ARTICLE X

In the Tenth Article We Ask a Question Which Arose Incidentally: CAN GOD MAKE INFINITES?

Difficulties:

It seems that He can, for

1. Natures existing in the divine mind are productive of things, and one does not impede another by its action. Since there are infinite natures in the divine mind, infinite effects could follow from them were the divine power to carry them into execution.

2. The power of the Creator infinitely surpasses that of a creature. But a creature can produce infinites successively. Therefore, God can produce infinites simultaneously.

3. A power is useless if it is not put into act; it is especially useless if it cannot be put into act. But God's power extends to infinites. Hence, such a power would be useless if He could not actually make infinites.

Difficulties to the contrary:

1'. Seneca's opinion is to the contrary: "An idea is an exemplar of things coming into being naturally." But, since there cannot be infinite things naturally, it would seem that they cannot come to be; for what cannot be cannot come to be. Therefore, there will be no idea of infinites in God. But God cannot make anything except through an idea. Therefore, He cannot make infinites.

2'. When God is said to create a thing, nothing new on the part of the Creator is affirmed but only on the part of the creature. Hence, it seems the same to say that God creates things as to say that things come forth into being from God. For the same reason, therefore, to say that God can create things is to say that things are able to come forth from God into being. But infinite things cannot come to be, for no creature has the capacity for infinite act. Hence, even God cannot make actual infinites.

REPLY:

The infinite can be distinguished in two ways. In one way, it is distinguished by means of potency and act. A potential infinite is that which consists in an endless succession. For example, we find potential infinity in generation, in time, and in the division of a continuum; for, when one member is given, another always follows. An example of an actual infinite, however, would be a line which we would assume to have no termini.

In the second way, an essential infinite is distinguished from an accidental infinite. This distinction is explained as follows: "The character of the infinite," as mentioned above, "belongs to quantity." Now, quantity is predicated first of all of discrete quantity rather than of continuous quantity. Hence, in order to see what is infinite essentially and what is infinite accidentally, we must consider that a multitude is sometimes required essentially and sometimes merely accidentally. Essentially a multitude is required in ordered causes and effects where one has an essential dependence upon another. For example, the soul sets in motion the natural heat by which nerves and muscles are moved, which, in turn, move the hands, which move a stick by which a stone is moved. In this series, each of the later members essentially depends upon every one that precedes. But an accidental multitude is found when all the members of the multitude are posited, as it were, in place of one; and their mutual relation is such that it is a matter of indifference whether they be one or many, or more or fewer. For example, if a builder makes a house in whose construction he wears out many saws successively, a multitude of saws is required for the erection of the house only accidentally, that is, because one saw cannot last forever. It does not matter to the house how many saws are used; hence, one saw does not have that dependence upon another which we find when a multitude is required essentially.

There are many different opinions about the infinite. Some ancient philosophers posited actual infinites, both essential and accidental, thinking that an infinite would necessarily be a result of what they posited as a beginning. For this reason, they also posited an infinite process of causes. The Philosopher refutes this position, however.

Others, following Aristotle, conceded that an essential infinite cannot be found either in act or in potency, because it is impossible for a thing to depend essentially upon an infinite number of things; for, if this were true, then its own act of existence would never be formally constituted. But they posited an accidental infinite, both in potency and in act. Algazel holds: "There are an infinite number of human souls separated from bodies" -something which he thought followed from his view that the world is eternal. He saw no difficulty since they have no mutual dependence, and so in their multiplicity they constituted merely an accidental infinity.

Others asserted that there cannot be an actual infinite, either essential or accidental. They admitted a potential infinite, which, as is taught in the Physics, consists in succession; and this is the position of the Commentator. But for either of two reasons it can happen that an actual infinite cannot exist: either because to be in act is contradictory to the infinite by the very fact that it is infinite; or because of some extrinsic reason--as being lifted up is repugnant to a lead triangle, not because it is a triangle, but because it is lead.

But if an actual infinite is not contradictory to the infinite as such and can exist, as I hold, or if it cannot exist merely because of some impediment extrinsic to the notion of an infinite, then I say that God can make an actual infinite. If, however, actual existence is repugnant to the very notion of an infinite, then God cannot make one, just as, for example, He cannot make a man be an irrational animal. This would mean that two contradictories would coincide in one act of existence. However, whether or not it is intrinsically repugnant for an actual infinite to exist must be discussed elsewhere, since this question arose only incidentally. Answers, however, must be given to the difficulties on both sides.

Answers to Difficulties:

1. Natures in the divine mind are not reproduced in a creature the way in which they are in God, but in the way which the nature of a creature allows. Hence, although they themselves are immaterial, from them are brought forth things with a material act of existence. If, therefore, as the Philosopher says, it is of the essence of an infinite to exist, not actually and simultaneously, but merely successively, then the infinite natures in the divine mind cannot all be produced in creatures simultaneously but only successively. So, it does not follow that there are actual infinites.

2. The power of a creature is said to be wanting in two ways. First, it can be wanting because of a lack of strength. In this respect, it is correct to argue that what a creature cannot do God can do. Second, it can be wanting because that which is said to be impossible for a creature to do contains in itself some intrinsic repugnance. In this respect, it is possible neither for a creature nor for God--as, for instance, that contradictories should exist simultaneously, and that an infinite actually exist falls into this class, if to exist actually is repugnant to the nature of an infinite.

3. As is said in the Physics, a being is useless if it does not attain the end for which it exists. Hence, a power is not said to be had in vain simply because it is not put into act, but only because its effect or the very act, being distinct from the power itself, is the end for which the power exists. However, no effect of the divine power is its end, nor is its act distinct from it. Hence, the argument does not follow.

Answers to Contrary Difficulties:

1'. Although the members of infinites may not naturally be able to exist simultaneously, they may, however, come into being. For the essence of an infinite does not consist in simultaneous existence; but it is like things which are in a state of becoming, such as a day or a contest, as is said in the Physics. Nor does it follow that God is able to make only things which come into being naturally. It is true that according to the meaning given previously an idea was taken as applying to practical knowledge, which is an idea for this reason that it is determined by the divine will to an act. However, by His will God is able to make many things other than those which He has determined to exist now, in the past, or in the future.

2'. Although in creation there is nothing new except in reference to the creature, the word creation implies not only this newness but also something on the part of God; for it signifies a divine action, which is His essence, and connotes an effect in a creature, which is the reception of being from God. So, it does not follow that it is the same to say that God can create something as to say that something can be created by Him. Otherwise, before there was a creature, nothing could be created unless the potency of a creature first existed. This would be positing eternal matter. Therefore, although the potency of a creature does not extend to the existence of actual infinites, this does not exclude ability on the part of God to make actual infinites.