Article 2 — Whether God’s power is infinite

The second point of inquiry is whether God’s power is infinite. (Parallel texts: ST I.25.2; SCG I.43; In I Sent. 43.1.1; Compendium theologiae, ch. 19; Commentary on Physics, bk. 8, lect. 2; Commentary on Metaphysics, bk. 12, lect. 2.)

Obj. 1: And it would seem that it is not. For it is stated in Metaphysics 9 (Aristotle, Metaphysics 9.1, 1046a4–35.) that in nature any active power that has no corresponding passive power is in vain. But no passive power in nature corresponds to the infinite divine power. Therefore, the infinite divine power would be in vain.

Obj. 2: The Philosopher proves that there is no infinite power with an infinite magnitude, for it would act in no time. (Aristotle, Physics 8.10, 266a10–267b26.) For the greater power acts in less time; hence, the greater the power, the less the time. But there is no proportion between an infinite and a finite power. Neither, therefore, is there proportion between the time taken by the action of an infinite power and that taken by the action of a finite power. Yet between any time and any other time there is proportion. Therefore, since a finite power takes time to move, an infinite power will move in no time. For the same reason, if God’s power is infinite, it will always act without time. But this is false.

Obj. 3: To this you may reply that the divine will determines in how much time he will bring his effects to completion; and thus, it is not necessary that the divine power always acts in no time.

On the contrary, God’s will cannot change his power. But the very account of an infinite power requires that it act in no time. Therefore, this cannot be changed by God’s will.

Obj. 4: Every power is made known by its effect. But God cannot produce an infinite effect. Therefore, his power is not infinite.

Obj. 5: Power is proportionate to activity. But God’s activity is simple. Therefore, so is his power. But the simple and the infinite are mutually incompatible. Therefore, the same conclusion follows as before.

Obj. 6: Infinity is an attribute of quantity, according to the Philosopher. (Aristotle, Physics 1.2, 185a20–b5.) But in God there is neither quantity nor magnitude. Therefore, his power cannot be infinite.

Obj. 7: Whatever is distinct is finite. But God’s power is distinct from other realities. Therefore, it is finite.

Obj. 8: “Infinite” denotes something endless. Now, there are three kinds of end: the end of a magnitude, like a point; an end of perfection, like a form; and an end of intention, like a final cause. But since the last two belong to perfection, they must not be removed from God. Therefore, the divine power should not be called “infinite.”

Obj. 9: If God’s power is infinite, this can only be because it is concerned with infinite effects. But there are many other things which have potentially infinite effects; for example, the intellect can potentially understand an infinite number of things, and the sun can produce an infinity of effects. If, then, God’s power be infinite, many other powers will be infinite by the same account: which is impossible.

Obj. 10: An end is something pertaining to nobility. But all that is such should be ascribed to divine realities. Therefore, God’s power should be described as having an end.

Obj. 11: According to the Philosopher, infinity belongs to a part and matter, (Aristotle, Physics 3.6, 206a9–207a30.) which themselves belong to imperfection and are unbecoming to God. Therefore, there is no infinity in God’s power.

Obj. 12: According to the Philosopher, a terminus is neither finite nor infinite. (Aristotle, Physics 1.6, 189a11–20.) But God’s power is the terminus of all realities. Therefore, it is not infinite.

Obj. 13: God works with his whole power. If, then, his power is infinite, his effect will be always infinite. And this is impossible.

On the contrary (1), Damascene says that the infinite is that which is bounded neither by time nor by place nor by comprehension. (John Damascene (d. ca. 749 AD), On the Orthodox Faith 1.4, 1.8 (PG 94:798–99, 807).) Now, this belongs to the divine power. Therefore, God’s power is infinite.

Furthermore (2), Hilary says that God’s power is immeasurable; he is the living mighty one, ever present, never failing. (Hilary of Poitiers (ca. 315–368 AD), On the Trinity 8.24 (PL 10:253–54).) Now, that which is immeasurable is infinite. Therefore, God’s power is infinite.

I answer that a thing is said to be infinite in two ways.

First, by way of privation. Thus a thing is said to be “infinite” when it is in its nature to have an end, and yet it has none. But such infinity is found only in quantities.

Second, by way of negation; that is, when it has no end.

Infinity cannot be ascribed to God in the former sense, both because God is without quantity, and because all privation denotes imperfection, which is far removed from God.

On the other hand, infinity in the second sense is ascribed to God and to all that is in him, because he himself is not limited by anything—not his essence, not his wisdom, not his power, and not his goodness. Hence, in him all is infinite. But with special regard to the infinity of his power, it must be observed that since an active power follows act, the quantity of a power follows the quantity of act; for the more actual a thing is, the more it abounds in the power to act.

Now, God is infinite act; this is clear from the fact that act can be finite in only two ways.

First, on the part of the agent; thus, the beauty of a house receives its quantity and terminus from the will of the architect.

Second, on the part of the recipient; thus, the heat in pieces of wood is limited by and receives its quantity according to the disposition of the wood pieces.

Now, the divine act itself is not limited by any agent, because it is not from another, but from its very self; nor is it limited by any recipient, because, since nothing of passive power is blended with him, he is pure act, not received in anything; for God is his being itself received in nothing. Thus, it is clear that God is infinite.

And this can be made evident as follows. The being of a man is limited to the species of man because it is received into the nature of the human species; the same applies to the being of a horse or of any other creature. But the being of God, since it is not received into anything but is pure being, is not limited to any particular mode of a perfection of being but contains the whole of being within itself. And thus, as “being” taken in its widest sense can extend to an infinity of things, so the divine being is infinite. And hence it is clear that his might or active power is infinite.

But we must note that, although his power is infinite by reason of his essence, nevertheless it holds a certain mode of infinity which the essence does not possess, because we refer it to the things of which it is the source. For in the objects of a power there is a certain multitude; in action also there is a certain intensity according to the efficiency of acting, such that a certain infinity may be ascribed to active power according to its conformity to the infinity of quantity, whether continuous or discrete. Of discrete quantity, insofar as the quantity of a power is measured by many or few objects—and this is called its “extensive quantity.” Of continuous quantity, insofar as the quantity of a power is measured by the intensity or slackness of its action—and this is called its “intensive quantity.” The former quantity is ascribed to power in respect of its objects, the latter in respect of its action; for active power is the principle of both.

In both ways, the divine power is infinite. For it never produces so many effects that it cannot produce more, nor does it ever act with such intensity that it cannot act more intensely. But in the divine operation, intensity should not be viewed in reference to the operation being in the operator, for then it is always infinite, since God’s operation is his essence; rather, it should be viewed in reference to its attaining its effect, for in this way some things are moved by God more efficaciously, some less.

Reply Obj. 1: Nothing in God can be called “in vain,” for the vain is what is directed to an end that it cannot attain, whereas God and all that is in him are not for an end, but are the end. Or we may reply that the Philosopher is speaking of a natural active power. For natural things, and even all created things, are coordinated with each other. But God is outside that order since this whole order is ordered to him as its extrinsic good, like the army to the general, according to the Philosopher. (Aristotle, Metaphysics 12.10, 1075a13.) Consequently, there is no need that there be something in created things corresponding to what is in God.

Reply Obj. 2: According to the Commentator on Physics 8, this demonstration drawn from the proportion between time and the mover’s power proceeds in reference to a magnitude’s infinite power, which is proportionate to an infinity of time, since they both belong to one definite genus, namely, continuous quantity; (Averroes (1126–1196 AD), Commentary on the Physics, in Aristotelis opera cum Averrois commentariis, 4 vols. (Venice: Apud Junctas, 1562–1574; reprinted, Frankfurt am Main: Minerva, 1962), bk. 8, folios 423C–426G TC78–79); hereafter, citations from this edition will be given in abbreviated format, with the first number referring the folio and letter division and the second number referring to the paragraph being commented on: LC 423C–426G TC 78–79. Cf. Aristotle, Physics 8.10, 266a10–30.) but it does not hold for an infinity apart from magnitude, which is not proportionate to an infinity of time, since it is of a different account. It may also be replied, as hinted in the objection, that, since God acts by his will, he adapts the movement of whatever he moves according as he wills.

Reply Obj. 3: Although God’s will cannot change his power, it nevertheless can determine its effect. For the will moves power.

Reply Obj. 4: The very account of being made or created is incompatible with the infinite. For from the very fact that it comes to be from nothing, it has a certain defect and is in potency, not pure act: consequently, it cannot be equated with the infinite as though it also were infinite.

Reply Obj. 5: “Infinity” spoken of privatively, which is an attribute of quantity, is repugnant to simplicity; but “infinity” spoken of negatively is not.

Reply Obj. 6: This argument applies to infinity taken as a privation.

Reply Obj. 7: A thing may be distinct in two ways.

First, by something adjoined to it, as man is distinct from ass by the difference “rational.” And a distinct thing of this kind must be finite because the adjunct determines it as a particular thing.

Second, by itself; and thus God is distinct from other things; and this for the simple reason that it is impossible to add anything to him. Hence, it does not follow that he is finite, either in himself or as regards anything that is attributed to him.

Reply Obj. 8: Since an end belongs to perfection, it is ascribed to God in the noblest way—namely, that he himself is essentially the end and not denominatively finite.

Reply Obj. 9: As in quantities we may consider infinity in regard to one dimension and not in regard to another (or again, in regard to all dimensions), even so may we consider infinity in effects. For it is possible for a creature considered in itself to be able to produce an infinity of effects in some particular respect—for instance, as regards number in one species. And then the nature of all those effects is finite, being confined to one particular species, such as if one were to take an infinite number of men or asses. But it is impossible for a creature to be able to produce an infinity of effects in every way, in point of number, species, and genera. Rather, this belongs to God alone; and hence his power alone is simply infinite.

Reply Obj. 10: The reply to the tenth objection is the same as to the eighth.

Reply Obj. 11: This argument takes infinity as a privation.

Reply Obj. 12: The same answer applies to the twelfth objection.

Reply Obj. 13: God always works with the whole of his power. But his effect is limited according to the determination of his will and the order of reason.