2. God knows His own power perfectly (Chap. XLVII, XLIX). But power cannot be perfectly known, unless all the objects to which it extends are known, since according to that extent the amount of the power may be said to be determined. But His power being infinite (Chap. XLIII) extends to things infinite, and therefore also His knowledge.
3. If the knowledge of God extends to all things that in any sort of way are, He must not only know actual being, but also potential being. But in the physical world there is potential infinity, though not actual infinity, as the Philosopher proves. God therefore knows infinite things, in the way that unity, which is the principle of number, would know infinite species of number if it knew whatever is in its potentiality: for unity is in promise and potency every number.*
4. God in His essence, as in a sort of exemplar medium, knows other things. But as He is a being of infinite perfection, there can be modelled upon Him infinite copies with finite perfections, because no one of these copies, nor any number of them put together, can come up to the perfection of their exemplar; and thus there always remains some new way for any copy taken to imitate Him.
10. The infinite defies knowledge in so far as it defies counting. To count the parts of the infinite is an intrinsic impossibility, as involving a contradiction. To know a thing by enumeration of its parts is characteristic of a mind that knows part after part successively, not of a mind that comprehends the several parts together. Since then the divine mind knows all things together without succession, it has no more difficulty in knowing things infinite than in knowing things finite.
11. All quantity consists in a certain multiplication of parts; and therefore number is the first of quantities.* Where then plurality makes no difference, no difference can be made there by anything that follows upon quantity. But in God's knowledge many things are known in one, not by many different presentations, but by that one species, or presentation, which is the essence of God. Hence a multitude of things is known by God all at once; and thus plurality makes no difference in God's knowledge: neither then does infinity, which follows upon quantity.
In accordance with this is what is said in Psalm cxlvi: And of his wisdom there is no telling.
From what has been said it is clear why our mind does not know the infinite as the divine mind does. Our mind differs from the divine mind in four respects; and they make all the difference. The first is that our mind is simply finite, the divine mind infinite. The second is that as our mind knows different things by different impressions, it cannot extend to an infinity of things, as the divine mind can. The third results in this way, that as our mind is cognisant of different things by different impressions, it cannot be actually cognisant of a multitude of things at the same time;* and thus it could not know an infinity of things except by counting them in succession, which is not the case with the divine mind, which discerns many things at once as seen by one presentation. The fourth thing is that the divine mind is cognisant of things that are and of things that are not (Chap. LXVI).
It is also clear how the saying of the Philosopher, that the infinite, as infinite, is unknowable, is in no opposition with the opinion now put forth: because the notion of infinity attaches to quantity; consequently, for infinite to be known as infinite, it would have to be known by the measurement of its parts, for that is the proper way of knowing quantity: but God does not know the infinite in that way. Hence, so to say, God does not know the infinite inasmuch as it is infinite, but inasmuch as, to His knowledge, it is as though it were finite.*
It is to be observed however that God does not know an infinity of things with the 'knowledge of vision,' because infinite things neither actually are, nor have been, nor shall be, since, according to the Catholic faith, there are not infinite generations either in point of time past or in point of time to come. But He does know an infinity of things with the 'knowledge of simple understanding': for He knows infinite things that neither are, nor have been, nor shall be, and yet are in the power of the creature;* and He also knows infinite things that are in His own power, which neither are, nor shall be, nor have been. Hence to the question of the knowledge of particular things it may be replied by denial of the major: for particular things are not infinite: if however they were, God would none the less know them.*
1.68 : That God knows the Motions of the Will
1.70 : That God knows Base and Mean Things