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 fellowship between light and darkness (2 Cor.
6:14). Therefore G.o.d is not in all things.
_On the contrary,_ A thing is wherever it operates. But G.o.d operates in all things, according to Isa. 26:12, "Lord ... Thou hast wrought all our works in [Vulg.: "for"] us." Therefore G.o.d is in all things.
_I answer that,_ G.o.d is in all things; not, indeed, as part of their essence, nor as an accident, but as an agent is present to that upon which it works. For an agent must be joined to that wherein it acts immediately and touch it by its power; hence it is proved in Phys. vii that the thing moved and the mover must be joined together. Now since G.o.d is very being by His own essence, created being must be His proper effect; as to ignite is the proper effect of fire. Now G.o.d causes this effect in things not only when they first begin to be, but as long as they are preserved in being; as light is caused in the air by the sun as long as the air remains illuminated. Therefore as long as a thing has being, G.o.d must be present to it, according to its mode of being.
But being is innermost in each thing and most fundamentally inherent in all things since it is formal in respect of everything found in a thing, as was shown above (Q. 7, A. 1). Hence it must be that G.o.d is in all things, and innermostly.
Reply Obj. 1: G.o.d is above all things by the excellence of His nature; nevertheless, He is in all things as the cause of the being of all things; as was shown above in this article.
Reply Obj. 2: Although corporeal things are said to be in another as in that which contains them, nevertheless, spiritual things contain those things in which they are; as the soul contains the body.
Hence also G.o.d is in things containing them; nevertheless, by a certain similitude to corporeal things, it is said that all things are in G.o.d; inasmuch as they are contained by Him.
Reply Obj. 3: No action of an agent, however powerful it may be, acts at a distance, except through a medium. But it belongs to the great power of G.o.d that He acts immediately in all things. Hence nothing is distant from Him, as if it could be without G.o.d in itself.
But things are said to be distant from G.o.d by the unlikeness to Him in nature or grace; as also He is above all by the excellence of His own nature.
Reply Obj. 4: In the demons there is their nature which is from G.o.d, and also the deformity of sin which is not from Him; therefore, it is not to be absolutely conceded that G.o.d is in the demons, except with the addition, "inasmuch as they are beings." But in things not deformed in their nature, we must say absolutely that G.o.d is.
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SECOND ARTICLE [I, Q. 8, Art. 2]
Whether G.o.d Is Everywhere?
Objection 1: It seems that G.o.d is not everywhere. For to be everywhere means to be in every place. But to be in every place does not belong to G.o.d, to Whom it does not belong to be in place at all; for "incorporeal things," as Boethius says (De Hebdom.), "are not in a place." Therefore G.o.d is not everywhere.
Obj. 2: Further, the relation of time to succession is the same as the relation of place to permanence. But one indivisible part of action or movement cannot exist in different times; therefore neither can one indivisible part in the genus of permanent things be in every place. Now the divine being is not successive but permanent. Therefore G.o.d is not in many places; and thus He is not everywhere.
Obj. 3: Further, what is wholly in any one place is not in part elsewhere. But if G.o.d is in any one place He is all there; for He has no parts. No part of Him then is elsewhere; and therefore G.o.d is not everywhere.
_On the contrary,_ It is written, "I fill heaven and earth." (Jer.
23:24).
_I answer that,_ Since place is a thing, to be in place can be understood in a twofold sense; either by way of other things--i.e. as one thing is said to be in another no matter how; and thus the accidents of a place are in place; or by a way proper to place; and thus things placed are in a place. Now in both these senses, in some way G.o.d is in every place; and this is to be everywhere. First, as He is in all things giving them being, power and operation; so He is in every place as giving it existence and locative power. Again, things placed are in place, inasmuch as they fill place; and G.o.d fills every place; not, indeed, like a body, for a body is said to fill place inasmuch as it excludes the co-presence of another body; whereas by G.o.d being in a place, others are not thereby excluded from it; indeed, by the very fact that He gives being to the things that fill every place, He Himself fills every place.
Reply Obj. 1: Incorporeal things are in place not by contact of dimensive quant.i.ty, as bodies are but by contact of power.
Reply Obj. 2: The indivisible is twofold. One is the term of the continuous; as a point in permanent things, and as a moment in succession; and this kind of the indivisible in permanent things, forasmuch as it has a determinate site, cannot be in many parts of place, or in many places; likewise the indivisible of action or movement, forasmuch as it has a determinate order in movement or action, cannot be in many parts of time. Another kind of the indivisible is outside of the whole genus of the continuous; and in this way incorporeal substances, like G.o.d, angel and soul, are called indivisible. Such a kind of indivisible does not belong to the continuous, as a part of it, but as touching it by its power; hence, according as its power can extend itself to one or to many, to a small thing, or to a great one, in this way it is in one or in many places, and in a small or large place.
Reply Obj. 3: A whole is so called with reference to its parts. Now part is twofold: viz. a part of the essence, as the form and the matter are called parts of the composite, while genus and difference are called parts of species. There is also part of quant.i.ty into which any quant.i.ty is divided. What therefore is whole in any place by totality of quant.i.ty, cannot be outside of that place, because the quant.i.ty of anything placed is commensurate to the quant.i.ty of the place; and hence there is no totality of quant.i.ty without totality of place. But totality of essence is not commensurate to the totality of place. Hence it is not necessary for that which is whole by totality of essence in a thing, not to be at all outside of it. This appears also in accidental forms which have accidental quant.i.ty; as an example, whiteness is whole in each part of the surface if we speak of its totality of essence; because according to the perfect idea of its species it is found to exist in every part of the surface. But if its totality be considered according to quant.i.ty which it has accidentally, then it is not whole in every part of the surface. On the other hand, incorporeal substances have no totality either of themselves or accidentally, except in reference to the perfect idea of their essence. Hence, as the soul is whole in every part of the body, so is G.o.d whole in all things and in each one.
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THIRD ARTICLE [I, Q. 8, Art. 3]
Whether G.o.d Is Everywhere by Essence, Presence and Power?
Objection 1: It seems that the mode of G.o.d"s existence in all things is not properly described by way of essence, presence and power. For what is by essence in anything, is in it essentially. But G.o.d is not essentially in things; for He does not belong to the essence of anything. Therefore it ought not to be said that G.o.d is in things by essence, presence and power.
Obj. 2: Further, to be present in anything means not to be absent from it. Now this is the meaning of G.o.d being in things by His essence, that He is not absent from anything. Therefore the presence of G.o.d in all things by essence and presence means the same thing.