunt specie, etiam si utrique imponatur aliquod nomen; ut si homo albus dicatur a et homo niger b. Hoc autem addit, quia homo albus non videtur esse aliquid unum. Sed si imponeretur nomen, videtur esse aliquid unum. Et similiter est de homine nigro. Et ideo dicit, quod homo albus et homo niger non differunt specie, quia homo, scilicet particularis, cui conveniunt album et nigrum, est quasi materia. Non enim dicitur quod homo sit albus, nisi quia hic homo est albus. Et sic, cum homo particularis conceptus sit cum materia, et materia non facit differentiam secundum speciem, sequitur quod hic homo et ille homo non differant specie: quia plures homines non propter hoc sunt plures species hominis, quia sunt plures; quia non sunt plures nisi propter diversitatem materiae, quia scilicet sunt diversae carnes et ossa ex quibus est hic et ille. Sed simul totum, idest individuum congregatum ex materia et forma, est diversum: sed non est diversum specie, quia non est contrarietas ex parte formae. Sed hoc, scilicet homo, est ultimum individuum secundum speciem, quia non dividitur ulterius divisione formali. Vel hoc, scilicet particulare, est ultimum individuum, quia non dividitur ulterius, nec materiali nec formali differentia. Sed quamvis in diversis individuis non sit contrarietas ex parte formae, est tamen diversitas individuorum particularium; quia particulare aliquod, ut Callias, non solum est forma, sed est forma cum materia individuata. Et ita, sicut diversitas formae facit differentiam specierum, ita diversitas materiae individualis facit differentiam individuorum. Album autem non praedicatur de homine nisi ratione individui. Non enim dicitur homo albus, nisi quia aliquis homo dicitur albus, ut Callias. Et sic patet, quod homo per accidens dicitur albus; quia non inquantum homo, sed inquantum hic homo, albus dicitur. Hic autem homo dicitur propter materiam. Unde patet quod album et nigrum non pertinent ad differentiam formalem hominis, sed solum ad materialem. Et propter hoc non differunt specie homo albus et niger, sicut nec circulus aereus et ligneus differunt specie. Et in his etiam quae differunt specie, non est differentia speciei propter materiam, sed propter formam; sicut triangulus aereus et circulus ligneus non differunt specie propter materiam, sed propter diversitatem formae.	2132. Hence whiteness and blackness do not cause men to differ specifically; for white man and black man do not differ specifically, even if a one-word name were given to each of them, say, “white man” were called A and “black man” were called B. He adds this because “white man” does not seem to be one thing, and the same is true of “black man.” Hence he says that “white man” and “black man” do not differ specifically, because man, i.e., a particular man, to whom both white and black belong, serves as matter; for man is said to be white only because this man is white. Thus since a particular man is conceived along with matter, and matter does not cause difference in species, it. follows that this particular man and that particular man do not differ specifically. For many men are not many species of man on the grounds that they are many, since they are many only by reason of the diversity of their matter, i.e., because the flesh and bones of which this man and that man are composed are different. But “the concrete whole,” i.e., the individual constituted of matter and form, is distinct; yet it is not specifically different because there is no contrariety as regards form. But this, namely, man, is the ultimate individual from the viewpoint of species, because the species is not further divided by a formal division. Or this, namely, the particular thing, is the ultimate individual, because it is not further divided either by a material difference or a formal one. But while there is no contrariety in distinct individuals as regard form, nevertheless there is a distinction between particular individuals; because a particular thing, such as Callias, is not a form alone but a form with individuated matter. Hence, just as difference of form causes difference of species, so too otherness in individual matter causes difference of individuals. And white is predicated’ of man only by way of the individual; for man is said to be white only because some particular man, such as Callias, is said to be white. Hence it is evident that man is said to be white accidentally, because a man is said to be white, not inasmuch as he is man, but inasmuch as he is this man. And this man is called “this” because of matter. Thus it is clear that white and black do not pertain to the formal difference of man but only to his material difference. Therefore “white man” and “black man” do not differ specifically, and neither do a bronze circle and a wooden circle differ specifically. And even those things which differ specifically do not do so by reason of their matter but only by reason of their form. Thus a bronze triangle and a wooden circle do not differ specifically by reason of their matter but because they have a different form.
lib. 10 l. 11 n. 7 Unde si quaeratur, utrum materia faciat diversa specie aliquo modo, videtur quod faciat; quia hic equus ab hoc homine est diversus specie, et tamen manifestum est quod ratio utriusque est cum materia individuali. Et sic videtur quod materia aliqualiter faciat differre specie. Sed tamen manifestum est, quod hoc non contingit propter diversitatem materiae, sed quia contrarietas est ex parte formae, quia homo albus et equus niger differunt specie. Sed hoc non est propter album et nigrum, quia si ambo essent albi, adhuc specie differrent. Sic igitur apparet quod contrarietas quae est ex parte ipsius formae, facit differre specie; non autem illa quae est ex parte materiae.	2133. If one were to ask, then, whether matter somehow causes difference in species, the answer would seem to be that it does, because this horse is specifically different from this man, and it is no less evident that the notion of each contains individual matter. Thus it appears that matter somehow causes difference in species.—But on the other hand it is also evident that this does not come about by reason of any difference in their matter, but because there is contrariety with regard to their form. For “white man” and “black horse” differ specifically, yet they do not do so by reason of whiteness and blackness; for even if both were white they would still differ specifically. It appears, then, that the kind of contrariety which pertains to form causes difference in species, but not the kind which pertains to matter.
lib. 10 l. 11 n. 8 Deinde cum dicit masculus vero solutionem generalem positam adaptat ad terminos speciales, in quibus primo quaestionem moverat, scilicet ad masculum et feminam; dicens, quod masculus et femina sunt proprie passiones animalis, quia animal ponitur in definitione utriusque. Sed non conveniunt animali secundum substantiam et formam, sed ex parte materiae et corporis. Quod patet ex hoc, quod idem sperma potest fieri masculus et femina, secundum quod diversimode patitur aliquam passionem; quia cum fuerit calor operans fortis, fiet masculus; cum autem erit debilis, fiet femina. Hoc autem non posset esse vel contingere, si masculus et femina differrent specie. Non enim ex uno semine diversa secundum speciem producuntur. Quia in semine vis est activa, et omne agens naturale agit ad determinatam speciem, quia agit sibi simile. Unde relinquitur quod masculus et femina non differant secundum formam, nec sunt diversa secundum speciem.	2134. However, male and female (893). Next he adapts the general answer which he has given to the special terms in reference to which he first raised the question, namely, male and female. He says that male and female are proper affections of animal, because animal is included in the definition of each. But they do not pertain to animal by reason of its substance or form, but by reason of its matter or body. This is clear from the fact that the same sperm insofar as it undergoes a different kind of change can become a male or a female animal; because, when the heat at work is strong, a male is generated, but when it is weak, a female is generated. But this could not be the case or come about if male and female differed specifically; for specifically different things are not generated from one and the same kind of sperm, because it is the sperm that contains the active power, and every natural agent acts by way of a determinate form by which it produces its like. It follows, then, that male and female do not differ formally, and that they do not differ specifically.
lib. 10 l. 11 n. 9 Deinde cum dicit quod quidem epilogat quod dixerat: quod planum est in litera.	2135. What it is (894). Here he sums up what has been said. This is clear in the text.

Lecture 12

Latin	English
lib. 10 l. 12 n. 1 Postquam philosophus ostendit quae sunt contraria quae non faciunt differre specie, hic ostendit quae sunt contraria quae etiam genere differre faciunt. Et circa hoc tria facit. Primo determinat veritatem. Secundo excludit quorumdam falsam opinionem, ibi, nunc ergo diximus et cetera. Tertio infert quoddam corollarium ex dictis, ibi, palam igitur quod non contingit et cetera. Primo ergo praemittit duo ad ostendendum propositum: quorum primum est, quod contraria sunt diversa specie, ut supra ostensum est.	2136. After having shown what contraries do not cause things to differ specifically, here the Philosopher explains what contraries cause things to differ generically. In regard to this he does three things. First (895)C 2136), he establishes the truth. Second (896:C 2138), he rejects the false opinion of certain men (“Now we have already”). Third (898:C 214.3), he draws a corollary from his discussion (“It is clearly”). He accordingly first of all (895) lays down two premises necessary for the proof of his thesis. The first of these is that contraries are formally different, as was explained above (888:C 2.120). Corruptible & incorruptible are generically different.
lib. 10 l. 12 n. 2 Secundum est, quod corruptibile et incorruptibile sunt contraria. Quod probat ex hoc, quod impotentia opposita determinatae potentiae est quaedam privatio, ut in nono habitum est. Privatio autem est principium contrarietatis. Unde sequitur, quod impotentia sit contrarium potentiae. Corruptibile autem et incorruptibile opponuntur secundum potentiam et impotentiam. Sed diversimode. Nam si accipiatur potentia communiter, secundum quod se habet ad posse agere vel pati quodcumque, sic corruptibile secundum potentiam dicetur, incorruptibile secundum impotentiam. Si autem dicatur potentia secundum quod non est posse aliquid deterius, sic e converso, incorruptibile dicetur secundum potentiam, corruptibile vero secundum impotentiam.	2137. The second premise is that the corruptible and the incorruptible are contraries. He proves this from the fact that the incapacity opposed to a definite capacity is a kind of privation, as has been stated in Book IX (1784). Now privation is a principle of contrariety; and therefore it follows that incapacity is contrary to capacity, and that the corruptible and the incorruptible are opposed as capacity and incapacity. But they are opposed in a different way. For if capacity is taken (1) according to its general meaning, as referring to the ability to act or to be acted upon in some way, then the term corruptible is used like the term capacity, and the term incorruptible like the term incapacity. (2) But if the term capacity is used of something inasmuch as it is incapable of undergoing something for the worse, then contrariwise the term incorruptible is referred to capacity, and the term corruptible is referred to incapacity. 2137a. But although it seems necessary from these remarks to conclude that the corruptible and the incorruptible differ specifically, he concludes that they differ generically. And this is true because, just as form and actuality pertain to the species, so too matter and capacity pertain to the genus. Hence, just as the contrariety which pertains to form and actuality causes difference in species, so too the contrariety which pertains to capacity or potency causes difference in genus.
lib. 10 l. 12 n. 3 Cum autem ex his videretur concludendum quod corruptibile et incorruptibile differunt specie, concludit quod sunt diversa genere. Et hoc ideo, quia sicut forma et actus pertinent ad speciem, ita materia et potentia pertinent ad genus. Unde sicut contrarietas quae est secundum formas et actus, facit differentiam secundum speciem, ita contrarietas quae est secundum potentiam, facit generis diversitatem.	2137a. But although it seems necessary from these remarks to conclude that the corruptible and the incorruptible differ specifically, he concludes that they differ generically. And this is true because, just as form and actuality pertain to the species, so too matter and capacity pertain to the genus. Hence, just as the contrariety which pertains to form and actuality causes difference in species, so too the contrariety which pertains to capacity or potency causes difference in genus.
lib. 10 l. 12 n. 4 Deinde cum dicit nunc autem excludit quorumdam falsam opinionem. Et circa hoc duo facit. Primo proponit eam. Secundo improbat, ibi, sed contrariorum et cetera. Dicit ergo primo, quod probatio praemissa de corruptibili et incorruptibili est accepta ex ratione horum universalium nominum, secundum scilicet quod unum significat potentiam, et aliud impotentiam. Sed sicut quibusdam videtur, non necesse est quod corruptibile et incorruptibile differant specie, sicut non est hoc necesse in albo et nigro. Convenit enim idem esse album et nigrum. Sed diversimode. Quia si illud quod dicitur album et nigrum sit aliquod universale, simul est album et nigrum quantum ad diversos. Sicut simul verum est dicere, quod homo est albus propter Socratem et niger propter Platonem. Si vero fuerit aliquid singularium, non erit simul album et nigrum. Sed tamen potest nunc esse album, postea nigrum, cum tamen album et nigrum sint contraria. Et hoc modo dicunt quidam, quod simul in eadem specie possunt esse quaedam corruptibilia et quaedam incorruptibilia. Et idem singulariter quandoque corruptibile, et quandoque incorruptibile.	2138. Now we have already (896). Here he rejects the false opinion of certain men; and in regard to this he does two things. First, he gives this opinion. Second (997:C 213()), he shows that it is false (“But while some”). He accordingly says, first (896), that the proof which was given above regarding the corruptible and the incorruptible is based on the meaning of these universal terms, i.e., inasmuch as one signifies a capacity and the other an incapacity. But, as it seems to certain men, it is not necessary that the corruptible and the incorruptible should differ specifically, just as this is not necessary for white and black, because it is admissible for the same thing to be both white and black, although in different ways. For if what is said to be white and black is something universal, it is white and black at the same time in different subjects. Thus it is true to say that man is at the same time both white, because of Socrates, and black, because of Plato. But if it is a singular thing, it will not be both white and black at the same time (although it can now be white and afterward black) since white and black are contraries. Thus some say that some things can be corruptible and some incorruptible within the same genus, and that the same singular thing can sometimes be corruptible and sometimes incorruptible.
lib. 10 l. 12 n. 5 Deinde cum dicit sed contrariorum excludit praedictam opinionem; dicens, quod contrariorum quaedam sunt in his de quibus dicuntur secundum accidens, sicut album et nigrum homini, de quibus nunc dictum est: et alia multa sunt huiusmodi contraria, in quibus locum habet quod dictum est, scilicet quod possunt simul esse in eadem specie, et successive in eodem singulari. Sed quaedam contraria sunt, de quibus hoc est impossibile; de quorum numero sunt corruptibile et incorruptibile.	2139. But while some (897). Here he rejects the foregoing opinion. He says that some contraries belong accidentally to the things of which they are predicated, as white and black belong to man, as has been mentioned already (892:C 2131); and there are many other contraries of this kind in reference to which the view stated is verified, i.e., that contraries can exist simultaneously in the same species and successively in the same singular thing. But there are other contraries which are incapable of this, and among these are the corruptible and the incorruptible.
lib. 10 l. 12 n. 6 Non enim corruptibile inest secundum accidens alicui eorum de quibus praedicatur; quia quod est secundum accidens, contingit non inesse. Corruptibile autem ex necessitate inest his quibus inest. At si hoc non sit verum, sequeretur, quod unum et idem sit quandoque corruptibile et quandoque incorruptibile: quod est impossibile secundum naturam. (Licet per hoc non excludatur, quin virtus divina possit aliqua corruptibilia secundum suam naturam, incorruptibiliter conservare).	2140. For corruptible does not belong accidentally to any of the things of which it is predicated, because what is accidental is capable of not belonging to a thing. But corruptible belongs necessarily to the things in which it is present. If this were not so it would follow that the very same thing would sometimes be corruptible and sometimes incorruptible; but this is naturally impossible. (However, this does not prevent the divine power from being able to keep some things which are corruptible by their very nature from being corrupted.)
lib. 10 l. 12 n. 7 Sic igitur necesse est, cum corruptibile non praedicetur secundum accidens, quod aut significet substantiam eius de quo praedicatur, aut aliquid quod est in substantia. Est enim unumquodque corruptibile per materiam, quae est de substantia rei. Et similis ratio est de incorruptibili; quia utrumque ex necessitate inest. Sic igitur patet, quod corruptibile et incorruptibile opponuntur sicut secundum se praedicata; quae scilicet praedicantur de aliquo inquantum huiusmodi, secundum quod tale, et primo.	2141. Since the term corruptible, then, is not an accidental predicate, it must signify either the substance of the thing of which it is predicated or something belonging to the substance; for each thing is corruptible by reason of its matter, which belongs to its substance. The same argument applies to incorruptibility, because both belong to a thing necessarily. Hence it is evident that corruptible and incorruptible are opposed as essential predicates, which are predicated of a thing inasmuch as it is a thing of this kind, as such and primarily.
lib. 10 l. 12 n. 8 Et ex hoc sequitur ex necessitate, quod corruptibile et incorruptibile sint genere diversa. Manifestum est enim quod contraria quae sunt in uno genere, non sunt de substantia illius generis. Non enim rationale et irrationale sunt de substantia animalis. Sed animal est potentia utrumque. Quodcumque autem genus accipiatur, oportet quod corruptibile et incorruptibile sint de intellectu eius. Unde impossibile est quod communicent in aliquo genere. Et hoc rationabiliter accidit. Nam corruptibilium et incorruptibilium non potest esse materia una. Genus autem, physice loquendo, a materia sumitur. Unde supra dictum est, quod ea quae non communicant in materia, sunt genere diversa. Logice autem loquendo, nihil prohibet quod conveniant in genere, inquantum conveniunt in una communi ratione, vel substantiae, vel qualitatis, vel alicuius huiusmodi.	2142. And from this it necessarily follows that the corruptible and the incorruptible differ generically; for it is evident that contraries which belong to one genus do not belong to the substance of that genus; for “rational” and “irrational” do not belong to the substance of animal. But animal is the one or the other potentially. And whatever genus may be taken, corruptible and incorruptible must pertain to its intelligible make-up. It is impossible, then, that they should have a common genus. And this is reasonable, for there cannot be a single matter for both corruptible and incorruptible things. Now speaking from the viewpoint of the philosophy of nature, genus is taken from the matter; and thus it was said above (890:C 2125) that things which do not have a common matter are other or different in genus. But speaking from the viewpoint of logic, nothing prevents them from having the same common genus inasmuch as they have one common definition, either that of substance or of quality or of quantity or something of this sort.
lib. 10 l. 12 n. 9 Deinde cum dicit palam igitur infert quoddam corollarium ex dictis; scilicet quod non possunt esse species separatae, sicut Platonici posuerunt. Ponunt enim duos homines, unum sensibilem qui est corruptibilis, et unum separatum qui est incorruptibilis, quem dicunt speciem vel ideam hominis. Species autem sive ideae dicuntur esse eadem specie, secundum Platonicos, cum singularibus. Et nomen speciei non aequivoce praedicatur de specie et de singulari, cum tamen incorruptibile et corruptibile etiam genere differant. Et ea quae sunt diversa genere plus distant, quam quae differunt specie.	2143. It is clearly impossible (898). Next he draws a corollary from his discussion, namely, that there cannot be separate Forms as the Platonists claimed; for they maintained that there are two men: a sensible man who is corruptible, and a separate man who is incorruptible, which they called the separate Form or Idea of man. But the separate Forms or Ideas are said to be specifically the same as individual things, according to the Platonists. And the name of the species is not predicated equivocally of the separate Form and of singular things, although the corruptible and the incorruptible differ even generically. And those things which differ generically are more widely separated than those which differ specifically.
lib. 10 l. 12 n. 10 Attendendum est autem, quod licet philosophus ostenderit, quod quaedam contraria non faciunt differre specie, et quaedam faciunt differre etiam genere; tamen omnia contraria aliquo modo faciunt differre specie, si fiat comparatio contrariorum ad aliquod determinatum genus. Nam album et nigrum, licet non faciant differre specie in genere animalis, faciunt tamen differre specie in genere coloris. Et masculinum et femininum faciunt differre specie in genere sexus. Et animatum et inanimatum, licet faciant differre genere quantum ad infimas species, tamen quantum ad genus quod per se dividitur in animatum et inanimatum, faciunt differre specie tantum. Nam omnes differentiae generis sunt constitutivae specierum quarumdam, licet illae species possint genere esse diversa.	2144. Now it must be observed that although the Philosopher has shown that some contraries do not cause things to differ specifically, and that some cause things to differ even generically, none the less all contraries cause things to differ specifically in some way if the comparison between contraries is made with reference to some definite genus. For even though white and black do not cause difference in species within the same genus of animal, they do cause difference in species in the genus of color. And male and female cause difference in species in the genus of sex. And while living and nonliving cause difference in genus in reference to the lowest species, still in reference to the genus which is divided essentially into living and non-living they merely cause difference in species. For all differences of a genus constitute certain species, although these species can differ generically.
lib. 10 l. 12 n. 11 Corruptibile autem et incorruptibile dividunt per se ens: quia corruptibile est quod potest non esse, incorruptibile autem quod non potest non esse. Unde, cum ens non sit genus, non mirum si corruptibile et incorruptibile non conveniant in aliquo uno genere. Et haec de decimo libro.	2145. But corruptible and incorruptible divide being essentially, because that is corruptible which is capable of not being, and that is incorruptible which is incapable of not being. Hence, since being is not a genus, it is not surprising if the corruptible and the incorruptible do not have a common genus. This brings our treatment of Book X to a close.