Part I (Prima Pars) Part 10 (1/2)

Whether an Infinite Mult.i.tude Can Exist?

Objection 1: It seems that an actually infinite mult.i.tude is possible.

For it is not impossible for a potentiality to be made actual. But number can be multiplied to infinity. Therefore it is possible for an infinite mult.i.tude actually to exist.

Obj. 2: Further, it is possible for any individual of any species to be made actual. But the species of figures are infinite. Therefore an infinite number of actual figures is possible.

Obj. 3: Further, things not opposed to each other do not obstruct each other. But supposing a mult.i.tude of things to exist, there can still be many others not opposed to them. Therefore it is not impossible for others also to coexist with them, and so on to infinitude; therefore an actual infinite number of things is possible.

_On the contrary,_ It is written, ”Thou hast ordered all things in measure, and number, and weight” (Wis. 11:21).

_I answer that,_ A twofold opinion exists on this subject. Some, as Avicenna and Algazel, said that it was impossible for an actually infinite mult.i.tude to exist absolutely; but that an accidentally infinite mult.i.tude was not impossible. A mult.i.tude is said to be infinite absolutely, when an infinite mult.i.tude is necessary that something may exist. Now this is impossible; because it would entail something dependent on an infinity for its existence; and hence its generation could never come to be, because it is impossible to pa.s.s through an infinite medium.

A mult.i.tude is said to be accidentally infinite when its existence as such is not necessary, but accidental. This can be shown, for example, in the work of a carpenter requiring a certain absolute mult.i.tude; namely, art in the soul, the movement of the hand, and a hammer; and supposing that such things were infinitely multiplied, the carpentering work would never be finished, forasmuch as it would depend on an infinite number of causes. But the mult.i.tude of hammers, inasmuch as one may be broken and another used, is an accidental mult.i.tude; for it happens by accident that many hammers are used, and it matters little whether one or two, or many are used, or an infinite number, if the work is carried on for an infinite time. In this way they said that there can be an accidentally infinite mult.i.tude.

This, however, is impossible; since every kind of mult.i.tude must belong to a species of mult.i.tude. Now the species of mult.i.tude are to be reckoned by the species of numbers. But no species of number is infinite; for every number is mult.i.tude measured by one. Hence it is impossible for there to be an actually infinite mult.i.tude, either absolute or accidental. Likewise mult.i.tude in nature is created; and everything created is comprehended under some clear intention of the Creator; for no agent acts aimlessly. Hence everything created must be comprehended in a certain number. Therefore it is impossible for an actually infinite mult.i.tude to exist, even accidentally. But a potentially infinite mult.i.tude is possible; because the increase of mult.i.tude follows upon the division of magnitude; since the more a thing is divided, the greater number of things result. Hence, as the infinite is to be found potentially in the division of the continuous, because we thus approach matter, as was shown in the preceding article, by the same rule, the infinite can be also found potentially in the addition of mult.i.tude.

Reply Obj. 1: Every potentiality is made actual according to its mode of being; for instance, a day is reduced to act successively, and not all at once. Likewise the infinite in mult.i.tude is reduced to act successively, and not all at once; because every mult.i.tude can be succeeded by another mult.i.tude to infinity.

Reply Obj. 2: Species of figures are infinite by infinitude of number. Now there are various species of figures, such as trilateral, quadrilateral and so on; and as an infinitely numerable mult.i.tude is not all at once reduced to act, so neither is the mult.i.tude of figures.

Reply Obj. 3: Although the supposition of some things does not preclude the supposition of others, still the supposition of an infinite number is opposed to any single species of mult.i.tude. Hence it is not possible for an actually infinite mult.i.tude to exist.

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QUESTION 8

THE EXISTENCE OF G.o.d IN THINGS (In Four Articles)

Since it evidently belongs to the infinite to be present everywhere, and in all things, we now consider whether this belongs to G.o.d; and concerning this there arise four points of inquiry:

(1) Whether G.o.d is in all things?

(2) Whether G.o.d is everywhere?

(3) Whether G.o.d is everywhere by essence, power, and presence?

(4) Whether to be everywhere belongs to G.o.d alone?

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FIRST ARTICLE [I, Q. 8, Art. 1]

Whether G.o.d Is in All Things?

Objection 1: It seems that G.o.d is not in all things. For what is above all things is not in all things. But G.o.d is above all, according to the Psalm (Ps. 112:4), ”The Lord is high above all nations,” etc.

Therefore G.o.d is not in all things.

Obj. 2: Further, what is in anything is thereby contained. Now G.o.d is not contained by things, but rather does He contain them.

Therefore G.o.d is not in things but things are rather in Him. Hence Augustine says (Octog. Tri. Quaest. qu. 20), that ”in Him things are, rather than He is in any place.”

Obj. 3: Further, the more powerful an agent is, the more extended is its action. But G.o.d is the most powerful of all agents. Therefore His action can extend to things which are far removed from Him; nor is it necessary that He should be in all things.

Obj. 4: Further, the demons are beings. But G.o.d is not in the demons; for there is no fellows.h.i.+p between light and darkness (2 Cor.