Part 3 Commentary
QUESTION FIVE: The division of speculative science
Article 1: Is Speculative Science Appropriately Divided into these Three Parts: Natural, Mathematical, and Divine?
Article 2 Does Natural Philosophy Treat of What Exists in Motion and Matter?
Article 3: Does Mathematics Treat, Without Motion and Matter, of What Exists in Matter?
Article 4: Does Divine Science Treat of What Exists Without Matter and Motion?
| Latin | English |
|---|---|
| Sancti Thomae de Aquino | Thomas Aquinas |
| Super Boetium De Trinitate | On Boethius on the Trinity |
| Textum a Bruno Decker Lugduni Batauorum 1959 editum ac automato translatum a Roberto Busa SJ in taenias magneticas denuo recognovit Enrique Alarcón atque instruxit | Questions 5-6, translated by Armand Mauer (Toronto, 1953) |
| Pars 3 | |
| Prooemium | |
| Pars 3 pr. 1 | |
| Proposuit superius Boethius sententiam Catholicae fidei de unitate Trinitatis et rationem sententiae prosecutus est. Nunc intendit procedere ad inquisitionem praedictorum. Et quia secundum sententiam philosophi in II metaphysicae ante scientiam oportet inquirere modum scientiae, ideo pars ista dividitur in duas. In prima Boethius ostendit modum proprium huius inquisitionis, quae est de rebus divinis. In secunda vero parte secundum modum assignatum procedit ad propositum inquirendum, ibi: quae vere forma est et cetera. | 1.1 Boethius has previously set forth the doctrine of the Catholic faith regarding the unity of the Trinity, and indicated the reason of this belief. Now he intends to proceed to an investigation of the aforesaid doctrine. Since, according to the opinion of the Philosopher in II Metaph., inquiry into the method of a science ought to precede science itself, he therdore divides this section into two parts. In the first place Boethius points out the method proper for this kind of inquiry, which is concerned with divine things. In the second place he proceeds, according to the method he has indicated, to inquire into the proposition determined upon, where he says, "Which form, indeed." |
| Prima pars dividitur in duas. In prima ponit necessitatem ostendendi modum inquisitionis. In secunda modum congruum inquisitioni praesenti ostendit, ibi: nam cum tres sint et cetera. Dicit ergo: igitur, ex quo constat hanc esse sententiam Catholicae fidei de unitate Trinitatis et indifferentiam esse rationem unitatis, | The first part is again divided into two sections: first, he indicates the necessity of making clear the method of investigation. Secondly, he shows that the method of the present inquiry is suitable, saying: "Speculative science may be divided into three kinds." Therefore he says: "Wherefore it is certain that this is the doctrine of the Catholic faith regarding the unity of the Trinity, and the nature of that unity without difference." |
| Age, adverbium exhortandi, ingrediamur, id est interius inquiramus ipsa intima rerum principia considerantes et veritatem quasi velatam et absconditam perscrutantes, et hoc modo convenienti; unde subdit: et unumquodque dicendorum discutiamus, ut potest intelligi atque capi, id est per modum quo possit intelligi et capi. | Thereupon, he says by way of exhortation, "Let us now begin," that is, let us inquire more deeply, carrying our investigation to an examination of the intimate principle of things and of truth which is, as it were, veiled and hidden away from view. And that method which he deems fitting is indicated by the words: "Let us now begin a careful consideration of each several point, as far as it can be grasped and understood," that is, according to the mode by which. understanding and apprehension are possible. |
| Pars 3 pr. 2 | |
| Et dicit haec duo, quia modus, quo aliqua discutiuntur, debet congruere et rebus et nobis. Nisi enim rebus congrueret, res intelligi non possent; nisi vero congrueret nobis, nos capere non possemus, utpote res divinae ex natura sua habent quod non cognoscantur nisi intellectu. Unde si aliquis vellet sequi imaginationem in consideratione earum, non posset intelligere, quia ipsae res non sunt sic intelligibiles. Si autem aliquis vellet res divinas per se ipsas videre ea certitudine et comprehendere, sicut comprehenduntur sensibilia et demonstrationes mathematicae, non posset hoc modo capere propter defectum intellectus sui, quantumvis ipsae res sint secundum se hoc modo intelligibiles. | Moreover, he uses the two words ("grasped" and "understood") because the method of any investigation ought to be in harmony both with things and with us. For if it is not suited to the matter, things will not be understood; and if it is not suited to us, we shall not be able to apprehend the matter; for example, divine things are such by their very nature that they cannot be known except by intellect. Wherefore, if anyone wished to follow another way and to use imagination instead, he would not be able to understand anything of them as a result of his consideration, because truths, of this kind are not thus to be known. But if, on the other hand, one wished to know divine things so as to see them in themselves, and to comprehend them with the same certitude with which sensible things or mathematical demonstrations are comprehended, this too would be impossible; even things which are, in themselves, understandable in this way cannot be perfectly grasped because of the weakness of our intellect. |
| Et quod modus congruus sit in inquisitione qualibet observandus, probat inducendo auctoritatem philosophi in principio Ethicorum, et hoc est quod subiungit: nam sicut optime dictum videtur, scilicet ab Aristotele in principio Ethicorum: eruditi hominis est ut unumquodque ipsum est, id est per modum congruum ipsi rei, ita de eo fidem capere temptare. Non enim de omnibus rebus potest aequalis certitudo et evidentia demonstrationis servari. Et sunt haec verba philosophi in I Ethicorum: disciplinati enim est in tantum certitudinem inquirere secundum unumquodque genus, in quantum natura rei recipit. | He also shows that the mode of inquiry used must always correspond to the kind of investigation undertaken, by reference to the authority of the Philosopher in I Ethic. when he says: "For it has been wisely said that it is a scholar’s duty to formulate his belief about anything according to its real nature." So, in regard to a doctrine of faith, the same principle must be applied: for in all cases, equal certitude and demonstrative evidence cannot be demanded. And these are the very words of the Philosopher in I Ethic.: "It is the duty of the scholar to demand as much certitude in his investigation of each thing as the nature of that thing permits." |
| Pars 3 pr. 3 | |
| Deinde cum dicit: nam cum tres etc., inquirit modum congruum huic inquisitioni per distinctionem a modis qui observantur in aliis scientiis. Et quia modus debet esse congruus rei de qua est perscrutatio, ideo dividitur haec pars in duas. | 1.2 In the second place, when he says: "Speculative science may be divided into three kinds," he inquires into the method of his own investigation, testing its congruousness by distinguishing it from the methods employed in other sciences; and, since method ought to correspond to the matter under investigation, he therefore divides this part of his consideration into two sections. |
| In prima enim distinguit scientias secundum res, de quibus determinant. | First, he distinguishes sciences according to the matter with which each is concerned. |
| In secunda ostendit modos singulis earum congruos, ibi: in naturalibus igitur et cetera. | Secondly, he indicates the methods suitable for each kind of matter, beginning, "Physics deals." |
| Circa primum tria facit. Primo ostendit, de quibus consideret naturalis philosophia. Secundo, de quibus mathematica, ibi: mathematica et cetera. Tertio, de quibus considerat divina scientia, ibi: theologia est sine motu et cetera. | In regard to the first point, he does three things. First, he shows what the objects of natural philosophy are. Secondly, he indicates the objects of mathematics. Thirdly, he speaks of the truths with which divine science is concerned, when he says: "Theology does not." |
| Dicit ergo: bene dictum est quod ut unumquodque est, ita debet de eo fides capi. Nam cum tres sint partes speculativae, scilicet philosophiae - hoc dicit ad differentiam Ethicae, quae est activa sive practica - in omnibus requiritur modus competens materiae. Sunt autem tres partes praedictae: physica sive naturalis, mathematica, divina sive theologia. Cum, inquam, sint tres partes, naturalis, quae est una earum, est in motu, inabstracta, id est versatur eius consideratio circa res mobiles a materia non abstractas, quod probat per exempla, ut patet in littera. Quod autem dicit: habetque motum forma materiae coniuncta, sic intelligendum est: ipsum compositum ex materia et forma, in quantum huiusmodi, habet motum sibi debitum, vel ipsa forma in materia exsistens est principium motus; et ideo eadem est consideratio de rebus secundum quod sunt materiales et secundum quod sunt mobiles. | 1.2.1.1 Therefore he says: "It has been wisely said that it is a scholar’s duty to formulate his belief about anything according to its real nature." For, since there are three divisions of speculative science (or philosophy), and he calls it "speculative" to differentiate it from ethics, which is operative or practical; in each of these the method must be in conformity with the matter. The three divisions of speculative science indicated are physics or natural science, mathematics, and divine science or theology. While, I say, there are three divisions, natural philosophy, which is one of the, three, "deals with motion and,is not abstract," that is, it is concerned with things in motion and not abstracted from matter. This he proves by examples, as is evident in his treatise. When, however, he says: "Form takes on the movement of the particular thing to which it is annexed," his words should be understood as follows: that what is composite of matter and form, inasmuch as it is due the nature of a thing of this kind, has motion; or, in other words, a form existing in matter is the principle of motion. Therefore the consideration of things that are material and of things that are in motion is the same. |
| Pars 3 pr. 4 | |
| Deinde exponit de quibus sit mathematica: mathematica est sine motu, id est sine motus et mobilium consideratione, in quo differt a naturali, inabstracta, id est considerat formas quae secundum esse suum non sunt a materia abstractae, in quo convenit cum naturali; quod quomodo sit exponit. Haec enim, scilicet mathematica, speculatur formas sine materia ac per hoc sine motu, quia ubicumque est motus, est materia, ut probatur in IX metaphysicae, eo modo quo est ibi motus, et sic ipsa speculatio mathematici est sine materia et motu. Quae formae, scilicet de quibus mathematicus speculatur, cum sint in materia, non possunt ab his separari secundum esse, et sic secundum speculationem sunt separabiles, non secundum esse. | 1.2.1.2 He then indicates the subject matter of mathematics, saying: "Mathematics does not deal with motion"; that is, it involves no consideration of motion or of movable things, and on this point it differs from natural philosophy. Mathematics, moreover, is said to be "not abstract"; that is, it considers forms which according to their existence are not abstract from matter, and in this respect it is in agreement with natural philosophy. He then explains. how this is: Mathematics considers forms which are without matter and hence without motion, because wherever there is matter there is motion, as is proved in X Metaph. For according as things have matter there will also be motion, and thus the speculations of a mathematician are without matter and without motion, although these forms, namely, those about which the mathematician speculates, "being connected with matter, cannot really be separated from bodies," according to their being [real existence]; but according to speculation, they can be considered as separable. |
| Pars 3 pr. 5 | |
| Deinde ostendit de quibus sit tertia, scilicet divina: theologia, id est tertia pars speculativae, quae dicitur divina vel metaphysica vel philosophia prima, est sine motu, in quo convenit cum mathematica et differt a naturali, abstracta, scilicet a materia, atque inseparabilis, per quae duo differt a mathematica. Res enim divinae sunt secundum esse abstractae a materia et motu, sed mathematicae inabstractae, sunt autem consideratione separabiles; sed res divinae inseparabiles, quia nihil est separabile nisi quod est coniunctum. Unde res divinae non sunt secundum considerationem separabiles a materia, sed secundum esse abstractae; res vero mathematicae e contrario. Et hoc probat per Dei substantiam, de qua scientia divina considerat principaliter, unde et inde nominatur. | 1.2.1.3 Then he indicates the objects of divine science, calling it, ‘theology," that is, the third division of speculative science, which is termed divine, or metaphysics, or first philosophy; and it deals with objects apart from motion, in which it agrees with mathematics and differs from natural philosophy. It also is "abstract," namely, from matter, and "inseparable"; and because of these two facts it differs from mathematics. For the objects of divine science are of themselves abstract from matter and motion, but those of mathematics are not thus naturally abstract, but separable in thought. The objects of divine science, however, are called "inseparable" because a thing is not separable unless there is some conjunction with matter. Hence the objects of divine science are not separable from matter by thought, but are abstract according to their very being; while the converse is true in the case of the objects of mathematics. This he proves by the fact that the substance with which divine science is principally concerned is that of God, and on this account it is called "divine." |
| Pars 3 pr. 6 | |
| Deinde cum dicit: in naturalibus igitur etc., ostendit, quis sit modus congruus praedictis partibus. Et circa hoc duo facit. Primo concludit modos congruos singulis partium praedictarum, et huius partis expositio relinquitur disputationi. Secundo exponit ultimum modum qui est proprius praesenti inquisitioni. Et hoc dupliciter. Primo removendo id quod est impeditivum dicens: neque oportet in divinis deduci ad imaginationes, ut scilicet de eis iudicando sequamur imaginationis iudicium. | 1.2.2.1 In the next place, when he says, "In physics, then, we are bound to use scientific concepts, in mathematics systematic concepts, in theology intellectual concepts." He points out the methods that correspond to the aforesaid divisions. Here he treats of two things. First, he draws conclusions about the methods appropriate for each of the divisions named, and the disposition of this section is left open for discussion. Secondly, he describes the last mode, which is that proper to the present investigation, and indicates a twofold procedure: first, by the removal of that which is an impediment to speculation saying, ‘In theology we will not let ourselves be diverted to play with imaginations (that is, in such a way that in formulating judgments we follow the judgment of the imagination) but will consider simply form." |
| Secundo ostendendo id quod est proprium, ibi: sed potius ipsam inspicere formam sine motu et materia, cuius condiciones consequenter exponit ingrediens ad propositam inquisitionem. | 1.2.2.2 Secondly, he indicates the method which is the proper one when he says: "but will consider simply form" (apart from motion and matter), the nature of which he consequently explains in beginning his treatment of the proposed question. |
| Quaestio 5 | QUESTION FIVE |
| Pars 3 q. 5 pr. | |
| Hic est duplex quaestio. Prima de divisione speculativae, quam in littera ponit. Secunda de modis, quos partibus speculativae attribuit. Circa primum quaeruntur quattuor. | The Division of Speculative Science. There are two questions here. The first concerns the division of speculative science which the text proposes, the second concerns the methods it attributes to the parts of speculative science. With regard to the first question there are four points of inquiry: |
| Pars 3 q. 5 pr. 1 | |
| Primo. Utrum sit conveniens divisio qua dividitur speculativa in has tres partes: naturalem, mathematicam et divinam. | 1. Is speculative science appropriately divided into these three parts: natural, mathematical, and divine? |
| Pars 3 q. 5 pr. 2 | |
| Secundo. Utrum naturalis philosophia sit de his quae sunt in motu et materia. | 2. Does natural philosophy treat of what exists in motion and matter? |
| Pars 3 q. 5 pr. 3 | |
| Tertio. Utrum mathematica consideratio sit sine motu et materia de his quae sunt in materia. | 3. Does mathematics treat, without motion and matter, of what exists in matter? |
| Pars 3 q. 5 pr. 4 | |
| Quarto. Utrum divina scientia sit de his quae sunt sine materia et motu. | 4. Does divine science treat of what exists without matter and motion? |
| Articulus 1 | ARTICLE ONE Is Speculative Science Appropriately Divided into these Three Parts: Natural, Mathematical, and Divine? |
| Pars 3 q. 5 a. 1 arg. 1 | |
| Ad primum sic proceditur. Videtur quod speculativa inconvenienter in has partes dividatur. Partes enim speculativae sunt illi habitus qui partem contemplativam animae perficiunt. Sed philosophus in VI Ethicorum ponit quod scientificum animae, quod est pars eius contemplativa, perficitur tribus habitibus, scilicet sapientia, scientia et intellectu. Ergo ista tria sunt partes speculativae et non illa quae in littera ponuntur. | We proceed as follows to the first article: It seems that speculative science is not appropriately divided into these three parts, for: 1. The parts of speculative science are the habits that perfect the contemplative part of the soul. But the Philosopher says in the Ethics that the scientific part of the soul, which is its contemplative part, is perfected by three habits, namely, wisdom, science, and understanding. Therefore these are the three divisions of speculative science, not those proposed in the text. |
| Pars 3 q. 5 a. 1 arg. 2 | |
| Praeterea, Augustinus dicit in VIII de civitate Dei quod rationalis philosophia, quae est logica, sub contemplativa philosophia vel speculativa continetur. Cum ergo de ea mentionem non faciat, videtur quod divisio sit insufficiens. | 2. Again, Augustine says that rational philosophy, or logic, is included under contemplative or speculative philosophy. Consequently, since no mention is made of it, it seems the division is inadequate. |
| Pars 3 q. 5 a. 1 arg. 3 | |
| Praeterea, communiter dividitur philosophia in septem artes liberales, inter quas neque naturalis neque divina continetur, sed sola rationalis et mathematica. Ergo naturalis et divina non debuerunt poni partes speculativae. | 3. Again, philosophy is commonly divided into seven liberal arts, which include neither natural nor divine science, but only rational and mathematical science. Hence natural and divine should not be called parts of speculative science. |
| Pars 3 q. 5 a. 1 arg. 4 | |
| Praeterea, scientia medicinae maxime videtur esse operativa, et tamen in ea ponitur una pars speculativa et alia practica. Ergo eadem ratione in omnibus aliis operativis scientiis aliqua pars est speculativa, et ita debuit in hac divisione mentio fieri de Ethica sive morali, quamvis sit activa, propter partem eius speculativam. | 4. Again, medicine seems to be the most practical science, and yet it is said to contain a speculative part and a practical part. By the same token, therefore, all the other practical sciences have a speculative part. Consequently, even though it is a practical science, ethics or moral science should be mentioned in this division because of its speculative part. |
| Pars 3 q. 5 a. 1 arg. 5 | |
| Praeterea, scientia medicinae quaedam pars physicae est, et similiter quaedam aliae artes quae dicuntur mechanicae, ut scientia de agricultura, alchimia et aliae huiusmodi. Cum ergo istae sint operativae, videtur quod non debuerit naturalis absolute sub speculativa poni. | 5. Again, the science of medicine is a branch of physics, and similarly certain other arts called "mechanical," like the science of agriculture, alchemy, and others of the same sort. Therefore, since these sciences are practical, it seems that natural science should not be included without qualification under speculative science. |
| Pars 3 q. 5 a. 1 arg. 6 | |
| Praeterea, totum non debet dividi contra partem. Sed divina scientia esse videtur ut totum respectu physicae et mathematicae, cum subiecta illarum sint partes subiecti istius. Divinae enim scientiae, quae est prima philosophia, subiectum est ens, cuius pars est substantia mobilis, quam considerat naturalis, et similiter quantitas quam considerat mathematicus, ut patet in III metaphysicae. Ergo scientia divina non debet dividi contra naturalem et mathematicam. | 6. Again, a whole should not be contra-distinguished from its part. But divine science seems to be a whole in relation to physics mathematics, since their subjects are parts of its subject of divine science or first philosophy is being; and changeable substance, which the natural scientist considers, and also quantity, which the mathematician considers, are parts of being. This is clear in the Metaphysics. Therefore, divine science should not be contra-distinguished from natural science and mathematics. |
| Pars 3 q. 5 a. 1 arg. 7 | |
| Praeterea, scientiae dividuntur quemadmodum et res, ut dicitur in III de anima. Sed philosophia est de ente; est enim cognitio entis, ut dicit Dionysius in epistula ad Polycarpum. Cum ergo ens primo dividatur per potentiam et actum, per unum et multa, per substantiam et accidens, videtur quod per huiusmodi deberent partes philosophiae distingui. | 7. Again, as it is said in the De Anima, sciences are divided in the same manner as things. But philosophy concerns being, for it is knowledge of being, as Dionysius says. Now being is primarily divided into potency and act, one and many, substance and accident. So it seems that the parts of philosophy ought to be distinguished by such divisions of being. |
| Pars 3 q. 5 a. 1 arg. 8 | |
| Praeterea, multae aliae divisiones sunt entium, de quibus sunt scientiae, magis essentiales quam istae quae sunt per mobile et immobile, per abstractum et non abstractum, utpote per corporeum et incorporeum, animatum et inanimatum et per alia huiusmodi. Ergo magis deberet divisio partium philosophiae accipi per huiusmodi differentias quam per illas quae hic tanguntur. | 8. Again, there are many other divisions of beings studied by sciences more essential than the divisions into mobile and immobile and into abstract and non-abstract; for example, the divisions into corporeal and incorporeal and into living and non-living, and the like. Therefore differences of this sort should be the basis for the division of the parts of philosophy rather than those mentioned here. |
| Pars 3 q. 5 a. 1 arg. 9 | |
| Praeterea, illa scientia, a qua aliae supponunt, debet esse prior eis. Sed omnes aliae scientiae supponunt a scientia divina, quia eius est probare principia aliarum scientiarum. Ergo debuit scientiam divinam aliis praeordinare. | 9. Again, that science on which others depend must be prior to them. Now all the other sciences depend on divine science because it is its business to prove their principles. Therefore Boethius should have placed divine science before the others. |
| Pars 3 q. 5 a. 1 arg. 10 | |
| Praeterea, mathematica prius occurrit addiscenda quam naturalis, eo quod mathematicam facile possunt addiscere pueri, non autem naturalem nisi provecti, ut dicitur in VI Ethicorum. Unde et apud antiquos hic ordo in scientiis addiscendis fuisse dicitur observatus, ut primo logica, deinde mathematica, post quam naturalis et post hanc moralis, et tandem divinae scientiae homines studerent. Ergo mathematicam naturali scientiae praeordinare debuit. Et sic videtur divisio haec insufficiens. | 10. Again, mathematics should be studied before natural science, for the young can easily learn mathematics, but only the more advanced natural science, as is said in the Ethics. This is why the ancients are said to have observed the following order in learning the sciences: first logic, then mathematics, then natural science, after that moral science, and finally men studied divine science. Therefore, Boethius should have placed mathematics before natural science. And so it seems that this division is unsuitable. |
| Pars 3 q. 5 a. 1 s. c. 1 | |
| Sed e contra, quod haec divisio sit conveniens, probatur per philosophum in VI metaphysicae, ubi dicit: quare tres erunt philosophicae et theoricae: mathematica, physica, theologia. | On the contrary, the Philosopher proves the appropriateness of this division in the Metaphysics, where he says, "There will be three philosophical and theoretical sciences, mathematics, physics, and theology. |
| Pars 3 q. 5 a. 1 s. c. 2 | |
| Praeterea, in II physicorum ponuntur tres modi scientiarum, qui ad has etiam tres pertinere videntur. | Moreover, in the Physics three methods of the sciences are proposed which indeed seem to belong to these three. |
| Pars 3 q. 5 a. 1 s. c. 3 | |
| Praeterea, Ptolemaeus etiam in principio Almagesti hac divisione utitur. | Moreover, Ptolemy also uses this division in the beginning of his Almagest. |
| Pars 3 q. 5 a. 1 co. 1 | |
| Responsio. Dicendum quod theoricus sive speculativus intellectus in hoc proprie ab operativo sive practico distinguitur quod speculativus habet pro fine veritatem quam considerat, practicus vero veritatem consideratam ordinat in operationem tamquam in finem. Et ideo dicit philosophus in III de anima quod differunt ad invicem fine, et in II metaphysicae dicitur quod finis speculativae est veritas, sed finis operativae scientiae est actio. | Reply: The theoretical or speculative intellect is properly distinguished from the operative or practical intellect by the fact that the speculative intellect has for its end the truth that it contemplates, while the practical intellect directs the truth under consideration to activity as to an end. So the Philosopher says in the De Anima that they differ from each other by their ends; and in the Metaphysics he states that "the end of speculative knowledge is truth, but the end of practical knowledge is action." |
| Cum ergo oporteat materiam fini esse proportionatam, oportet practicarum scientiarum materiam esse res illas quae a nostro opere fieri possunt, ut sic earum cognitio in operationem quasi in finem ordinari possit. | Now, since matter must be proportionate to the end, the subject-matter of the practical sciences must be things that can be made or done by us, so that we can direct the knowledge of them to activity as to an end. |
| Speculativarum vero scientiarum materiam oportet esse res quae a nostro opere non fiunt; unde earum consideratio in operationem ordinari non potest sicut in finem. Et secundum harum rerum distinctionem oportet scientias speculativas distingui. | On the other hand, the subject-matter of the speculative sciences must be things that cannot be made or done by us, so that our knowledge of them cannot be directed to activity as to an end. And the speculative sciences must differ according to the distinctions among these things. |
| Pars 3 q. 5 a. 1 co. 2 | |
| Sciendum tamen quod, quando habitus vel potentiae penes obiecta distinguuntur, non distinguuntur penes quaslibet differentias obiectorum, sed penes illas quae sunt per se obiectorum in quantum sunt obiecta. Esse enim animal vel plantam accidit sensibili in quantum est sensibile, et ideo penes hoc non sumitur distinctio sensuum, sed magis penes differentiam coloris et soni. Et ideo oportet scientias speculativas dividi per differentias speculabilium, in quantum speculabilia sunt. | Now we must realize that when habits or powers are differentiated by their objects they do not differ according to just any distinction among these objects, but according to the distinctions that are essential to the objects as objects. For example, it is incidental to a sense object as such whether it be an animal or a plant. Accordingly, the distinction between the senses is not based upon this difference but rather upon the difference between color and sound. So the speculative sciences must be divided according to differences between objects of speculation, considered precisely as such. |
| Speculabili autem, quod est obiectum speculativae potentiae, aliquid competit ex parte intellectivae potentiae et aliquid ex parte habitus scientiae quo intellectus perficitur. Ex parte siquidem intellectus competit ei quod sit immateriale, quia et ipse intellectus immaterialis est; ex parte vero scientiae competit ei quod sit necessarium, quia scientia de necessariis est, ut probatur in I posteriorum. Omne autem necessarium, in quantum huiusmodi, est immobile; quia omne quod movetur, in quantum huiusmodi, est possibile esse et non esse vel simpliciter vel secundum quid, ut dicitur in IX metaphysicae. Sic ergo speculabili, quod est obiectum scientiae speculativae, per se competit separatio a materia et motu vel applicatio ad ea. Et ideo secundum ordinem remotionis a materia et motu scientiae speculativae distinguuntur. | Now an object of this kind - namely, an object of a speculative power - derives one characteristic from the side of the power of intellect and another from the side of the habit of science that perfects the intellect. From the side of the intellect it has the fact that it is immaterial, because the intellect itself is immaterial. From the side of habit of science it has the fact that it is necessary, for science treats of necessary matters, as is shown in the Posterior Analytics. Now everything that is necessary is, as such, immobile, because everything changeable is, as such, able to be or not to be, either absolutely or in a certain respect, as is said in the Metaphysics. Consequently, separation from matter and motion, or connection with them, essentially belongs to an object of speculation, which is the object of speculative science. As a result, the speculative sciences are differentiated according to their degree of separation from matter and motion. |
| Pars 3 q. 5 a. 1 co. 3 | |
| Quaedam ergo speculabilium sunt, quae dependent a materia secundum esse, quia non nisi in materia esse possunt. Et haec distinguuntur, quia quaedam dependent a materia secundum esse et intellectum, sicut illa, in quorum diffinitione ponitur materia sensibilis; unde sine materia sensibili intelligi non possunt, ut in diffinitione hominis oportet accipere carnem et ossa. Et de his est physica sive scientia naturalis. Quaedam vero sunt, quae quamvis dependeant a materia secundum esse, non tamen secundum intellectum, quia in eorum diffinitionibus non ponitur materia sensibilis, sicut linea et numerus. Et de his est mathematica. | (1) Now there are some objects of speculation that depend on matter for their being, for they can exist only in matter. And these are subdivided. (a) Some depend on matter both for their being (+) and for their being understood, as do those things whose definition contains sensible matter and which, as a consequence, cannot be understood without sensible matter. For example, it is necessary to include flesh and bones in the definition of man. It is things of this sort that physics or natural science studies. (b) On the other hand, there are some things that, although dependent upon matter for their being, do not depend upon it (~) for their being understood, because sensible matter is not included in their definitions. This is the case with lines and numbers - the kind of objects with which mathematics deals. |
| Quaedam vero speculabilia sunt, quae non dependent a materia secundum esse, quia sine materia esse possunt, sive numquam sint in materia, sicut Deus et Angelus, sive in quibusdam sint in materia et in quibusdam non, ut substantia, qualitas, ens, potentia, actus, unum et multa et huiusmodi. De quibus omnibus est theologia, id est scientia divina, quia praecipuum in ea cognitorum est Deus, quae alio nomine dicitur metaphysica, id est trans physicam, quia post physicam discenda occurrit nobis, quibus ex sensibilibus oportet in insensibilia devenire. Dicitur etiam philosophia prima, in quantum aliae omnes scientiae ab ea sua principia accipientes eam consequuntur. Non est autem possibile quod sint aliquae res quae secundum intellectum dependeant a materia et non secundum esse, quia intellectus, quantum est de se, immaterialis est. Et ideo non est quartum genus philosophiae praeter praedicta. | (2) There are still other objects of speculative knowledge that do not depend upon matter(~) for their being, because they can exist without matter; (a) either they never exist in matter, as in the case of God and the angels, or (b) they exist in matter in some instances and not in others, as in the case of substance, quality, being, potency, act, one and many, and the like. The science that treats of all these is theology or divine science, which is so called because its principal object is God. By another name it is called metaphysics; that is to say, "beyond physics", because it ought to be learned by us after physics; for we have to proceed from sensible things to those that are non-sensible. It is also called first philosophy, inasmuch as all the other sciences, receiving their principles from it, come after it. Now there can be nothing that depends upon matter for its being understood but not for its being, because by it; very nature the intellect is immaterial. So there is no fourth kind of philosophy besides the ones mentioned. |
| Pars 3 q. 5 a. 1 ad 1 | |
| Ad primum ergo dicendum quod philosophus in VI Ethicorum determinat de habitibus intellectualibus, in quantum sunt virtutes intellectuales. Dicuntur autem virtutes, in quantum perficiunt in sua operatione. Virtus enim est quae bonum facit habentem et opus eius bonum reddit; et ideo secundum quod diversimode perficitur per huiusmodi habitus speculativos, diversificat huiusmodi virtutes. Est autem alius modus quo pars animae speculativa perficitur per intellectum, qui est habitus principiorum, quo aliqua ex se ipsis nota fiunt et quo cognoscuntur conclusiones ex huiusmodi principiis demonstratae, sive demonstratio procedat ex causis inferioribus, sicut est in scientia, sive ex causis altissimis, ut in sapientia. Cum autem distinguuntur scientiae ut sunt habitus quidam, oportet quod penes obiecta distinguantur, id est penes res, de quibus sunt scientiae. Et sic distinguuntur hic et in VI metaphysicae tres partes philosophiae speculativae. | Reply to 1. ln the Ethics the Philosopher considers the intellectual habits insofar as they are intellectual virtues. Now they are called virtues because they perfect the intellect in its operation; for "virtue makes its possessor good and renders his work good." So he distinguishes between virtues of this sort in as much as speculative habits perfect the intellect in different ways. In one way the speculative part of the soul is perfected by understanding, which is the habit of principles, through which some things become known of themselves. In another way it is perfected by a habit through which conclusions demonstrated from these principles are known, whether the demonstration proceeds from inferior causes, as in science, or from the highest causes, as in wisdom. But when sciences are differentiated insofar as they are habits, they must be distinguished according to their objects, that is, according to the things of which the sciences treat. And it is in this way that both here and in the Metaphysics speculative philosophy is distinguished into three parts. |
| Pars 3 q. 5 a. 1 ad 2 | |
| Ad secundum dicendum quod scientiae speculativae, ut patet in principio metaphysicae, sunt de illis quorum cognitio quaeritur propter se ipsa. Res autem, de quibus est logica, non quaeruntur ad cognoscendum propter se ipsas, sed ut adminiculum quoddam ad alias scientias. Et ideo logica non continetur sub speculativa philosophia quasi principalis pars, sed sicut quiddam reductum ad philosophiam speculativam, prout ministrat speculationi sua instrumenta, scilicet syllogismos et diffinitiones et alia huiusmodi, quibus in scientiis speculativis indigemus. Unde secundum Boethium in commento super Porphyrium non tam est scientia quam scientiae instrumentum. | Reply to 2. As is evident in the beginning of the Metaphysics, the speculative sciences concern things the knowledge of which is sought for their own sake. However, we do not seek to know the things studied by logic for themselves, but as a help to the other sciences. So logic is not included under speculative philosophy as a principal part but as something brought under speculative philosophy as furnishing speculative thought with its instruments, namely, syllogisms, definitions, and the like, which we need in the speculative sciences. Thus, according to Boethius, logic is not so much a science as the instrument of science. |
| Pars 3 q. 5 a. 1 ad 3 | |
| Ad tertium dicendum quod septem liberales artes non sufficienter dividunt philosophiam theoricam, sed ideo, ut dicit Hugo de sancto Victore in III sui didascalicon, praetermissis quibusdam aliis septem connumerantur, quia his primum erudiebantur, qui philosophiam discere volebant, et ideo distinguuntur in trivium et quadrivium, eo quod his quasi quibusdam viis vivax animus ad secreta philosophiae introeat. Et hoc etiam consonat verbis philosophi qui dicit in II metaphysicae quod modus scientiae debet quaeri ante scientias; et Commentator ibidem dicit quod logicam, quae docet modum omnium scientiarum, debet quis addiscere ante omnes alias scientias, ad quam pertinet trivium. Dicit etiam in VI Ethicorum quod mathematica potest sciri a pueris, non autem physica, quae experimentum requirit. Et sic datur intelligi quod post logicam consequenter debet mathematica addisci, ad quam pertinet quadrivium; et ita his quasi quibusdam viis praeparatur animus ad alias philosophicas disciplinas. Vel ideo hae inter ceteras scientias artes dicuntur, quia non solum habent cognitionem, sed opus aliquod, quod est immediate ipsius rationis, ut constructionem syllogismi vel orationem formare, numerare, mensurare, melodias formare et cursus siderum computare. | Reply to 3. The seven liberal arts do not adequately divide theoretical philosophy; but, as Hugh of St. Victor says, seven arts are grouped together (leaving out certain other ones), because those who wanted to learn philosophy were first instructed in them. And the reason why they are divided into the trivium and quadrivium is that "they are as it were paths (viae) introducing the quick mind to the secrets of philosophy." This is also in harmony with the Philosopher’s statement in the Metaphysics that we must investigate the method of scientific thinking before the sciences themselves. And the Commentator says in the same place that before all the other sciences a person should learn logic, which teaches the method of all the sciences; and the trivium concerns logic. The Philosopher also says in the Ethics that the young can know mathematics but not physics, because it requires experience. So we are given to understand that after logic we should learn mathematics, which the quadrivium concerns. These, then, are like paths leading the mind to the other philosophical disciplines. We may add that among the other sciences these are called arts because they involve not only knowledge but also a work that is directly a product of reason itself; for example, producing a composition, syllogism or discourse, numbering, measuring, composing melodies, and reckoning the course of the stars. |
| Aliae vero scientiae vel non habent opus, sed cognitionem tantum, sicut scientia divina et naturalis; unde nomen artis habere non possunt, cum ars dicatur ratio factiva, ut dicitur in VI metaphysicae. Vel habent opus corporale, sicut medicina, alchimia et aliae huiusmodi. Unde non possunt dici artes liberales, quia sunt hominis huiusmodi actus ex parte illa, qua non est liber, scilicet ex parte corporis. Scientia vero moralis, quamvis sit propter operationem, tamen illa operatio non est actus scientiae, sed magis virtutis, ut patet in libro Ethicorum. Unde non potest dici ars, sed magis in illis operationibus se habet virtus loco artis. Et ideo veteres diffinierunt virtutem esse artem bene recteque vivendi, ut Augustinus dicit in IV de civitate Dei. | Other sciences (such as divine and natural science) either do not involve a work produced but only knowledge, and so we cannot call them arts, because, as the Metaphysics says, art is "productive reason"; or they involve some bodily activity, as in the case of medicine, alchemy, and other sciences of this kind. These latter, then, cannot be called liberal arts because such activity belongs to man on the side of his nature in which he is not free, namely, on the side of his body. And although moral science is directed to action, still that action is not the act of the science but rather of virtue, as is clear in the Ethics. So we cannot call moral science an art; but rather in these actions virtue takes the place of art. Thus, as Augustine says, the ancients defined virtue as the art of noble and well-ordered living. |
| Pars 3 q. 5 a. 1 ad 4 | |
| Ad quartum dicendum quod, sicut dicit Avicenna in principio suae medicinae, aliter distinguitur theoricum et practicum, cum philosophia dividitur in theoricam et practicam, aliter cum artes dividuntur in theoricas et practicas, aliter cum medicina. Cum enim philosophia vel etiam artes per theoricum et practicum distinguuntur, oportet accipere distinctionem eorum ex fine, ut theoricum dicatur illud, quod ordinatur ad solam cognitionem veritatis, practicum vero, quod ordinatur ad operationem. Hoc tamen interest, cum in hoc dividitur philosophia totalis et artes, quod in divisione philosophiae habetur respectus ad finem beatitudinis, ad quem tota humana vita ordinatur. Ut enim dicit Augustinus XX de civitate Dei ex verbis Varronis, nulla est homini alia causa philosophandi nisi ut beatus sit. Unde cum duplex felicitas a philosophis ponatur, una contemplativa et alia activa, ut patet in X Ethicorum, secundum hoc etiam duas partes philosophiae distinxerunt, moralem dicentes practicam, naturalem et rationalem dicentes theoricam. Cum vero dicuntur artium quaedam esse speculativae, quaedam practicae, habetur respectus ad aliquos speciales fines illarum artium, sicut si dicamus agriculturam esse artem practicam, dialecticam vero theoricam. Cum autem medicina dividitur in theoricam et practicam, non attenditur divisio secundum finem. Sic enim tota medicina sub practica continetur, utpote ad operationem ordinata. | Reply to 4. As Avicenna says, the distinction between theoretical and practical is not the same when philosophy is divided into theoretical and practical, when the arts are divided into theoretical and practical, and when medicine is so divided. For when we distinguish philosophy or the arts into theoretical and practical we must do so on the basis of their end, calling that theoretical which is directed solely to knowledge of the truth, and that practical which is directed to operation. However, there is this difference when we distinguish the whole of philosophy and the arts on this basis. We divide philosophy with respect to the final end or happiness, to which the whole of human life is directed. For, as Augustine says, following Varro, "There is no other reason for a man philosophizing except to be happy." And since the philosophers teach that there is a twofold happiness, one contemplative and the other active, as is clear in the Ethics, they have accordingly a]so distinguished between two parts of philosophy, calling moral philosophy practical and natural and rational philosophy theoretical. But when they call some arts speculative and some practical, this is on the basis of some special ends of those arts; as when we say that agriculture is a Practical art but dialectic is theoretical. However, when we divide medicine into theoretical and practical, the division is not on the basis of the end. For on that basis the whole of medicine is practical, since it is directed to practice. |
| Sed attenditur praedicta divisio secundum quod ea, quae in medicina tractantur, sunt propinqua vel remota ab operatione. Illa enim pars medicinae dicitur practica, quae docet modum operandi ad sanationem, sicut quod talibus apostematibus sunt talia remedia adhibenda, theorica vero illa pars, quae docet principia, ex quibus homo dirigitur in operatione, sed non proxime, sicut quod virtutes sunt tres et quod genera febrium sunt tot. Unde non oportet, ut si alicuius activae scientiae aliqua pars dicatur theorica, quod propter hoc illa pars sub philosophia speculativa ponatur. | But the above division is made on the basis of whether what is studied in medicine is proximate to, or remote from practice. Thus we call that part of medicine practical which teaches the method of healing; for instance, that these particular medicines should be given for these abscesses. On the other hand, we call that part theoretical which teaches the principles directing a man in his practice, although not immediately; for instance, that there are three virtues, and that there are so many kinds of fever. Consequently, if we call some part of a practical science theoretical, we should not on that account place that part under speculative philosophy. |
| Pars 3 q. 5 a. 1 ad 5 | |
| Ad quintum dicendum quod aliqua scientia continetur sub alia dupliciter, uno modo ut pars ipsius, quia scilicet subiectum eius est pars aliqua subiecti illius, sicut planta est quaedam pars corporis naturalis; unde et scientia de plantis continetur sub scientia naturali ut pars. Alio modo continetur una scientia sub alia ut ei subalternata, quando scilicet in superiori scientia assignatur propter quid eorum, de quibus scitur in scientia inferiori solum quia, sicut musica ponitur sub arithmetica. Medicina ergo non ponitur sub physica ut pars. Subiectum enim medicinae non est pars subiecti scientiae naturalis secundum illam rationem, qua est subiectum medicinae. Quamvis enim corpus sanabile sit corpus naturale, non tamen est subiectum medicinae, prout est sanabile a natura, sed prout est sanabile ab arte. | Reply to 5. One science is contained under another in two ways: in one way, as its part, because its subject is part of the subject of that other science, as plant is part of natural body. So the science of plants is also contained under natural science as one of its parts. In another way, one science is contained under another as subalternated to it. This occurs when in a higher science there is given the reason for what a lower science knows only as a fact. This is how music is contained under arithmetic. Medicine, therefore, is not contained under physics as a part, for the subject of medicine is not part of the subject of natural science from the point of view from which it is the subject of medicine. For although the curable body is a natural body, it is not the subject of medicine insofar as it is curable by nature, but insofar as it is curable by art. |
| Sed quia in sanatione, quae fit etiam per artem, ars est ministra naturae, quia ex aliqua naturali virtute sanitas perficitur auxilio artis, inde est quod propter quid de operatione artis oportet accipere ex proprietatibus rerum naturalium. Et propter hoc medicina subalternatur physicae, et eadem ratione alchimia et scientia de agricultura et omnia huiusmodi. Et sic relinquitur quod physica secundum se et secundum omnes partes suas est speculativa, quamvis aliquae scientiae operativae subalternentur ei. | But because art is nature’s handmaid in healing (in which art too plays a part, for health is brought about through the power of nature with the assistance of art), it follows that the reason for the practices used in the art must be based on the properties of natural things. So medicine is subalternated to physics, and for the same reason so too are alchemy, the science of agriculture, and all sciences of this sort. We conclude, then, that physics in itself and in all its parts is speculative, although some practical sciences are subalternated to it. |
| Pars 3 q. 5 a. 1 ad 6 | |
| Ad sextum dicendum quod quamvis subiecta aliarum scientiarum sint partes entis, quod est subiectum metaphysicae, non tamen oportet quod aliae scientiae sint partes ipsius. Accipit enim unaquaeque scientiarum unam partem entis secundum specialem modum considerandi alium a modo, quo consideratur ens in metaphysica. Unde proprie loquendo subiectum illius non est pars subiecti metaphysicae; non enim est pars entis secundum illam rationem, qua ens est subiectum metaphysicae, sed hac ratione considerata ipsa est specialis scientia aliis condivisa. Sic autem posset dici pars ipsius scientia, quae est de potentia vel quae est de actu aut de uno vel de aliquo huiusmodi, quia ista habent eundem modum considerandi cum ente, de quo tractatur in metaphysica. | Reply to 6. Although the subjects of the other sciences are parts of being, which is the subject of metaphysics, the other sciences are not necessarily parts of metaphysics. For each science treats of one part of being in a special way distinct from that in which metaphysics treats of being. So its subject is not properly speaking a part of the subject of metaphysics, for it is not a part of being from the point of view from which being is the subject of metaphysics; from this viewpoint it is a special science distinct from the others. However, the science treating of potency, or that treating of act or unity or anything of this sort, could be called a part of metaphysics because these are considered in the same manner as being, which is the subject of metaphysics. |
| Pars 3 q. 5 a. 1 ad 7 | |
| Ad septimum dicendum quod illae partes entis exigunt eundem modum tractandi cum ente communi, quia etiam ipsa non dependent ad materiam, et ideo scientia de ipsis non distinguitur a scientia quae est de ente communi. | Reply to 7. These parts of being require the same manner of consideration as being-in-general (ens commune) because they too are independent of matter. For this reason the science dealing with them is not distinct from the science of being-in-general. |
| Pars 3 q. 5 a. 1 ad 8 | |
| Ad octavum dicendum quod aliae diversitates rerum, quas obiectio tangit, non sunt differentiae per se earum in quantum sunt scibiles; et ideo penes eas scientiae non distinguuntur. | Reply to 8. The other diversities of things mentioned in the objection do not differentiate those things essentially as objects of knowledge. So the sciences are not distinguished according to them. |
| Pars 3 q. 5 a. 1 ad 9 | |
| Ad nonum dicendum quod quamvis scientia divina sit prima omnium scientiarum naturaliter, tamen quoad nos aliae scientiae sunt priores. Ut enim dicit Avicenna in principio suae metaphysicae, ordo huius scientiae est, ut addiscatur post scientias naturales, in quibus sunt multa determinata, quibus ista scientia utitur, ut generatio, corruptio, motus et alia huiusmodi. Similiter etiam post mathematicas. Indiget enim haec scientia ad cognitionem substantiarum separatarum cognoscere numerum et ordinem orbium caelestium, quod non est possibile sine astrologia, ad quam tota mathematica praeexigitur. Aliae vero scientiae sunt ad bene esse ipsius, ut musica et morales vel aliae huiusmodi. | Reply to 9. Although divine science is by nature the first of all the sciences, with respect to us the other sciences come before it. For as Avicenna says, the position Or this science is that it be learned after the natural sciences, which explain many things used by metaphysics, such as generation, corruption, motion, and the like. It should also be learned after mathematics, because to know the separate substances metaphysics has to know the number and disposition of the heavenly spheres, and this is impossible without astronomy, which presupposes the whole of mathematics. Other sciences, such as music, ethics, and the like, contribute to its fullness of perfection. |
| Nec tamen oportet quod sit circulus, quia ipsa supponit ea, quae in aliis probantur, cum ipsa aliarum principia probet, quia principia, quae accipit alia scientia, scilicet naturalis, a prima philosophia, non probant ea quae item philosophus primus accipit a naturali, sed probantur per alia principia per se nota; et similiter philosophus primus non probat principia, quae tradit naturali, per principia quae ab eo accipit, sed per alia principia per se nota. Et sic non est aliquis circulus in diffinitione. Praeterea, effectus sensibiles, ex quibus procedunt demonstrationes naturales, sunt notiores quoad nos in principio, sed cum per eos pervenerimus ad cognitionem causarum primarum, ex eis apparebit nobis propter quid illorum effectuum, ex quibus probabantur demonstratione quia. Et sic et scientia naturalis aliquid tradit scientiae divinae, et tamen per eam sua principia notificantur. Et inde est quod Boethius ultimo ponit scientiam divinam, quia est ultima quoad nos. | Nor is there necessarily a vicious circle because metaphysics presupposes conclusions proved in the other sciences while it itself proves their principles. For the principles that another science (such as natural philosophy) takes from first philosophy do not prove the points which the first philosopher takes from the natural philosopher, but they are proved through other self-evident principles. Similarly the first philosopher does not prove the principles he gives the natural philosopher by principles he receives from him, but by other self-evident principles. So there is no vicious circle in their definitions. Moreover, the sensible effects on which the demonstrations of natural science are based are more evident to us in the beginning. But when we come to know the first causes through them, these causes will reveal to us the reason for the effects, from which they were proved by a demonstration quia. In this way natural science also contributes something to divine science, and nevertheless it is divine science that explains its principles. That is why Boethius places divine science last, because it is the last relative to us. |
| Pars 3 q. 5 a. 1 ad 10 | |
| Ad decimum dicendum quod quamvis naturalis post mathematicam addiscenda occurrat, ex eo quod universalia ipsius documenta indigent experimento et tempore, tamen res naturales, cum sint sensibiles, sunt naturaliter magis notae quam res mathematicae a sensibili materia abstractae. | Reply to 10. Although we should learn natural science after mathematics because the general proofs of natural science require experience and time, still, since natural things fall under the senses, they are by nature better known than the mathematical entities abstracted from sensible matter. |
| Articulus 2 | ARTICLE TWO Does Natural Philosophy Treat of What Exists in Motion and Matter? |
| Pars 3 q. 5 a. 2 arg. 1 | |
| Ad secundum sic proceditur. Videtur quod scientia naturalis non sit de his quae sunt in motu et materia. Materia enim est individuationis principium. Sed nulla scientia est de individuis, sed de solis universalibus, secundum sententiam Platonis, quae ponitur in Porphyrio. Ergo scientia naturalis non est de his quae sunt in materia. | We proceed as follows to the second article: It seems that natural science does not treat of things that exist in motion and matter, for 1. Matter is the principle of individuation, Now, according to Plato’s doctrine, which is followed by Porphyry, no science treats of individual things but only of universals. Therefore, natural science does not treat of what is in matter. |
| Pars 3 q. 5 a. 2 arg. 2 | |
| Praeterea, scientia ad intellectum pertinet. Sed intellectus cognoscit abstrahendo a materia et a condicionibus materiae. Ergo de his, quae non sunt a materia abstracta, nulla scientia esse potest. | 2. Again, science pertains to the intellect. But the intellect knows by abstracting from matter and from the conditions of matter. Therefore, no science can treat of what is not abstracted from matter. |
| Pars 3 q. 5 a. 2 arg. 3 | |
| Praeterea, in scientia naturali agitur de primo motore, ut patet in VIII physicorum. Sed ipse est immunis ab omni materia. Ergo scientia naturalis non est de his solis quae sunt in materia. | 3. Again, as is clear in the Physics, the First Mover is considered in natural science. But The First Mover is free from all matter. Therefore, natural science does not treat only of what is in matter. |
| Pars 3 q. 5 a. 2 arg. 4 | |
| Praeterea, omnis scientia de necessariis est. Sed omne quod movetur, in quantum huiusmodi, est contingens, ut probatur in IX metaphysicae. Ergo nulla scientia potest esse de rebus mobilibus, et sic nec scientia naturalis. | 4. Again, every science has to do with what is necessary. But whatever is moved, as such is contingent, as is proved in the Metaphysics. Therefore, no science can treat of what is subject to motion; and so neither can natural science. |
| Pars 3 q. 5 a. 2 arg. 5 | |
| Praeterea, nullum universale movetur; homo enim universalis non sanatur, sed hic homo, ut dicitur in principio metaphysicae. Sed omnis scientia de universalibus est. Ergo naturalis scientia non est de his quae sunt in motu. | 5. Again, no universal is subject to motion; for as is said in the beginning of the Metaphysics, it is not man in general who is healed, but this man. But every science concerns that which is universal. Therefore natural science does not treat of what is in motion. |
| Pars 3 q. 5 a. 2 arg. 6 | |
| Praeterea, in scientia naturali determinatur de quibusdam quae non moventur, sicut est anima, ut probatur in I de anima, et terra, ut probatur in II caeli et mundi; et etiam omnes formae naturales non fiunt nec corrumpuntur, et eadem ratione non moventur nisi per accidens, ut probatur in VII metaphysicae. Ergo non omnia, de quibus est physica, sunt in motu. | 6. Again, some of the things with which natural science deals are not subject to motion; for instance, the soul, as is shown in De Anima, and the earth, as is proved in the De Caelo et Mundo. What is more, all natural forms neither come into being nor perish, and for the same reason they are not subject to motion, except accidentally. This is shown in the Metaphysics. Therefore everything that physics considers is in motion. |
| Pars 3 q. 5 a. 2 arg. 7 | |
| Praeterea, omnis creatura est mutabilis, cum vera immutabilitas soli Deo conveniat, ut Augustinus dicit. Si ergo ad naturalem pertinet consideratio de his, quae in motu sunt, eius erit considerare de omnibus creaturis, quod apparet expresse esse falsum. | 7. Again, every creature is mutable for, as Augustine says, true immutability belongs to God alone. So if it is the task of natural science to consider what is in motion, it will be its business to consider all creatures, which clearly appears to be false. |
| Pars 3 q. 5 a. 2 s. c. 1 | |
| Sed contra, ad scientiam naturalem pertinet de rebus naturalibus determinare. Sed res naturales sunt, in quibus est principium motus. Ubicumque autem est motus, oportet et esse materiam, ut dicitur in IX metaphysicae. Ergo scientia naturalis est de his quae sunt in motu et materia. | On the contrary, it is the work of natural science to reach conclusions about natural things. Now, natural things are those in which there is a principle of motion; and, as the Metaphysics says, wherever there is motion there must be matter. So natural science treats of what is in motion and matter. |
| Pars 3 q. 5 a. 2 s. c. 2 | |
| Praeterea, de his, quae sunt in materia et motu, oportet esse aliquam scientiam speculativam, alias non esset perfecta traditio philosophiae quae est cognitio entis. Sed nulla alia speculativa scientia est de his, quia neque mathematica nec metaphysica. Ergo est de his naturalis. | Moreover, these must be some speculative science dealing with what is in matter and motion, for otherwise the teaching of philosophy, which is knowledge of being, would be incomplete. Now no other speculative science treats of these things, for neither mathematics nor metaphysics does so. Therefore, natural science treats of them. |
| Pars 3 q. 5 a. 2 s. c. 3 | |
| Praeterea, hoc apparet ex hoc quod dicit philosophus in VI metaphysicae et in II physicorum. | Moreover, the fact is clear from the statements of the Philosopher in the Metaphysics and the Physics. |
| Pars 3 q. 5 a. 2 co. 1 | |
| Responsio. Dicendum quod propter difficultatem huius quaestionis coactus est Plato ad ponendum ideas. Cum enim, ut dicit philosophus in I metaphysicae, crederet omnia sensibilia semper esse in fluxu, secundum opinionem Cratyli et Heracliti, et ita existimaret de eis non posse esse scientiam, posuit quasdam substantias a sensibilibus separatas, de quibus essent scientiae et darentur diffinitiones. Sed hic defectus accidit ex eo quod non distinxit quod est per se ab eo quod est secundum accidens, nam secundum accidens falluntur plerumque etiam sapientes, ut dicitur in I elenchorum. Ut autem probatur in VII metaphysicae, cum in substantia sensibili inveniatur et ipsum integrum, id est compositum, et ratio, id est forma eius, per se quidem generatur et corrumpitur compositum, non autem ratio sive forma, sed solum per accidens. Non enim fit domum esse, ut ibidem dicitur, sed hanc domum. | Reply: It was the difficulty of this problem that drove Plato to posit Ideas. Believing that all sensible things were always in flux, as Cratylus and Heraclitus taught, he thought there can be no science concerning them, as the Philosopher says in the Metaphysics. So he claimed that there were substances separated from the sense world, which might serve as the objects of science and of definitions. He made this mistake because he failed to distinguish what is essential from what is accidental. For it happens that by accident even the wise often fall into error, as is said in the Sophistic Refutations. Now, as is shown in the Metaphysics, we find in a sensible substance both the whole or the composite itself, and also its nature (ratio) or form; and it is the composite that is essentially generated and corrupted and not the nature or form, except accidentally. As the Metaphysics says, "It is not house that is made, but this house. |
| Unumquodque autem potest considerari sine omnibus his quae ei non per se comparantur. Et ideo formae et rationes rerum quamvis in motu exsistentium, prout in se considerantur, absque motu sunt. Et sic de eis sunt scientiae et diffinitiones, ut ibidem philosophus dicit. Non autem scientiae sensibilium substantiarum fundantur super cognitione aliquarum substantiarum a sensibilibus separatarum, ut ibidem probatur. | Now anything can be thought of without all the items that are not essentially related to it. Consequently, forms and natures, though belonging to things existing in motion, are without motion when they are considered in themselves; and so they can be the objects of sciences and of definitions, as the Philosopher says. As he proves, the sciences of sensible reality are not based upon the knowledge of certain substances separated from the sense world. |
| Pars 3 q. 5 a. 2 co. 2 | |
| Huiusmodi autem rationes, quas considerant scientiae quae sunt de rebus, considerantur absque motu. Sic oportet quod considerentur absque illis, secundum quae competit motus rebus mobilibus. Cum autem omnis motus tempore mensuretur et primus motus sit motus localis, quo remoto nullus alius motus inest, oportet quod secundum hoc aliquid sit mobile, quod est hic et nunc. Hoc autem consequitur rem ipsam mobilem, secundum quod est individuata per materiam exsistentem sub dimensionibus signatis. | Natures of this kind, which are the objects of the sciences of real beings, are thought of without motion; and so they must be thought of without those conditions by reason of which motion belongs to mobile things. Now, because every motion is measured by time, and the primary motion is local motion (for without it there is no other motion), a thing must be subject to motion inasmuch as it exists here and now; and it exists under these conditions insofar as it is individuated by matter having determinate dimensions. |
| Unde oportet quod huiusmodi rationes, secundum quas de rebus mobilibus possunt esse scientiae, considerantur absque materia signata et absque omnibus his quae consequuntur materiam signatam, non autem absque materia non signata, quia ex eius notione dependet notio formae quae determinat sibi materiam. Et ideo ratio hominis, quam significat diffinitio et secundum quam procedit scientia, consideratur sine his carnibus et sine his ossibus, non autem sine carnibus et ossibus absolute. Et quia singularia includunt in sui ratione materiam signatam, universalia vero materiam communem, ut dicitur in VII metaphysicae, ideo praedicta abstractio non dicitur formae a materia absolute, sed universalis a particulari. | Consequently, natures of this kind, which make possible sciences of things subject to motion, must be thought of without determinate matter and everything following upon such matter; but not without indeterminate matter, because on its notion depends the notion of form that determines matter to itself. Thus the nature of man, which his definition signifies and which is the object of science, is considered without this flesh and these bones, but not absolutely without flesh and bones. And because individuals include determinate matter in their nature, whereas universals include common matter, as is said in the Metaphysics, the above-mentioned abstraction is not said to be the abstraction of form from matter absolutely, but the abstraction of the universal from the particular. |
| Pars 3 q. 5 a. 2 co. 3 | |
| Possunt ergo huiusmodi rationes sic abstractae considerari dupliciter. Uno modo secundum se, et sic considerantur sine motu et materia signata, et hoc non invenitur in eis nisi secundum esse quod habent in intellectu. Alio modo secundum quod comparantur ad res, quarum sunt rationes; quae quidem res sunt in materia et motu. Et sic sunt principia cognoscendi illa, quia omnis res cognoscitur per suam formam. Et ita per huiusmodi rationes immobiles et sine materia particulari consideratas habetur cognitio in scientia naturali de rebus mobilibus et materialibus extra animam exsistentibus. | Natures of this sort, thus abstracted, can be considered in two ways. First, in themselves; and then they are thought of without motion and determinate matter. This happens to them only by reason of the being they have in the intellect. Second, they can be viewed in relation to the things of which they are the natures; and these things exist with matter and motion. Thus they are principles by which we know these things, for everything is known through its form. Consequently, in natural science we know mutable and material things existing outside the soul through natures of this kind; that is to say, natures that are immobile and considered without particular matter. |
| Pars 3 q. 5 a. 2 ad 1 | |
| Ad primum ergo dicendum quod materia non est individuationis principium nisi secundum quod est sub dimensionibus signatis exsistens. Et sic etiam scientia naturalis a materia abstrahit. | Reply to 1. Matter is the principle of individuation only insofar as it exists with determinate dimensions, and in this sense natural science indeed abstracts from matter. |
| Pars 3 q. 5 a. 2 ad 2 | |
| Ad secundum dicendum quod forma intelligibilis est quiditas rei. Obiectum enim intellectus est quid, ut dicitur in III de anima. Quiditas autem compositi universalis, ut hominis aut animalis, includit in se materiam universalem, non autem particularem, ut dicitur in VII metaphysicae. Unde intellectus communiter abstrahit a materia signata et condicionibus eius, non autem a materia communi in scientia naturali, quamvis etiam in scientia naturali non consideretur materia nisi in ordine ad formam. Unde etiam forma per prius est de consideratione naturalis quam materia. | Reply to 2. The intelligible form is a thing’s quiddity, for, as the De Anima says, the object of the intellect is the quiddity of a thing. Now, as is said in the Metaphysics, the quiddity of a universal composite, like man or animal, includes within itself common but not particular matter. So the intellect regularly abstracts from determinate matter and its conditions; but in natural science it does not abstract from common matter, although matter itself is considered in natural science only in relation to form. For this reason the natural scientist is more concerned with form than with matter. |
| Pars 3 q. 5 a. 2 ad 3 | |
| Ad tertium dicendum quod de primo motore non agitur in scientia naturali tamquam de subiecto vel de parte subiecti, sed tamquam de termino ad quem scientia naturalis perducit. Terminus autem non est de natura rei, cuius est terminus, sed habet aliquam habitudinem ad rem illam, sicut terminus lineae non est linea, sed habet ad eam aliquam habitudinem, ita etiam et primus motor est alterius naturae a rebus naturalibus, habet tamen ad eas aliquam habitudinem, in quantum influit eis motum, et sic cadit in consideratione naturalis, scilicet non secundum ipsum, sed in quantum est motor. | Reply to 3. Natural science does not treat of the First Mover as its subject or as part of its subject, but as the end to which natural science leads. Now the end does not belong to the nature of the thing of which it is the end, but it has a relation to it; as the end of a line is not the line but is related to it. So also the First Mover is of a different nature from natural things, but it is related to them because it moves them. So it falls under the consideration of natural science, not in itself, but insofar as it is a mover. |
| Pars 3 q. 5 a. 2 ad 4 | |
| Ad quartum dicendum quod scientia est de aliquo dupliciter. Uno modo primo et principaliter, et sic scientia est de rationibus universalibus, supra quas fundatur. Alio modo est de aliquibus secundario et quasi per reflexionem quandam, et sic de illis rebus, quarum sunt illae rationes, in quantum illas rationes applicat ad res etiam particulares, quarum sunt, adminiculo inferiorum virium. Ratione enim universali utitur sciens et ut re scita et ut medio sciendi. Per universalem enim hominis rationem possum iudicare de hoc vel de illo. Rationes autem universales rerum omnes sunt immobiles, et ideo quantum ad hoc omnis scientia de necessariis est. Sed rerum, quarum sunt illae rationes, quaedam sunt necessariae et immobiles, quaedam contingentes et mobiles, et quantum ad hoc de rebus contingentibus et mobilibus dicuntur esse scientiae. | Reply to 4. Science treats of something in two ways: in one way, primarily and principally; and in this sense science is concerned universal natures, which are its very foundation. In another way it treats of something secondarily, as by a sort of reflection; and in this sense it is concerned with the things whose natures they are, inasmuch as, using the lower powers, it relates those natures to the particular things possessing them. For a knower uses a universal nature both as a thing known and as a means of knowing. Thus, through the universal nature of man we can judge of this or that particular man. Now, all universal natures of things are immutable; and so, in this respect, all science is concerned with what is necessary. But some of the things possessing these natures are necessary and immutable, whereas others are contingent and subject to movement, and in this respect sciences are said to be concerned with the contingent and mutable. |
| Pars 3 q. 5 a. 2 ad 5 | |
| Ad quintum dicendum quod quamvis universale non moveatur, est tamen ratio rei mobilis. | Reply to 5. Although a universal is not mutable, it is nevertheless the nature of a mutable thing. |
| Pars 3 q. 5 a. 2 ad 6 | |
| Ad sextum dicendum quod anima et aliae formae naturales, quamvis non moveantur per se, moventur tamen per accidens, et insuper sunt perfectiones rerum mobilium, et secundum hoc cadunt in consideratione naturalis. Terra vero, quamvis secundum totum non moveatur, quod accidit ei, in quantum est in suo loco naturali, in quo aliquid quiescit per eandem naturam, per quam movetur ad locum, tamen partes eius moventur ad locum, cum sunt extra locum proprium. Et sic terra et ratione quietis totius et ratione motus partium cadit in considerationem naturalis. | Reply to 6. Although the soul and other natural forms are not themselves subject to motion, they are moved accidentally, and they are, moreover, the perfections of mutable things; and for this reason they come within the domain of natural science. But even though the earth as a whole is not moved (for it happens to be in its natural place, where a thing is at rest in virtue of the same nature through which it is moved to a place), nevertheless, when its parts are outside their proper place, they are moved to a place. Thus the earth falls within the domain of natural science both by reason of the immobility of the whole earth and by reason of the movement of its parts. |
| Pars 3 q. 5 a. 2 ad 7 | |
| Ad septimum dicendum quod mutabilitas illa, quae competit omni creaturae, non est secundum aliquem motum naturalem, sed secundum dependentiam ad Deum, a quo si sibi deserentur, deficerent ab eo quod sunt. Dependentia autem ista pertinet ad considerationem metaphysici potius quam naturalis. Creaturae etiam spirituales non sunt mutabiles nisi secundum electionem, et talis mutatio non pertinet ad naturalem, sed magis ad divinum. | Reply to 7. The mutability characteristic of all creatures is not with respect to any natural motion, but with respect to their dependence on God, separation from whom entails destruction of their very being. And that dependence falls under the consideration of metaphysics rather than under that of natural philosophy. Spiritual creatures, moreover, are mutable only with regard to choice; and this sort of motion is not the concern of the natural philosopher but rather of the metaphysician. |
| Articulus 3 | ARTICLE THREE Does Mathematics Treat, Without Motion and Matter, of What Exists in Matter? |
| Pars 3 q. 5 a. 3 arg. 1 | |
| Ad tertium sic proceditur. Videtur quod mathematica consideratio non sit sine materia de his quae habent esse in materia. Cum enim veritas consistat in adaequatione rei ad intellectum, oportet esse falsitatem, quandocumque res consideratur aliter quam sit. Si ergo res, quae sunt in materia, sine materia considerat mathematica, eius consideratio erit falsa, et sic non erit scientia, cum omnis scientia sit verorum. | We proceed as follows to the third article: It seems that mathematical thinking does not treat, without motion and matter, of what exists in matter, for: 1. Since truth consists in the conformity of thing to intellect, there must be falsehood whenever we think of something otherwise than it is. If then in mathematics we consider what is in matter in abstraction from matter, we will consider it falsely; and so mathematics will not be a science, for every science is concerned with what is true. |
| Pars 3 q. 5 a. 3 arg. 2 | |
| Praeterea, secundum philosophum in I posteriorum cuiuslibet scientiae est considerare subiectum et partes subiecti. Sed omnium materialium secundum esse materia pars est. Ergo non potest esse quod aliqua scientia consideret de his quae sunt in materia, absque hoc quod materiam consideret. | 2. Again, as the Philosopher states, every science has the task of considering a subject and the parts of the subject. Now in actual existence matter is a part of all material things. So it is impossible for a science to treat of what is in matter without treating of matter. |
| Pars 3 q. 5 a. 3 arg. 3 | |
| Praeterea, omnes lineae rectae sunt eiusdem speciei. Sed mathematicus considerat lineas rectas numerando eas, alias non consideraret triangulum et quadratum. Ergo considerat lineas, secundum quod differunt numero et conveniunt specie. Sed principium differendi his, quae secundum speciem conveniunt, est materia, ut ex supra dictis patet. Ergo materia consideratur a mathematico. | 3. Again, all straight lines are specifically the same. But the mathematician treats of straight lines by numbering them; otherwise he would not treat of the triangle and the square. It follows that he considers lines as specifically the same and numerically different. But it is clear from the above that matter is the principle differentiating things specifically the same. So the mathematician treats of matter. |
| Pars 3 q. 5 a. 3 arg. 4 | |
| Praeterea, nulla scientia, quae penitus abstrahit a materia, demonstrat per causam materialem. Sed in mathematica fiunt aliquae demonstrationes, quae non possunt reduci nisi ad causam materialem, sicut cum demonstratur aliquid de toto ex partibus. Partes enim sunt materia totius, ut dicitur in II physicorum. Unde et in II posteriorum reducitur ad causam materialem demonstratio, qua demonstratur quod angulus qui est in semicirculo est rectus ex hoc quod utraque pars eius est semirectus. Ergo mathematica non omnino abstrahit a materia. | 4. Again, no science completely abstracting from matter demonstrates through a material cause. But in mathematics some demonstrations are made which can only be reduced to a material cause, as when we demonstrate something about a whole by its parts. For, as the Physics says, parts are the matter of the whole. Thus in the Posterior Analytics the demonstration that the angle in a semi-circle is a right angle from the fact that each of its two parts is half of a right angle, is reduced to a material cause. Therefore, mathematics does not entirely abstract from matter. |
| Pars 3 q. 5 a. 3 arg. 5 | |
| Praeterea, motus non potest esse sine materia. Sed mathematicus debet considerare motum, quia cum motus mensuretur secundum spatium, eiusdem rationis et scientiae videtur esse considerare quantitatem spatii, quod pertinet ad mathematicum, et quantitatem motus. Ergo mathematicus non omnino dimittit considerationem materiae. | 5. Again, motion cannot exist without matter. But the mathematician ought to consider motion, because, since motion is measured relative to space, to consider the quantity of space, which pertains to the mathematician, and the quantity of motion, has the same nature and belongs to the same science. Therefore, the mathematician does not entirely leave matter out of consideration. |
| Pars 3 q. 5 a. 3 arg. 6 | |
| Praeterea, astrologia quaedam pars mathematicae est; et similiter scientia de sphaera mota et scientia de ponderibus et musica, in quibus omnibus fit consideratio de motu et rebus mobilibus. Ergo mathematica non abstrahit totaliter a materia et motu. | 6. Again, astronomy is a part of mathematics, and so too is the science of the moved sphere, the science of weights, and music, all of which treat of motion and mobile things So mathematics does not entirely abstract from matter and motion. |
| Pars 3 q. 5 a. 3 arg. 7 | |
| Praeterea, naturalis consideratio tota est circa materiam et motum. Sed quaedam conclusiones demonstrantur communiter a mathematico et naturali, ut utrum terra sit rotunda, et utrum sit in medio caeli. Ergo non potest esse quod mathematica omnino abstrahat a materia. Si dicatur quod abstrahit tantum a materia sensibili, contra. Materia sensibilis videtur esse materia particularis, quia sensus particularium est, a qua omnes scientiae abstrahunt. Ergo mathematica consideratio non debet dici magis abstracta quam aliqua aliarum scientiarum. | 7. Again, natural science is entirely concerned with matter and motion. But some conclusions are demonstrated alike by the mathematician and the natural scientist, for instance, whether the earth is round and whether it is in the middle of the universe. Therefore, mathematics cannot entirely abstract from matter. If it be said that mathematics abstracts only from sensible matter, the contrary seems true. Sensible matter seems to be particular matter, because what the senses perceive are particular things, and all the sciences abstract from this kind of matter. So mathematical thinking should not be called more abstract than that of the other sciences. |
| Pars 3 q. 5 a. 3 arg. 8 | |
| Praeterea, philosophus in II physicorum dicit tria esse negotia. Primum est de mobili et corruptibili, secundum de mobili et incorruptibili, tertium de immobili et incorruptibili. Primum autem est naturale, tertium divinum, secundum mathematicum, ut Ptolemaeus exponit in principio Almagesti. Ergo mathematica est de mobilibus. | 8. Again, the Philosopher says that there are three branches of study: the first concerns what is mutable and corruptible, the second what is mutable and incorruptible, and the third what is immutable and incorruptible. As Ptolemy explains, the first is natural science the third divine science, and the second mathematics. Therefore mathematics concerns what is mutable. |
| Pars 3 q. 5 a. 3 s. c. 1 | |
| Sed contra est quod philosophus dicit in VI metaphysicae. | To the contrary is the Philosopher’s statement in the Metaphysics. |
| Pars 3 q. 5 a. 3 s. c. 2 | |
| Praeterea, quaedam res sunt, quae quamvis sint in materia, tamen non recipiunt in sui diffinitione materiam, ut curvum, et in hoc differt a simo. Sed philosophia debet de omnibus entibus considerare. Ergo oportet de huiusmodi esse aliquam partem philosophiae, et haec est mathematica, cum ad nullam aliam pertineat. | Moreover, some things, although existing in matter, do not contain matter in their definition; for instance, curve, which differs in this respect from snub. Now philosophy should treat of all beings. Hence some part of philosophy must consider beings of this sort; and this is mathematics, for this does not belong to any other part. |
| Pars 3 q. 5 a. 3 s. c. 3 | |
| Praeterea, ea, quae sunt priora secundum intellectum, possunt sine posterioribus considerari. Sed mathematica sunt priora naturalibus, quae sunt in materia et motu; habent enim se ex additione ad mathematica, ut dicitur in III caeli et mundi. Ergo mathematica consideratio potest esse sine materia et motu. | Moreover, what is prior from the point of view of the intellect can be considered without what is posterior. Now mathematicals are prior to natural things existing in matter and motion, for the latter are so related to mathematicals that they add something to them, as is said in the De Caelo et Mundo. Therefore, mathematical investigation can be without matter and motion. |
| Pars 3 q. 5 a. 3 co. 1 | |
| Responsio. Dicendum quod ad evidentiam huius quaestionis oportet videre, qualiter intellectus secundum suam operationem abstrahere possit. | Reply: In order to throw light on this question we must understand how the intellect in its operation is able to abstract. |
| Sciendum est igitur quod secundum philosophum in III de anima duplex est operatio intellectus. Una, quae dicitur intelligentia indivisibilium, qua cognoscit de unoquoque, quid est. Alia vero, qua componit et dividit, scilicet enuntiationem affirmativam vel negativam formando. Et hae quidem duae operationes duobus, quae sunt in rebus, respondent. Prima quidem operatio respicit ipsam naturam rei, secundum quam res intellecta aliquem gradum in entibus obtinet, sive sit res completa, ut totum aliquod, sive res incompleta, ut pars vel accidens. Secunda vero operatio respicit ipsum esse rei, quod quidem resultat ex congregatione principiorum rei in compositis vel ipsam simplicem naturam rei concomitatur, ut in substantiis simplicibus. | We must realize that, as the Philosopher says, the intellect has two operations, one called the "understanding of indivisibles," by which it knows what a thing is, and another by which it joins and divides, that is to say, by forming affirmative and negative statements. Now these two operations correspond to two principles in things, The first operation concerns the nature itself of a thing, in virtue of which the object known holds a certain rank among beings, whether it be a complete thing, like some whole, or an incomplete thing, like a part or an accident. The second operation has to do with a thing’s being (esse), which results from the union of the principles of a thing in composite substances, or, as in the case of simple substances, accompanies the thing’s simple nature. |
| Et quia veritas intellectus est ex hoc quod conformatur rei, patet quod secundum hanc secundam operationem intellectus non potest vere abstrahere quod secundum rem coniunctum est, quia in abstrahendo significaretur esse separatio secundum ipsum esse rei, sicut si abstraho hominem ab albedine dicendo: homo non est albus, significo esse separationem in re. Unde si secundum rem homo et albedo non sint separata, erit intellectus falsus. Hac ergo operatione intellectus vere abstrahere non potest nisi ea quae sunt secundum rem separata, ut cum dicitur: homo non est asinus. | Now, since the truth of the intellect results from its conformity with reality, it is clear that in this second operation the intellect cannot truthfully abstract what is united in reality, because the abstraction would signify a separation with regard to the very being of the thing. For example, if I abstract man from whiteness by saying, "Man is not white," I signify that there is a separation in reality. So if in reality man and whiteness are not separate, the intellect will be false. Through this operation, then, the intellect can truthfully abstract only those things that are separate in reality, as when we say, "Man is not an ass." |
| Sed secundum primam operationem potest abstrahere ea quae secundum rem separata non sunt, non tamen omnia, sed aliqua. Cum enim unaquaeque res sit intelligibilis, secundum quod est in actu, ut dicitur in IX metaphysicae, oportet quod ipsa natura sive quiditas rei intelligatur: vel secundum quod est actus quidam, sicut accidit de ipsis formis et substantiis simplicibus, vel secundum id quod est actus eius, sicut substantiae compositae per suas formas, vel secundum id quod est ei loco actus, sicut materia prima per habitudinem ad formam et vacuum per privationem locati. Et hoc est illud, ex quo unaquaeque natura suam rationem sortitur. | Through the first operation, however, we can abstract things that are not separate in reality; not all, it is true, but some. For, since everything is intelligible insofar as it is in act, as the Metaphysics says, we must understand the nature itself or the quiddity of a thing either inasmuch as it is a certain act (as happens in the case of forms themselves and simple substances); or through that which is its act (as we know composite substances through their forms); or through that which takes the place of act in it (as we know prime matter through its relation to form, and a vacuum through the absence of a body in place). And it is from this that each nature is given its definition. |
| Quando ergo secundum hoc, per quod constituitur ratio naturae et per quod ipsa natura intelligitur, natura ipsa habet ordinem et dependentiam ad aliquid aliud, tunc constat quod natura illa sine illo alio intelligi non potest, sive sint coniuncta coniunctione illa, qua pars coniungitur toti, sicut pes non potest intelligi sine intellectu animalis, quia illud, a quo pes habet rationem pedis, dependet ab eo, a quo animal est animal, sive sint coniuncta per modum quo forma coniungitur materiae, vel ut pars comparti vel accidens subiecto, sicut simum non potest intelligi sine naso, sive etiam sint secundum rem separata, sicut pater non potest intelligi sine intellectu filii, quamvis istae relationes inveniantur in diversis rebus. Si vero unum ab altero non dependeat secundum id quod constituit rationem naturae, tunc unum potest ab altero abstrahi per intellectum ut sine eo intelligatur, non solum si sint separata secundum rem, sicut homo et lapis, sed etiam si secundum rem coniuncta sint, sive ea coniunctione, qua pars et totum coniunguntur, sicut littera potest intelligi sine syllaba, sed non e converso, et animal sine pede, sed non e converso, sive etiam sint coniuncta per modum quo forma coniungitur materiae et accidens subiecto, sicut albedo potest intelligi sine homine, et e converso. | Therefore, when the nature itself is related to, and depends on something else, with regard to that which forms the definition (ratio) of the nature, and through which the nature itself is understood, clearly we cannot know the nature without that other thing. This is true whether they are connected as a part is united to a whole (as we cannot know foot without knowing animal, because that whereby foot has the nature of foot depends on that whereby animal is animal); or whether they are connected as form is united to matter, or as one part to another part, or as accident to subject (as we cannot know snub without nose); or even whether they are separated in reality (as we cannot know father without knowing son, although these relationships are found in different things). But if one thing does not depend on another with regard to that which forms the definition of the nature, then the intellect can abstract the one from the other so as to know it without the other. This is true not only if they are separated in reality, like man and stone, but also if they are united in reality, whether they are joined as part and whole (as letter can be understood without syllable, but not vice versa, and animal without foot, but not conversely); or even if they are joined as form is united to matter and accident to subject (as whiteness can be understood without man and vice versa). |
| Pars 3 q. 5 a. 3 co. 2 | |
| Sic ergo intellectus distinguit unum ab altero aliter et aliter secundum diversas operationes; quia secundum operationem, qua componit et dividit, distinguit unum ab alio per hoc quod intelligit unum alii non inesse. In operatione vero qua intelligit, quid est unumquodque, distinguit unum ab alio, dum intelligit, quid est hoc, nihil intelligendo de alio, neque quod sit cum eo, neque quod sit ab eo separatum. Unde ista distinctio non proprie habet nomen separationis, sed prima tantum. Haec autem distinctio recte dicitur abstractio, sed tunc tantum quando ea, quorum unum sine altero intelligitur, sunt simul secundum rem. Non enim dicitur animal a lapide abstrahi, si animal absque intellectu lapidis intelligatur. | Accordingly, through its various operations the intellect distinguishes one thing from another in different ways. Through the operation by which it composes and divides, it distinguishes one thing from another by understanding that the one does not exist in the other. Through the operation, however, by which it understands what a thing is, it distinguishes one thing from another by knowing what one is without knowing anything of the other, either that it is united to it or separated from it. So this distinction is not properly called separation, but only the first. lt is correctly called abstraction, but only when the objects, one of which is known without the other, are one in reality. For if we consider animal without considering stone, we do not say that we abstract animal from stone. |
| Unde cum abstractio non possit esse, proprie loquendo, nisi coniunctorum in esse, secundum duos modos coniunctionis praedictos, scilicet qua pars et totum uniuntur vel forma et materia, duplex est abstractio, una, qua forma abstrahitur a materia, alia, qua totum abstrahitur a partibus. | It follows that since, properly speaking, we can only abstract objects united in existence, there are two sorts of abstraction corresponding to the two modes of union mentioned above, namely, the union of part and whole, and the union of form and matter. The first is that in which we abstract form from matter, and the second is that in which we abstract a whole from its parts. |
| Forma autem illa potest a materia aliqua abstrahi, cuius ratio essentiae non dependet a tali materia.Ab illa autem materia non potest forma abstrahi per intellectum, a qua secundum suae essentiae rationem dependet. Unde cum omnia accidentia comparentur ad substantiam subiectam sicut forma ad materiam et cuiuslibet accidentis ratio dependeat ad substantiam, impossibile est aliquam talem formam a substantia separari. Sed accidentia superveniunt substantiae quodam ordine. Nam primo advenit ei quantitas, deinde qualitas, deinde passiones et motus. Unde quantitas potest intelligi in materia subiecta, antequam intelligantur in ea qualitates sensibiles, a quibus dicitur materia sensibilis. Et sic secundum rationem suae substantiae non dependet quantitas a materia sensibili, sed solum a materia intelligibili. Substantia enim remotis accidentibus non manet nisi intellectu comprehensibilis, eo quod sensitivae potentiae non pertingunt usque ad substantiae comprehensionem. Et de huiusmodi abstractis est mathematica, quae considerat quantitates et ea quae quantitates consequuntur, ut figuras et huiusmodi. | Now a form can be abstracted from matter if the essential nature of the form does not depend on that particular kind of matter; but the intellect cannot abstract form from the kind of matter upon which the form depends according to its essential nature. Consequently, because all accidents are related to the underlying substance as form to matter, and because it is the nature of every accident to depend upon substance, no form of this kind can be separated from substance. But accidents befall substance in a definite order. Quantity comes to it first, then quality, after that passivities (passiones) and actions. So quantity can be thought of in substance before the sensible qualities (because of which matter is called sensible) are considered in it. Quantity, then, according to its essential nature does not depend upon sensible matter but only upon intelligible matter. For, after accidents have been abstracted, substance is intelligible only to the intellect, because it is beyond the sense powers to comprehend substance. And abstract objects of this kind are the concern of mathematics; it treats of quantities and the properties of quantity, such as figures and the like. |
| Pars 3 q. 5 a. 3 co. 3 | |
| Totum etiam non a quibuslibet partibus abstrahi potest. Sunt enim quaedam partes, ex quibus ratio totius dependet, quando scilicet hoc est esse tali toti quod ex talibus partibus componi, sicut se habet syllaba ad litteras et mixtum ad elementa; et tales partes dicuntur partes speciei et formae, sine quibus totum intelligi non potest, cum ponantur in eius diffinitione. | Moreover, we cannot abstract a whole from just any parts. For there are some parts upon which the nature of the whole depends, namely, when the being of a particular whole consists in the composition of particular parts. It is in this way that a syllable is related to letters and a mixed body to the elements. Parts of this sort, which are necessary for understanding the whole because they enter into its definition, are called parts of the species and of the form. |
| Quaedam vero partes sunt quae accidunt toti, in quantum huiusmodi, sicut semicirculus se habet ad circulum. Accidit enim circulo, quod sumantur per divisionem duae eius partes aequales vel inaequales vel etiam plures; non autem accidit triangulo, quod in eo designentur tres lineae, quia ex hoc triangulus est triangulus. Similiter etiam per se competit homini quod inveniatur in eo anima rationalis et corpus compositum ex quattuor elementis, unde sine his partibus homo intelligi non potest, sed haec oportet poni in diffinitione eius; unde sunt partes speciei et formae. Sed digitus, pes et manus et aliae huiusmodi partes sunt post intellectum hominis, unde ex eis ratio essentialis hominis non dependet; et homo sine his intelligi potest. Sive enim habeat pedes sive non, dummodo ponatur coniunctum ex anima rationali et corpore mixto ex elementis propria mixtione, quam requirit talis forma, erit homo. | There are some parts, however, that are accidental to the whole as such. The semicircle, for instance, is related to the circle in this way, for it is accidental to a circle that it be divided into two or more equal or unequal parts. But it is not accidental to a triangle that three lines are designated in it, for because of this a triangle is a triangle. Similarly, it is an essential characteristic of man that there be found in him a rational soul and a body composed of the four elements. So man cannot be understood without these parts and they must be included in his definition; so they are parts of his species and form. But finger, foot, and hand, and other parts of this kind are outside the definition of man; and thus the essential nature of man does not depend on them and he can be understood without them. For whether or not he has feet, as long as he is constituted of a rational soul and a body composed of the elements in the proper mixture required by this sort of form, he will be a man. |
| Et hae partes dicuntur partes materiae, quae non ponuntur in diffinitione totius, sed magis e converso. Et hoc modo se habent ad hominem omnes partes signatae, sicut haec anima et hoc corpus et hic unguis et hoc os et huiusmodi. Hae enim partes sunt quidem partes essentiae sortis et Platonis, non autem hominis, in quantum homo; et ideo potest homo abstrahi per intellectum ab istis partibus, et talis abstractio est universalis a particulari. | These parts are called parts of matter: they are not included in the definition of the whole, but rather the converse is true. This is how all determinate (signatae) parts are related to man; for instance, this soul, this body, this nail, this bone, etc. These indeed are parts of the essence of Socrates and Plato, but not of man precisely as man; and therefore the intellect can abstract man from these parts. And this is the abstraction of the universal from the particular. |
| Pars 3 q. 5 a. 3 co. 4 | |
| Et ita sunt duae abstractiones intellectus. Una quae respondet unioni formae et materiae vel accidentis et subiecti, et haec est abstractio formae a materia sensibili. Alia quae respondet unioni totius et partis, et huic respondet abstractio universalis a particulari, quae est abstractio totius, in quo consideratur absolute natura aliqua secundum suam rationem essentialem, ab omnibus partibus, quae non sunt partes speciei, sed sunt partes accidentales. Non autem inveniuntur abstractiones eis oppositae, quibus pars abstrahatur a toto vel materia a forma; quia pars vel non potest abstrahi a toto per intellectum, si sit de partibus materiae, in quarum diffinitione ponitur totum, vel potest etiam sine toto esse, si sit de partibus speciei, sicut linea sine triangulo vel littera sine syllaba vel elementum sine mixto. In his autem quae secundum esse possunt esse divisa, magis habet locum separatio quam abstractio. | So there are two abstractions of the intellect. One corresponds to the union of form and matter or accident and subject. This is the abstraction of form from sensible matter. The other corresponds to the union of whole and part; and to this corresponds the abstraction of the universal from the particular. This is the abstraction of a whole, in which we consider a nature absolutely, according to its essential character, in independence of all parts that do not belong to the species but are accidental parts. But we do not find abstractions opposed to these, by which a part is abstracted from a whole by the intellect if it is one of the parts of matter in whose definition the whole is included, or it can even exist without the whole if it is one of the parts of the species, for instance, a line without a triangle, a letter without a syllable, or an element without a mixed body. But in the case of things that can exist separately, separation rather than abstraction obtains. |
| Similiter autem cum dicimus formam abstrahi a materia, non intelligitur de forma substantiali, quia forma substantialis et materia sibi correspondens dependent ad invicem, ut unum sine alio non possit intelligi, eo quod proprius actus in propria materia fit. Sed intelligitur de forma accidentali, quae est quantitas et figura, a qua quidem materia sensibilis per intellectum abstrahi non potest, cum qualitates sensibiles non possint intelligi non praeintellecta quantitate, sicut patet in superficie et colore, nec etiam potest intelligi esse subiectum motus, quod non intelligitur quantum. Substantia autem, quae est materia intelligibilis quantitatis, potest esse sine quantitate; unde considerare substantiam sine quantitate magis pertinet ad genus separationis quam abstractionis. | Similarly, when we say from is abstracted from matter, we do not mean substantial form, because substantial form and the matter correlative to it are interdependent, so that one is not intelligible without the other, because the appropriate act is in its appropriate matter. Rather, we mean the accidental forms of quantity and figure, from which indeed sensible matter cannot be abstracted by the intellect, because sensible qualities cannot be understood unless quantity is presupposed, as is clear in the case of surface and color. And neither can we understand something to be the subject of motion unless we understand it to possess quantity. Substance, however, which is the intelligible matter of quantity, can exist without quantity. Consequently, the consideration of substance without quantity belongs to the order of separation rather than to that of abstraction. |
| Pars 3 q. 5 a. 3 co. 5 | |
| Sic ergo in operatione intellectus triplex distinctio invenitur. Una secundum operationem intellectus componentis et dividentis, quae separatio dicitur proprie; et haec competit scientiae divinae sive metaphysicae. Alia secundum operationem, qua formantur quiditates rerum, quae est abstractio formae a materia sensibili; et haec competit mathematicae. Tertia secundum eandem operationem quae est abstractio universalis a particulari; et haec competit etiam physicae et est communis omnibus scientiis, quia in scientia praetermittitur quod per accidens est et accipitur quod per se est. Et quia quidam non intellexerunt differentiam duarum ultimarum a prima, inciderunt in errorem, ut ponerent mathematica et universalia a sensibilibus separata, ut Pythagorici et Platonici. | We conclude that there are three kinds of distinction in the operation of the intellect. There is one through the operation of the intellect joining and dividing which is properly called separation and this belongs to divine science or metaphysics. There is another through the operation by which the quiddities of things are conceived which is the abstraction of form from sensible matter, and this belongs to mathematics. And there is a third through the same operation which is the abstraction of a universal from a particular, and this belongs to physics and to all the sciences in general, because science disregards accidental features and treats of necessary matters. And because certain men (for example, the Pythagoreans and the Platonists) did not understand the difference between the last two kinds of distinction and the first, they fell into error, asserting that the objects of mathematics and universals exist separate from sensible things. |
| Pars 3 q. 5 a. 3 ad 1 | |
| Ad primum ergo dicendum quod mathematicus abstrahens non considerat rem aliter quam sit. Non enim intelligit lineam esse sine materia sensibili, sed considerat lineam et eius passiones sine consideratione materiae sensibilis, et sic non est dissonantia inter intellectum et rem, quia etiam secundum rem id, quod est de natura lineae, non dependet ab eo, quod facit materiam esse sensibilem, sed magis e converso. Et sic patet quod abstrahentium non est mendacium, ut dicitur in II physicorum. | Reply to 1. When the mathematician abstracts he does not consider something otherwise than it is. Thus, he does not think that a line exists without sensible matter, but he treats of a line and its properties without considering sensible matter. So there is no disagreement between his intellect and reality, because even in reality what belongs to the nature of a line does not depend upon that which makes matter sensible, but vice versa. Consequently, it is evident that "there is no error in the one who abstracts," as is said in the Physics. |
| Pars 3 q. 5 a. 3 ad 2 | |
| Ad secundum dicendum quod materiale dicitur non solum id, cuius pars est materia, sed etiam illud, quod in materia esse habet, secundum quem modum linea sensibilis materiale quoddam dici potest. Unde per hoc non prohibetur quin linea sine materia intelligi possit. Non enim materia sensibilis comparatur ad lineam sicut pars, sed magis sicut subiectum, in quo esse habet, et similiter est de superficie et corpore. Non enim mathematicus considerat corpus, quod est in genere substantiae, prout eius pars est materia et forma, sed secundum quod est in genere quantitatis tribus dimensionibus perfectum, et sic comparatur ad corpus quod est in genere substantiae, cuius pars est materia physica, sicut accidens ad subiectum. | Reply to 2. By "material" is meant not only that which has matter as a part, but also that which exists in matter; and in this way sensible line can be called something material. So this does not prevent a line from being understood without matter. For sensible matter is not related to a line as a part, but rather as the subject in which it exists, and this is also the case with a surface or body. Obviously, the mathematician does not treat of the kind of body that is in the category of substance, whose parts are matter and form, but rather the body in the category of quantity, constituted by three dimensions. Body, in this sense of the term, is related to body the category of substance (of which physical matter is a part) as accident to its subject. |
| Pars 3 q. 5 a. 3 ad 3 | |
| Ad tertium dicendum quod materia non est principium diversitatis secundum numerum nisi secundum quod in multas partes divisa in singulis partibus formam recipiens eiusdem rationis plura individua eiusdem speciei constituit. Materia autem dividi non potest nisi ex praesupposita quantitate, qua remota omnis substantia indivisibilis remanet, et sic prima ratio diversificandi ea, quae sunt unius speciei, est penes quantitatem. Quod quidem quantitati competit, in quantum in sui ratione situm quasi differentiam constitutivam habet, qui nihil est aliud quam ordo partium. Unde etiam abstracta quantitate a materia sensibili per intellectum adhuc contingit imaginari diversa secundum numerum unius speciei, sicut plures triangulos aequilateros et plures lineas rectas aequales. | Reply to 3. Matter is the principle of numerical diversity or inasmuch as, being divided into many parts, and receiving in each part a form of the same nature, it constitutes many individuals of the same species. Now matter can be divided only if we presuppose quantity in it; if that is taken away, even substance remains indivisible. So the primary reason for the diversification of things of one species lies in quantity. And this is due to quantity because position, which is the arrangement of parts in place, is contained in its notion as a kind of formal difference. So even when the intellect has abstracted quantity from sensible matter, it is still possible to imagine numerically different things in the same species, for example, several equilateral triangles and several equal straight lines. |
| Pars 3 q. 5 a. 3 ad 4 | |
| Ad quartum dicendum quod mathematica non abstrahuntur a qualibet materia, sed solum a materia sensibili. Partes autem quantitatis, a quibus demonstratio sumpta quodammodo a causa materiali videtur sumi, non sunt materia sensibilis, sed pertinent ad materiam intelligibilem, quae etiam in mathematicis invenitur, ut patet in VII metaphysicae. | Reply to 4. Mathematics does not abstract from every kind of matter but only from sensible matter. Now the parts of quantity that seem to be in a way the basis for a demonstration by means of a material cause are not sensible matter; rather, they pertain to intelligible matter, which indeed is found in mathematics, as is clear in the Metaphysics. |
| Pars 3 q. 5 a. 3 ad 5 | |
| Ad quintum dicendum quod motus secundum naturam suam non pertinet ad genus quantitatis, sed participat aliquid de natura quantitatis aliunde, secundum quod divisio motus sumitur vel ex divisione spatii vel ex divisione mobilis; et ideo considerare motus non pertinet ad mathematicum, sed tamen principia mathematica ad motum applicari possunt. Et ideo secundum hoc, quod principia quantitatis ad motum applicantur, naturalis considerat de divisione et continuitate motus, ut patet in VI physicorum. Et in scientiis mediis inter mathematicam et naturalem tractatur de mensuris motuum, sicut in scientia de sphaera mota et in astrologia. | Reply to 5. By its very nature motion is not in the category of quantity, but it partakes somewhat of the nature of quantity from another source, namely, according as the division of motion derives from either the division of space or the division of the thing subject to motion. So it does not belong to the mathematician to treat of motion, although mathematical principles can be applied to motion. Therefore, inasmuch as the principles of quantity are applied to motion, the natural scientist treats of the division and continuity of motion, as is clear in the Physics. And the measurements of motions are studied in the intermediate sciences between mathematics and natural science: for instance, in the science of the moved sphere and in astronomy. |
| Pars 3 q. 5 a. 3 ad 6 | |
| Ad sextum dicendum quod in compositis simplicia salvantur et proprietates eorum, licet per alium modum, sicut propriae qualitates elementorum et motus ipsorum proprii inveniuntur in mixto; quod autem est compositorum proprium, non invenitur in simplicibus. Et inde est quod quanto aliqua scientia est abstractior et simpliciora considerans, tanto eius principia sunt magis applicabilia aliis scientiis. Unde principia mathematicae sunt applicabilia naturalibus rebus, non autem e converso, propter quod physica est ex suppositione mathematicae, sed non e converso, ut patet in III caeli et mundi. Et inde est quod de rebus naturalibus et mathematicis tres ordines scientiarum inveniuntur. | Reply to 6. Simple bodies and their properties remain in composite bodies although in a different way, as the proper qualities of the elements and their proper movements are found in a mixed body. What is proper to composite bodies, however, is not found in simple bodies. And so it is that the more abstract and simple the objects of a science are, the more applicable its principles are to the other sciences. Thus the principles of mathematics are applicable to natural things, but not visa versa, because physics presupposes mathematics; but the converse is not true, as is clear in the De Caelo et Mundo. So there are three levels of sciences concerning natural and mathematical entities. |
| Quaedam enim sunt pure naturales, quae considerant proprietates rerum naturalium, in quantum huiusmodi, sicut physica et agricultura et huiusmodi. | Some are purely natural and treat of the properties of natural things as such, like physics, agriculture, and the like. |
| Quaedam vero sunt pure mathematicae, quae determinant de quantitatibus absolute, sicut geometria de magnitudine et arithmetica de numero. | Others are purely mathematical and treat of quantities absolutely, as geometry considers magnitude and arithmetic numbers. |
| Quaedam vero sunt mediae, quae principia mathematica ad res naturales applicant, ut musica, astrologia et huiusmodi. Quae tamen magis sunt affines mathematicis, quia in earum consideratione id quod est physicum est quasi materiale, quod autem est mathematicum est quasi formale; sicut musica considerat sonos, non in quantum sunt soni, sed in quantum sunt secundum numeros proportionabiles, et similiter est in aliis. Et propter hoc demonstrant conclusiones suas circa res naturales, sed per media mathematica; et ideo nihil prohibet, si in quantum cum naturali communicant, materiam sensibilem respiciunt. In quantum enim cum mathematica communicant, abstractae sunt. | Still others are intermediate, and these apply mathematical principles to natural things; for instance, music, astronomy, and the like. These sciences, however, have a closer affinity to mathematics, because in their thinking that which is physical is, as it were, material, whereas that which is mathematical is, as it were, formal. For example, music considers sounds, not inasmuch as they are sounds, but inasmuch as they are proportionable according to numbers; and the same holds in other sciences. Thus they demonstrate their conclusions concerning natural things, but by means of mathematics. Therefore nothing prevents their being concerned with sensible matter insofar as they have something in common with natural science, but insofar as they have something in common with mathematics they are abstract. |
| Pars 3 q. 5 a. 3 ad 7 | |
| Ad septimum dicendum quod, quia scientiae mediae, de quibus dictum est, communicant cum naturali secundum id quod in earum consideratione est materiale, differunt autem secundum id quod in earum consideratione est formale, ideo nihil prohibet has scientias cum naturali habere interdum easdem conclusiones. Non tamen per eadem demonstrant nisi secundum quod scientiae sunt immixtae et una interdum utitur eo quod est alterius, sicut rotunditatem terrae naturalis probat ex motu gravium, astrologus autem per considerationem lunarium eclipsium. | Reply to 7. Because the intermediate sciences mentioned above have something in common with natural science as regards what is material in their procedure, but differ from it as regards what is formal in it, nothing prevents these sciences from occasionally having the same conclusions as natural science. Nevertheless, they do not use the same means of demonstration, unless the sciences are mixed and one occasionally uses what belongs to another, as the natural scientist proves that the earth is round from the movement of heavy bodies, while the astronomer proves it by considering eclipses of the moon. |
| Pars 3 q. 5 a. 3 ad 8 | |
| Ad octavum dicendum quod, sicut dicit Commentator ibidem, philosophus non intendit ibi distinguere scientias speculativas, quia de quolibet mobili, sive sit corruptibile sive incorruptibile, determinat naturalis. Mathematicus autem, in quantum huiusmodi, non considerat aliquod mobile. Intendit autem distinguere res, de quibus scientiae speculativae determinant, de quibus seorsum et secundum ordinem agendum est, quamvis illa tria genera rerum tribus scientiis appropriari possint. Entia enim incorruptibilia et immobilia praecise ad metaphysicum pertinent. Entia vero mobilia et incorruptibilia propter sui uniformitatem et regularitatem possunt determinari quantum ad suos motus per principia mathematica, quod de mobilibus corruptibilibus dici non potest; et ideo secundum genus entium attribuitur mathematicae ratione astrologiae. Tertium vero remanet proprium soli naturali. Et sic loquitur Ptolemaeus. | Reply to 8. As the Commentator says, the Philosopher there did not intend to distinguish between the speculative sciences, because the natural scientist treats of everything subject to motion, whether it be corruptible or incorruptible, while the mathematician as such does not treat of anything subject to motion. But he intended to distinguish between the things studied by the speculative sciences, which must be treated separately and in order, although these three sorts of things can be apportioned to the three sciences. For incorruptible and immobile beings pertain precisely to the metaphysician. However, mobile and incorruptible beings, owing to their uniformity and regularity, can be determined in their movements by mathematical principles; this cannot be said of beings that are mobile and corruptible. Therefore, as Ptolemy says, the second kind of beings is ascribed to mathematics through astronomy, while the third kind remains the proper domain of natural science alone. |
| Articulus 4 | ARTICLE FOUR Does Divine Science Treat of What Exists Without Matter and Motion? |
| Pars 3 q. 5 a. 4 arg. 1 | |
| Ad quartum sic proceditur. Videtur quod scientia divina non sit de rebus a motu et materia separatis. Scientia enim divina maxime videtur esse de Deo. Sed ad Dei cognitionem pervenire non possumus nisi per effectus visibiles, qui sunt in materia et motu constituti, Rom. 1: invisibilia enim ipsius et cetera. Ergo scientia divina non abstrahit a materia et motu. | We proceed as follows to the fourth article: It seems that divine science does not treat of things separate from motion and matter, for: 1. Divine science seems to he especially concerned with God. Now we can come to know God only by way of his visible effects, which are created in matter and motion, as it is said in the Epistle to the Romans, "The invisible things of him, from the creation of the world, are clearly seen, being understood by the things that are made." Therefore, divine science does not abstract from matter and motion. |
| Pars 3 q. 5 a. 4 arg. 2 | |
| Praeterea, illud, cui aliquo modo motus convenit, non est omnino a motu et materia separatum. Sed motus aliquo modo Deo convenit; unde dicitur Sap. 7 de spiritu sapientiae quod est mobilis et mobilior omnibus mobilibus. Et Augustinus dicit VIII super Genesim quod Deus movet se sine tempore et loco, et Plato posuit primum movens movere se ipsum. Ergo scientia divina, quae de Deo determinat, non est omnino a motu separata. | 2. Again, that to which motion in some way belongs is not entirely separate from motion and matter. But motion in some way belongs to God. Thus it is said in Wisdom that the Spirit of Wisdom is "mobile" and "more mobile than all mobile things." And Augustine says that God moves himself without time and place. Plato also asserted that the First Mover moves itself. Therefore divine science, which treats of God, is not entirely separate from motion. |
| Pars 3 q. 5 a. 4 arg. 3 | |
| Praeterea, scientia divina non solum habet considerare de Deo, sed etiam de Angelis. Sed Angeli moventur et secundum electionem, quia de bonis facti sunt mali, et secundum locum, ut patet in illis qui mittuntur. Ergo illa, de quibus scientia divina considerat, non sunt omnino a motu separata. | 3. Again, divine science must treat not only of God but also of angels. But angels change both with regard to choice, because they became bad after having been good, and also with regard to place, as is evident in the case of those who are sent as messengers. So the objects of divine science are not entirely separated from motion. |
| Pars 3 q. 5 a. 4 arg. 4 | |
| Praeterea, ut videtur Commentator dicere in principio physicorum, omne, quod est, vel est materia pura vel forma pura vel compositum ex materia et forma. Sed Angelus non est forma pura, quia sic esset actus purus, quod solius Dei est, nec iterum est materia pura. Ergo est compositus ex materia et forma. Et sic scientia divina non abstrahit a materia. | 4. Again, as the Commentator seems to say in the beginning of the Physics, every being is either pure matter, or pure form, or a composite of matter and form. But an angel is not a pure form, because then he would be pure act, which is true of God alone. Neither is he pure matter. So he is a composite of matter and form. Therefore divine science does not abstract from matter. |
| Pars 3 q. 5 a. 4 arg. 5 | |
| Praeterea, scientia divina, quae ponitur tertia pars speculativae philosophiae, est idem quod metaphysica, cuius subiectum est ens, et principaliter ens quod est substantia, ut patet in IV metaphysicae. Sed ens et substantia non abstrahit a materia, alias nullum ens inveniretur quod haberet materiam. Ergo scientia divina non est a materia abstrahens. | 5. Again, divine science, the third part of speculative philosophy, is the same as metaphysics, whose subject is being, and especially substantial being. This is clear in the Metaphysics. But being and substance do not abstract from matter; otherwise there would be no material being. So divine science does not abstract from matter. |
| Pars 3 q. 5 a. 4 arg. 6 | |
| Praeterea, secundum philosophum in I posteriorum ad scientiam pertinet considerare non solum subiectum, sed partes et passiones subiecti. Sed ens est subiectum scientiae divinae, ut dictum est. Ergo ad ipsam pertinet considerare de omnibus entibus. Sed materia et motus sunt quaedam entia. Ergo pertinent ad considerationem metaphysicae, et sic scientia divina ab eis non abstrahit. | 6. Again, according to the Philosopher, it is the business of a science to consider not only a subject but also the divisions and attributes of that subject. Now, as we have said, being is the subject of divine science. Therefore it is the business of this science to treat of all beings. But matter and motion are beings. Therefore they come under the consideration of metaphysics, and so divine science does not abstract from them. |
| Pars 3 q. 5 a. 4 arg. 7 | |
| Praeterea, sicut dicit Commentator in I physicorum, scientia divina demonstrat per tres causas, scilicet efficientem, formalem et finalem. Sed causa efficiens non potest considerari sine consideratione motus, similiter nec finis, ut dicitur in III metaphysicae. Unde in mathematicis propter hoc quod sunt immobilia nulla demonstratio per huiusmodi causas datur. Ergo scientia divina non abstrahit a motu. | 7. Again, divine science demonstrates by means of three causes: efficient, formal, and final, as the Commentator says, But we cannot consider an efficient cause without taking motion into account; and the same thing is true of a final cause, as the Metaphysics says. Thus, because the objects of mathematics are immobile, there are no demonstrations through these causes in that science. Consequently, divine science does not abstract from motion. |
| Pars 3 q. 5 a. 4 arg. 8 | |
| Praeterea, in theologia determinatur de creatione caeli et terrae et actibus hominum et multis huiusmodi, quae in se materiam et motum continent. Ergo non videtur theologia a materia et motu abstrahere. | 8. Again, in theology we treat of the creation of the heavens and the earth, of acts of men, and many similar things that involve matter and motion. So theology does not seem to abstract from matter and motion. |
| Pars 3 q. 5 a. 4 s. c. 1 | |
| Sed contra est quod philosophus dicit in VI metaphysicae quod prima philosophia est circa separabilia, scilicet a materia, et immobilia. Prima autem philosophia est scientia divina, ut ibidem dicitur. Ergo scientia divina est abstracta a materia et motu. | On the contrary, the Philosopher says in the Metaphysics that "first philosophy deals with things that can exist separately," that is, from matter, "and with immobile things." Now first philosophy is divine science, as he says in the same place. Therefore divine science abstracts from matter and motion. |
| Pars 3 q. 5 a. 4 s. c. 2 | |
| Praeterea, nobilissima scientia est de nobilissimis entibus. Sed scientia divina est nobilissima. Cum ergo entia immaterialia et immobilia sint nobilissima, de eis erit scientia divina. | Moreover, the most excellent science deals with the most excellent beings. But the most excellent science is divine science. Therefore, since immaterial and immobile beings are the most excellent, divine science will treat of them. |
| Pars 3 q. 5 a. 4 s. c. 3 | |
| Praeterea, philosophus dicit in principio metaphysicae quod scientia divina est de primis principiis et causis. Huiusmodi autem sunt immaterialia et immobilia. Ergo de talibus est scientia divina. | Moreover, the Philosopher says in the beginning of the Metaphysics that divine science concerns first principles and causes. Now these are immaterial and immobile. Therefore things of this sort are the objects of divine science. |
| Pars 3 q. 5 a. 4 co. 1 | |
| Responsio. Dicendum quod ad evidentiam huius quaestionis scire oportet quae scientia divina scientia dici debeat. Sciendum siquidem est quod quaecumque scientia considerat aliquod genus subiectum, oportet quod consideret principia illius generis, cum scientia non perficiatur nisi per cognitionem principiorum, ut patet per philosophum in principio physicorum. Sed principiorum duo sunt genera. Quaedam enim sunt quae et sunt in se ipsis quaedam naturae completae et sunt nihilominus principia aliorum, sicut corpora caelestia sunt quaedam principia inferiorum corporum et corpora simplicia corporum mixtorum. | Reply: In order to throw light on this question we must understand what science should be called divine science. We must realize indeed that if a science considers a subject-genus, it must investigate the principles of that genus, since science is perfected only through knowledge of principles, as the Philosopher explains in the beginning of the Physics. Now there are two kinds of principles. (1) Some are complete natures in themselves and nevertheless they are the principles of other things, as the heavenly bodies are principles of lower bodies and simple bodies are principles of mixed bodies. In the sciences, therefore, we study them not only insofar as they are principles, but also insofar as they are certain things in themselves. |
| Et ideo ista non solum considerantur in scientiis ut principia sunt, sed etiam ut sunt in se ipsis res quaedam; et propter hoc de eis non solum tractatur in scientia quae considerat ipsa principiata, sed etiam habent per se scientiam separatam, sicut de corporibus caelestibus est quaedam pars scientiae naturalis praeter illam, in qua determinatur de corporibus inferioribus, et de elementis praeter illam, in qua tractatur de corporibus mixtis. Quaedam autem sunt principia, quae non sunt naturae completae in se ipsis, sed solum sunt principia naturarum, sicut unitas numeri et punctus lineae et forma et materia corporis physici, unde huiusmodi principia non tractantur nisi in scientia, in qua de principiatis agitur. | And for this reason they are considered not only in the science of the beings of which they are the principles, but also in a separate science. Thus there is a branch of natural science treating of heavenly bodies distinct from that treating of lower bodies, and there is one treating of the elements distinct from that treating of mixed bodies. (2) There are some principles, however, that are not complete natures in themselves, but only principles of natures, as unity is the principle of number, point the principle of line, and form and matter principles of natural bodies. Principles of this sort, then, are investigated only in the science dealing with the things of which they are principles. |
| Pars 3 q. 5 a. 4 co. 2 | |
| Sicut autem uniuscuiusque determinati generis sunt quaedam communia principia quae se extendunt ad omnia principia illius generis, ita etiam et omnia entia, secundum quod in ente communicant, habent quaedam principia quae sunt principia omnium entium. Quae quidem principia possunt dici communia dupliciter secundum Avicennam in sua sufficientia: uno modo per praedicationem, sicut hoc quod dico: forma est commune ad omnes formas, quia de qualibet praedicatur; alio modo per causalitatem, sicut dicimus solem unum numero esse principium ad omnia generabilia. | Now just as there are certain common principles of any particular genus extending to all the principles of that genus, so too all beings, inasmuch as they share in being, have certain principles that are the principles of all beings. And as Avicenna says," these principles can be called common in two ways, (1) first, by predication, as when I say that form is common to all forms because it is predicated of all; (2) second, by causality, as we say that the sun, which is numerically one, is the principle of all things subject to generation. |
| Omnium autem entium sunt principia communia non solum secundum primum modum, quod appellat philosophus in XI metaphysicae omnia entia habere eadem principia secundum analogiam, sed etiam secundum modum secundum, ut sint quaedam res eadem numero exsistentes omnium rerum principia, prout scilicet principia accidentium reducuntur in principia substantiae et principia substantiarum corruptibilium reducuntur in substantias incorruptibiles, et sic quodam gradu et ordine in quaedam principia omnia entia reducuntur. | Now there are principles common to all beings not only in the first way (in this sense the Philosopher says that all beings have proportionately the same principles), but also in the second way, so that there are certain beings, each numerically one, which are the principles of all things. Thus the principles of accidents are reducible to the principles of substance, and the principles of perishable substances are reducible to imperishable ones, with the result that all beings are reducible to certain principles in a definite graded order. |
| Et quia id, quod est principium essendi omnibus, oportet esse maxime ens, ut dicitur in II metaphysicae, ideo huiusmodi principia oportet esse completissima, et propter hoc oportet ea esse maxime actu, ut nihil vel minimum habeant de potentia, quia actus est prior et potior potentia, ut dicitur in IX metaphysicae. Et propter hoc oportet ea esse absque materia, quae est in potentia, et absque motu, qui est actus exsistentis in potentia. Et huiusmodi sunt res divinae; quia si divinum alicubi exsistit, in tali natura, immateriali scilicet et immobili, maxime exsistit, ut dicitur in VI metaphysicae. | And since the principle of the being of all things must be being in the highest degree as the Metaphysics says, these principles must be most perfect and therefore supremely in act, so that they have no potentiality whatsoever, or the least possible, because actuality is prior to, and more excellent than potentiality, as the Metaphysics says. For this reason they must be free from matter, which is in potency, and free from motion, which is actuality of that which exists in potency. Divine beings are of this sort, "because if the divine exists anywhere, it exists especially in such a nature" (that is to say, in a nature that is immaterial and immutable), as is sad in the Metaphysics. |
| Pars 3 q. 5 a. 4 co. 3 | |
| Huiusmodi ergo res divinae, quia sunt principia omnium entium et sunt nihilominus in se naturae completae, dupliciter tractari possunt: uno modo, prout sunt principia communia omnium entium; alio modo, prout sunt in se res quaedam. Quia autem huiusmodi prima principia quamvis sint in se maxime nota, tamen intellectus noster se habet ad ea ut oculus noctuae ad lucem solis, ut dicitur in II metaphysicae, per lumen naturalis rationis pervenire non possumus in ea nisi secundum quod per effectus in ea ducimur; et hoc modo philosophi in ea pervenerunt, quod patet Rom. 1: invisibilia Dei per ea quae facta sunt intellecta conspiciuntur. Unde et huiusmodi res divinae non tractantur a philosophis, nisi prout sunt rerum omnium principia. Et ideo pertractantur in illa doctrina, in qua ponuntur ea quae sunt communia omnibus entibus, quae habet subiectum ens in quantum est ens; et haec scientia apud eos scientia divina dicitur. | Accordingly, because these divine beings are the principles of all things and nevertheless they are complete natures in themselves, they can be studied in two ways: (1) first, insofar as they are the common principles of all things, and (2) second insofar as they are beings in their own right. But even though these first principles are most evident in themselves, our intellect regards them as the eye of an owl does the light of the sun, as the Metaphysics says. We can reach them by the light of natural reason only to the extent that their effects reveal them to us. It was in this way that the philosophers came to know them as is clear from the Epistle to the Romans: "The invisible things of God... are clearly seen, being understood by the things that are made." Philosophers, then, study these divine beings only insofar as they are the principles of all things. Consequently, they are the objects of the science that investigates what is common to all beings, which has for its subject being as being. The philosophers call this divine science. |
| Est autem alius modus cognoscendi huiusmodi res, non secundum quod per effectus manifestantur, sed secundum quod ipsae se ipsas manifestant. Et hunc modum ponit apostolus 1 Cor. 2: quae sunt Dei, nemo novit nisi spiritus Dei. Nos autem non spiritum huius mundi accepimus, sed spiritum qui a Deo est, ut sciamus. Et ibidem: nobis autem revelavit Deus per spiritum suum. Et per hunc modum tractantur res divinae, secundum quod in se ipsis subsistunt et non solum prout sunt rerum principia. | There is, however, another way of knowing beings of this kind, (a) not as their effects reveal them, but (b) as they reveal themselves. The Apostle mentions this way in his First Epistle to the Corinthians: "So the things also that are of God no man knows, but the Spirit of God. Now we have received not the spirit of this world, but the Spirit that is of God, that we may understand." And again, "But to us God has revealed them by his Spirit." In this way we consider divine beings as they subsist in themselves and not only inasmuch as they are the principles of things. |
| Pars 3 q. 5 a. 4 co. 4 | |
| Sic ergo theologia sive scientia divina est duplex. Una, in qua considerantur res divinae non tamquam subiectum scientiae, sed tamquam principia subiecti, et talis est theologia, quam philosophi prosequuntur, quae alio nomine metaphysica dicitur. Alia vero, quae ipsas res divinas considerat propter se ipsas ut subiectum scientiae et haec est theologia, quae in sacra Scriptura traditur. | Accordingly, there are two kinds of theology or divine science. (1) There is one that treats of divine things, not as the subject of the science but as the principles of the subject. This is the kind of theology pursued by the philosophers and that is also called metaphysics. (2) There is another theology, however, that investigates divine things for their own sakes as the subject of the science. This is the theology taught in Sacred Scripture. |
| Utraque autem est de his quae sunt separata a materia et motu secundum esse, sed diversimode, secundum quod dupliciter potest esse aliquid a materia et motu separatum secundum esse. Uno modo sic, quod de ratione ipsius rei, quae separata dicitur, sit quod nullo modo in materia et motu esse possit, sicut Deus et Angeli dicuntur a materia et motu separati. Alio modo sic, quod non sit de ratione eius quod sit in materia et motu, sed possit esse sine materia et motu, quamvis quandoque inveniatur in materia et motu. Et sic ens et substantia et potentia et actus sunt separata a materia et motu, quia secundum esse a materia et motu non dependent, sicut mathematica dependebant, quae numquam nisi in materia esse possunt, quamvis sine materia sensibili possint intelligi. | Both treat of beings that exist separate from matter and motion, but with a difference, for something can exist separate from matter and motion in two distinct ways: (1) first, because by its nature the thing that is called separate in no way can exist in matter and motion, as God and the angels are said to be separate from matter and motion. (2) Second, because by its nature it does not exist in matter and motion; but it can exist without them, though we sometimes find it with them. In this way being, substance, potency, and act are separate from matter and motion, because they do not depend on them for their existence, unlike the objects of mathematics, which can only exist in matter, though they can be understood without sensible matter. |
| Theologia ergo philosophica determinat de separatis secundo modo sicut de subiectis, de separatis autem primo modo sicut de principiis subiecti. Theologia vero sacrae Scripturae tractat de separatis primo modo sicut de subiectis, quamvis in ea tractentur aliqua quae sunt in materia et motu, secundum quod requirit rerum divinarum manifestatio. | Thus philosophical theology investigates beings separate in the second sense as its subjects, and beings separate in the first sense as the principles of its subject. But the theology of Sacred Scripture treats of beings separate in the first sense as its subjects, though it concerns some items in matter and motion insofar as this is needed to throw light on divine things. |
| Pars 3 q. 5 a. 4 ad 1 | |
| Ad primum ergo dicendum quod illa, quae non assumuntur in scientia nisi ad alterius manifestationem, non pertinent per se ad scientiam, sed quasi per accidens. Sic enim in naturalibus quaedam mathematica assumuntur, et per hunc modum nihil prohibet in scientia divina esse quaedam quae sunt in materia et motu. | Reply to 1. When something is incorporated into a science only to throw light on something else, it does not belong to the science essentially, but, in a way, incidentally, as some mathematics are incorporated into the natural sciences. In this way nothing prevents some things in matter and motion being in divine science. |
| Pars 3 q. 5 a. 4 ad 2 | |
| Ad secundum dicendum quod moveri non attribuitur Deo proprie, sed quasi metaphorice, et hoc dupliciter. Uno modo, secundum quod improprie operatio intellectus vel voluntatis motus dicitur, et secundum hoc dicitur aliquis movere se ipsum, quando intelligit vel diligit se. Et per hunc modum potest verificari dictum Platonis qui dixit quod primus motor movet se ipsum, quia scilicet intelligit et diligit se, ut Commentator dicit in VIII physicorum. Alio modo, secundum quod ipse effluxus causatorum a suis causis nominari potest processio sive motus quidam causae in causatum, in quantum in ipso effectu relinquitur similitudo causae, et sic causa, quae prius erat in se ipsa, postmodum fit in effectu per suam similitudinem. Et hoc modo Deus, qui similitudinem suam omnibus creaturis impartitus est, quantum ad aliquid dicitur per omnia moveri vel ad omnia procedere, quo modo loquendi utitur frequenter Dionysius. Et secundum hunc etiam modum videtur intelligi quod dicitur Sap. 7 quod omnium mobilium mobilior est sapientia et quod attingit a fine usque ad finem fortiter. Hoc autem non est proprie moveri, et ideo ratio non sequitur. | Reply to 2. We do not attribute motion to God properly, but by a kind of metaphor, and this in two ways, first, according as the operation of the intellect or will is improperly called motion; and in this way a person is said to move himself when he knows or loves himself. ln this sense, as the Commentator says, the statement of Plato is true, that the First Mover moves himself because he knows and loves himself. Second, according as the flowing forth of effects From their causes can be called a procession or motion of cause to effect insofar as the likeness of the cause is left in the effect itself; and so the cause, which previously existed in itself, afterward comes to be in the effect through its likeness. And in this way God, who has communicated his likeness to all creatures, in a certain respect is said to be moved by all of them or to go forward to all things. Dionysius frequently uses this manner of speaking. This also seems to be the meaning of the statement in Wisdom, that "Wisdom is more mobile than all mobile things," and that "She reaches from end to end mightily." However, this is not motion in the proper sense the term, and so the argument does not follow. |
| Pars 3 q. 5 a. 4 ad 3 | |
| Ad tertium dicendum quod scientia divina, quae est per inspirationem divinam accepta, non est de Angelis sicut de subiecto, sed solum sicut de his, quae assumuntur ad manifestationem subiecti. Sic enim in sacra Scriptura agitur de Angelis sicut et de ceteris creaturis. Sed in scientia divina, quam philosophi tradunt, consideratur de Angelis, quos intelligentias vocant, eadem ratione qua et de prima causa, quae Deus est, in quantum ipsi etiam sunt rerum principia secunda, saltem per motum orbium, quibus quidem nullus motus physicus accidere potest. Motus autem, qui est secundum electionem, reducitur ad illum modum, quo actus intellectus vel voluntatis motus dicitur, quod est improprie dictum motu pro operatione sumpto. Motus etiam, quo dicuntur secundum locum moveri, non est secundum circumscriptionem localem, sed secundum operationem, quam exercent in hoc vel in illo loco, aut secundum aliquam aliam habitudinem, quam habent ad locum, omnino aequivocam ab illa habitudine, quam habet corpus locatum ad locum. Et ideo patet quod eis non convenit motus, secundum quod naturalia in motu esse dicuntur. | Reply to 3. Divine science received through divine inspiration does not treat of the angels as its subject, but only as something incorporated into the science to throw light on its subject. For Sacred Scripture treats of the angels just as it does other creatures. In the divine science taught by the philosophers, however, the angels, which they call Intelligences, are considered from the same point of view as the First Cause or God, insofar as they are also secondary principles of things, at least through the movement of the spheres, though the angels themselves are subject to no physical motion. Moreover, motion with respect to choice is reducible to the sense in which the act of the intellect or will is called motion, which is an improper sense of the term, motion being understood as operation. Further, when angels are said to move in place, their motion is not with reference to enclosure in place but with reference to the activity they exercise in this or that place, or with reference to some other relation they have to place, although that relation is absolutely equivocal to that which a localized body has to place. So it is clear that they do not move in the sense in which we say natural things move. |
| Pars 3 q. 5 a. 4 ad 4 | |
| Ad quartum dicendum quod actus et potentia sunt communiora quam materia et forma; et ideo in Angelis, etsi non inveniatur compositio formae et materiae, potest tamen inveniri in eis potentia et actus. Materia enim et forma sunt partes compositi ex materia et forma, et ideo in illis tantum invenitur compositio materiae et formae, quorum una pars se habet ad aliam ut potentia ad actum. Quod autem potest esse, potest et non esse; et ideo possibile est unam partem inveniri cum alia et sine alia, et ideo compositio materiae et formae non invenitur secundum Commentatorem in I caeli et mundi et in VIII metaphysicae nisi in his quae sunt per naturam corruptibilia. Nec obstat quod aliquod accidens in aliquo subiecto perpetuo conservetur, sicut figura in caelo, cum tamen corpus caeleste impossibile sit esse sine tali figura et omnia accidentia consequuntur substantiam sicut causam, et ideo subiectum se habet ad accidentia non solum ut potentia passiva, sed etiam quodammodo ut potentia activa, et ideo aliqua accidentia naturaliter perpetuantur in suis subiectis. Materia autem non est hoc modo causa formae, et ideo omnis materia, quae subest alicui formae, potest etiam non subesse, nisi fortassis a causa extrinseca contineatur; sicut virtute divina ponimus aliqua corpora etiam ex contrariis composita esse incorruptibilia, ut corpora resurgentium. | Reply to 4. Act and potency are more common than matter and form. Therefore, even though we do not find the composition of form and matter in the angels we can still find potency and act in them. For matter and form are parts of a thing composed of matter and form; and so we find the composition of matter and form only in things with parts, one of which is related to the other as potency to act. Now what can be, can also not be; and so one part can be found with or without the other; and therefore, as the Commentator says, we find the composition of matter and form only in those things that are by nature corruptible. Nor is the objection valid, that an accident may be eternally conserved in a subject, like shape in the heavens. For a heavenly body cannot exist without such a shape, since shape and all accidents in general follow upon substance as their cause. So a subject is related to its accidents not only as passive potency, but also in a way as an active power; and for this reason some accidents are naturally conserved forever in their subjects. But matter is not the cause of form in this way; and therefore all matter subject to form can cease to be subject to it, unless perhaps an extrinsic cause preserves it; thus we maintain that by the divine power even some bodies composed of contraries, like the bodies of those arisen from the dead, are incorruptible. |
| Essentia autem Angeli secundum naturam suam incorruptibilis est, et ideo non est in ea compositio formae et materiae. Sed quia non habet esse a se ipso Angelus, ideo se habet in potentia ad esse quod accipit a Deo, et sic esse a Deo acceptum comparatur ad essentiam eius simplicem ut actus ad potentiam. Et hoc est quod dicitur quod sunt compositi ex quod est et quo est, ut ipsum esse intelligatur quo est, ipsa vero natura Angeli intelligatur quod est. Tamen si ex materia et forma Angeli compositi essent, non tamen ex materia sensibili, a qua oportet et mathematica abstracta esse et metaphysica separata. | Now, since the essence of an angel is incorruptible by its nature, it is not composed of form and matter. But an angel does not exist of himself, and so he is potential to the being (esse) he receives from God. Consequently, the being (esse) received from God is related to his simple essence as act to potency. This is what is meant by saying that angels are composed of what they are (quod est) and that by which they are (quo est); being (esse) is understood as that by which they are and the angelic nature as what they are. However, even if angels were composed of matter and form, they would not be composed of sensible matter, from which both the objects of mathematics must be abstracted and those of metaphysics must be separated. |
| Pars 3 q. 5 a. 4 ad 5 | |
| Ad quintum dicendum quod ens et substantia dicuntur separata a materia et motu non per hoc quod de ratione ipsorum sit esse sine materia et motu, sicut de ratione asini est sine ratione esse, sed per hoc quod de ratione eorum non est esse in materia et motu, quamvis quandoque sint in materia et motu, sicut animal abstrahit a ratione, quamvis aliquod animal sit rationale. | Reply to 5. We say that being and substance are separate from matter and motion not because it is of their nature to be without them, as it is of the nature of ass to be without reason, but because it is not of their nature to be in matter and motion, although sometimes they are in matter and motion, as animal abstracts from reason, although some animals are rational. |
| Pars 3 q. 5 a. 4 ad 6 | |
| Ad sextum dicendum quod metaphysicus considerat etiam de singularibus entibus non secundum proprias rationes, per quas sunt tale vel tale ens, sed secundum quod participant communem rationem entis, et sic etiam pertinet ad eius considerationem materia et motus. | Reply to 6. The metaphysician deals with individual beings too, not with regard to their special natures, in virtue of which they are special kinds of being, but insofar as they share the common character of being. And in this way matter and motion also fall under his consideration. |
| Pars 3 q. 5 a. 4 ad 7 | |
| Ad septimum dicendum quod agere et pati non convenit entibus secundum quod sunt in consideratione, sed secundum quod sunt in esse. Mathematicus autem considerat res abstractas secundum considerationem tantum, et ideo illae res, prout cadunt in consideratione mathematici, non convenit esse principium et finis motus, et ideo mathematicus non demonstrat per causas efficientem et finalem. Res autem, quas considerat divinus, sunt separatae exsistentes in rerum natura, tales quae possunt esse principium et finis motus; unde nihil prohibet quin per causas efficientem et finalem demonstret. | Reply to 7. Action and passion do not belong to things as they exist in thought but as they exist in reality. Now since the mathematician deals with things that are abstract only in thought, insofar as they come under his consideration they cannot be the principle or the end of motion. So the mathematician does not demonstrate by means of efficient and final causes. But the things the metaphysician deals with are separate, existing in reality, and these can be the principle and end of motion. So nothing prevents his demonstrating by means of efficient and final causes. |
| Pars 3 q. 5 a. 4 ad 8 | |
| Ad octavum dicendum quod sicut fides, quae est quasi habitus principiorum theologiae, habet pro obiecto ipsam veritatem primam et tamen quaedam alia ad creaturas pertinentia in articulis fidei continentur, in quantum contingunt aliquo modo veritatem primam, per eundem modum theologia est principaliter de Deo sicut de subiecto, de creaturis autem multa assumit ut effectus eius vel quomodolibet habentia habitudinem ad ipsum. | Reply to 8. Just as faith, which is in a way the habit of the principles of theology, has for its object the First Truth itself, and yet the articles of faith contain certain other things relating to creatures insofar as they have some connection with the First Truth, in the same way theology is primarily concerned with God as its subject, but it includes many things about creatures as his effects, or as being in some way related to him. |
THE LOGIC MUSEUM
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