Greco-Christian stream·Opera Omnia Sancti Thomae (Complete Works of Thomas Aquinas)·Summa Theologiae·Prima Pars·Q7. The infinity of God
Source context
- Theme
- divine infinity as absolute, unlimited being
Steiner
- GA 46In treating the three sonships of God, Steiner characterizes a state of divine self-illuminating infinity in which no differentiation or individuation has yet occurred — only the one undivided God is perceivable.
- GA 52, 1903-11-07Steiner paraphrases a neo-Platonic position holding that God does not derive from being but from transcendence, and that this generates a feeling of infinity that cannot be grasped through sensory mental images.
Cross-tradition
- Neoplatonism (Plotinus, Proclus)The Neoplatonic One is characterized as beyond being and measure, a structural parallel to Aquinas's argument that God's essence, being its own act of being, admits no limiting principle and is therefore simply infinite.
- Kabbalah (Ein Sof)The kabbalistic concept of Ein Sof — the limitless, boundless aspect of divinity prior to all emanation — exhibits cross-tradition congruence with Aquinas's demonstration that God's being is unrestricted by any potentiality or matter.
- Vedanta (Brahman as ananta)Advaita Vedanta describes Brahman as ananta (without end) and aparichchhinna (unconditioned), a structural parallel to Aquinas's claim that divine infinity follows from God's act of being subsisting without any receiving essence to delimit it.
Q7. The infinity of God
Article 2
[I.q.7.a.2.arg.1] It seems that something else besides God can be essentially infinite. For the power of anything is proportioned to its essence. Now if the essence of God is infinite, His power must also be infinite. Therefore He can produce an infinite effect, since the extent of a power is known by its effect.
[I.q.7.a.2.arg.1] Ad secundum sic proceditur. 4. Videtur quod aliquid aliud quam Deus possit esse infinitum per essentiam. Virtus enim rei proportionatur essentiæ ejus. Si igitur essentia Dei est infinita, oportet quod ejus virtus sit infinita. Ergo potest producere effectum infinitum, cum quantitas virtutis per effectum cognoscatur.
[I.q.7.a.2.arg.2] Further, whatever has infinite power, has an infinite essence. Now the created intellect has an infinite power; for it apprehends the universal, which can extend itself to an infinitude of singular things. Therefore every created intellectual substance is infinite.
[I.q.7.a.2.arg.2] 2. Præterea, quidquid habet virtutem in- Non ut prius in editis: « si enim essentia, etc. » Sociniani Deum esse in omni perfectionis genere infinitum negarunt. Omnes autem theologi infinitatem ponunt ac probant, sed diversimode probant.
[I.q.7.a.2.arg.3] Further, primary matter is something other than God, as was shown above (Question 3, Article 8). But primary matter is infinite. Therefore something besides God can be infinite.
[I.q.7.a.2.arg.3] 3. Præterea, materia prima aliud est a Deo, ut supra ostensum est. Sed materia prima est infinita. Ergo aliquid aliud præter Deum potest esse infinitum.
[I.q.7.a.2.sc] The infinite cannot have a beginning, as said in Phys. iii. But everything outside God is from God as from its first principle. Therefore besides God nothing can be infinite.
[I.q.7.a.2.sc] Sed contra est quod infinitum non potest esse ex principio aliquo, ut dicitur in III Physic., text. 30. Omne autem quod est præter Deum, est ex Deo sicut ex primo principio. Ergo nihil quod est præter eum est infinitum.
[I.q.7.a.2.co] Things other than God can be relatively infinite, but not absolutely infinite. For with regard to infinite as applied to matter, it is manifest that everything actually existing possesses a form; and thus its matter is determined by form. But because matter, considered as existing under some substantial form, remains in potentiality to many accidental forms, which is absolutely finite can be relatively infinite; as, for example, wood is finite according to its own form, but still it is relatively infinite, inasmuch as it is in potentiality to an infinite number of shapes. But if we speak of the infinite in reference to form, it is manifest that those things, the forms of which are in matter, are absolutely finite, and in no way infinite. If, however, any created forms are not received into matter, but are self-subsisting, as some think is the case with angels, these will be relatively infinite, inasmuch as such kinds of forms are not terminated, nor contracted by any matter. But because a created form thus subsisting has being, and yet is not its own being, it follows that its being is received and contracted to a determinate nature. Hence it cannot be absolutely infinite.
[I.q.7.a.2.co] Respondeo dicendum, quod aliquid præter Deum potest esse infinitum secundum quid, sed non simpliciter. Si enim loquamur de infinito secundum quod competit materiæ, manifestum est quod omne existens in actu habet aliquam formam, et sic materia ejus est determinata per formam. Sed quia materia, secundum quod est sub una forma substantiali, remanet in potentia ad multas formas accidentales; quod est finitum simpliciter, potest esse infinitum secundum quid: utpote lignum est finitum secundum suam formam, sed tamen est infinitum secundum quid, in quantum est in potentia ad figuras infinitas. Si autem loquamur de infinito secundum quod convenit formæ, sic manifestum est quod illa quorum formæ sunt in materia, sunt simpliciter finita, et nullo modo infinita. Si autem sint aliquæ formæ creata non receptæ in materia, sed per se subsistentes, ut quidam de angelis opinantur; erunt quidem infinitæ secundum quid, in quantum hujusmodi formæ non terminantur neque contrahuntur per aliquam materiam. Sed quia forma creata sic subsistens habet esse, et non est suum esse; necesse est quod ipsum ejus esse sit receptum, et contractum ad terminatam naturam. Unde non potest esse infinitum simpliciter.
[I.q.7.a.2.ad.1] It is against the nature of a made thing for its essence to be its existence; because subsisting being is not a created being; hence it is against the nature of a made thing to be absolutely infinite. Therefore, as God, although He has infinite power, cannot make a thing to be not made (for this would imply that two contradictories are true at the same time), so likewise He cannot make anything to be absolutely infinite.
[I.q.7.a.2.ad.1] Ad primum ergo dicendum, quod hoc est contra rationem facti, quod essentia rei sit ipsum esse ejus, quia esse subsistens non est esse creatum; unde contra rationem facti est quod sit simpliciter infinitum. Sicut ergo Deus, licet habeat potentiam infinitam, non tamen potest facere aliquid non factum, hoc enim esset contradictoria esse simul, ita non potest facere aliquid infinitum simpliciter.
[I.q.7.a.2.ad.2] The fact that the power of the intellect extends itself in a way to infinite things, is because the intellect is a form not in matter, but either wholly separated from matter, as is the angelic substance, or at least an intellectual power, which is not the act of any organ, in the intellectual soul joined to a body.
[I.q.7.a.2.ad.2] Ad secundum dicendum, quod hoc ipsum quod virtus intellectus extendit se quodammodo ad infinita, procedit ex hoc quod intellectus est forma non in materia, sed vel totaliter separata, sicut sunt substantiae angelorum, vel ad minus potentia intellectiva, quae non est actus alicujus organi in anima intellectiva corpori conjuncta.
[I.q.7.a.2.ad.3] Primary matter does not exist by itself in nature, since it is not actually being, but potentially only; hence it is something concreated rather than created. Nevertheless, primary matter even as a potentiality is not absolutely infinite, but relatively, because its potentiality extends only to natural forms.
[I.q.7.a.2.ad.3] Ad tertium dicendum, quod materia prima non existit in rerum natura per se ipsam, cum non sit ens in actu, sed potentia tantum; unde magis est aliquid concreatum, quam creatum. Nihilominus tamen materia prima, etiam secundum potentiam, non est infinita simpliciter, sed secundum quid; quia ejus potentia non se extendit nisi ad formas naturales.
Article 3
[I.q.7.a.3.arg.1] It seems that there can be something actually infinite in magnitude. For in mathematics there is no error, since "there is no lie in things abstract," as the Philosopher says (Phys. ii). But mathematics uses the infinite in magnitude; thus, the geometrician in his demonstrations says, "Let this line be infinite." Therefore it is not impossible for a thing to be infinite in magnitude.
[I.q.7.a.3.arg.1] Ad tertium sic proceditur. 4. Videtur quod possit esse aliquid infinitum actu secundum magnitudinem. In scientiis enim mathematiciis non inventur falsum; quia « abstrahentium non est mendacium, » ut dicitur in II Physic., text. 48. Sed scientiæ mathematicae utuntur infinito secundum magnitudinem; dicit enim geometra in suis demonstrationibus: « Sit linea talis infinita. » Ergo non est impossibile aliquid esse infinitum secundum magnitudinem.
[I.q.7.a.3.arg.2] Further, what is not against the nature of anything, can agree with it. Now to be infinite is not against the nature of magnitude; but rather both the finite and the infinite seem to be properties of quantity. Therefore it is not impossible for some magnitude to be infinite.
[I.q.7.a.3.arg.2] 2. Præterea, id quod non est contra rationem alicujus, non est impossibile convenire sibi. Sed esse infinitum non est contra rationem magnitudinis; sed magis finitum et infinitum videntur esse passiones quantitatis. Ergo non est impossibile aliquid magnitudinem esse infinitam.
[I.q.7.a.3.arg.3] Further, magnitude is infinitely divisible, for the continuous is defined that which is infinitely divisible, as is clear from Phys. iii. But contraries are concerned about one and the same thing. Since therefore addition is opposed to division, and increase opposed to diminution, it appears that magnitude can be increased to infinity. Therefore it is possible for magnitude to be infinite.
[I.q.7.a.3.arg.3] 3. Præterea, magnitudo divisibilis est in infinitum; sic enim definitur continuum, « quod est in infinitum divisibile, » ut patet in III Physic., text. 4. Sed contraria nata sunt fieri circa idem. Cum ergo divisioni « De angelis opinantur. »—Inferius D. Thomas substantias angelorum substantias separatas vocat; sed quidam ex antiquis Patribus vel affirmarunt angelorum corporeitatem, vel saltem de illa dubiopponatur additio, et diminutioni augmentum, videtur quod magnitudo possit crescere in infinitum. Ergo possibile est esse magnitudinem infinitam.
[I.q.7.a.3.arg.4] Further, movement and time have quantity and continuity derived from the magnitude over which movement passes, as is said in Phys. iv. But it is not against the nature of time and movement to be infinite, since every determinate indivisible in time and circular movement is both a beginning and an end. Therefore neither is it against the nature of magnitude to be infinite.
[I.q.7.a.3.arg.4] 4. Præterea, motus et tempus habent quantitatem et continuitatem a magnitudine super quam transit motus, ut dicitur in IV Physic., text. 99. Sed non est contra rationem temporis et motus quod sint infinita, cum unumquodque indivisibile signatum in tempore et motu circulari sit principium et finis. Ergo nec contra rationem magnitudinis erit quod sit infinita.
[I.q.7.a.3.sc] Every body has a surface. But every body which has a surface is finite; because surface is the term of a finite body. Therefore all bodies are finite. The same applies both to surface and to a line. Therefore nothing is infinite in magnitude.
[I.q.7.a.3.sc] Sed contra, omne corpus superficiem habet. Sed omne corpus superficiem habens est finitum, quia superficies est terminus corporis. Ergo omne corpus est finitum. Et similiter potest objici de superficie et linea. Nihil est ergo infinitum secundum magnitudinem.
[I.q.7.a.3.co] It is one thing to be infinite in essence, and another to be infinite in magnitude. For granted that a body exists infinite in magnitude, as fire or air, yet this could not be infinite in essence, because its essence would be terminated in a species by its form, and confined to individuality by matter. And so assuming from these premises that no creature is infinite in essence, it still remains to inquire whether any creature can be infinite in magnitude.
We must therefore observe that a body, which is a complete magnitude, can be considered in two ways; mathematically, in respect to its quantity only; and naturally, as regards its matter and form.
Now it is manifest that a natural body cannot be actually infinite. For every natural body has some determined substantial form. Since therefore the accidents follow upon the substantial form, it is necessary that determinate accidents should follow upon a determinate form; and among these accidents is quantity. So every natural body has a greater or smaller determinate quantity. Hence it is impossible for a natural body to be infinite. The same appears from movement; because every natural body has some natural movement; whereas an infinite body could not have any natural movement; neither direct, because nothing moves naturally by a direct movement unless it is out of its place; and this could not happen to an infinite body, for it would occupy every place, and thus every place would be indifferently its own place. Neither could it move circularly; forasmuch as circular motion requires that one part of the body is necessarily transferred to a place occupied by another part, and this could not happen as regards an infinite circular body: for if two lines be drawn from the centre, the farther they extend from the centre, the farther they are from each other; therefore, if a body were infinite, the lines would be infinitely distant from each other; and thus one could never occupy the place belonging to any other.
The same applies to a mathematical body. For if we imagine a mathematical body actually existing, we must imagine it under some form, because nothing is actual except by its form; hence, since the form of quantity as such is figure, such a body must have some figure, and so would be finite; for figure is confined by a term or boundary.
[I.q.7.a.3.co] Respondeo dicendum, quod aliud est esse infinitum secundum suam essentiam et secundum magnitudinem. Dato enim quod esset aliquod corpus infinitum secundum magnitudinem, utpote ignis vel aer, non tamen esset infinitum secundum essentiam; quia essentia sua esset terminata ad aliquam speciem per formam, et ad aliquod individuum per materiam. Et ideo, habito ex præmissis quod nulla creatura est infinita secundum essentiam, adhuc restat inquirere, utrum aliquid creatum sit infinitum secundum magnitudinem. Sciendum est igitur quod corpus, quod est magnitudo completa, dupliciter sumitur; scilicet mathematice, secundum quod consideratur in eo sola quantitas; et naturaliter, secundum quod consideratur in eo materia et forma. Et de corpore quidem naturali, quod non possit esse infinitum in actu, manifestum est. Nam omne corpus naturale aliquam formam substantialem habet determinatam. Cum igitur ad formam substantialem consequentur accidentia, necesse est quod ad determinatam formam consequentur determinata accidentia, inter quæ est quantitas. Unde omne corpus naturale, habet determinatam quantitatem et in majus et in minus. Unde impossibile est aliquod corpus naturale infinitum esse. Hoc etiam ex motu patet; quia omne corpus naturale habet aliquem motum naturalem; corpus autem infinitum non posset habere aliquem motum naturalem; nec rectum, quia nihil movetur naturaliter motu recto, nisi cum est extra suum locum, quod corpori infinito accidere non posset; occuparet enim omnia loca, et sic indifferenter quilibet locus esset locus ejus; et similiter etiam neque secundum motum circularem, quia in motu circulari oportet quod una pars corporis, transferatur ad locum in quo fuit alia pars, quod in corpore circulari, si ponatur infinitum, esse non posset: quia duæ lineæ protractæ a centro, quanto longius protrahuntur a centro, tanto longius distant ab invicem. Si ergo corpus esset infinitum, in infinitum lineæ distarent ab invicem, et sic una nunquam posset pervenire ad locum alterius. De corpore etiam mathematico eadem ratio est. Quia si imaginemur corpus mathematicum existens actu, oportet quod imaginemur ipsum sub aliqua forma; quia nihil est actu nisi per suam formam: unde cum forma quanti, in quantum hujusmodi, sit figura, oportebit quod habeat aliquam figuram; et sic erit finitum: est enim figura, quæ termino vel terminis comprehenditur.
[I.q.7.a.3.ad.1] A geometrician does not need to assume a line actually infinite, but takes some actually finite line, from which he subtracts whatever he finds necessary; which line he calls infinite.
[I.q.7.a.3.ad.1] Ad primum ergo dicendum, quod geometer non indiget assumere aliquam lineam esse infinitam actu; sed indiget accipere aliquam lineam a qua possit subtrahi quantum necesse est, et hanc nominat lineam infinitam.
[I.q.7.a.3.ad.2] Although the infinite is not against the nature of magnitude in general, still it is against the nature of any species of it; thus, for instance, it is against the nature of a bicubical or tricubical magnitude, whether circular or triangular, and so on. Now what is not possible in any species cannot exist in the genus; hence there cannot be any infinite magnitude, since no species of magnitude is infinite.
[I.q.7.a.3.ad.2] Ad secundum dicendum, quod licet infinitum non sit contra rationem magnitudinis in communi, est tamen contra rationem cujuslibet speciei ejus, scilicet contra rationem magnitudinis bicubitæ vel tricubitæ, sive circularis vel triangularis, et similium. Non autem est possibile in genere esse quod in nulla specie est; unde non est possibile esse aliquam magnitudinem infinitam, cum nulla species magnitudinis sit infinita.
[I.q.7.a.3.ad.3] The infinite in quantity, as was shown above, belongs to matter. Now by division of the whole we approach to matter, forasmuch as parts have the aspect of matter; but by addition we approach to the whole which has the aspect of a form. Therefore the infinite is not in the addition of magnitude, but only in division.
[I.q.7.a.3.ad.3] Ad tertium dicendum, quod infinitum, quod convenit quantitati, ut dictum est, se tenet ex parte materiae; per divisionem autem totius acceditur ad materiam, nam partes se habent in ratione materiae; per additionem autem acceditur ad totum, quod se habet in ratione formæ: et ideo III Physic., text. 40. — I De cælo, text. 35. Editio Rom.: « Ad totum, secundum quod se habet, etc. » Non ut in editis: « Est terminus corporis finiti.» non invenitur infinitum in additione magnitudinis, sed in divisione tantum.
[I.q.7.a.3.ad.4] Movement and time are whole, not actually but successively; hence they have potentiality mixed with actuality. But magnitude is an actual whole; therefore the infinite in quantity refers to matter, and does not agree with the totality of magnitude; yet it agrees with the totality of time and movement: for it is proper to matter to be in potentiality.
[I.q.7.a.3.ad.4] Ad quartum dicendum, quod motus et tempus non sunt secundum totum in actu, sed successive; unde habent potentiam per mixtam actui. Sed magnitudo est tota in actu; et ideo infinitum quod convenit quantitati, et se tenet ex parte materiæ, repugnat totalitati magnitudinis, non autem totalitati temporis vel motus; esse enim in potentia convenit materiæ.
Article 4
[I.q.7.a.4.arg.1] It seems that an actually infinite multitude is possible. For it is not impossible for a potentiality to be made actual. But number can be multiplied to infinity. Therefore it is possible for an infinite multitude actually to exist.
[I.q.7.a.4.arg.1] Ad quartum sic proceditur. 1. Videtur quod possibile sit esse multa infinita secundum actum. Non enim est impossibile, id quod est in potentia, reduci ad actum. Sed numerus est in infinitum multiplicabilis. Ergo non est impossibile esse multitudinem infinitam in actu.
[I.q.7.a.4.arg.2] Further, it is possible for any individual of any species to be made actual. But the species of figures are infinite. Therefore an infinite number of actual figures is possible.
[I.q.7.a.4.arg.2] 2. Præterea, cujuslibet speciei possibile est esse aliquod individuum in actu. Sed species figuræ sunt infinitæ. Ergo possibile est esse infinitas figuras in actu.
[I.q.7.a.4.arg.3] Further, things not opposed to each other do not obstruct each other. But supposing a multitude of things to exist, there can still be many others not opposed to them. Therefore it is not impossible for others also to coexist with them, and so on to infinitude; therefore an actual infinite number of things is possible.
[I.q.7.a.4.arg.3] 3. Præterea, ea quæ non opponuntur ad invicem, non impediunt se invicem. Sed posita aliqua multitudine rerum, adhuc possunt sumi alia multa, quæ eis non opponuntur. Ergo non est impossibile alia iterum simul esse cum eis, et sic in infinitum; ergo possibile est esse infinita in actu.
[I.q.7.a.4.sc] It is written, "Thou hast ordered all things in measure, and number, and weight" (Wisdom 11:21).
[I.q.7.a.4.sc] Sed contra est quod dicitur Sap., xi, 21: Omnia in pondere, numero et mensura* disposuisti.
[I.q.7.a.4.co] A twofold opinion exists on this subject. Some, as Avicenna and Algazel, said that it was impossible for an actually infinite multitude to exist absolutely; but that an accidentally infinite multitude was not impossible. A multitude is said to be infinite absolutely, when an infinite multitude is necessary that something may exist. Now this is impossible; because it would entail something dependent on an infinity for its existence; and hence its generation could never come to be, because it is impossible to pass through an infinite medium.
A multitude is said to be accidentally infinite when its existence as such is not necessary, but accidental. This can be shown, for example, in the work of a carpenter requiring a certain absolute multitude; namely, art in the soul, the movement of the hand, and a hammer; and supposing that such things were infinitely multiplied, the carpentering work would never be finished, forasmuch as it would depend on an infinite number of causes. But the multitude of hammers, inasmuch as one may be broken and another used, is an accidental multitude; for it happens by accident that many hammers are used, and it matters little whether one or two, or many are used, or an infinite number, if the work is carried on for an infinite time. In this way they said that there can be an accidentally infinite multitude.
This, however, is impossible; since every kind of multitude must belong to a species of multitude. Now the species of multitude are to be reckoned by the species of numbers. But no species of number is infinite; for every number is multitude measured by one. Hence it is impossible for there to be an actually infinite multitude, either absolute or accidental. Likewise multitude in nature is created; and everything created is comprehended under some clear intention of the Creator; for no agent acts aimlessly. Hence everything created must be comprehended in a certain number. Therefore it is impossible for an actually infinite multitude to exist, even accidentally. But a potentially infinite multitude is possible; because the increase of multitude follows upon the division of magnitude; since the more a thing is divided, the greater number of things result. Hence, as the infinite is to be found potentially in the division of the continuous, because we thus approach matter, as was shown in the preceding article, by the same rule, the infinite can be also found potentially in the addition of multitude.
[I.q.7.a.4.co] Respondeo dicendum, quod circa hoc fuit duplex opinio. Quidam enim, sicut Avicenna, et Algazel, dixerunt, super III Phys., quod impossibile est esse multitudinem actu infinitam per se, sed infinitam per accidens multitudinem esse non est impossibile. Dicitur enim multitud esse infinita per se, quando requiritur ad aliquid quod sit multitudo infinita; et hoc est impossibile esse; quia sic oporteret quod aliquid dependeret ex infinitis; unde talis generatio nunquam compleretur, cum non sit infinita pertransire. Per accidens autem dicitur multitudo infinita, quando non requiritur ad aliquid infinitas multitudines, sed accidit ita esse. Et hoc sic manifestari potest in operatione fabri, ad quam quaedam multitudo requiritur per se, scilicet quod sit ars in anima, et manus movens, et martellus; et si hæc in infinitum multiplicarentur, nunquam opus fabrile compleretur, quia dependeret ex infinitis causis. Sed multitudo martellorum, quæ accidit ex hoc quod unum frangitur, et accipit aliud, est multitudo per accidens; accidit enim, quod multis martellis operetur, et nihil differt utrum uno vel duobus vel pluribus operetur vel infinitis, si infinito tempore operaretur. Per hunc igitur modum posuerunt, quod possibile est esse actu multitudinem infinitam per accidens. Sed hoc est impossibile, quia omnem multitudinem oportet esse in aliqua specie multitudinis. Species autem multitudinis sunt secundum species numerorum. Nulla autem species numeri est infinita, quia quilibet numerus est multitudo mensurata per unum. Unde impossibile est esse multitudinem infinitam actu, sive per se, sive per accidens. Item omnis multitudo in rerum natura existens est creata, et omne creatum sub aliqua certa intentione creantis comprehenditur: non enim in vanum agens aliquod operatur. Unde necesse est quod sub certo numero omnia creata comprehendantur. Impossibile est ergo esse multitudinem infinitam in actu, etiam per accidens. Sed esse multitudinem infinitam in potentia possibile est; quia augmentum multitudinis consequitur divisionem magnitudinis. Quanto enim aliquid plus dividitur, tanto plura secundum numerum resultant. Unde sicut infinitum invenitur in potentia divisione continui, quia proceditur ad materiam, ut supra ostensum est, eadem ratione etiam infinitum invenitur in potentia in additione multitudinis.
[I.q.7.a.4.ad.1] Every potentiality is made actual according to its mode of being; for instance, a day is reduced to act successively, and not all at once. Likewise the infinite in multitude is reduced to act successively, and not all at once; because every multitude can be succeeded by another multitude to infinity.
[I.q.7.a.4.ad.1] Ad primum ergo dicendum, quod unum-quoque quod est in potentia, reducitur in actum secundum modum sui esse; dies agat. Sed etiam in hoc casu propter finem quemdam agit, et consequenter non praecise in vanum. Quod ad Deum spectat, in vanum nec agit, nec agere potest. enim non reducitur in actum ut sit tota simul, sed successive; et similiter infinitum multitudinis non reducitur in actum ut sit totum simul, sed successive; quia post quamlibet multitudinem potest sumi alia multitudo in infinitum.
[I.q.7.a.4.ad.2] Species of figures are infinite by infinitude of number. Now there are various species of figures, such as trilateral, quadrilateral and so on; and as an infinitely numerable multitude is not all at once reduced to act, so neither is the multitude of figures.
[I.q.7.a.4.ad.2] Ad secundum dicendum, quod species figurarum habent infinitatem ex infinitate numeri. Sunt enim species figurarum: trilaterum, quadrilaterum, et sic inde. Unde sicut multitudin infinita numerabilis non reducitur in actum quod sit tota simul, ita nec multitudino figurarum.
[I.q.7.a.4.ad.3] Although the supposition of some things does not preclude the supposition of others, still the supposition of an infinite number is opposed to any single species of multitude. Hence it is not possible for an actually infinite multitude to exist.
The Summa Theologica of St. Thomas AquinasSecond and Revised Edition, 1920Literally translated by Fathers of the English Dominican ProvinceOnline Edition Copyright © 2009 by Kevin Knight Nihil Obstat. F. Innocentius Apap, O.P., S.T.M., Censor. Theol.Imprimatur. Edus. Canonicus Surmont, Vicarius Generalis. Westmonasterii.APPROBATIO ORDINISNihil Obstat. F. Raphael Moss, O.P., S.T.L. and F. Leo Moore, O.P., S.T.L.Imprimatur. F. Beda Jarrett, O.P., S.T.L., A.M., Prior Provincialis AngliæMARIÆ IMMACULATÆ - SEDI SAPIENTIÆ
[I.q.7.a.4.ad.3] Ad tertium dicendum, quod, licet quibusdam positis, alia poni non sit eis oppositum, tamen infinita poni opponitur cuilibet speciei multitudinis. Unde non est possibile esse aliquam multitudinem actu infinitam.
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