Summa contra Gentiles1.69 Chapter LXIX. That God knows infinite things

We must next prove that God knows infinite things. For in knowing that He is the cause of things He knows things other than Himself, as was shown above. Now He is the cause of infinite things, if there be infinite things, since He is the cause of whatever is. Therefore He knows infinite things.

Again. God knows His own power perfectly, as was proved above. Now a power cannot be known perfectly unless all the things to which it extends be known, since its quantity is gauged in a manner according to them. But His power, being infinite as we have shown, extends to infinite things. Therefore God knows infinite things.

Moreover. If God's knowledge extends to all things that exist, in whatever way they exist, as we have shown, it follows that He knows not only actual being but also potential being. Now in natural things there is the infinite potentially although not actually, as the Philosopher proves in 3 Phys. Therefore God knows infinite things: even as unity, which is the principle of number, would know infinite species of numbers, if it knew whatever is potentially in it; for unity is every number potentially.

Again. God knows other things in His essence as in a prototypical medium. Now since He is infinitely perfect, as was shown above, it is possible for an infinite number of things with finite perfections to be copied from Him; since it is impossible for any single one, or any number of copies, to equal the example of their prototype, and thus there always remains some new way in which some copy can imitate it. Nothing therefore prevents Him from knowing infinite things by His essence.

Further. God's being is His act of understanding. Therefore even as His being is infinite, as shown above, so His act of understanding is infinite. Now as finite is to finite so is infinite to infinite. If therefore by our act of understanding which is finite we are able to understand finite things, God also by His act of understanding is able to understand infinite things.

Moreover. According to the Philosopher (3 De Anima) an intellect which knows the supremely intelligible knows the less intelligible not less but more: and the reason for this is that the intellect is not corrupted by the excellence of the intelligible, as the sense is, but is the more perfected. Now if we take an infinite number of beings, whether they be of the same species—as an infinite number of men—or of an infinite number of species, even though some or all of them be infinite in quantity, if this were possible; all of them together would be of less infinity than God: since each one and all together would have being confined and limited to a certain species or genus, and thus would be in some way finite: wherefore it would fall short from the infinity of God Who is infinite simply, as we proved above. Since, therefore, God knows Himself perfectly, nothing prevents Him from also knowing that infinite number of things.

Further. The more efficacious and clear an intellect is in knowing, the greater the number of things is it able to know from one: even as every power, the stronger it is, the more united it is. Now the divine intellect is infinite in effiacy or perfection, as was shown above. Therefore it can know an infinite number of things by one which is His essence.

Further. The divine intellect like the divine essence is perfect simply. Wherefore no intellectual perfection is lacking thereto. Now that to which our intellect is in potentiality is its intellectual perfection: and it is in potentiality to all intelligible species. But these species are infinite in number: since the species of numbers and figures are infinite. It follows therefore that God knows all like infinite things.

Again. Since our intellect is cognizant of the infinite in potentiality, for as much as it is able to multiply the species of numbers indefinitely; if the divine intellect knew not also the infinite in act, it would follow either that our intellect knows more things than the divine intellect knows, or that the divine intellect knows not actually all the things that it knows potentially: and each of these is impossible, as proved above.

Further. The infinite is repugnant to knowledge in so far as it is incompatible with being counted: for it is in itself impossible, as implying a contradiction, for the parts of the infinite to be numbered. Now the knowledge of a thing by counting its parts belongs to an intellect that knows one part after another in succession, and not to one that understands the various parts together. Since then the divine intellect knows things together without succession, it is no more hindered from knowing the infinite than from knowing the finite.

Moreover. All quantity consists in a certain plurality of parts, for which reason number is the first of quantities. Accordingly where plurality involves no difference, neither does it cause any difference consequent upon quantity. Now in God's knowledge many things are known in the same way as one, since they are known, not by various species, but by one which is God's essence. Wherefore many things are known by God simultaneously: and consequently plurality makes no difference in God's know- 1 Ch. xlv. 2 Cf. chs. xvi., xxix. 3 Ch. xlvi.

ledge. Neither therefore does the infinite which is consequent upon quantity. Therefore knowledge, whether of infinite or of finite things, differs not to the divine intellect. And consequently, since it knows finite things, nothing prevents it from knowing also infinite things.

The words of the psalm are in agreement with this: And of His wisdom there is no number.

From the foregoing it is clear why our intellect knows not the infinite, as the divine intellect does. For our intellect differs from the divine intellect in four respects, which constitute this difference. In the first place, our intellect is simply finite, whereas the divine intellect is infinite. Secondly our intellect knows different things by different species: wherefore it cannot grasp infinite things by one knowledge, as the divine intellect can. The third difference results from the fact that our intellect, since it knows different things by different species, cannot know many things at the same time, so that it cannot know an infinite number of things except by taking them one after the other. Whereas it is not so in the divine intellect, which considers many things simultaneously, as seen by one species. Fourthly, because the divine intellect is about things that are and things that are not, as we proved above.

It is also clear how the saying of the Philosopher that the infinite as such is unknown, is not in contradiction with this statement. For since, as he says, the notion of infinity is becoming to quantity, the infinite would be known as such, if it were known by the measuring of its parts: because this is proper knowledge of quantity. But God does not know thus. Wherefore, so to say, He knows the infinite, not as such, but in as much as in comparison with His knowledge it is finite, as we have shown.

It must be observed, however, that God does not know infinite things by His knowledge of vision, to use the expression employed by others, because the infinite neither is, nor was, nor will be actual; since, according to the Catholic faith, generation is not infinite on either part. Yet He knows the infinite by His knowledge of simple intelligence. For God knows the infinite number of things that neither are, nor will be, nor have been, and nevertheless are in the power of a creature. He knows also the infinite things that are in His power, that neither are, nor have been, nor shall be.

Wherefore as regards the question about the knowledge of singulars, we might reply by denying the major premiss: since singulars are not infinite. If, however, they were, God would know them none the less.