Sed contra est quod dicitur in Psalmo CIII, Qui facit angelos suos spiritus. On the contrary, It is said (Ps 103:4): Who makes His angels spirits. Respondeo dicendum quod necesse est ponere aliquas creaturas incorporeas. Id enim quod praecipue in rebus creatis Deus intendit est bonum quod consistit in assimilatione ad Deum. Perfecta autem assimilatio effectus ad causam attenditur, quando effectus imitatur causam secundum illud per quod causa producit effectum; sicut calidum facit calidum. Deus autem creaturam producit per intellectum et voluntatem, ut supra ostensum est. Unde ad perfectionem universi requiritur quod sint aliquae creaturae intellectuales. Intelligere autem non potest esse actus corporis, nec alicuius virtutis corporeae, quia omne corpus determinatur ad hic et nunc. Unde necesse est ponere, ad hoc quod universum sit perfectum, quod sit aliqua incorporea creatura. I answer that, There must be some incorporeal creatures. For what is principally intended by God in creatures is good, and this consists in assimilation to God Himself. And the perfect assimilation of an effect to a cause is accomplished when the effect imitates the cause according to that whereby the cause produces the effect; as heat makes heat. Now, God produces the creature by His intellect and will (Q. 14, A. 8; Q. 19, A. 4). Hence the perfection of the universe requires that there should be intellectual creatures. Now intelligence cannot be the action of a body, nor of any corporeal faculty; for every body is limited to here and now. Hence the perfection of the universe requires the existence of an incorporeal creature. Antiqui autem, ignorantes vim intelligendi, et non distinguentes inter sensum et intellectum, nihil esse existimaverunt in mundo, nisi quod sensu et imaginatione apprehendi potest. Et quia sub imaginatione non cadit nisi corpus, existimaverunt quod nullum ens esset nisi corpus; ut Philosophus dicit in IV Physic. Et ex his processit Sadducaeorum error, dicentium non esse spiritum. The ancients, however, not properly realizing the force of intelligence, and failing to make a proper distinction between sense and intellect, thought that nothing existed in the world but what could be apprehended by sense and imagination. And because bodies alone fall under imagination, they supposed that no being existed except bodies, as the Philosopher observes (Phys. iv, 52,57). Thence came the error of the Sadducees, who said there was no spirit (Acts 23:8). Sed hoc ipsum quod intellectus est altior sensu, rationabiliter ostendit esse aliquas res incorporeas, a solo intellectu comprehensibiles. But the very fact that intellect is above sense is a reasonable proof that there are some incorporeal things comprehensible by the intellect alone. Ad primum ergo dicendum quod substantiae incorporeae medium sunt inter Deum et creaturas corporeas. Medium autem comparatum ad unum extremum, videtur alterum extremum; sicut tepidum comparatum calido, videtur frigidum. Et hac ratione dicitur quod angeli, Deo comparati, sunt materiales et corporei, non quod in eis sit aliquid de natura corporea. Reply Obj. 1: Incorporeal substances rank between God and corporeal creatures. Now the medium compared to one extreme appears to be the other extreme, as what is tepid compared to heat seems to be cold; and thus it is said that angels, compared to God, are material and corporeal, not, however, as if anything corporeal existed in them. Ad secundum dicendum quod motus ibi accipitur prout intelligere et velle motus quidam dicuntur. Dicitur ergo angelus substantia semper mobilis, quia semper est actu intelligens, non quandoque actu et quandoque potentia, sicut nos. Unde patet quod ratio procedit ex aequivoco. Reply Obj. 2: Movement is there taken in the sense in which it is applied to intelligence and will. Therefore an angel is called an ever mobile substance, because he is ever actually intelligent, and not as if he were sometimes actually and sometimes potentially, as we are. Hence it is clear that the objection rests on an equivocation. Ad tertium dicendum quod circumscribi terminis localibus est proprium corporum, sed circumscribi terminis essentialibus est commune cuilibet creaturae, tam corporali quam spirituali. Unde dicit Ambrosius, in libro de Spir. Sanct., quod licet quaedam locis corporalibus non contineantur, circumscriptione tamen substantiae non carent. Reply Obj. 3: To be circumscribed by local limits belongs to bodies only; whereas to be circumscribed by essential limits belongs to all creatures, both corporeal and spiritual. Hence Ambrose says (De Spir. Sanct. i, 7) that although some things are not contained in corporeal place, still they are none the less circumscribed by their substance. Articulus 2 Article 2 Utrum angelus sit compositus ex materia et forma Whether an angel is composed of matter and form? Ad secundum sic proceditur. Videtur quod angelus sit compositus ex materia et forma. Omne enim quod continetur sub aliquo genere, est compositum ex genere et differentia, quae, adveniens generi, constituit speciem. Sed genus sumitur ex materia, differentia vero ex forma, ut patet in VIII Metaphys. Ergo omne quod est in genere, est compositum ex materia et forma. Sed angelus est in genere substantiae. Ergo est compositus ex materia et forma. Objection 1: It would seem that an angel is composed of matter and form. For everything which is contained under any genus is composed of the genus, and of the difference which added to the genus makes the species. But the genus comes from the matter, and the difference from the form (Metaph. viii, 6). Therefore everything which is in a genus is composed of matter and form. But an angel is in the genus of substance. Therefore he is composed of matter and form. Praeterea, in quocumque inveniuntur proprietates materiae, ibi invenitur materia. Proprietates autem materiae sunt recipere et substare; unde dicit Boetius, in libro de Trin., quod forma simplex subiectum esse non potest. Haec autem inveniuntur in angelo. Ergo angelus est compositus ex materia et forma. Obj. 2: Further, wherever the properties of matter exist, there is matter. Now the properties of matter are to receive and to substand; whence Boethius says (De Trin.) that a simple form cannot be a subject: and the above properties are found in the angel. Therefore an angel is composed of matter and form. Praeterea, forma est actus. Quod ergo est forma tantum, est actus purus. Sed angelus non est actus purus, hoc enim solius Dei est. Ergo non est forma tantum, sed habet formam in materia. Obj. 3: Further, form is act. So what is form only is pure act. But an angel is not pure act, for this belongs to God alone. Therefore an angel is not form only, but has a form in matter. Praeterea, forma proprie limitatur et finitur per materiam. Forma ergo quae non est in materia, est forma infinita. Sed forma angeli non est infinita, quia omnis creatura finita est. Ergo forma angeli est in materia. Obj. 4: Further, form is properly limited and perfected by matter. So the form which is not in matter is an infinite form. But the form of an angel is not infinite, for every creature is finite. Therefore the form of an angel is in matter. Sed contra est quod Dionysius dicit, IV cap. de Div. Nom., quod primae creaturae sicut incorporales et immateriales intelliguntur. On the contrary, Dionysius says (Div. Nom. iv): The first creatures are understood to be as immaterial as they are incorporeal. Respondeo dicendum quod quidam ponunt angelos esse compositos ex materia et forma. Et hanc opinionem astruere nititur Avicebron in libro Fontis Vitae. Supponit enim quod quaecumque distinguuntur secundum intellectum, sint etiam in rebus distincta. In substantia autem incorporea intellectus apprehendit aliquid per quod distinguitur a substantia corporea, et aliquid per quod cum ea convenit. Unde ex hoc vult concludere quod illud per quod differt substantia incorporea a corporea, sit ei quasi forma, et illud quod subiicitur huic formae distinguenti quasi commune, sit materia eius. Et propter hoc ponit quod eadem est materia universalis spiritualium et corporalium, ut intelligatur quod forma incorporeae substantiae sic sit impressa in materia spiritualium, sicut forma quantitatis est impressa in materia corporalium. I answer that, Some assert that the angels are composed of matter and form; which opinion Avicebron endeavored to establish in his book of the Fount of Life. For he supposes that whatever things are distinguished by the intellect are really distinct. Now as regards incorporeal substance, the intellect apprehends that which distinguishes it from corporeal substance, and that which it has in common with it. Hence he concludes that what distinguishes incorporeal from corporeal substance is a kind of form to it, and whatever is subject to this distinguishing form, as it were something common, is its matter. Therefore, he asserts that the universal matter of spiritual and corporeal things is the same; so that it must be understood that the form of incorporeal substance is impressed in the matter of spiritual things, in the same way as the form of quantity is impressed in the matter of corporeal things. Sed primo aspectu apparet esse impossibile unam esse materiam spiritualium et corporalium. Non enim est possibile quod forma spiritualis et corporalis recipiatur in una parte materiae, quia sic una et eadem res numero esset corporalis et spiritualis. Unde relinquitur quod alia pars materiae sit quae recipit formam corporalem, et alia quae recipit formam spiritualem. Materiam autem dividi in partes non contingit nisi secundum quod intelligitur sub quantitate, qua remota, remanet substantia indivisibilis, ut dicitur in I Physic. Sic igitur relinquitur quod materia spiritualium sit subiecta quantitati, quod est impossibile. Impossibile est ergo quod una sit materia corporalium et spiritualium. But one glance is enough to show that there cannot be one matter of spiritual and of corporeal things. For it is not possible that a spiritual and a corporeal form should be received into the same part of matter, otherwise one and the same thing would be corporeal and spiritual. Hence it would follow that one part of matter receives the corporeal form, and another receives the spiritual form. Matter, however, is not divisible into parts except as regarded under quantity; and without quantity substance is indivisible, as Aristotle says (Phys. i, 15). Therefore it would follow that the matter of spiritual things is subject to quantity; which cannot be. Therefore it is impossible that corporeal and spiritual things should have the same matter. Sed adhuc ulterius impossibile est quod substantia intellectualis habeat qualemcumque materiam. Operatio enim cuiuslibet rei est secundum modum substantiae eius. Intelligere autem est operatio penitus immaterialis. Quod ex eius obiecto apparet, a quo actus quilibet recipit speciem et rationem; sic enim unumquodque intelligitur, inquantum a materia abstrahitur; quia formae in materia sunt individuales formae, quas intellectus non apprehendit secundum quod huiusmodi. Unde relinquitur quod omnis substantia intellectualis est omnino immaterialis. It is, further, impossible for an intellectual substance to have any kind of matter. For the operation belonging to anything is according to the mode of its substance. Now to understand is an altogether immaterial operation, as appears from its object, whence any act receives its species and nature. For a thing is understood according to its degree of immateriality; because forms that exist in matter are individual forms which the intellect cannot apprehend as such. Hence it must be that every intellectual substance is altogether immaterial. Non est autem necessarium quod ea quae distinguuntur secundum intellectum, sint distincta in rebus, quia intellectus non apprehendit res secundum modum rerum, sed secundum modum suum. Unde res materiales, quae sunt infra intellectum nostrum, simpliciori modo sunt in intellectu nostro, quam sint in seipsis. Substantiae autem angelicae sunt supra intellectum nostrum. Unde intellectus noster non potest attingere ad apprehendendum eas secundum quod sunt in seipsis; sed per modum suum, secundum quod apprehendit res compositas. Et sic etiam apprehendit Deum, ut supra dictum est. But things distinguished by the intellect are not necessarily distinguished in reality; because the intellect does not apprehend things according to their mode, but according to its own mode. Hence material things which are below our intellect exist in our intellect in a simpler mode than they exist in themselves. Angelic substances, on the other hand, are above our intellect; and hence our intellect cannot attain to apprehend them, as they are in themselves, but by its own mode, according as it apprehends composite things; and in this way also it apprehends God (Q. 3). Ad primum ergo dicendum quod differentia est quae constituit speciem. Unumquodque autem constituitur in specie, secundum quod determinatur ad aliquem specialem gradum in entibus, quia species rerum sunt sicut numeri, qui differunt per additionem et subtractionem unitatis, ut dicitur in VIII Metaphys. In rebus autem materialibus aliud est quod determinat ad specialem gradum, scilicet forma, et aliud quod determinatur, scilicet materia, unde ab alio sumitur genus, et ab alio differentia. Sed in rebus immaterialibus non est aliud determinans et determinatum, sed unaquaeque earum secundum seipsam tenet determinatum gradum in entibus. Et ideo genus et differentia in eis non accipitur secundum aliud et aliud, sed secundum unum et idem. Quod tamen differt secundum considerationem nostram, inquantum enim intellectus noster considerat illam rem ut indeterminate, accipitur in eis ratio generis; inquantum vero considerat ut determinate, accipitur ratio differentiae. Reply Obj. 1: It is difference which constitutes the species. Now everything is constituted in a species according as it is determined to some special grade of being because the species of things are like numbers, which differ by addition and subtraction of unity, as the Philosopher says (Metaph. viii, 10). But in material things there is one thing which determines to a special grade, and that is the form; and another thing which is determined, and this is the matter; and hence from the latter the genus is derived, and from the former the difference. Whereas in immaterial things there is no separate determinator and thing determined; each thing by its own self holds a determinate grade in being; and therefore in them genus and difference are not derived from different things, but from one and the same. Nevertheless, this differs in our mode of conception; for, inasmuch as our intellect considers it as indeterminate, it derives the idea of their genus; and inasmuch as it considers it determinately, it derives the idea of their difference. Ad secundum dicendum quod ratio illa ponitur in libro Fontis Vitae, et esset necessaria, si idem esset modus quo recipit intellectus, et quo recipit materia. Sed hoc patet esse falsum. Materia enim recipit formam, ut secundum ipsam constituatur in esse alicuius speciei, vel aeris, vel ignis, vel cuiuscumque alterius. Sic autem intellectus non recipit formam, alioquin verificaretur opinio Empedoclis, qui posuit quod terram terra cognoscimus, et ignem igne. Sed forma intelligibilis est in intellectu secundum ipsam rationem formae, sic enim cognoscitur ab intellectu. Unde talis receptio non est receptio materiae, sed est receptio substantiae immaterialis. Reply Obj. 2: This reason is given in the book on the Fount of Life, and it would be cogent, supposing that the receptive mode of the intellect and of matter were the same. But this is clearly false. For matter receives the form, that thereby it may be constituted in some species, either of air, or of fire, or of something else. But the intellect does not receive the form in the same way; otherwise the opinion of Empedocles (De Anima i, 5, 26) would be true, to the effect that we know earth by earth, and fire by fire. But the intelligible form is in the intellect according to the very nature of a form; for as such is it so known by the intellect. Hence such a way of receiving is not that of matter, but of an immaterial substance. Ad tertium dicendum quod, licet in angelo non sit compositio formae et materiae, est tamen in eo actus et potentia. Quod quidem manifestum potest esse ex consideratione rerum materialium, in quibus invenitur duplex compositio. Prima quidem formae et materiae, ex quibus constituitur natura aliqua. Natura autem sic composita non est suum esse, sed esse est actus eius. Unde ipsa natura comparatur ad suum esse sicut potentia ad actum. Subtracta ergo materia, et posito quod ipsa forma subsistat non in materia, adhuc remanet comparatio formae ad ipsum esse ut potentiae ad actum. Et talis compositio intelligenda est in angelis. Et hoc est quod a quibusdam dicitur, quod angelus est compositus ex quo est et quod est, vel ex esse et quod est, ut Boetius dicit, nam quod est est ipsa forma subsistens; ipsum autem esse est quo substantia est, sicut cursus est quo currens currit. Sed in Deo non est aliud esse et quod est, ut supra ostensum est. Unde solus Deus est actus purus. Reply Obj. 3: Although there is no composition of matter and form in an angel, yet there is act and potentiality. And this can be made evident if we consider the nature of material things which contain a twofold composition. The first is that of form and matter, whereby the nature is constituted. Such a composite nature is not its own existence but existence is its act. Hence the nature itself is related to its own existence as potentiality to act. Therefore if there be no matter, and supposing that the form itself subsists without matter, there nevertheless still remains the relation of the form to its very existence, as of potentiality to act. And such a kind of composition is understood to be in the angels; and this is what some say, that an angel is composed of, whereby he is, and what is, or existence, and what is, as Boethius says. For what is, is the form itself subsisting; and the existence itself is whereby the substance is; as the running is whereby the runner runs. But in God existence and what is are not different as was explained above (Q. 3, A. 4). Hence God alone is pure act. Ad quartum dicendum quod omnis creatura est finita simpliciter, inquantum esse eius non est absolutum subsistens, sed limitatur ad naturam aliquam cui advenit. Sed nihil prohibet aliquam creaturam esse secundum quid infinitam. Creaturae autem materiales habent infinitatem ex parte materiae, sed finitatem ex parte formae, quae limitatur per materiam in qua recipitur. Substantiae autem immateriales creatae sunt finitae secundum suum esse, sed infinitae secundum quod eorum formae non sunt receptae in alio. Sicut si diceremus albedinem separatam existentem esse infinitam quantum ad rationem albedinis, quia non contrahitur ad aliquod subiectum; esse tamen eius esset finitum, quia determinatur ad aliquam naturam specialem. Reply Obj. 4: Every creature is simply finite, inasmuch as its existence is not absolutely subsisting, but is limited to some nature to which it belongs. But there is nothing against a creature being considered relatively infinite. Material creatures are infinite on the part of matter, but finite in their form, which is limited by the matter which receives it. But immaterial created substances are finite in their being; whereas they are infinite in the sense that their forms are not received in anything else; as if we were to say, for example, that whiteness existing separate is infinite as regards the nature of whiteness, forasmuch as it is not contracted to any one subject; while its being is finite as determined to some one special nature. Et propter hoc dicitur in libro de Causis, quod intelligentia est finita superius, inquantum scilicet recipit esse a suo superiori; sed est infinita inferius, inquantum non recipitur in aliqua materia. Whence it is said (De Causis, prop. 16) that intelligence is finite from above, as receiving its being from above itself, and is infinite from below, as not received in any matter. Articulus 3 Article 3 Utrum angeli sint in aliquo magno numero Whether the angels exist in any great number? Ad tertium sic proceditur. Videtur quod angeli non sint in aliquo magno numero. Numerus enim species quantitatis est, et sequitur divisionem continui. Hoc autem non potest esse in angelis cum sint incorporei, ut supra ostensum est. Ergo angeli non possunt esse in aliquo magno numero. Objection 1: It would seem that the angels are not in great numbers. For number is a species of quantity, and follows the division of a continuous body. But this cannot be in the angels, since they are incorporeal, as was shown above (A. 1). Therefore the angels cannot exist in any great number. Praeterea, quanto aliquid est magis propinquum uni, tanto minus est multiplicatum, ut in numeris apparet. Natura autem angelica inter alias naturas creatas est Deo propinquior. Cum ergo Deus sit maxime unus, videtur quod in natura angelica inveniatur minimum de multitudine. Obj. 2: Further, the more a thing approaches to unity, so much the less is it multiplied, as is evident in numbers. But among other created natures the angelic nature approaches nearest to God. Therefore since God is supremely one, it seems that there is the least possible number in the angelic nature. Praeterea, proprius effectus separatarum substantiarum videtur esse motus corporum caelestium. Sed motus corporum caelestium sunt secundum aliquem determinatum numerum paucum, qui a nobis comprehendi potest. Ergo angeli non sunt in maiori multitudine, quam motus corporum caelestium. Obj. 3: Further, the proper effect of the separate substances seems to be the movements of the heavenly bodies. But the movements of the heavenly bodies fall within some small determined number, which we can apprehend. Therefore the angels are not in greater number than the movements of the heavenly bodies. Praeterea, Dionysius dicit, IV cap. de Div. Nom., quod propter radios divinae bonitatis subsistunt intelligibiles et intellectuales omnes substantiae. Sed radius non multiplicatur nisi secundum diversitatem recipientium. Non autem potest dici quod materia sit receptiva intelligibilis radii, cum substantiae intellectuales sint immateriales, ut supra ostensum est. Ergo videtur quod multiplicatio substantiarum intellectualium non possit esse nisi secundum exigentiam primorum corporum, scilicet caelestium, ut ad ea quodammodo processus praedictorum radiorum terminetur. Et sic idem quod prius. Obj. 4: Dionysius says (Div. Nom. iv) that all intelligible and intellectual substances subsist because of the rays of the divine goodness. But a ray is only multiplied according to the different things that receive it. Now it cannot be said that their matter is receptive of an intelligible ray, since intellectual substances are immaterial, as was shown above (A. 2). Therefore it seems that the multiplication of intellectual substances can only be according to the requirements of the first bodies—that is, of the heavenly ones, so that in some way the shedding form of the aforesaid rays may be terminated in them; and hence the same conclusion is to be drawn as before. Sed contra est quod dicitur Dan. VII, millia millium ministrabant ei, et decies millies centena millia assistebant ei. On the contrary, It is said (Dan 7:10): Thousands of thousands ministered to Him, and ten thousand times a hundred thousand stood before Him. Respondeo dicendum quod circa numerum substantiarum separatarum, diversi diversis viis processerunt. Plato enim posuit substantias separatas esse species rerum sensibilium, utpote si poneremus ipsam naturam humanam esse separatam. Et secundum hoc oportebat dicere quod substantiae separatae sint secundum numerum specierum sensibilium. Sed hanc positionem improbat Aristoteles, ex eo quod materia est de ratione speciei horum sensibilium. Unde substantiae separatae non possunt esse species exemplares horum sensibilium, sed habent quasdam naturas altiores naturis rerum sensibilium. Posuit tamen Aristoteles quod illae naturae perfectiores habent ordinem ad sensibilia ista, secundum rationem moventis et finis. Et ideo secundum numerum primorum motuum, conatus est adinvenire numerum substantiarum separatarum. I answer that, There have been various opinions with regard to the number of the separate substances. Plato contended that the separate substances are the species of sensible things; as if we were to maintain that human nature is a separate substance of itself: and according to this view it would have to be maintained that the number of the separate substances is the number of the species of sensible things. Aristotle, however, rejects this view (Metaph. i, 31) because matter is of the very nature of the species of sensible things. Consequently the separate substances cannot be the exemplar species of these sensible things; but have their own fixed natures, which are higher than the natures of sensible things. Nevertheless Aristotle held (Metaph. xi, 43) that those more perfect natures bear relation to these sensible things, as that of mover and end; and therefore he strove to find out the number of the separate substances according to the number of the first movements. Sed quia hoc videtur repugnare documentis sacrae Scripturae, Rabbi Moyses, Iudaeus, volens utrumque concordare, posuit quod angeli, secundum quod dicuntur substantiae immateriales, multiplicantur secundum numerum motuum vel corporum caelestium, secundum Aristotelem. Sed posuit quod angeli in Scriptura dicuntur etiam homines divina annuntiantes; et iterum virtutes rerum naturalium, quae Dei omnipotentiam manifestant. Sed hoc est alienum a consuetudine Scripturae, quod virtutes rerum irrationabilium angeli nominentur. But since this appears to militate against the teachings of Sacred Scripture, Rabbi Moses the Jew, wishing to bring both into harmony, held that the angels, in so far as they are styled immaterial substances, are multiplied according to the number of heavenly movements or bodies, as Aristotle held (Metaph. xi, 43); while he contended that in the Scriptures even men bearing a divine message are styled angels; and again, even the powers of natural things, which manifest God’s almighty power. It is, however, quite foreign to the custom of the Scriptures for the powers of irrational things to be designated as angels. Unde dicendum est quod etiam angeli secundum quod sunt immateriales substantiae, in quadam multitudine maxima sunt, omnem materialem multitudinem excedentes. Et hoc est quod dicit Dionysius, XIV cap. Caelest. Hierarch., multi sunt beati exercitus supernarum mentium, infirmam et constrictam excedentes nostrorum materialium numerorum commensurationem. Et huius ratio est quia, cum perfectio universi sit illud quod praecipue Deus intendit in creatione rerum, quanto aliqua sunt magis perfecta tanto in maiori excessu sunt creata a Deo. Sicut autem in corporibus attenditur excessus secundum magnitudinem, ita in rebus incorporeis potest attendi excessus secundum multitudinem. Videmus autem quod corpora incorruptibilia, quae sunt perfectiora inter corpora, excedunt quasi incomparabiliter secundum magnitudinem corpora corruptibilia, nam tota sphaera activorum et passivorum est aliquid modicum respectu corporum caelestium. Unde rationabile est quod substantiae immateriales excedant secundum multitudinem substantias materiales, quasi incomparabiliter. Hence it must be said that the angels, even inasmuch as they are immaterial substances, exist in exceeding great number, far beyond all material multitude. This is what Dionysius says (Coel. Hier. xiv): There are many blessed armies of the heavenly intelligences, surpassing the weak and limited reckoning of our material numbers. The reason whereof is this, because, since it is the perfection of the universe that God chiefly intends in the creation of things, the more perfect some things are, in so much greater an excess are they created by God. Now, as in bodies such excess is observed in regard to their magnitude, so in things incorporeal is it observed in regard to their multitude. We see, in fact, that incorruptible bodies exceed corruptible bodies almost incomparably in magnitude; for the entire sphere of things active and passive is something very small in comparison with the heavenly bodies. Hence it is reasonable to conclude that the immaterial substances as it were incomparably exceed material substances as to multitude. Ad primum ergo dicendum quod in angelis non est numerus qui est quantitas discreta, causatus ex divisione continui, sed causatus ex distinctione formarum, prout multitudo est de transcendentibus, ut supra dictum est. Reply Obj. 1: In the angels number is not that of discrete quantity, brought about by division of what is continuous, but that which is caused by distinction of forms; according as multitude is reckoned among the transcendentals, as was said above (Q. 30, A. 3; Q. 11). Ad secundum dicendum quod ex hoc quod natura angelica est Deo propinqua, oportet quod habeat minimum de multitudine in sui compositione, non autem ita quod in paucis salvetur. Reply Obj. 2: From the angelic nature being the nighest unto God, it must needs have least of multitude in its composition, but not so as to be found in few subjects. Ad tertium dicendum quod ratio illa est Aristotelis in XII Metaphys; et ex necessitate concluderet, si substantiae separatae essent propter substantias corporales, sic enim frustra essent immateriales substantiae, nisi ex eis aliquis motus in rebus corporalibus appareret. Non est autem hoc verum, quod substantiae immateriales sint propter corporales, quia finis nobilior est his quae sunt ad finem. Unde etiam Aristoteles dicit ibidem quod haec ratio non est necessaria, sed probabilis. Coactus autem fuit hac ratione uti, quia ad cognoscendum intelligibilia non possumus pervenire nisi per sensibilia. Reply Obj. 3: This is Aristotle’s argument (Metaph. xii, 44), and it would conclude necessarily if the separate substances were made for corporeal substances. For thus the immaterial substances would exist to no purpose, unless some movement from them were to appear in corporeal things. But it is not true that the immaterial substances exist on account of the corporeal, because the end is nobler than the means to the end. Hence Aristotle says (Metaph. xii, 44) that this is not a necessary argument, but a probable one. He was forced to make use of this argument, since only through sensible things can we come to know intelligible ones.