Articulus 1 Article 1 Utrum Deus sit infinitus Whether God is infinite? Ad primum sic proceditur. Videtur quod Deus non sit infinitus. Omne enim infinitum est imperfectum, quia habet rationem partis et materiae, ut dicitur in III Physic. Sed Deus est perfectissimus. Ergo non est infinitus. Objection 1: It seems that God is not infinite. For everything infinite is imperfect, as the Philosopher says; because it has parts and matter, as is said in Phys. iii. But God is most perfect; therefore He is not infinite. Praeterea, secundum Philosophum in I Physic., finitum et infinitum conveniunt quantitati. Sed in Deo non est quantitas, cum non sit corpus, ut supra ostensum est. Ergo non competit sibi esse infinitum. Obj. 2: Further, according to the Philosopher (Phys. i), finite and infinite belong to quantity. But there is no quantity in God, for He is not a body, as was shown above (Q. 3, A. 1). Therefore it does not belong to Him to be infinite. Praeterea, quod ita est hic quod non alibi, est finitum secundum locum, ergo quod ita est hoc quod non est aliud, est finitum secundum substantiam. Sed Deus est hoc, et non est aliud, non enim est lapis nec lignum. Ergo Deus non est infinitus secundum substantiam. Obj. 3: Further, what is here in such a way as not to be elsewhere, is finite according to place. Therefore that which is a thing in such a way as not to be another thing, is finite according to substance. But God is this, and not another; for He is not a stone or wood. Therefore God is not infinite in substance. Sed contra est quod dicit Damascenus, quod Deus est infinitus et aeternus et incircumscriptibilis. On the contrary, Damascene says (De Fide Orth. i, 4) that God is infinite and eternal, and boundless. Respondeo dicendum quod omnes antiqui philosophi attribuunt infinitum primo principio, ut dicitur in III Physic., et hoc rationabiliter, considerantes res effluere a primo principio in infinitum. Sed quia quidam erraverunt circa naturam primi principii, consequens fuit ut errarent circa infinitatem ipsius. Quia enim ponebant primum principium materiam, consequenter attribuerunt primo principio infinitatem materialem, dicentes aliquod corpus infinitum esse primum principium rerum. I answer that, All the ancient philosophers attribute infinitude to the first principle, as is said (Phys. iii), and with reason; for they considered that things flow forth infinitely from the first principle. But because some erred concerning the nature of the first principle, as a consequence they erred also concerning its infinity; forasmuch as they asserted that matter was the first principle; consequently they attributed to the first principle a material infinity to the effect that some infinite body was the first principle of things. Considerandum est igitur quod infinitum dicitur aliquid ex eo quod non est finitum. Finitur autem quodammodo et materia per formam, et forma per materiam. Materia quidem per formam, inquantum materia, antequam recipiat formam, est in potentia ad multas formas, sed cum recipit unam, terminatur per illam. Forma vero finitur per materiam, inquantum forma, in se considerata, communis est ad multa, sed per hoc quod recipitur in materia, fit forma determinate huius rei. We must consider therefore that a thing is called infinite because it is not finite. Now matter is in a way made finite by form, and the form by matter. Matter indeed is made finite by form, inasmuch as matter, before it receives its form, is in potentiality to many forms; but on receiving a form, it is terminated by that one. Again, form is made finite by matter, inasmuch as form, considered in itself, is common to many; but when received in matter, the form is determined to this one particular thing. Materia autem perficitur per formam per quam finitur, et ideo infinitum secundum quod attribuitur materiae, habet rationem imperfecti; est enim quasi materia non habens formam. Forma autem non perficitur per materiam, sed magis per eam eius amplitudo contrahitur; unde infinitum secundum quod se tenet ex parte formae non determinatae per materiam, habet rationem perfecti. Now matter is perfected by the form by which it is made finite; therefore infinite as attributed to matter, has the nature of something imperfect; for it is as it were formless matter. On the other hand, form is not made perfect by matter, but rather is contracted by matter; and hence the infinite, regarded on the part of the form not determined by matter, has the nature of something perfect. Illud autem quod est maxime formale omnium, est ipsum esse, ut ex superioribus patet. Cum igitur esse divinum non sit esse receptum in aliquo, sed ipse sit suum esse subsistens, ut supra ostensum est, manifestum est quod ipse Deus sit infinitus et perfectus. Now being is the most formal of all things, as appears from what is shown above (Q. 4, A. 1, Obj. 3). Since therefore the divine being is not a being received in anything, but He is His own subsistent being as was shown above (Q. 3, A. 4), it is clear that God Himself is infinite and perfect. Et per hoc patet responsio ad primum. From this appears the Reply to the First Objection. Ad secundum dicendum quod terminus quantitatis est sicut forma ipsius, cuius signum est, quod figura, quae consistit in terminatione quantitatis, est quaedam forma circa quantitatem. Unde infinitum quod competit quantitati, est infinitum quod se tenet ex parte materiae, et tale infinitum non attribuitur Deo, ut dictum est. Reply Obj. 2: Quantity is terminated by its form, which can be seen in the fact that a figure which consists in quantity terminated, is a kind of quantitative form. Hence the infinite of quantity is the infinite of matter; such a kind of infinite cannot be attributed to God; as was said above, in this article. Ad tertium dicendum quod, ex hoc ipso quod esse Dei est per se subsistens non receptum in aliquo, prout dicitur infinitum, distinguitur ab omnibus aliis, et alia removentur ab eo, sicut, si esset albedo subsistens, ex hoc ipso quod non esset in alio, differret ab omni albedine existente in subiecto. Reply Obj. 3: The fact that the being of God is self-subsisting, not received in any other, and is thus called infinite, shows Him to be distinguished from all other beings, and all others to be apart from Him. Even so, were there such a thing as a self-subsisting whiteness, the very fact that it did not exist in anything else, would make it distinct from every other whiteness existing in a subject. Articulus 2 Article 2 Utrum aliquid aliud quam Deus possit esse infinitum per essentiam Whether anything but God can be essentially infinite? Ad secundum sic proceditur. Videtur quod aliquid aliud quam Deus possit esse infinitum per essentiam. Virtus enim rei proportionatur essentiae eius. Si igitur essentia Dei est infinita, oportet quod eius virtus sit infinita. Ergo potest producere effectum infinitum, cum quantitas virtutis per effectum cognoscatur. Objection 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. Praeterea, quidquid habet virtutem infinitam, habet essentiam infinitam. Sed intellectus creatus habet virtutem infinitam, apprehendit enim universale, quod se potest extendere ad infinita singularia. Ergo omnis substantia intellectualis creata est infinita. Obj. 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. Praeterea, materia prima aliud est a Deo, ut supra ostensum est. Sed materia prima est infinita. Ergo aliquid aliud praeter Deum potest esse infinitum. Obj. 3: Further, primary matter is something other than God, as was shown above (Q. 3, A. 8). But primary matter is infinite. Therefore something besides God can be infinite. Sed contra est quod infinitum non potest esse ex principio aliquo, ut dicitur in III Physic. Omne autem quod est praeter Deum, est ex Deo sicut ex primo principio. Ergo nihil quod est praeter Deum, potest esse infinitum. On the contrary, 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. Respondeo dicendum quod aliquid praeter Deum potest esse infinitum secundum quid, sed non simpliciter. I answer that, Things other than God can be relatively infinite, but not absolutely infinite. Si enim loquamur de infinito secundum quod competit materiae, manifestum est quod omne existens in actu, habet aliquam formam, et sic materia eius est terminata 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, inquantum est in potentia ad figuras infinitas. 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, that 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. Si autem loquamur de infinito secundum quod convenit formae, sic manifestum est quod illa quorum formae sunt in materia, sunt simpliciter finita, et nullo modo infinita. Si autem sint aliquae formae creatae non receptae in materia, sed per se subsistentes, ut quidam de Angelis opinantur, erunt quidem infinitae secundum quid, inquantum huiusmodi formae non terminantur neque contrahuntur per aliquam materiam, sed quia forma creata sic subsistens habet esse, et non est suum esse, necesse est quod ipsum eius esse sit receptum et contractum ad determinatam naturam. Unde non potest esse infinitum simpliciter. 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. Ad primum ergo dicendum quod hoc est contra rationem facti, quod essentia rei sit ipsum esse eius, 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. Reply Obj. 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. 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 alicuius organi, in anima intellectiva corpori coniuncta. Reply Obj. 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. Ad tertium dicendum quod materia prima non existit in rerum natura per seipsam, 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 eius potentia non se extendit nisi ad formas naturales. Reply Obj. 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. Articulus 3 Article 3 Utrum possit esse aliquid infinitum actu secundum magnitudinem Whether an actually infinite magnitude can exist? Ad tertium sic proceditur. Videtur quod possit esse aliquid infinitum actu secundum magnitudinem. In scientiis enim mathematicis non invenitur falsum, quia abstrahentium non est mendacium, ut dicitur in II Physic. Sed scientiae mathematicae utuntur infinito secundum magnitudinem, dicit enim geometra in suis demonstrationibus, sit linea talis infinita. Ergo non est impossibile aliquid esse infinitum secundum magnitudinem. Objection 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. Praeterea, id quod non est contra rationem alicuius, 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 aliquam magnitudinem esse infinitam. Obj. 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. Praeterea, magnitudo divisibilis est in infinitum, sic enim definitur continuum, quod est in infinitum divisibile, ut patet in III Physic. Sed contraria nata sunt fieri circa idem. Cum ergo divisioni opponatur additio, et diminutioni augmentum, videtur quod magnitudo possit crescere in infinitum. Ergo possibile est esse magnitudinem infinitam. Obj. 3: Further, magnitude is infinitely divisible, for the continuous is defined as 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. Praeterea, motus et tempus habent quantitatem et continuitatem a magnitudine super quam transit motus, ut dicitur in IV Physic. 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. Obj. 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. Sed contra, omne corpus superficiem habet. Sed omne corpus superficiem habens est finitum, quia superficies est terminus corporis finiti. Ergo omne corpus est finitum. Et similiter potest dici de superficie et linea. Nihil est ergo infinitum secundum magnitudinem. On the contrary, 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. 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 praemissis quod nulla creatura est infinita secundum essentiam, adhuc restat inquirere utrum aliquid creatum sit infinitum secundum magnitudinem. I answer that, 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. 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. 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. 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 consequantur accidentia, necesse est quod ad determinatam formam consequantur determinata accidentia; inter quae est quantitas. Unde omne corpus naturale habet determinatam quantitatem et in maius et in minus. Unde impossibile est aliquod corpus naturale infinitum esse. 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. 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 eius. 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 duae lineae protractae a centro, quanto longius protrahuntur a centro, tanto longius distant ab invicem; si ergo corpus esset infinitum, in infinitum lineae distarent ab invicem, et sic una nunquam posset pervenire ad locum alterius. 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 center, the farther they extend from the center, 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.