That God is Infinite

INFINITY cannot be attributed to God on the score of multitude, seeing there is but one God. Nor on the score of quantitative extension, seeing He is incorporeal. It remains to consider whether infinity belongs to Him in point of spiritual greatness. Spiritual greatness may be either in power or in goodness (or completeness) of nature. Of these two greatnesses the one follows upon the other: for by the fact of a thing being in actuality it is capable of action. According then to the completeness of its actuality is the measure of the greatness of its power. Thus it follows that spiritual beings are called great according to the measure of their completeness, as Augustine says: "In things in which greatness goes not by bulk, being greater means being better" (De Trinit. vi, 9). But in God infinity can be understood negatively only, inasmuch as there is no term or limit to His perfection. And so infinity ought to be attributed to God.

2. Every actuality inhering in another takes limitation from that wherein it is: for what is in another is therein according to the measure of the recipient. An actuality therefore that is in none, is bounded by none: thus, if whiteness were self-existent, the perfection of whiteness in it would have no bounds till it attained all the perfection of whiteness that is attainable.* But God is an actuality in no way existent in another: He is not a form inherent in matter; nor does His being inhere in any form or nature; since He is His own being, His own existence (Chap. XXI). The conclusion is that He is infinite.

4. Actuality is more perfect, the less admixture it has of potentiality. Every actuality, wherewith potentiality is blended, has bounds set to its perfection: while that which is without any blend of potentiality is without bounds to its perfection. But God is pure actuality without potentiality (Chap. XVI), and therefore infinite.

6. There cannot be conceived any mode in which any perfection can be had more perfectly than by him, who is perfect by his essence, and whose being is his own goodness. But such is God: therefore anything better or more perfect than God is inconceivable. He is therefore infinite in goodness.

7. Our intellect, in understanding anything, reaches out to infinity; a sign whereof is this, that, given any finite quantity, our intellect can think of something greater. But this direction of our intellect to the infinite would be in vain, if there were not something intelligible that is infinite. There must therefore be some infinite intelligible reality, which is necessarily the greatest of realities; and this we call God.

8. An effect cannot reach beyond its cause: now our understanding cannot come but of God, who is the First Cause. If then our understanding can conceive something greater than any finite being, the conclusion remains that God is not finite.*

9. Every agent shows greater power in action, the further from actuality is the potentiality which it reduces to actuality, as there is need of greater power to warm water than to warm air. But that which is not at all, is infinitely distant from actuality, and is not in any way in potentiality: therefore if the world was made a fact from being previously no fact at all, the power of the Maker must be infinite. This argument avails to prove the infinity of the divine power even to the mind of those who assume the eternity of the world. For they acknowledge God to be the cause of the substantial being of the world, although they think that substance to have been from eternity, saying that the eternal God is the cause of an ever-existing world in the same way that a foot would be the cause of an everlasting foot-print, if it had been from eternity stamped on the dust. Still, even accepting the position thus defined, it follows that the power of God is infinite. For whether He produced things in time, according to us, or from eternity, according to them, there can be nothing in the world of reality that He has not produced, seeing that He is the universal principle of being; and thus He has brought things to be, without presupposition of any matter or potentiality. Now the measure of active power must be taken according to the measure of potentiality or passivity; for the greater the pre-existing or preconceived passivity, the greater the active power required to reduce it to complete actuality. The conclusion remains that, as finite power in producing an effect is conditioned on the potentiality of matter, the power of God, not being conditioned on any potentiality, is not finite, but infinite, and so is His essence infinite. To this truth Holy Scripture bears witness: Great is the Lord and exceedingly to he praised, and of his greatness there is no end (Ps. cxliv, 3).

1.42 : That God is One
1.44 : That God has Understanding