Authors/Thomas Aquinas/metaphysics/liber10/lect4

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).