Authors/Thomas Aquinas/metaphysics/liber5/lect4

Lecture 4

Latin	English
lib. 5 l. 4 n. 1 Hic distinguit hoc nomen elementum. Circa quod duo facit. Primo assignat diversos modos elementi. Secundo ostendit quid in omnibus sit commune, ibi, omnium autem commune. Circa primum duo facit. Primo ostendit quomodo elementum proprie dicatur. Secundo quomodo dicatur transumptive, ibi, et transferentes elementum et cetera. Ponit ergo primo, quamdam elementi descriptionem; ex qua colligi potest, quod quatuor sunt de ratione elementi. Quorum primum est, ut sit causa sicut ex quo: per quod patet, quod elementum ponitur in genere causae materialis.	795. Here he distinguishes the different senses of the term element, and in regard to this lie does two things. First, he gives the different senses in which the term element is used. Second (807), he indicates what all of them have in common (“And in all these”). In regard to the first he does two things. First, he explains how the term element is used in its proper sense; and second (802), how it is used in transferred senses (“People also use”). First, he gives a sort of description of an element, and from this one can gather the four notes contained in its definition. The first is that an element is a cause in the sense of that from which a thing comes to be; and from this it is clear that an element is placed in the class of material cause.
lib. 5 l. 4 n. 2 Secundum est, quod sit principium ex quo aliquid fiat primo. Cuprum enim est ex quo fit statua; non tamen est elementum, quia habet aliquam aliam materiam ex qua fit.	796. The second is that an element is the principle from which something first comes to be. For copper is that from which a statue comes to be, but it is still not an element because it has some matter from which it comes to be.
lib. 5 l. 4 n. 3 Tertium est, quod sit inexistens sive intrinsecum: per quod differt elementum ab omni eo ex quo fit aliquid sicut ex transeunte, sive sit privatio, aut contrarium, sive materia contrarietati et privationi subiecta, quae est materia transiens. Ut cum dicimus, quod homo musicus fit ex homine non musico, vel musicum ex non musico. Elementa enim oportet manere in his quorum sunt elementa.	797. The third is that an element is inherent or intrinsic; and for this reason. it differs from everything of a transitory nature from which a thing comes to be, whether it be a privation or a contrary or the matter subject to contrariety and privation, which is transitory; for example, when we say that a musical man comes from a nonmusical man, or that the musical comes from the non-musical. For elements must remain in the things of which they are the elements.
lib. 5 l. 4 n. 4 Quartum est, quod habeat aliquam speciem, quae non dividatur in diversas species: per quod differt elementum a materia prima, qua nullam speciem habet, et etiam ab omnibus materiis, quae in diversas species resolvi possunt, sicut sanguis et huiusmodi. Propter hoc dicit, quod elementum est ex quo aliquid componitur, quantum ad primum. Primo, quantum ad secundum. Inexistente, quantum ad tertium. Indivisibili specie in aliam speciem, quantum ad quartum.	798. The fourth is that an element has a species which is not divisible into different species; and thus an element differs from first matter, which has no species, and also from every sort of matter which is capable of being divided into different species, as blood and things of this kind. Hence he says, as the first note, that an element is that of which a thing is composed; as the second, that it is that of which a thing is “first” composed; as the third, that it is “an inherent principle”; and as the fourth, that it is “not divisible into another species.”
lib. 5 l. 4 n. 5 Hanc autem definitionem manifestat in quatuor, in quibus utimur nomine elementi. Dicimus enim ipsas literas esse elementa vocis, quia ex eis omnis vox componitur, et primo. Quod ex hoc patet, quia omnes voces in literas resolvuntur, sicut in ultima. Quod est enim ultimum in resolutione, oportet esse primum in compositione. Literae autem non resolvuntur ulterius in alias voces specie diversas. Sed, si aliquo modo dividantur, particulae in quas fit divisio, erunt conformes, idest unius speciei, sicut omnes particulae aquae sunt aqua. Dividitur autem litera secundum tempora prolationis, prout litera longa dicitur habere duo tempora, brevis vero unum. Nec tamen partes, in quas sic dividuntur literae, sunt diversae secundum speciem vocis. Non est autem ita de syllaba: nam eius partes sunt diversae secundum speciem: alius enim sonus est secundum speciem, quem facit vocalis et consonans, ex quibus syllaba componitur.	799. He illustrates this definition of element in four cases in which we use the term element. For we say that letters are the elements of a word because every word is composed of them, and of them primarily. This is evident from the fact that all words are divided into letters as ultimate things; for what is last in the process of dissolution must be first in the process of composition. But letters are not further divided into other words which are specifically different. Yet if they should be divided in any way, the parts in which the division results would be “alike,” i.e., specifically the same, just as all parts of water are water. Now letters are divided according to the amount of time required to pronounce them, inasmuch as a long letter is said to require two periods of time, and a short letter one. But while the parts into which letters are so divided do not differ as the species of words do, this is not the case with a syllable; for its parts are specifically different, since the sounds which a vowel and a consonant make, of which a syllable is composed, are specifically different.
lib. 5 l. 4 n. 6 Secundum exemplum ponit in corporibus naturalibus, in quibus etiam quaedam dicimus elementa quorumdam. Illa enim dicuntur corporum esse elementa, in quae ultimo resolvuntur omnia corpora mixta: et per consequens ea sunt, ex quibus primo componuntur huiusmodi corpora. Ipsa autem corpora, quae elementa dicuntur, non dividuntur in alia corpora specie differentia, sed in partes consimiles, sicut quaelibet pars aquae est aqua. Et quicumque posuerunt tale corpus esse unum, scilicet in quod omnia resolvuntur, et ipsum non resolvitur in alia, dixerunt unum esse elementum. Quidam vero aquam, quidam autem aerem, quidam autem ignem. Qui vero posuerunt plura talia corpora, dixerunt etiam esse elementa plura. Sciendum est, quod cum in definitione elementi ponatur, quod non dividitur in diversa secundum speciem, non est intelligendum de partibus in quas aliquid dividitur divisione quantitatis: sic enim lignum esset elementum, quia quaelibet pars ligni est lignum: sed de divisione, quae fit secundum alterationem, sicut corpora mixta resolvuntur in simplicia.	800. He gives as a second example natural bodies, certain of which we also call the elements of certain others. For those things into which all compounds are ultimately dissolved are called their elements; and therefore they are the things of which bodies of this kind are composed. But those bodies which are called elements are not divisible into other bodies which are specifically different, but into like parts, as any part of water is water. And all those who held for one such body into which every body is dissolved and which is itself incapable of being further divided , said that there is one element. Some said that it is water, some air, and some fire. But those who posited many such bodies also said there are many elements. Now it should be borne in mind that when it is set down in the definition of an element that an element is not divisible into different species, this should not be understood of the parts into which a thing is divided in a quantitative division (for wood would then be an element, since any part of wood is wood), but in a division made by alteration, as compounds are dissolved into simple bodies.
lib. 5 l. 4 n. 7 Tertium exemplum ponit in demonstrationibus; in quibus etiam utimur nomine elementi, sicut dicitur liber elementorum Euclidis. Et dicit, quod modo simili et propinquo dictis dicuntur elementa, quae sunt diagrammatum, idest descriptionum geometralium elementa. Et non solum hoc potest dici in geometria, sed universaliter in omnibus demonstrationibus. Illae enim demonstrationes, quae existunt in tribus terminis tantum, dicuntur esse aliorum elementa. Nam ex his componuntur aliae demonstrationes, et in ea resolvuntur. Quod sic patet. Secunda enim demonstratio accipit pro principio conclusionem primae demonstrationis, inter cuius terminos intelligitur medium, quod fuit primae demonstrationis principium. Et sic secunda demonstratio erit ex quatuor terminis; prima ex tribus tantum, tertia vero ex quinque, quarta ex sex, et sic quaelibet demonstratio unum terminum addit. In quo manifestum est demonstrationes primas in postremis includi: ut si sit haec demonstratio prima: omne b est a: omne c est b: ergo omne c est a: hoc includetur in hac, omne c est a: omne d est c: ergo omne d est a. Et ulterius ista in alia, quae concludit, omne e est a: ut quasi videatur esse ad hanc ultimam conclusionem unus syllogismus ex pluribus syllogismis compositus plura media habens, ut dicatur sic, omne b est a: et omne c est b: et omne d est c: et omne e est d: ergo omne e est a. Prima igitur demonstratio, quae habebat unum medium et solum tres terminos, est simplex et non resolvitur in aliam demonstrationem, sed omnes aliae resolvuntur in ipsam. Et ideo syllogismi primi, qui fiunt ex terminis tribus per unum medium, elementa dicuntur.	801. As a third example he gives the order of demonstrations, in which we also employ the word element; for example, we speak of Euclid’s Book of Elements. And he says that, in a way similar and close to those mentioned, those things which “are parts of diagrams,” i.e., the constituents of geometrical figures, are called elements. This can be said not only of the demonstrations in geometry but universally of all demonstrations. For those demonstrations which have only three terms are called the elements of other demonstrations, because the others are composed of them and resolved into them. This is shown as follows: a second demonstration takes as its starting point the conclusion of a first demonstration, whose terms are understood to contain the middle term which was the starting point of the first demonstration. Thus the second demonstration will proceed from four terms the first from three only, the third from five, and the fourth from six; so that each demonstration adds one term. Thus it is clear that first demonstrations are included in subsequent ones, as when this first demonstration—every B is A, every C is B, therefore every C is A—is included in this demonstration—every C is A, every D is C, therefore every D is A; and this again is included in the demonstration whose conclusion is that every E is A, so that for this final conclusion there seems to be one syllogism composed of several syllogisms having several middle terms. This may be expressed thus: every B is A, every C is B, every D is C, every E is D, therefore every E is A. Hence a first demonstration, which has one middle term and only three terms, is simple and not reducible to another demonstration, whereas all other demonstrations are reducible to it. Hence first syllogisms, which come from three terms by way of one middle term, are called elements.
lib. 5 l. 4 n. 8 Deinde cum dicit et transferentes ostendit quomodo elementum dicatur transumptive; dicens, quod ex hac praemissa ratione et significatione elementi transtulerunt quidam hoc nomen elementum ad significandum aliquid, quod est unum, et parvum, et ad multa utile. Ex hoc enim quod elementum est indivisibile in diversas species, acceperunt quod sit unum. Ex eo vero quod est primum, quod sit simplex. Ex eo vero, quod ex elementis alia componuntur, acceperunt quod sit utile ad multa. Unde hanc rationem elementi constituerunt, ut elementum dicerent omne illud, quod est parvum in quantitate, et simplex, quasi ex aliis non compositum, et indivisibile in diversa.	802. People also use (412). Here he shows how the term element is used in a transferred sense. He says that some men, on the basis of the foregoing notion or meaning of element, have used the term in a transferred sense to signify anything that is one and small and useful for many purposes. For from the fact that an element is indivisible they understood that it is one; and from the fact that it is first they understood that it is simple; and from the fact that other things are composed of elements they understood that an element is useful for many purposes. Hence they set up this definition of an element in order that they might say that everything which is smallest in quantity and simple (inasmuch as it is not composed of other things) and incapable of division into different species, is an element.
lib. 5 l. 4 n. 9 Hac autem ratione elementi constituta, per transumptionem contingebat eis ut duos modos elementorum adinvenirent; quorum primus est, ut ea quae sunt maxime universalia, dicerent elementa. Universale enim est unum secundum rationem, et est simplex, quia eius definitio non componitur ex diversis, et est in multis, et sic est ad multa utile, sive sit in omnibus, sicut unum et ens; sive in pluribus, sicut alia genera. Per eamdem vero rationem contingebat eis secundo, quod punctum et unitatem dicerent esse principia vel elementa, quia utrumque eorum est unum simplex et ad multa utile.	803. But when they had set up this definition of element, it turned out that by using it in a transferred sense they had invented two senses of element. First, they called the most universal things elements; for a universal is one in definition and is simple (because its definition is not composed of different parts) and is found in many things, and thus is useful for many purposes, whether it be found in all things, as unity and being are, or in most things, as the other genera. And by the same reasoning it came about, second, that they called points and units principles or elements because each of them is one simple thing and useful for many purposes.
lib. 5 l. 4 n. 10 Sed in hoc a vera ratione elementi defecerunt, quia universalia non sunt materia, ex quibus componuntur particularia, sed praedicant eorum substantiam. Similiter et punctus non est materia linearum; non enim linea ex punctis componitur.	804. But in this respect they fell short of the true notion of a principle, because universals are not the matter of which particular things are composed but predicate their very substance. And similarly points are not the matter of a line, for a line is not composed of points.
lib. 5 l. 4 n. 11 Hac autem transumptiva elementi ratione constituta, patet solutio cuiusdam quaestionis in tertio libro disputatae; scilicet quid sit magis elementum, utrum genus vel species, et utrum genus magis quam differentia. Patet enim consequi quod genera magis sunt elementa, quia genera magis sunt universalia et indivisibilia. Non enim est ratio eorum et definitio, quam oporteat componi ex genere et differentia; sed definitiones proprie dantur de speciebus. Et si aliquod genus definitur, non definitur inquantum est genus, sed inquantum est species; et ideo species dividitur in diversa, et propter hoc non habent rationem elementi. Genus autem non dividitur in diversa: et ideo dixerunt genera esse elementa magis quam species. Alia translatio habet una enim est eorum ratio idest indivisibilis, quia genera, etsi non habeant definitionem, tamen id quod significatur per nomen generis, est quaedam conceptio intellectus simplex, quae ratio dici potest.	805. Now with this transferred notion of element established, the solution to a question disputed in Book III (431-36) becomes clear, i.e., whether a genus or a species is more an element, and whether a genus or a difference is more an element; for it clearly follows that genera are elements to a greater degree because genera are more universal and indivisible. For there is no concept or definition of them which must be composed of genera and differences, but it is species which are properly defined. And if a genus is defined, it is not defined insofar as it is a genus but insofar as it is a species. Hence a species is divided into different parts and thus does not have the character of an element. But a genus is not divisible into different parts, and therefore they said that genera are elements more than species. Another translation reads, “For their formal character is one,” that is, indivisible, because even though genera do not have a definition, still what is signified by the term genus is a simple conception of the intellect which can be called a definition.
lib. 5 l. 4 n. 12 Et sicut genus est magis elementum quam species, quia est simplicius; ita etiam magis quam differentia, licet ipsa simplex sit, quia genus est universalius. Quod ex hoc patet: quia cuicumque inest differentia, inest genus, cum per se differentiae non transcendant genus: non tamen oportet quod ad omne id sequatur differentia cui convenit genus.	806. And just as a genus is more an element than a species is because it is simpler, in a similar way it is more an element than a difference is, even though a difference is simple, because a genus is more universal. This is clear from the fact that anything which has a difference has a genus, since essential differences do not transcend a genus; but not everything which has a genus necessarily has a difference.
lib. 5 l. 4 n. 13 Ultimo autem dicit, quod omnibus praedictis modis elementi hoc est commune, esse primum in unoquoque, sicut dictum est.	807. Last of all he says that all of the foregoing senses of element have this note in common, that an element is the primary component of each being, as has been stated.