Chapter 43 — That God is infinite

Now while the infinite is a sequel of quantity, as philosophers teach, (Aristotle, Physics 1.2, 185a20–b5.) infinity cannot be ascribed to God in respect of multitude, seeing that it has been proved that there is but one God, (Ch. 42.) and that there is no composition either of parts or of accidents in him. (Cc. 18, 23.) Nor may we say that he is infinite in respect of continuous quantity, since we have shown that he is incorporeal. (Ch. 20.) It remains, therefore, to inquire whether infinity is becoming to him in respect of spiritual magnitude.

This spiritual magnitude is referable to two things, namely, to power and to the goodness or perfection of a thing’s very nature. For a thing is said to be more or less white according to the degree of perfection in its whiteness. And the magnitude of power is gauged from the magnitude of deeds or of things made. Now in these things the magnitude of one follows the magnitude of the other, because from the very fact that a thing is in act it is active, and consequently the degree of magnitude in its power is according to the degree in which it is perfected in its act. And thus spiritual things are said to be great according to their degree of perfection: for Augustine says that in things which are great not by bulk, to be great is to be good. (Augustine, On the Trinity, bk. 6, ch. 8.)

Accordingly, we have to show that God is infinite according to this kind of magnitude. Not, however, so that infinite be understood privatively, as in dimensive or numeral quantity: for a quantity of this kind is naturally finite, so that we speak of infinity by subtraction of that which it has by nature, and for this reason infinity in those quantities denotes imperfection. But in God the infinite is understood only negatively, because there is no bound or end to his perfection, and he is the supremely perfect being. And it is thus that the infinite should be ascribed to God.

For whatever is finite by its nature is confined to some generic notion. Now God is in no genus, and his perfection contains the perfections of all genera, as we have shown above. (Cc. 25, 28.) Therefore, he is infinite.

Moreover. Every act inherent to something else receives its limitation from that in which it is, since that which is in another is in it according to the mode of the recipient. Therefore, an act that exists in no subject has no limitations: for instance, if whiteness were essentially existent, the perfection of whiteness in it would not be limited from having whatever it is possible to have of the perfection of whiteness. Now God is an act in no way existing in another: for neither is he form in matter, as we have proved, (Cc. 26, 27.) nor is his being inherent to any form or nature, since he is his own being, as we have shown above. (Ch. 22.) Therefore, it follows that he is infinite.

Again. In things we find something that is pure potency, as prime matter; something that is pure act, namely, God, as we have shown above; (Ch. 16.) and something that is act and potency, namely, other things. Now as potency, since it bears relation to an act, cannot exceed that act in any particular thing, so neither can it simply. Therefore, since primary matter is infinite in its potency, it follows that God, who is pure act, is infinite in his act.

Again. An act is the more perfect according as it is less mingled with potency. Therefore, every act that has an admixture of potency has a limit to its perfection, while the act which has no admixture of potency has no limit to its perfection. Now God is pure act without any potency, as we have proved above. (Ch. 16.) Therefore, he is infinite.

Again. Being itself, considered absolutely, is infinite; for it can be participated by an infinite number of things in an infinite number of ways. Hence if we take a thing with finite being, this being must be limited by some other thing which is in some way the cause of that being. Now there can be no cause of God’s being, since he is necessary of himself. (Ch. 13.) Therefore, he has infinite being, and himself is infinite.

Moreover. Whatever has a particular perfection is the more perfect according as it more fully participates that perfection. Now there cannot be, nor even be imagined, a way in which a perfection is possessed more fully than by that which is perfect by its essence, and whose being is its goodness: and such is God. Therefore, in no way can anything be imagined better or more perfect than God. Therefore, he is infinite in goodness.

Further. Our intellect reaches the infinite in understanding, a sign of which is that, given any finite quantity, our intellect can imagine a greater. Now, it would be to no purpose for the intellect to be thus directed to the infinite unless there were infinite intelligible being. Therefore, there must be some infinite intelligible thing, which must be the greatest of all beings: and this we call God. Therefore, God is infinite.

Again. An effect cannot extend beyond its cause. Now our intellect cannot be but from God, who is the first cause of all things. Therefore, our intellect cannot think of anything greater than God. If, then, it is possible to think of something greater than every finite thing, it follows that God is not finite.

Moreover. Infinite power cannot be in a finite essence, because everything acts by its form, which is either its essence or part thereof, and power denotes a principle of action. But God has not a finite active power, for he moves in infinite time, and this cannot be save from an infinite power, as we have shown above. (Ch. 20.) Therefore, it follows that God’s essence is infinite.

This argument, however, avails for those who hold to the eternity of the world. If this is not supposed, our opinion about the infinity of the divine power is confirmed yet more. For every agent is the more powerful to act according as it reduces to act a potency the further removed from act: thus a greater power is needed to heat water than air. Now that which is not at all is infinitely distant from act, nor is it in any way in potency. Therefore, if the world was made after previously not being at all, the maker’s power must be infinite.

This argument, even for those who hold to the eternity of the world, is strong enough to prove the infinity of the divine power. For they confess that God is the cause of the substance of the world, although they aver that it is eternal, since they say that the eternal God is the cause of an eternal world in the same way as a foot would have been from eternity the cause of a footprint, if it had trod on the dust from eternity. (Cf. Augustine, City of God 10.31.) Now this opinion being presupposed, it nevertheless follows from the above argument that the power of God is infinite. For whether he fashioned things from time, as we hold, or from eternity, as they maintain, there cannot be in things anything that he has not produced, since he is the universal source of being, and so he produced them without any preexisting matter or potency. Now active power must be in proportion to passive potency, because the greater the passive potency that is preexistent or presupposed, the greater the active power which completes its act. Hence it follows, since a finite power produces an effect if we presuppose the potency of matter, that God’s power, which presupposes no potency, is not finite but infinite: and that consequently his essence is infinite.

Moreover. A thing lasts so much the longer as its cause is more efficacious. Consequently, a thing which is of infinite duration must have being through a cause of infinite efficacy. Now God is of infinite duration, for it has been shown above (Ch. 15.) that he is eternal. Since, then, he has no cause of his being besides himself, it follows that he is infinite.

The authority of Sacred Scripture bears witness to this truth; for the Psalmist says: great is the Lord and greatly to be praised: and of his greatness there is no end (Ps 145[144]:3).

The same truth is attested by the statements of the oldest philosophers, since all of them, compelled as it were by truth itself, asserted that the first principle of things is infinite. (Aristotle, Physics 3.4.) For they knew not what they said, believing the infinity of the first principle to be after the manner of a discrete quantity, as Democritus maintained, asserting an infinite number of atoms to be the principles of things, and as Anaxagoras held, stating that the principles of things are an infinite number of similar parts; or after the manner of continuous quantity, as those who held that some element, or some undefined infinite body, is the first principle of all. But since it was proved by the researches of subsequent philosophers that there is no infinite body, and if to this we add that the first principle must be infinite in some way, it follows that the infinite which is the first principle is neither a body nor a power residing in a body. (Cf. ch. 20.)

God’s knowledge