Thomas Aquinas - Summa Theologica, Part I (Prima Pars)

Everything is therefore called good from the divine goodness, as from the first exemplary effective and final principle of all goodness. Nevertheless, everything is called good by reason of the similitude of the divine goodness belonging to it, which is formally its own goodness, whereby it is denominated good. And so of all things there is one goodness, and yet many goodnesses.

This is a sufficient Reply to the Objections.

After considering the divine perfection we must consider the divine infinity, and God's existence in things: for God is everywhere, and in all things, inasmuch as He is boundless and infinite.

Concerning the first, there are four points of inquiry:

(1) Whether God is infinite?

(2) Whether anything besides Him is infinite in essence?

(3) Whether anything can be infinitude in magnitude?

(4) Whether an infinite multitude can exist? _______________________

FIRST ARTICLE [I, Q. 7, Art. 1]

Whether God Is Infinite?

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.

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.

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.

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 (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.

From this appears the Reply to the First Objection.

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.

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. _______________________

SECOND ARTICLE [I, Q. 7, Art. 2]

Whether Anything but God Can Be Essentially Infinite?

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.

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.

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.

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.

I answer that, 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.

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.

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.

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. _______________________