Authors/Thomas Aquinas/metaphysics/liber8/lect3

Lecture 3

Latin	English
lib. 8 l. 3 n. 1 Postquam inquisivit philosophus principia substantiae sensibilis, ostendens quod substantia sensibilis componitur ex materia et forma; nunc de principio materiali et formali determinare intendit, inquirendo ea quae sunt consideranda circa utrumque. Et dividitur in duas partes. In prima inquirit ea quae sunt consideranda circa principium formale. In secunda, ea quae sunt consideranda circa principium materiale, ibi, de materiali autem substantia.	1703. Having investigated the principles of sensible substances~ and having shown that sensible substances are composed of matter and form, the Philosopher’s aim here is to establish the truth about the formal and material principles of things by investigating the points which must be considered about each. This is divided into two parts. In the first (708)C 1705), he investigates the things which must be considered about the formal principle. In the second (722:C 1729), he investigates the things which must be considered about the material principle (“Concerning material substances”).
lib. 8 l. 3 n. 2 Et, quia Plato praecipue principium formale tetigit, ideo determinat de principio formali secundum ea quae Plato posuit. Ponit autem Plato, formas rerum esse species et numeros. Unde prima pars dividitur in duas partes. In prima determinat de principio formali per comparationem ad species. In secunda per comparationem ad numeros, ibi, palam autem. Ponebat autem Plato quatuor de formis per comparationem ad species. Quorum primum est, quod nomina specierum significent tantum formam, non autem formam cum materia. Secundum, quod forma est aliquid praeter partes materiae. Tertium est, quod est ingenerabilis et incorruptibilis. Quartum est, quod formae sunt separatae a sensibilibus. Unde prima pars dividitur in quatuor, secundum quod Aristoteles de quatuor praedictis inquirit. Secunda pars incipit, ibi, non videtur. Tertia, ibi, necessarium itaque et cetera. Quarta, ibi, si autem sunt corruptibilium.	1704. And since Plato was the one who devoted special treatment to the formal principle, therefore Aristotle deals with the formal principle in reference to those things which Plato posited. Now Plato claimed that species [i.e., separate Forms or Ideas] and numbers are the forms of things. Hence the first part is divided into two sections. In the first (708:C 1705), he deals with the formal principle in relation to the species [or Ideas]; and in the second (717:C 1722), in relation to numbers (“Further, it is also clear”). Now Plato held four things about forms in relation to the species [or Ideas]. The first of these is that specific names signify form alone and not form with matter. The second is that form is something besides the material parts. The third is that form can neither be generated nor corrupted. The fourth is that forms are separate from sensible things. The first part is divided into four sections inasmuch as Aristotle investigates the four points just mentioned. The second (711:C 1712) begins where he says “Accordingly, to those.” The third (712:C 1715) begins where he says “Now this must.” The fourth (713:C 1717) begins where he says “But whether.”
lib. 8 l. 3 n. 3 Circa primum tria facit. Primo movet quaestionem; dicens quod necessarium est scire quod apud aliquos dubium est: utrum nomen speciei significet substantiam compositam, aut formam tantum, sive aliquid, quod est loco actus. Ut hoc nomen domus, utrum significet communiter materiam et formam, puta quod domus significet tegumentum constitutum ex caemento et lapidibus ordinatum ut decet (nam tegumentum est sicut forma, caementum et lapides ut materia); aut praedictum nomen significet tantum actum et speciem, scilicet tegumentum.	1705. In regard to the first he does three things. First (708) he raises a question. We must understand, he says, that for some men there is the problem whether a specific name signifies the composite substance or only the form or something having the status of actuality; for example, whether the word house signifies both matter and form together so that a house means a shelter made of bricks and stones properly arranged (for shelter is as form, and bricks and stones as matter), or whether this word signifies only the actuality or form, a shelter.
lib. 8 l. 3 n. 4 Similiter, utrum hoc nomen linea significet dualitatem et longitudinem, aut dualitatem tantum. Hoc autem ideo dicit, quia Platonici posuerunt numeros esse formas magnitudinum. Dicebant enim quod punctus nihil aliud est quam unitas positionem habens; ita quod positio sit quasi materiale unitas ut formale. Et similiter ponebant, quod dualitas erat forma lineae, ita quod linea nihil aliud est quam dualitas in longitudine. Quaerit ergo philosophus, utrum hoc nomen linea significet dualitatem tantum, quasi formam; aut dualitatem in longitudine, sicut formam in materia. Et similiter, utrum hoc nomen animal significet animam in corpore, quasi formam in materia; aut animam tantum, quae est forma corporis organici.	1706. Similarly, there is the problem whether the word line signifies twoness and length or twoness alone. He mentions this because the Platonists claimed that numbers are the forms of continuous quantities; for they said that a point is merely the number one having position, so that position is a sort of material principle, and the number one a formal principle. They likewise claimed that the number two is the form of a line, so that a line is merely twoness in length. Therefore the Philosopher asks whether the word line signifies twoness alone as form, or twoness grounded in length as form in matter. And again, there is the problem whether the word animal signifies a soul in a body as a form in matter, or only a soul, which is the form of an organic body.
lib. 8 l. 3 n. 5 Deinde cum dicit erit autem ostendit quid sequatur, si quis dicit, quod nomina specierum utroque modo se habent in significando: ut scilicet quandoque significent formam tantum, quandoque autem formam in materia: et est quod de utroque in utraque significatione animal accipietur non univoce, quasi una ratione dictum; sed analogice, sicut est in illis, quae habent nomen unum, propter hoc quod referuntur ad unum. Nomen enim speciei non dicetur de composito, nisi secundum ordinem ad hoc, quod dicitur secundum formam tantum, sicut Platonici posuerunt. Ponebant enim quod homo, qui est compositus ex materia et forma, dicitur per participationem hominis idealis, qui est forma tantum.	1707. Now animal will also apply (709). He shows what follows if one says that specific names are used in both senses, so that they sometimes signify form alone and sometimes form in matter. And the result is that animal will be taken of either in either meaning, not univocally, as though it were predicated with one meaning, but analogically, as happens in the case of those things which have one name because they are related to one thing. For the specific name will be predicated of the composite only by reason of relationship to that which is predicated according to form alone, as the Platonists held. For they maintained that man, who is a composite of matter and form, is so named because he participates in the Idea man, which is only a form.
lib. 8 l. 3 n. 6 Deinde cum dicit verum et haec ostendit philosophus ad quid tendit praedicta quaestio; dicens quod si nomen speciei significet substantiam compositam, aut significet formam tantum, hoc facit differentiam quantum ad aliquid; sed ad quaestionem substantiae sensibilis nullam differentiam facit. Manifestum enim est quod substantia sensibilis composita est ex materia et forma.	1708. These distinctions (710). Then the Philosopher shows the result to which the aforesaid search leads. He says that, while the question whether a specific name signifies the composite substance or only the form, (+) makes a difference in regard to something else, (~) it makes no difference to the investigation of sensible substance. For it is evident that a sensible substance is composed of matter and form.
lib. 8 l. 3 n. 7 Ad quid autem differat, utrum sic vel sic se habent, consequenter manifestat. Manifestum est enim quod si aliqua res est, quae sit forma tantum et actus, quod quid erat esse existit ei, idest quod quid erat esse eius, idem erit cum ea: sicut idem est anima et animae esse, idest anima est quidditas animae. Si vero aliquid est compositum ex materia et forma, non erit idem in ipso quod quid erat esse et res ipsa; sicut non idem est homini esse, et homo. Nisi forte dicatur anima tantum, secundum illos, qui dicunt, quod nomina specierum significant formam tantum. Et sic patet, quod aliqua res est, cui idem est quod quid erat esse suum; scilicet quae non est composita ex materia et forma, sed forma tantum.	1709. (+) Now to what kind of thing it makes a difference, whether to those in this state or in another, he makes clear next. For it is obvious that if there is something which is only form or actuality, its essence “consists of this,” i.e., the thing and its essence will be identical, as a soul is identical with its essence, or is its own quiddity. But if a thing is composed of matter and form, then in this case the thing itself and its essence will not be the same; for example, a man and the essence of a man are not the same, unless perhaps a man is said to be only a soul, as was held by those who say that specific names signify only the form. Thus it is evident that something does exist whose essence is the same as itself, namely, whatever is not composed of matter and form but is only a form.
lib. 8 l. 3 n. 8 Et huius ratio est, quia quod quid erat esse est id quod significat definitio. Definitio autem significat naturam speciei. Si autem aliqua res est, quae sit composita ex materia et forma, oportet quod in illa re sit aliquid praeter naturam speciei. Cum enim materia sit individuationis principium, oportet quod in quolibet composito ex materia et forma sint principia individuantia, quae sunt praeter naturam speciei. Unde huiusmodi res non tantum est quidditas sua, sed aliquid praeter hoc. Si qua vero res est, quae sit forma tantum, non habet aliqua principia individuantia praeter naturam speciei, cum ipsa forma per se existens per seipsam individuetur. Et ideo ipsa res nihil aliud est quam quod quid est esse suum.	1710. The reason for this position is that essence is what the definition signifies, and the definition signifies the nature of the species. But if there is something which is composed of matter and form, then in that thing there must be some other principle besides the nature of the species. For since matter is the principle of individuation, then in anything composed of matter and form there must be certain individuating principles distinct from the nature of the species. Hence such a thing is not just its own essence but is something in addition to this. But if such a thing exists which is only a form, it will have no individuating principles in addition to the nature of its species. For a form that exists of itself is individuated of itself. Therefore this thing is nothing else than its own essence.
lib. 8 l. 3 n. 9 Sic igitur patet, quod si nomen speciei significet formam tantum, cuiuslibet rei idem est quod quid erat esse et esse suum; sicut homo erit quod quid est esse suum, et equus, et omnia huiusmodi. Si autem nomina speciei significant compositum ex materia et forma, tunc non idem erit rebus quod quid erat esse earum.	1711. It is clear, then, that if the specific name signifies only the form, the essence of anything will be (+) the same as its being, as a man will be his essence, and a horse its essence, and so also will all other things of this kind. But if specific names signify things composed of matter and form, then such things will (~) not be the same as their essence.
lib. 8 l. 3 n. 10 Deinde cum dicit non videtur prosequitur secundum praedictorum, scilicet quod forma sit aliquid praeter partes materiae; dicens, quod Platonicis moventibus istam quaestionem, non videtur, quod syllaba sit ex elementis et ex compositione; quasi compositio, quae est forma syllabae, sit pars materialis syllabae, sicut elementa vel literae. Neque videtur eis quod domus sit caementum et compositio, quasi domus constituatur ex his quasi ex partibus materiae.	1712. Accordingly, to those who (711). Here he deals with the second point mentioned above, namely, that the form is something in addition to the material parts. He says that for the Platonists, in raising this question, it does not seem that a syllable consists of its elements and their combination, as if combination, which is the form of a syllable, were a material part of a syllable like its elements or letters. Nor does it seem to them that a house consists of stones and their combination, as if a house were constituted of these as material parts.
lib. 8 l. 3 n. 11 Et in hoc recte dicunt; quia si forma esset una de partibus materiae, dependeret ex materia. Et hoc videmus esse falsum; quia compositio et mixtio, quae sunt formalia principia, non constituuntur ex his quae componuntur aut miscentur, sicut nec aliquod aliud formale constituitur ex sua materia, sed e converso. Subliminare enim constituitur ex compositione, quae est forma eius, et non e converso.	1713. And on this point their remarks are true, because, if the form were one of the material parts, it would depend on matter. But we see that this is false; for combination or mixture, which are formal principles, are not constituted of those things which are combined or mixed; nor is any other formal principle constituted of its matter, but the reverse. For a threshold is constituted by position, which is its form, and not the reverse.
lib. 8 l. 3 n. 12 Ergo, si ponatur quod animal et bipes sint materia hominis, homo non erit animal et bipes, sed erit aliquid aliud praeter hoc. Nec erit elementum neque ex elementis, sed erit tantum forma, ut dicunt Platonici, qui auferunt materiam a definitionibus. Sed contra hanc positionem videtur esse dicendum, quod si id quod est forma tantum praeter materiam est substantia et principium essendi, non poterunt dicere quod hoc particulare sit illa substantia separata, scilicet quod homo sensibilis sit compositus ex materia et forma, homo autem sit forma tantum.	1714. Therefore, if one holds that animal and two-footed are the matter of man, man will not be animal and two-footed but will be something else in addition to these. And this will not be an element or anything composed of the elements but will be only a form as the Platonists claim, who omit matter from definitions. But it seems that we must hold, in opposition to this position, that, if form alone apart from matter is the substance or principle of being of a thing, they will not be able to say that this particular thing is that separate substance; i.e., they will not be able to say that this man as a sensible entity is composed of matter and form, but that man is only a form
lib. 8 l. 3 n. 13 Deinde cum dicit necessarium itaque prosequitur tertium praedictorum; scilicet quod formae secundum Platonicos sunt sempiternae et incorruptibiles. Unde concludit ex dictis quod necessarium est formam aut esse sempiternam, ut Platonici posuerunt ponentes ideas, quas dicebant formas rerum esse sempiternas: aut necesse est formam esse corruptibilem per accidens, sine hoc quod corrumpatur per se. Et similiter, facta per accidens, sine hoc quod fiat per se. Quod conceditur secundum sententiam Aristotelis, qui non posuit formas separatas, sed in materia existentes.	1715. Now this must (712). He considers the third point mentioned above, namely, the Platonists’ position that forms are eternal and Incorruptible. Hence he concludes, from what has been said, that either a form must be eternal, as the Platonists held when they claimed that the Ideas, which they called the forms of things, are eternal; or a form must be corruptible by reason of something else without being corrupted in itself, and similarly it must come to be by reason of something else without coming to be in itself. This is in agreement with the position of Aristotle, who does not hold that forms are separate but that they exist in matter.
lib. 8 l. 3 n. 14 Quod autem formae non possint corrumpi per se, nec generari, ex quo utrumque praedictorum dependet, monstrat consequenter per hoc quod superius probatum est, quod nullus facit formam, neque forma generatur, neque efficitur per se; sed per se efficitur et generatur hoc particulare. Et ratio est, quia omne quod fit, fit ex materia. Unde hoc particulare, cum sit compositum ex materia et forma, fit et generatur ex his, scilicet principiis materialibus et individuantibus. Supra autem dictum est quod forma non est elementum, neque ex elementis. Unde sequitur quod forma nec fit nec generatur per se.	1716. Further, the statement that forms can neither be corrupted nor generated in themselves (710)12:C 1708-15), on which each of the aforesaid points depends, Aristotle proceeds to demonstrate by reason of what was shown above, namely, that no one makes or produces a form, nor is a form generated or produced in itself; but it is this particular thing which comes to be or is generated in itself. And the reason is that everything which comes to be comes to be from matter. Hence, since this particular thing is composed of matter and form, it comes to be or is generated “from these principles,” i.e., from its material and individuating principles. But it was stated above (711:C 1714) that a form is not an element or anything composed of the elements. Therefore it follows that a form neither comes to he nor is generated in itself.
lib. 8 l. 3 n. 15 Deinde cum dicit si autem prosequitur quartum praedictorum; scilicet quod Plato ponebat formas separatas a materia. Et circa hoc tria facit. Primo ostendit quid sit dubium circa hanc positionem; dicens quod non est manifestum si substantiae, idest formae rerum corruptibilium, sint separabiles, ut Platonici posuerunt.	1717. But whether the substances (713). He examines the fourth point given above, namely, Plato’s position that forms are separate from matter. In regard to this he does three things. First, he exposes what the problem is in this position, saying that it is not clear whether “the substances,” i.e., the forms, of corruptible things are separable as the Platonists claimed.
lib. 8 l. 3 n. 16 Secundo attamen quia ostendit quid manifestum esse videtur circa hoc; et dicit manifestum esse, quod quorumdam corruptibilium formas non contingit separari, quaecumque scilicet non possibile est esse praeter materias suas, sicut domus aut vas, quia forma domus aut vasis non potest esse sine propria materia.	1718. It is evident, however (714). Second, he indicates what seems to be evident on this point. He says that it is evident that the forms of some corruptible things are not separate, namely, “all those” which are incapable of existing apart from their matters, as house or vessel, because neither the form of a house nor that of a vessel can exist apart from its proper matter.
lib. 8 l. 3 n. 17 Tertio forsan quidem excludit obviationem; dicens, quod formae artificialium forsan non sunt substantiae, nec ipsae sunt aliquid per se, unde separari non possunt. Et similiter nullum aliorum artificialium, quae non sunt secundum naturam; quia solum materia in rebus artificialibus ponitur esse substantia, formae autem artificiales accidentia sunt. Formae vero naturales sunt de genere substantiae. Et propter hoc Plato non posuit formas artificiales esse separatas a materia, sed solum formas substantiales.	1719. Indeed, perhaps (715). Third, he precludes an objection, saying that perhaps the forms of artifacts are not substances or anything in their own right, and so cannot have separate existence. Nor similarly can other artificial forms, which have no natural existence, because in artifacts the matter alone is held to be substance, whereas the forms of artifacts are accidents. Natural forms, however, belong to the class of substance; and this is why Plato did not hold that the forms of artifacts exist apart from matter but only substantial forms.
lib. 8 l. 3 n. 18 Deinde cum dicit quare dubitatio ostendit quid manifeste sit contra positionem Platonis; dicens, quod si quis ponat esse formas separatas, ut Platonici posuerant, dubitatio, quam Antisthenici dubitaverunt, licet viderentur indocti, habebit locum contra Platonicos. Dicebant enim quod non est aliquid definire definitione significante quidditatem rei. Quia, cum quidditas rei sit simplex, non convenienter significatur per orationem compositam ex multis. Videmus enim quod terminus, id est definitio, quae assignatur rei, est oratio longa ex multis composita; unde non significat quid est, sed quale quid, id est cui simile est aliquid. Sicut si aliquis dicat, quod definitio argenti non significat argentum, sed significat tale quale est plumbum vel stannum.	1720. For this reason (716). He advances arguments that are clearly opposed to Plato’s position. He says that if one holds that there are separate forms, as the Platonists maintained, the problem which the followers of Antisthenes raised, even though they seem to be uninstructed, may be used against the Platonists. For they argued that it is impossible to define a thing by means of a definition which signifies its quiddity, since a thing’s quiddity is simple and is not fittingly expressed by a statement composed of many parts. For we see that “the limit,” or definition, which is given to a thing, is a lengthy statement made up of many words. Therefore it does not signify what a thing is but “what it is like,” i.e., something to which it is similar; as if one were to say that the definition of silver does not signify silver but signifies something like lead or tin.
lib. 8 l. 3 n. 19 Unde ad solvendum istam dubitationem oportet dicere, quod substantia, quae definitur, sive sit intellectualis, sive sit sensibilis, oportet quod sit composita. Ea vero, ex quibus primo componitur, cum sint simplicia, non contingit definiri. Dictum est enim supra, quod ratio definitiva adiungit aliquid alteri, quorum unum est ut forma, aliud ut materia. Nam genus sumitur a materia, et differentia a forma, ut dictum est supra; unde, si species rerum essent tantum formae, ut Platonici posuerunt, non contingeret eas definiri.	1721. Hence in order to solve this problem we must say that the substance which is defined, whether it be intellectual or sensible, must be one that is composite. But since the primary parts of which a definition is composed are simple, they are incapable of definition. For it was stated above (706)C 1700) that the definitive statement joins one part to another, one of which is as form and the other as matter, because genus is derived from matter and difference from form, as was pointed out above (704:C 1696-8). Hence, if the species of things were forms only, as the Platonists held, they would be indefinable.
lib. 8 l. 3 n. 20 Deinde cum dicit palam autem postquam determinavit de formis secundum quod comparantur ad ideas introductas a Platone, nunc determinat de formis per comparationem ad numeros. Plato enim ponebat formas et substantias rerum, reducendo per modum cuiusdam assimilationis formas ad numeros. Et dividitur in quatuor, secundum quod quatuor modis assimilat formas numeris. Dicit ergo primo, quod manifestum est, quod si numeri aliquo modo sint substantiae rerum et formae, sic sunt, sicut ex praemissis accipi potest; non autem sunt numeri unitatum sicut Platonici dicunt. Dicitur autem numerus unitatum, numerus simplex et absolutus. Numerus autem applicatus ad res, dicitur numerus rerum, sicut quatuor canes vel quatuor homines, quo quidem modo substantiae rerum, quas significant definitiones, possunt dici numeri. Est enim definitio divisibilis in duo: quorum unum se habet ut forma, aliud ut materia, ut superius dictum est. Et iterum est in indivisibilia divisibilis. Divisio enim definitionis oportet quod per aliqua indivisibilia terminetur: non enim definitiones procedunt in infinitum. Puta, si definitio hominis dividatur in animal et rationale, definitio animalis in animatum et sensibile; non procedet hoc in infinitum, cum non sit procedere in infinitum in causis materialibus et formalibus, ut in secundo probatum est. Et sic definitionis divisio non assimilatur divisioni quantitatis continuae, quae est in infinitum; sed divisioni numeri, qui est divisibilis in indivisibilia.	1722. Further, it is also clear (717). Having determined what is true of forms in relation to the Ideas introduced by Plato, Aristotle now ‘determines what is true of forms in relation to numbers. For Plato held that numbers are the forms and substances of things by establishing a kind of likeness between forms and numbers. This is divided into four parts inasmuch as there are four ways in which he likens forms to numbers. First, he says that, if numbers are in any sense the substances or forms of things, it is evident that they are such in this way, as can be understood from the foregoing, but not as numbers of units as the Platonists said. Now a number of units is called a simple and absolute number [i.e., an abstract number], but the number applied to things is called a concrete number, as four dogs or four men; and in this way the substances of things, which are Signified by a definition, can be called numbers. For a definition is divisible into two parts, one of which is as form and the other as matter, as was pointed out above (706:C 1700). And it is divisible into indivisible parts; for since definitions cannot proceed to infinity, the division of a definition must terminate in certain indivisible parts. For example, if the definition of man is divided into animal and rational, and the definition of animal into animated and sensible, this will not go on to infinity. For it is impossible to have an infinite regress in material and formal causes, as was shown in Book II (152:C 299). Hence he explains that the division of a definition is not like the division of a continuous quantity, which is divisible to infinity, but is like the division of a number, which is divisible into indivisible parts.
lib. 8 l. 3 n. 21 Et quemadmodum ponit secundam assimilationem substantiae, quam significat definitio, ad numeros. Et dicit, quod si aliquid addatur vel subtrahatur alicui numero, etiam si sit minimum, non erit id idem numerus secundum speciem. Minimum enim in numeris est unitas; quae si addatur in ternario, surgit quaternarius, quae est alia species numeri: si vero abstrahatur ab eodem, remanet binarius, qui est etiam alia species numeri. Et hoc ideo, quia illa ultima differentia dat speciem numero.	1723. And just as when (718). He gives the second way in which the substance that the definition signifies is like number. He says that, if anything is added to or subtracted from any number, even if it is a bare minimum, the resulting number will not be specifically the same. For in the case of numbers the minimum is the number one, which, when added to the number three, gives rise to the number four, which is a specifically different number; but if it is subtracted from the same number, the number two remains, which is also a specifically different number. And this is true because the ultimate difference gives to a number its species.
lib. 8 l. 3 n. 22 Et similiter est in definitionibus, et in quod quid erat esse, quod significat definitio; quia quocumque minimo addito vel ablato, est alia definitio, et alia natura speciei. Sicut enim substantia animata sensibilis tantum, est definitio animalis: cui si addas et rationale, constituis speciem hominis: si autem subtrahas sensibile, constituis speciem plantae, quia etiam ultima differentia dat speciem.	1724. And it is similar in the case of definitions and of the essence, which the definition signifies; because, howsoever small a part has been added or subtracted, there results another definition and another specific nature. For animated sensible substance alone is the definition of animal, but if you also add rational to this, you establish the species man. And in a similar way if you subtract sensible, you establish the species plant, because the ultimate difference also determines the species.
lib. 8 l. 3 n. 23 Et numerum ponit tertiam assimilationem; et dicit, quod numerus est id quod est unum. Est enim per se unum numerus, inquantum ultima unitas dat numero speciem et unitatem; sicut etiam in rebus compositis ex materia et forma, per formam est aliquid unum, et unitatem et speciem sortitur. Et propter hoc loquentes de unitate numeri, ac si numerus non esset unus per seipsum, non possunt dicere quo est unus, si est unus. Cum enim componatur ex multis unitatibus, aut non est unus simpliciter, sed unitates aggregantur in eo per modum coacervationis, quae non facit simpliciter unum, et per consequens nec ens in aliqua specie constituunt: et sic numerus non est aliqua species entis; aut si numerus est unus simpliciter, et non per seipsum, dicendum est quid facit eum unum ex multis unitatibus: quod non est assignare.	1725. And there must be (719). He gives the third way in which forms are like numbers. He says that a number is one thing. For a number is an essential unity inasmuch as the ultimate unity gives to a number its species and unity, just as in things composed of matter and form a thing is one and derives its unity and species from its form. And for this reason those who speak about the unity of a number as though a number were not essentially one cannot say what makes it to be one thing, i.e., if it is one. For since a number is composed of many units, either it is not one thing in an absolute sense but its units are joined together in the manner of a heap, which does not constitute a unity in an absolute sense, and therefore not a being in any class of things (and thus number would not be a class of being); or if it is one thing in an absolute sense and a being in itself, it is still necessary to explain what makes it one thing out of a plurality of units. But they are unable to assign a reason for this.
lib. 8 l. 3 n. 24 Et similiter definitio est una per seipsam: et sic non habent aliquid assignare per quod fiat unum. Et hoc rationabiliter accidit: quia per eamdem rationem substantia, quam significat definitio, est ita unum sicut et numerus, scilicet per se, ex hoc quod una pars eius est ut forma alterius. Et non est una ut indivisibile, sicut unitas ac punctum, sicut quidam dixerunt; sed quia unaquaeque earum est una forma et natura quaedam.	1726. Similarly, a definition is one thing essentially, and thus they do not have to assign anything which makes it one. This is understandable, because the substance which the definition signifies is one thing for the very same reason that a number is, i.e., essentially, because one part of it is related to the other as form [to matter]. And it is one, not as being something indivisible such as a unit and a point, as some men claimed, but because each of them is one form and a kind of nature.
lib. 8 l. 3 n. 25 Et quemadmodum ponit quartam assimilationem; et dicit quod sicut numerus non suscipit magis aut minus, ita nec substantia quae dicitur secundum speciem, licet forte illa quae dicitur secundum materiam. Sicut enim ratio numeri in aliquo determinato consistit, cui non est addere nec subtrahere, ut dictum est, ita et ratio formae. Sed magis et minus contingit ex hoc quod materia perfectius vel minus perfecte formam participat. Unde etiam albedo non suscipit magis et minus, sed album.	1727. And just as number (720). He gives the fourth way in which forms are like numbers. He says that just as a number does not admit of (~) more or less, neither does substance in the sense of form, although perhaps substance in the sense of matter does admit of such difference. For just as the concept of number consists in some limit to which neither addition nor subtraction may be made, as has been pointed out (1723), so also does the concept of form. But things admit of (+) more or less because of the fact that matter participates in a form in a more or less perfect way. Hence too whiteness does not differ in terms of more or less, but a white thing does.
lib. 8 l. 3 n. 26 Deinde cum dicit de generatione epilogat quae dicta sunt; dicens, quod dictum est de generatione et corruptione talium substantiarum, scilicet formalium, quomodo contingit, quia per accidens; et quomodo est impossibile, quia per se; et de analogia, idest reductione earum ad numerum per viam assimilationis.	1728. In regard to the generation (721). He summarizes the points discussed. He says that he has dealt with “the generation and corruption of such substances,” or forms, both as to the way in which this is possible, namely, by reason of something else; and as to the way in which this is impossible, i.e., essentially; and also with the likeness which forms have to numbers, i.e., by reducing them to numbers by way of a likeness.