CHAPTER 7
Question 7: The Infinity of God
After a consideration of the divine perfection, the question of God's infinity is discussed, because infinity is a mode of perfection of the divine nature and of every divine attribute. This question
considers infinity in the divine nature, and is not concerned with the mode of this infinity in this or that particular divine attribute, such as wisdom or power.
First we consider God's infinity, then we discuss whether anything except God can be essentially infinite, or at least infinite in magnitude or multitude.
FIRST ARTICLE
WHETHER GOD IS INFINITE
State of the question. It concerns infinity of perfection or infinite perfection. The difficulty is: (I) that infinity is attributed also to matter, since there is in matter an infinite capacity for receiving all kinds of forms; (2) that it is attributed likewise to quantity, which can always be increased, as a series of days can; (3) that the coexistence of the finite and the infinite seems an impossibility, for, if the infinite in magnitude exists, no place is left for the finite.
The reply is in the affirmative, however, and it is of faith that God is infinite, or infinitely perfect.
I) Several texts in Holy Scripture assert this. Thus we read: "Great is the Lord and greatly to be praised; and of His greatness there is no end." (1) The Vatican Council declared: "God is incomprehensible and infinite in all perfection." (2)
2) The, reply is proved from reason by the following fundamental argument, which St. Thomas considers a simple corollary of the assertion that God is the self-subsisting Being.(3)
Whereas matter is called infinite by an infinity of imperfection, the unreceived form is infinite by an infinity of perfection, at least relatively so. Thus if whiteness were not received in anything, it would have the total perfection of whiteness without any limit. But being is the most formal of all things, as it is the actuality of forms themselves. Therefore being that is not received in anything - and this being is God -i s infinite by an infinity of perfection, and not merely relatively as included in some genus as would be the case with whiteness that is not received in anything, but is so absolutely, transcending every genus.
The major is explained in the beginning of the body of this article. The ancient philosophers of the Ionian school, such as Thales, Anaximenes, Anaximander, Heraclitus, attributed infinitude to the first principle because it is the source of an infinity of things. But they erred about the nature of the first principle, considering it to be something material, such as water, air, or fire. Hence they erred about its infinity, which they thought was something material and quantitative as consisting in an infinitely extended body. But infinity of matter is infinity of imperfection or something privative in that matter, which is pure potentiality and lacking in all determination, since it is made finite by the form, is perfected or determined by it.
On the contrary, the form is limited by the matter in which it is received, and the form considered in itself, or as not received in anything, has an infinity of perfection, since it is unlimited and is infinitely capable of being participated in, as in the case of whiteness. Hence if whiteness were not received in anything, it would have the total perfection of whiteness without any limit and would be infinitely perfect in a restricted sense, that is, in the genus of whiteness, though not of heat. Hence the common assertion: Matter is determined by the form, and the form is limited by the matter in which it is received. Thus determination is perfection or action; whereas limitation is imperfection.(4) It is a question of the form as such, which is thus infinitely perfect in a relative sense, if it is not received in anything. But such a form (for instance, that of an ox) is perfected together with matter, without which it cannot exist.
The minor, however, is evident, namely, that being is the most formal of all things, since it is the actuality of the forms themselves.(5) Therefore being that is not received in anything, which is God, is infinite with an infinity of perfection, and absolutely so.
Thus St. Thomas makes the transition from the relative infinity - for instance, of whiteness, that cannot be limited by matter; or of Michaelness, that is not indeed limited by matter- to the absolute infinity of the self-subsisting and unreceived Being, who is not limited by an essence which is distinct from Himself and in which He would be received.
Reply to the first and second objections. The infinity which is attributed to quantity has reference to matter and therefore does not apply to God.
Reply to third objection. Pure Act or being that is not received
in any other is really and essentially distinct from every finite being; for every finite being is a compound of limiting essence and of limited or participated existence. Thus is solved the difficulty of the coexistence of the finite and the infinite. The existence of the infinite does not prevent the existence of the finite, which is distinct from it. Even if it were to prevent the existence of the finite, this would be because the infinite could not produce anything external to itself; and thus this being would not be infinite, because the power of causing, or infinite power, would be denied this being. The infinite being can indeed not create, because He was most free in creating; but He must of necessity have the power to create.
Objection of Suarez. Suarez, who came after Scotus, says that the aforesaid argument presented by St. Thomas presupposes something not admitted by all theologians, namely, the real distinction between created essence and existence. In fact, Suarez denies this distinction and says: "Being is not finite, because it is received in some other; and it is not infinite, because it is not received in any
other." (7)
In reply to this, we say with John of St. Thomas (8) that, even apart from the direct consideration of the real distinction between essence and existence, the reason given by St. Thomas is still cogent. Indeed, before we consider that the existence of the creature is received subjectively in the created essence and is really distinct from it, we see that it is received objectively and by participation, since it is produced contingently by God and contingently belongs to the subject, which does not have to exist. On the contrary, self-subsisting Being is not received in any other objectively and by participation, because it is not produced, and is not a contingent but a necessary predicate of the subject.
But from this it follows that God alone is His own existence, and that contrary to this the creature,(9) before any consideration on our part, is not its existence, but has existence, just as matter is not form, but receives it. Thus it remains true, as St. Thomas says, that there is a real distinction between created essence and existence, and this for three reasons: (i) because actuality (which of itself is unlimited), is de facto limited only by the real capacity in which it is received; (2) because created essence and existence cannot be reduced to the same concept (as animality and rationality are reduced to the concept of humanity); (3) because existence is a contingent predicate for every creature, and is not included in the adequate concept of its essence.
But how does Suarez prove God's infinity? He proves that God is infinite because no being can be thought of greater than God; whereas it is possible to think of something greater than any finite being whatever.(10)
As John of St. Thomas remarks,(11) even St. Thomas proposed this argument; (12) but it does not bring out clearly what is the very foundation and reason for God's essential infinity, since it does not take as its starting point the very lack of terms limiting His existence.
On the contrary, when it is said that God is the self-subsisting and unreceived Being, the reason is given for His infinite perfection, just as, if whiteness were of itself subsistent and unreceived, it would have all the perfection of whiteness without limitation. The self-subsisting and unreceived Being has, without limitation, all the plenitude of being.
St. Thomas shows farther on (13) that there cannot be two angels of the same species, because the angel's nature is a subsistent form, which is not received in matter and is not capable of being participated in by matter. Thus, by the very fact that Michaelness is not received in any other, it is relatively infinite; the Deity, however, is absolutely infinite. Briefly stated: God is supremely determined or perfect, and therefore unlimited. The reference is to intensive infinite perfection.
But from the infinity of God's being is derived the infinite perfection of His operation, namely, of His intellection, love, and power: for operation follows being, and the mode of operation follows the mode of being.(14)
SECOND ARTICLE
WHETHER ANY BUT GOD CAN BE ESSENTIALLY INFINITE
State of the question. This article is written for the purpose of distinguishing more clearly between absolute infinity and relative
infinity. It begins by proposing three difficulties. (I) Why cannot God produce anything infinite, since His power is infinite? (2) The human intellect, for the very reason that it has knowledge of the universal, has infinite power in knowing all the singulars contained in the universal. (3) Prime matter itself is said to be infinite.
Conclusion. Things other than God can be relatively infinite, but not absolutely infinite.
This conclusion is of faith. Only God is infinitely perfect, "ineffably exalted above all things besides Himself which exist or are conceivable" 15 as the Vatican Council says.
The reason is that absolute infinity is the infinity of the being that is not received in any other, and there can be only one such infinity, just as, if whiteness were not received in any other, there would be but one whiteness.
However, immaterial forms, such as Michaelness, are relatively infinite with an infinity of perfection. Thus Michael has all the perfection that belongs to his species.(16) Infinity that is said to be secundum quid is also relative, or as referring to some genus of infinity, whereas infinity that is said to be so simpliciter, is absolute infinity. But matter is relatively infinite, with an infinity of imperfection, since it has a real capacity for receiving all natural forms.(17)
It must be noted that the end of the argumentative part of this article again affirms clearly the real distinction between created essence and existence in the following words: "Because a created subsisting form (as Michaelness) has being, yet is not its own being, it follows that its being is received and contracted to a determinate nature. Hence it cannot be absolutely infinite."
Likewise, in the reply to the first objection we read: "It is against the nature of a made thing for its essence to be its existence; because subsisting being is not a created being." Thus God, although He is omnipotent, cannot make something that is absolutely infinite, because this is really an impossibility.
Reply to second objection. Our intellect, since it transcends matter, naturally tends to extend itself in a way to know an infinity of things; yet it knows them in a finite way. Thus farther on (18), it will be stated that our intellect elevated by the light of glory can directly see God's essence, but in a finite way, not comprehensively as it is seen by God Himself.
THIRD ARTICLE
WHETHER AN ACTUALLY INFINITE MAGNITUDE CAN EXIST
State of the question. It is asked, for instance, whether it is possible for air to be infinite in extent, and yet for it to be finite according to the essence of air. The purpose of this article and the
following one is to distinguish between actual or categorematic
infinity, and, potential or syncategorematic infinity, which is the finite that is always perfectible, or which is always capable of having something added to it, as in the case of magnitude or a series of numbers. This distinction was already made by Aristotle,(l9) who
showed that everything which is continuous is, indeed, infinitely, divisible but is never infinitel divided for it consists indeed of parts that can always be divided and of terminating points. In like manner, the sides of a polygon inscribed in a circle can always be subdivided, and yet the polygon will never be equal to the circumference. It must be observed that Spinoza, not sufficiently distinguishing between infinity of perfection and infinity of imperfection - a distinction which St. Thomas had made in the first article of this question - said that actually infinite extension is one of God's attributes.
The conclusion of St. Thomas is: "No natural body, in fact, no mathematical body can be actually infinite."
A physical body is an existing subject of three dimensions; in it are matter, form, and sensible qualities. A mathematical body is merely quantity according to three dimensions. This distinction was not sufficiently upheld by Descartes.
The first part of the conclusion, concerning natural bodies, is proved in two ways; metaphysically and physically.
The metaphysical proof may be thus enunciated: Determinate accidents, and hence determinate quantity, follow upon a determinate form But every natural body, for instance, air or water, has a determinate specific form; so also has every created being. Therefore every natural body has a determinant form.
The major has its foundation in the principle that accidents inhere in substance, and, as it were, flow from it or are derived or emanate from it. Therefore an infinite accident is not derived from a finite substantial form; otherwise this finite form would be infinite in power.
It may be objected, however, that infinite air or infinite water would not constitute one individual body, but would be an aggregation of molecules of either water or air. In reply we say that then this would be another question, which is solved in the subsequent article about infinite multitude.
The physical proof is thus formulated:
Every natural body has some natural movement, either direct or circular. Thus the direct tendency of a stone is downward, but the movement of the planets is circular (or elliptical). But an infinite body could not be so moved; not indeed by a direct movement, because it would already occupy every place; nor could it be so moved by a circular movement because the lines, the farther they are drawn from the center of such a body as this toward the circumference (which would be in no place), would be infinitely distant from one another, and thus one of these lines could never reach the place occupied by another; but such a condition is required for the circular movement of any body revolving in the same place by a rotatory motion. There would be neither periphery nor circular motion in this periphery. Thus Paschal speaks of some sphere whose center would be everywhere and its circumference nowhere.
This physical argument presupposes the doctrine of natural motion as opposed to violent motion and as terminating at some natural place, as in the motion of a stone downward to the center of the earth. But after Galileo's experiments dealing with the falling of any body in a vacuum, this doctrine of the natural motion of bodies cannot now be admitted, at least without some modifications. However, modern physics has retained something of this teaching in the law of the diminution of energy. In accordance with this law, the heat required for the production of local motion cannot be fully restored by the conversion of this local motion into heat, and thus the whole world tends by a natural motion toward a certain state of equilibrium.
The proposed argument seems a sound one, if it is conceded that every natural body has a natural motion, at least in the same place. But some may say that this infinite body cannot be moved all at once as a compact mass, but perhaps the parts of this body can be moved.
In reply to this we say that then we are concerned with another question, namely, that of the actually infinite multitude of distinct parts, which is discussed in the following article.
But can one imagine an actually existing mathematical body that would be infinite in magnitude? St Thomas replies in the negative at the end of the argumentative part of this article. His reason is that this body could not be actual without some form or figure.
But every figure is finite. Therefore it is impossible to imagine an actually existing body that would be infinite in magnitude.
Nevertheless St. Thomas himself, commenting on this last proof, says: "It is not conclusive but only probable, because whoever would assert the existence of an infinite body would not concede that it is of the essence of a body to be bounded by a surface, unless perhaps potentially, although this view is probable and much argued.(20) Furthermore it must be said that a mathematical body cannot naturally exist without a subject that is a composite of matter and form and thus the previous arguments remain in force.
Reply to first objection. In geometry by the expression "infinite" is meant an actually finite line that can always be extended.
Reply to second objection. Infinite is not against the nature of magnitude in general, but it is against the nature of any of its species, because any species whatever of magnitude has a finite figure. "Now what is not possible in any species cannot exist in the gcnus." This last proposition confirms the probable argurnent about a mathematical body, given at the end of the argumentative part of this article.
Reply to third objection. "The infinite is not in the addition of magnitude, but only in division." The first part of this statement is true of a natural body, because it increases until it reaches a deter¬minate size that is proportionate to its specific form. Moreover, even if a body were capable of infinite increase, it would never be actually or categorematically infinite, but only potentially or syncategorematically.
Reply to fourth objection. It is conceded that infinite is not against the nature of time and movement, because time and movement differ from magnitude inasmuch as they are not in actuality as to the whole of their being, but only successively. Hence there seems to be no repugnance in the idea that the movement of the heavenly bodies and time should be from eternity, as Aristotle thought, and then there would be neither a first revolution of the sun nor a first day.
FOURTH ARTICLE
WHETHER AN INFINITE MULTITUDE CAN EXIST
State of the question. This question, is a very difficult one, this being the decision of St. Thomas, as will at once be seen, especially
Footnotes
1. Ps., 141: 3; also Bar. 3: 25.
2. Denz., no. 1782.
3. Summa theol., Ia, q.3, a.4.
4. Not understanding this distinction between determination and limitation, Spinoza said: "Every determination is a negation." In truth, God is in the highest degree determined or perfect, but He is unlimited.
5. Summa theol., Ia, q.4, a. 1.
6. Ibid., q.45, a.5.
7. De attributis Dei, Bk. III, chap. 1.
8. In Iam, q. 7, a. 1.
9. Summa theol., Ia, q.3, a.4.
10. De attributis Dei, loc. cit.
11. In Iam, q.7, a.1, no. 19.
12. Contra Gentes, Bk. I, chap. 43, §§ 7.
13. Summa theol., Ia, q.50, a.4.
14. Ibid., q.25, a.2.
15 Denz., nos. 1782, 1804.
16. Summa theol., Ia, q.50, a.4.
17. Ibid., ad 3um.
18. Ibid., q. 12, a.7.
19. Physics, Bk. III, chaps. 1 f.
20. Com. on Physics, Bk. III, chap. 5, lect. 8, no. 4.
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