Summa contra Gentiles1.43 Chapter XLIII. That God is infinite

Now while the infinite is a sequel of quantity, as philosophers teach, infinity cannot be ascribed to God in respect of multitude, seeing that it has been proved that there is but one God, and that there is no composition either of parts or of accidents in Him. Nor may we say that He is infinite in respect of continuous quantity, since we have shown that He is incorporeal. 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 according to the degree in which it is perfected in its act, is the degree of magnitude in its power. Wherefore 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.

'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. 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. Wherefore an act that exists in no subject has no limitations: for instance, if whiteness were per se existent, the perfection of whiteness therein would not be limited from having whatever it is possible to have of the perfection of whiteness. Now God is an act nowise existing in another: because neither is He form in matter, as we have proved, nor is His being inherent to any form or nature, since He is His own being, as we have shown above. Therefore it follows that He is infinite.

Again. In things we find something that is pure potentiality,' as primary matter; something that is pure act, namely God, as we have shown above; and something that is act and potentiality, namely other things. Now as potentiality, 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 potentiality, it follows that God, Who is pure act, is infinite in His actuality.

Again. An act is the more perfect, according as it is less mingled with potentiality. Wherefore every act that has an admixture of potentiality has a limit to its perfection: while the act which has no admixture of potentiality has no limit to its perfection. Now God is pure act without any potentiality, as we have proved above. 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. 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 perfect 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 needs 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 1 Ch. xvi. 2 Ch. xiii.

infinite power, as we have shown above. Therefore it follows that God's essence is infinite. This argument, however, avails for those who hold to the eternity of the world: and if this be not supposed, our opinion about the infinity of the divine power is confirmed yet more. Foi every agent is the more powerful to act according as it reduces to act.a potentiality 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 potentiality. Wherefore, if the world was made after previously not being at all, the maker's power must needs be infinite.

This argument, even for those who hold to the eternity of the world, avails 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. Now this opinion being presupposed, it follows none the less from the argument stated above, 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 sourse of being: and so He produced them without any pre-existing matter or potentiality. Now active power must needs be in proportion to passive potentiality; because the greater the passive potentiality that is pre-existent or presupposed, the greater the active power which completes its actuality. Hence it follows, since a finite power produces an effect if we presuppose the potentiality of matter, that God's power, which presupposes no potentiality, 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 1 Ch. xx. 2 Cf. Augustine, De Civ. Dei x. 31.

efficacy. Now God is of infinite duration, for it has been shown above that He is eternal. Since then He has no cause of His being besides Himself, it follows that He is infinite.

The authority of Holy Writ 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.

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. 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 needs 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.