Aquinas' In Librum Boetii de Trinitate Expositio

[The text of Boethius' On the Trinity upon which Aquinas' commentary is based is the following section from chapter two]

Let us begin, and consider (insofar as we can know and understand) each one of these [sciences]. For it was well said that it is the duty of an educated person to try to reach a conviction about each one, in regard to what it is in itself. There are, then, three parts of speculative science. The first is natural science, which is unabstracted, and concerns motion. It considers the forms of bodies along with their matter; forms which cannot in actuality be abstracted from bodies. These bodies are in motion, so that, as earth is moved downward and fire upward, the form possesses a motion conjoined to its matter.

Mathematical science is apart from motion but unabstract. This science speculates about the forms of bodies apart from matter, and, for this reason, apart from motion. Since these forms exist in matter, however, they cannot be separated from their bodies [in actuality]. Theology is apart from motion, is abstract, and is separable, for the substance of God lacks both matter and motion.

We must examine natural things rationally, mathematical things through discipline, divine things intellectually. Nor should we make our deductions [concerning divine things] with a view to imaginations, but we should regard the form itself---the form that is truly a form and not an image, and that is being itself, and is that from which being comes into existence. For every being is from form.

Hic est duplex quaestio. Prima de divisione speculativae, quam in littera ponit. Secunda de modis, quos partibus speculativae attribuit. Circa primum quaeruntur quattuor.	This question has two parts: first, concerning the division of speculative science that is stated in the text; second, concerning the methods that the text assigns to speculative science.1 With regard to the first part, there are four questions to ask:
Primo. Utrum sit conveniens divisio qua dividitur speculativa in has tres partes: naturalem, mathematicam et divinam.	In the first place, whether that division is proper which divides speculative science into these three parts: natural science, mathematical science, and divine science.
Secundo. Utrum naturalis philosophia sit de his quae sunt in motu et materia.	In the second place, whether natural philosophy is concerned with those things that exist in motion and matter.
Tertio. Utrum mathematica consideratio sit sine motu et materia de his quae sunt in materia.	Third, whether mathematics considers apart from motion and matter those things which exist in matter.
Quarto. Utrum divina scientia sit de his quae sunt sine materia et motu.	Fourth, whether divine science is concerned with those things that exist apart from matter and motion.
Utrum sit conveniens divisio qua dividitur speculativa in has tres partes: naturalem, mathematicam et divinam.	Article 1: Whether that division is proper which divides speculative science into three parts, namely, natural science, mathematical, and divine science.
Ad primum sic proceditur.	We proceed to the first article thus:
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.	1. It seems that speculative science is not properly divided into these three. The parts of speculative science, after all, are those habits which perfect the contemplative part of the soul. But the Philosopher states in the sixth book of the Ethics that what is scientific in the soul (that is, its contemplative part) is perfected by three habits: namely, wisdom, science, and intuitive reason. Therefore these three are the parts of speculative science, and not those stated in the text.
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. Similarly: Augustine says in the eighth book of the City of God that rational philosophy (which is logic) is comprised under speculative, or contemplative, philosophy. Therefore, since the division in the text makes no mention of this, it is insufficient.
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. Similarly: It is common to divide philosophy into the seven liberal arts, among which neither natural, nor divine, science is found, but only rational and mathematical science. Therefore natural and divine science should not be proposed as parts of speculative science.
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. Similarly: The science of medicine most entirely seems to be an operative [i.e., as distinct from theoretical] science, yet one part of it is said to be speculative, and another practical. By the same reasoning, then, in all other operative sciences there is some speculative part. Therefore, mention should have been made in this division of ethics, or moral science (even though it is an active science), on account of its speculative part.
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. Similarly: The science of medicine is a certain part of [natural] philosophy. So also are certain other arts---such as the science of agriculture, and of alchemy, and things of this sort---which are called mechanical. Since these are operative [i.e., rather than theoretical], it therefore seems that natural science should not have been put under speculative science without some qualification.
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. Similarly: A whole should not be divided otherwise than into its parts. But divine science appears to be the whole with respect to physics and mathematics, since their subjects are parts of its subject. For the subject of divine science (that is, of first philosophy) is being, one of whose parts is mobile substance (which natural science considers), and another quantity (which the mathematician considers), as is made clear in Book Three of the Metaphysics. Therefore divine science ought not to be divided other than into natural and mathematical science.
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. Similarly: Sciences are divided as things are, as is stated in Book Three of de Anima ("On the Soul"). But philosophy concerns being; it is, indeed, the knowledge of being, as Dionysius says in the Letter to Polycarp. Therefore, since being is divided first by potency and act, by the one and the many, and by substance and accident, it seems that the parts of philosophy should be distinguished through distinctions of this sort.
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. Similarly: With regard to the beings about which there are sciences, there are many other divisions that are more essential than the divisions into mobile and immobile, abstract and not abstract. Such are the divisions into corporeal and incorporeal, animate and inanimate, and others of this sort. Therefore the division of the parts of philosophy should be made more according to these distinctions than according to those that are touched on in the text.
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. Similarly: Any science which has others subordinated to it should be prior to them. But all other sciences are subordinated to divine science, since it is its function to prove the others' principles. Therefore, Boethius should have put divine science ahead of the others.
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. Similarly: Mathematical science in fact should be learned before natural science, since the young can learn mathematics easily, but not natural science, unless they are advanced, as is stated in the sixth book of the Ethics. And so it is said that even the ancients followed this order of acquiring the sciences: first logic, then mathematics, third natural science; afterwards moral science would be learned; finally, men would study divine science. Therefore, Boethius should have put mathematics ahead of natural science.
Sed contra,	To the contrary:
quod haec divisio sit conveniens, probatur per philosophum in VI metaphysicae, ubi dicit: quare tres erunt philosophicae et theoricae: mathematica, physica, theologia.	That this division is sufficient is proven by the Philosopher in the sixth book of the Metaphysics, when he says that there are three parts of philosophy and theoretical science: mathematics, physics, and theology.
Praeterea, in II physicorum ponuntur tres modi scientiarum, qui ad has etiam tres pertinere videntur.	Similarly: In the second book of the Physics, there are said to be three methods of science, which seem to apply to the three sciences here.
Praeterea, Ptolemaeus etiam in principio Almagesti hac divisione utitur.	Similarly: Ptolemy too makes use of this division in the beginning of the Almagest.
Responsio.	I reply:
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. 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. 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. 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.	It must be stated that the theoretical or speculative intellect is properly distinguished from the operative or practical intellect in this: that the speculative has for its end the truth it considers, while the practical orders the considered truth for operation as its end. For this reason the Philosopher states in the third book of the de Anima that they differ from each other by their end. In the second book of the Metaphysics, too, it is said that the end of speculative science is truth, the end of operative or practical science is action. Therefore, since material ought to be proportional to its end, the material of the practical sciences should be those things which can come to be through our efforts, so that understanding of them can be ordered for operation as for an end. But the material of the speculative sciences, then, should be things which do not come to be through our efforts; and therefore consideration of them cannot be ordered for operation as its end. The speculative sciences must be distinguished [from one another] by following the division of these latter things. It must be understood, however, that when habits or powers are distinguished according to their objects, they are not distinguished according to just any differences concerning the objects, but according to those which are essential differences of the objects insofar as they are objects. Whether it is an animal or plant is merely accidental to a sensible object insofar as it is sensible, and for this reason the distinctions among the sense are not drawn according to this difference, but rather according to the differences of color and sound. For this reason too the speculative sciences must be divided by means of the differences of speculable objects insofar as they are speculable.
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.	Two characteristics are appropriate to a speculable object in accordance with its being the object of a speculative power: one on account of the intellective power, another on account of the habit of science by which the intellect is perfected. On account of the intellect, it is proper that it be immaterial, since the intellect itself is also immaterial; but on account of the science, it is proper that it be necessary, since science concerns necessary things, as is proven in the first book of the Posterior Analytics. Everything that is necessary, however, as such is immobile, since everything that moves (insofar as it can) can either be or not be, either absolutely or in some respect, as is seen in the tenth book of the Metaphysics. And so, separation from both matter and motion---or attachment to them---belongs essentially to a speculable object that is the object of a speculative science; and for this reason the speculative sciences will be distinguished according to the order of their distance from both matter and motion.
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. 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.	(1) Now, certain speculable objects depend on matter for their being, because they cannot exist except in matter. These can be distinguished still further. (A) Some of them depend on matter for both being and being understood, namely those in whose definition sensible matter is assumed, so that they cannot be understood apart from sensible matter. As, for example, in the definition of man one must assume flesh and bones. Physics, or natural science, concerns these objects. (B) There are other speculable objects, however, which, although they depend on matter for their being, nonetheless do not with regard to their being understood, since sensible matter is not assumed in their definitions, such as line and number. Mathematics is about these objects. (2) On the other hand, there are some speculable objects which do not depend on matter for their being, because they can exist apart from matter. Either they never exist in matter, such as God and angels, or they exist in matter in some cases and not in others, such as substance, quality, potency and act, one and many, and objects of this sort. Concerned with all of these is theology---that is, divine science, because chief among the acknowledged subjects in it is God. It is also called metaphysics---that is, beyond physics---because it is in fact learned by us after physics, since it is characteristic of us to arrive at non-sensible objects from sensible ones. It is also called first philosophy inasmuch as the other sciences follow it, having received their principles from it. Finally, it is not possible that there be any things that depend on matter for being understood, but not for their being, since the intellect (as far as concerns it in itself) is immaterial. For this reason there is no fourth genus of philosophy beyond those already stated.
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.	To the first [objection], therefore, it must be said that the Philosopher in the sixth book of the Ethics is determining the intellectual habits insofar as they are intellectual virtues. But they are called virtues inasmuch as they perfect the intellect in its operation. A virtue, indeed, is something that makes its possessor good, and renders his work good. Therefore, it must be understood that as the intellect is perfected in various ways by speculative habits of different kinds, so Aristotle differentiates virtues of those sorts. One manner, indeed, in which the speculative part of the soul is perfected is by means of the intuitive reason, which is the habit of principles, by which things are known in themselves. But there is also another manner [of perfecting the speculative part of the soul] in which conclusions are known as having been demonstrated from principles of the aforementioned sort, whether the demonstration proceeds from lower causes, as in science, or from the highest causes, as in wisdom. When, therefore, the sciences are distinguished---since they are one particular habit---they must be distinguished from each other according to their objects---that is, according to the things of which they are the sciences. And it is thus that the three parts of speculative philosophy are distinguished here and in the Metaphysics.
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.	To the second it must be said that---as is clear in the first book of the Metaphysics---the speculative sciences concern those things about which knowledge is sought for their own sakes. But logic concerns things that one inquires into with a view to knowing not for their own sakes, but as a kind of support for the other sciences. Therefore logic is not contained in speculative philosophy as a principal part, but as something brought to it because it supplies the instruments for speculation---namely syllogisms and definitions and other such things that we require in the speculative sciences. Wherefore (as also according to Boethius in his Commentary on Porphyry) it is not so much a science as an instrument of science.
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;	To the third it must be said that the seven liberal arts do not adequately divide theoretical philosophy. Rather, as Hugh of St. Victor says in the third book of his Didascalon, they make up (along with certain other arts) the subjects in which those who intend to study philosophy are first instructed. Thus, they are divided into the trivium and the quadruvium so that by these---as if by certain roads---the vigorous mind may enter the innermost recesses of philosophy. This is consonant also with the statement of the Philosopher in the second book of the Metaphysics that the method of science should be sought before the sciences themselves.
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.	The Commentator too says (concerning the same statement) that logic---which teaches the method of all the sciences, and to which the trivium pertains---should be studied before all the other sciences. In the sixth book of the Ethics Aristotle also says that mathematics can be understood by the young, but not physics, which requires experience. From this is to be understood that first logic should be learned, and then mathematics---to which the quadrivium pertains. And thus the mind is prepared by these, as if by certain roads, for the remaining natural disciplines.
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. 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.	It is for this reason, indeed, that these among all other sciences are called arts, because they involve not only knowledge, but some operation (and one which results directly from the reason), such as forming grammatical constructions, syllogisms, and orations, or numbering, measuring, forming melodies, and computing the paths of the stars. Other sciences either (1) do not involve operation (but only knowledge), such as divine and natural science---for which reason they cannot possess the name "art," since "art" is used of productive reasoning, as is said in the sixth book of the Ethics--- or (2) they involve a physical operation, as in medicine, alchemy, and things of this sort. But these latter cannot, therefore, be called liberal arts [i.e. arts of "freedom"] since activities of this sort are the result of that side of man that is not free, namely, the physical side. As far as concerns moral science, even though it exists for the sake of action, nonetheless that action is not an act of science; it is an act of virtue, as the fifth book of the Ethics makes clear. Therefore, moral science cannot be said to be an art; but rather in these actions virtue stands in place of art. It is for this reason that the ancients defined virtue as the art of living rightly and well, as Augustine says in the tenth book of the City of God.2
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,	To the fourth it must be said that, just as Avicenna says in the beginning of his Canon on Medicine, theoretical and practical are distinguished in one way when philosophy is divided into theoretical and practical, in another way when the arts are divided into theoretical and practical, and yet another way when medicine is so divided. When philosophy and the arts are distinguished as theoretical or practical, the distinction between them must be understood as being based on their ends, so that what is ordered to an operation is called practical, but what is ordered solely to the understanding of truth is called theoretical. Nonetheless, there is a difference when philosophy as a whole is being divided this way, or when the arts are.
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. 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.	(1) In the division of philosophy consideration is given to happiness, the [general] end to which the whole of human life is ordered. Indeed, as Augustine says in the tenth book of the City of God, following Varro, there is no other cause for man philosophizing except that he be happy. For this philosophers have proposed a two-fold happiness: one contemplative and the other active, as the tenth book of the Ethics makes clear. And by following this they have divided philosophy into two parts: moral [philosophy], called practical; and natural and rational philosophy, called theoretical. (2) When certain arts are called speculative and others practical, however, consideration is being given to the special ends of those arts, as if we were to say, for example, that agriculture was a practical art, and dialectic, on the other hand, a theoretical one. (3) However, when medicine is divided into theoretical and practical, the division does not consider its end---for then the whole of medicine would be contained in the practical, inasmuch as it has been ordered to action. Rather, the aforesaid division considers the closeness to (or remoteness from) action of the subjects dealt with in medicine. Thus, that part of medicine is called practical which teaches ways of acting for the purpose of healing---for example, that certain sorts of medicines are to be applied to certain sorts of abscesses. That part of medicine is called theoretical, however, which teaches the principles according to which someone is guided in acting, yet not the most immediate principles---for example, that there are exactly three medicinal virtues [or powers], or that the number of kinds of fever is so many. For this reason, it is not proper, even if some part of an active science is called theoretical, that on those grounds that part should be placed under speculative science.
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. 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.	To the fifth it must be said that one science is contained in another in either of two ways: in one way as a part of it by virtue of its subject being a part of the other's subject, as for example that "plant" is a certain part of "natural body." Thus, the science of plants is contained in natural science as a part. But one science is contained in another in a different way when it is subalternated to it---when, that is, causes are assigned in the higher science for those things about which only the fact is known in the lower science. It is thus that music is contained in arithmetic. Medicine, then, is not contained in physics as a part, for the subject of medicine is not a part of the subject of natural science when considered in that special sense that makes it a subject of medicine. For although the curable body is a natural body, it is not a subject of medicine insofar as it is curable by nature, but insofar as it is curable by art. On the other hand, since in that curing which is accomplished by art art is the servant of nature (since it is as a result of some natural power that curing is accomplished with the assistance of art), the reasons for the practices of the art of medicine must be found in the properties of natural things; and on this account medicine is subordinated to physics, as for the same reason is alchemy, and the science of agriculture, and all things of this sort. What remains is that physics---both in respect of itself and all its parts---is a speculative science, albeit some operative sciences are subalternated to it.
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.	To the sixth it must be said that although the subjects of other sciences are parts of being---which is the subject of metaphysics---the other sciences need not be parts of metaphysics. For each particular science takes one part of being and examines it in a special way, a way different from the way in which being is examined in metaphysics. So, properly speaking, its subject is not a part of the subject of metaphysics, nor is it even a part of being for the same reason that being is the subject of metaphysics, but, rather, for that examined reason from which the science itself becomes a special science distinct from the others. By the same token, however, whatever science deals with potency and act, or the one, or something of this sort could be said to be a part of metaphysics, since these subjects are examined in the same way that being is, which metaphysics treats.
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.	To the seventh it must be said that these parts of being require the same mode of treatment as being in general, since they too do not depend on matter. And therefore the science which deals with them is not distinguished from the science which deals with being in general.
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.	To the eighth it must be said that those differences of things which the objection mentions are not essential differences of the things insofar as they are knowable, and therefore sciences are not distinguished according to them.
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. 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 definitione.	To the ninth it must be said that, although divine science is the first of all the sciences by nature, nevertheless to us other sciences are prior. Thus, Avicenna states at the beginning of his Metaphysics that the position of that science is that it is learned after the natural sciences, in which many things are determined which that science makes use of, such as generation and corruption, and motion, and this sort of thing. Similarly, [it is learned] after mathematics. For in order to understand separated substances metaphysics requires a knowledge of number and the celestial orbits, which is impossible without astronomy, for which the whole of mathematics is a prerequisite. Indeed, other sciences too are useful for metaphysics, such as music, and the moral sciences, and things of this sort. Nor is it a vicious circle that metaphysics assumes things which are proven in other sciences while itself proving the principles of these other sciences. For the principles which, for example, a natural philosopher receives for natural science from first philosophy do not prove those same things that the first philosopher receives from natural science. Rather, these [principles] are proven by other principles known in themselves; thus, the first philosopher does not prove the principles he gives to the natural philosopher by means of principles he has received from him, but by certain other principles known in themselves. And so there is no vicious circle in the definition.
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.	Moreover, sensible effects [i.e., rather than their causes]---from which natural demonstrations proceed---are better known to us at first. Once we come by means of them to an understanding of primary causes, the causes make clear the reason for the effects. Yet it was from the effects that the existence of the causes was proven by a demonstration quia.3 And thus natural science does bring something to divine science, though divine science's principles are made known through itself. This is the reason Boethius placed divine science last, since it is last in relation to us.
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.	To the tenth it must be said that, although natural philosophy is actually to be learned after mathematics because its universal proofs require experience and time, nevertheless natural things--- since they are sensible things---are naturally better known [to us] than mathematical things which are abstracted from sensible matter.

[From this point, Aquinas goes on to deal with the remaining three articles of Question 5, one each concerning the specific subject matters of natural science, mathematics, and theology. He then moves on to consider the third paragraph of Boethius' text that formed the basis of this section of his commentary (see text at the beginning of this translation). Question 6, which deals with that paragraph, concerns the manner in which we come to know, and can know, the subjects of these three speculative sciences.

The sixth Question is entitled, "Concerning the modes which Boethius attributes to speculative science." It is divided into four articles:

First, whether we must examine natural things rationally, mathematical things through discipline, and divine things intellectually.

Second, whether concerning divine things we must relinquish every use of the imagination.

Third, whether our intellect can regard the divine form itself.

Fourth, whether this can be done by means of any speculative science.]