Authors/Thomas Aquinas/metaphysics/liber5/lect15

Lecture 15

Latin	English
lib. 5 l. 15 n. 1 Quoniam ens non solum dividitur in potentiam et actum, sed etiam in decem praedicamenta, postquam philosophus distinxit hoc nomen potentia, hic incipit distinguere nomina, quae significant praedicamenta. Et primo nomen quantitatis. Secundo nomen qualitatis, ibi, quale autem. Tertio distinguit modos ad aliquid, ibi, ad aliquid dicuntur. Alia vero praedicamenta praetermittit, quia sunt determinata ad aliquod genus rerum naturalium; ut patet praecipue de agere et pati, et de ubi et quando. Circa primum tria facit. Primo ponit rationem quantitatis; dicens, quod quantum dicitur quod est divisibile in ea quae insunt. Quod quidem dicitur ad differentiam divisionis mixtorum. Nam corpus mixtum resolvitur in elementa, quae non sunt actu in mixto, sed virtute tantum. Unde non est ibi tantum divisio quantitatis; sed oportet quod adsit aliqua alteratio, per quam mixtum resolvitur in elementa. Et iterum addit, quod utrumque aut singulum, est natum esse unum aliquid, hoc est aliquid demonstratum. Et hoc dicit ad removendum divisionem in partes essentiales, quae sunt materia et forma. Nam neutrum eorum aptum natum est esse unum aliquid per se.	977. Since being is divided not only into potency and actuality but also into the ten categories, having given the different senses of the term potency (954-60), the Philosopher begins here to give the different senses of the terms which designate the categories. First, he considers the term quantity; and second (987), the term quality (“Quality means”). Third (1001), he gives the different meanings of the term relative (“Some things”). He omits the other categories because they are limited to one class of natural beings, as is especially evident of action and passion, and of place and time. In regard to the first he does three things. First, he gives the meaning of quantity. He says that quantity means what is divisible into constituent parts. Now this is said to distinguish this kind of division from that of compounds. For a compound is dissolved into the elements, and these are not present in it actually but only virtually. Hence, in the latter case there is not just division of quantity, but there must also be some alteration by means of which a compound is dissolved into its elements. He adds that both or one of these constituents is by nature “a one,” that is, something which is pointed out. He says this in order to exclude the division of a thing into its essential parts, which are matter and form; for neither one of these is fitted by nature to be a particular thing of itself.
lib. 5 l. 15 n. 2 Secundo ibi, multitudo ergo ponit species quantitatis; inter quas primae sunt duae; scilicet multitudo sive pluralitas, et magnitudo sive mensura. Utrumque autem eorum habet rationem quanti, inquantum multitudo numerabilis est et magnitudo est mensurabilis. Mensuratio enim propria pertinet ad quantitatem. Definitur autem multitudo sic. Multitudo est, quod est divisibile secundum potentiam in partes non continuas. Magnitudo autem quod est divisibile in partes continuas. Quod quidem contingit tripliciter: et secundum hoc sunt tres species magnitudinis. Nam, si sit divisibile secundum unam tantum dimensionem in partes continuas, erit longitudo. Si autem in duas, latitudo. Si autem in tres, profunditas. Ulterius autem, quando pluralitas vel multitudo est finita, dicitur numerus. Longitudo autem finita, dicitur linea. Latitudo finita, corpus. Si enim esset multitudo infinita, non esset numerus; quia quod infinitum est, numerari non potest. Similiter, si esset longitudo infinita, non esset linea. Linea enim est longitudo mensurabilis. Et propter hoc in ratione lineae ponitur, quod eius extremitates sunt duo puncta. Simile est de superficie et corpore.	978. Therefore plurality (483). Second, he gives the kinds of quantity; and of these there are two primary kinds: plurality or multitude, and magnitude or measure. And each of these has the character of something quantitative inasmuch as plurality is numerable and magnitude is measurable. For mensuration pertains properly to quantity. However, plurality is defined as what is divisible potentially into parts which are not continuous; and magnitude as what is divisible into parts which are continuous. Now this occurs in three ways, and therefore there are three kinds of magnitude. For if inagnitude is divisible into continuous parts in one dimension only, it will be length; if into two, width; and if into three, depth. Again, when plurality or multitude is limited, it is called number. And a limited length is called a line; a limited width, surface; and a limited depth, body. For if multitude were unlimited, number would not exist, because what is unlimited cannot be numbered. Similarly, if length were unlimited, a line would not exist, because a line is a measurable length (and this is why it is stated in the definition of a line that its extremities are two points). The same things holds true of surface and of body.
lib. 5 l. 15 n. 3 Tertio ibi, amplius autem distinguit modos quantitatis; et circa hoc tria facit. Primo distinguit quantum in id quod est quantum per se, sicut linea, et in id quod est quantum per accidens, sicut musicum.	979. Again, some things (484). Third, he gives the different ways in which things are quantitative; and in regard to this he does three things. First, he draws a distinction between what is essentially quantitative, as a line, and what is accidentally quantitative, as the musical.
lib. 5 l. 15 n. 4 Secundo ibi, eorum vero distinguit quantum per se; quod quidem duplex est. Quaedam enim significantur per modum substantiae et subiecti, sicut linea, vel superficies, vel numerus. Quodlibet enim istorum substantialiter est quantum, quia in definitione cuiuslibet ponitur quantitas. Nam linea est quantitas continua secundum longitudinem divisibilis, finita: et similiter est de aliis.	980. And of those (485). Second, he gives the different senses in which things are essentially quantitative, and there are two of these. For some things are said to be such after the manner of a substance or subject, as line, surface or number; for each of these is essentially quantitative because quantity is given in the definition of each. For a line is a limited quantity divisible in length. The same is true of the other dimensions.
lib. 5 l. 15 n. 5 Quaedam vero per se pertinent ad genus quantitatis, et significantur per modum habitus vel passionis talis substantiae, scilicet lineae, quae est substantialiter quantitas, vel aliarum similium quantitatum: sicut multum et paucum significantur ut passiones numeri: et productum et breve, ut passiones lineae: et latum et strictum, ut passiones superficiei: et profundum et humile sive altum, ut passiones corporis: et similiter grave et leve, secundum opinionem illorum, qui dicebant multitudinem superficierum vel atomorum esse causam gravitatis in corporibus, paucitatem vero eorumdem, causam levitatis. Sed secundum veritatem grave et leve non pertinent ad quantitatem, sed ad qualitatem, ut infra ponet. Et similiter est de aliis talibus.	981. And other things belong essentially to the genus of quantity and are signified after the manner of a state or property of such substance, i.e., of a line, which is essentially quantitative, or of other similar kinds of quantity. For example, much and little are signified as properties of number; long and short, as properties of a line; broad and narrow, as properties of surface; and high and low or deep, as properties of body. And the same is true of heavy and light according to the opinion of those who said that having many surfaces, or atoms, causes bodies to be heavy, and having few causes them to be light. But the truth of the matter is that heavy and light do not pertain to quantity but to quality, as he states below (993). The same thing is true of other such attributes as these.
lib. 5 l. 15 n. 6 Quaedam etiam sunt, quae communiter cuiuslibet quantitatis continuae passiones sunt, sicut magnum et parvum, maius et minus; sive haec dicantur secundum se, idest absolute, sive dicantur ad invicem, sicut aliquid dicitur magnum et parvum respective, sicut in praedicamentis habetur. Ista autem nomina, quae significant passiones quantitatis per se, transferuntur etiam ad alia quam ad quantitates. Dicitur enim albedo magna et parva, et alia huiusmodi.	982. There are also certain attributes which are common properties of any continuous quantity, as large and small, and larger and smaller, whether these are taken “essentially,” i.e., absolutely, or “in relation to each other,” its something is said to be large and small relatively, as is stated in the Categories. But these terms which signify the properties of quantity pure and simple are also transferred to other things besides quantities. For whiteness is said to be large and small, and so also are other accidents of this kind.
lib. 5 l. 15 n. 7 Sciendum autem est, quod quantitas inter alia accidentia propinquior est substantiae. Unde quidam quantitates esse substantias putant, scilicet lineam et numerum et superficiem et corpus. Nam sola quantitas habet divisionem in partes proprias post substantiam. Albedo enim non potest dividi, et per consequens nec intelligitur individuare nisi per subiectum. Et inde est, quod in solo quantitatis genere aliqua significantur ut subiecta, alia ut passiones.	983. But it must be borne in mind that of all the accidents quantity is closest to substance. Hence some men think that quantities, such as line, number, surface and body are substances. For next to substance only quantity can be divided into distinctive parts. For whiteness cannot be divided, and therefore it cannot be understood to be individuated except by its subject. And it is for this reason that only in the genus of quantity are some things designated as subjects and others as properties.
lib. 5 l. 15 n. 8 Tertio ibi, secundum accidens distinguit modos quantitatis per accidens: et ponit duos modos quantitatis per accidens: quorum unus est secundum quod aliqua dicuntur quanta per accidens ex hoc solo, quod sunt accidentia alicuius quanti, sicut album et musicum per hoc quod sunt accidentia alicuius subiecti, quod est quantum.	984. But of things (486). Then he gives the different senses in which things are said to be accidentally quantitative. These senses are two. (1) In one sense, things are said to be accidentally quantitative only because they are accidents of some quantity; for example, white and musical are said to be quantitative because they are accidents of a subject which is quantitative.
lib. 5 l. 15 n. 9 Alio modo dicuntur aliqua quanta per accidens non ratione subiecti, in quo sunt, sed eo quod dividuntur secundum quantitatem ad divisionem alicuius quantitatis; sicut motus et tempus, quae dicuntur quaedam quanta et continua, propterea quod ea, quorum sunt, sunt divisibilia, et ipsa dividuntur ad divisionem eorum. Tempus enim est divisibile et continuum propter motum; motus autem propter magnitudinem; non quidem propter magnitudinem eius quod movetur, sed propter magnitudinem eius in quo aliquid movetur. Ex eo enim quod illa magnitudo est quanta, et motus est quantus. Et propter hoc quod motus est quantus, sequitur tempus esse quantum. Unde haec non solum per accidens quantitates dici possunt, sed magis per posterius, inquantum quantitatis divisionem ab aliquo priori sortiuntur.	985. (2) In another sense, some things are said to be accidentally quantitative, not because of the subject in which they exist, but because they are divided quantitatively as a result of the division of some quantity; for example, motion and time (which are said to be quantitative and continuous because of the subjects to which they belong) are divisible and are themselves divided as a result of the division of the subjects to which they belong. For time is divisible and continuous because of motion, and motion is divisible because of magnitude—not because of the magnitude of the thing which is moved, but because of the magnitude of the space through which it is moved. For since that magnitude is quantitative, motion is also quantitative; and since motion is quantitative, it follows that time is quantitative. Hence these can be said to be quantitative not merely accidentally but rather subsequently, inasmuch as they receive quantitative division from something prior.
lib. 5 l. 15 n. 10 Sciendum est autem, quod philosophus in praedicamentis posuit tempus quantitatem per se, cum hic ponat ipsum quantitatem per accidens; quia ibi distinxit species quantitatis secundum diversas rationes mensurae. Aliam enim rationem mensurae habet tempus, quod est mensura extrinseca, et magnitudo, quae est mensura intrinseca. Et ideo ponitur ibi ut alia species quantitatis. Hic autem considerat species quantitatis quantum ad ipsum esse quantitatis. Et ideo illa, quae non habent esse quantitatis nisi ex alio, non ponit hic species quantitatis, sed quantitates per accidens, ut motum et tempus. Motus autem non habet aliam rationem mensurae quam tempus et magnitudo. Et ideo nec hic nec ibi ponitur quantitatis species. Locus autem ponitur ibi species quantitatis, non hic, quia habet aliam rationem mensurae, sed non aliud esse quantitatis.	986. However, it must be noted that in the Categories the Philosopher held that time is essentially quantitative, while here he holds that it is accidentally quantitative. There he distinguished between the species of quantity from the viewpoint of the different kinds of measure. For time, which is an external measure, has the character of one kind of measure, and continuous quantity, which is an internal measure, has a different one. Hence in the Categories time is given as another species of quantity, whereas here he considers the species of quantity from the viewpoint of the being of quantity. Therefore those things which only receive their quantitative being from something else he does not give here as species of quantity, but as things which are accidentally quantitative, as motion and time. But motion has no other manner of measure than time and magnitude. Hence neither in this work nor in the Categories does he give it as a species of quantity. Place, however, is given there as a species of quantity. But it is not given as such here because it has a different manner of measure, although not a different quantitative being. LESSON 16 The Senses of Quality ARISTOTLE'S TEXT Chapter 14: 1020a 33-1020b 25