Thomas Aquinas, Summa Theologiae

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.

Objection 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 (Question 3, Article 1). Therefore it does not belong to Him to be infinite.

Objection 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.

On the contrary, Damascene says (De Fide Orth. i, 4) that "God is infinite and eternal, and boundless."

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.

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. 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. Now being is the most formal of all things, as appears from what is shown above (Question 4, Article 1, Objection 3). Since therefore the divine being is not a being received in anything, but He is His own subsistent being as was shown above (Question 3, Article 4), it is clear that God Himself is infinite and perfect.

From this appears the Reply to the First Objection.

Reply to Objection 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.

Reply to Objection 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 1

Argumentum 1

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.

Argumentum 2

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.

Argumentum 3

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.

Sed Contra

Sed contra est quod dicit Damascenus, quod deus est infinitus et aeternus et incircumscriptibilis.

Corpus

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.

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. 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.

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.

Ad 1

Et per hoc patet responsio ad primum.

Ad 2

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.

Ad 3

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.