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.
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 - is 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
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)
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.
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.
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 from what he wrote on this subject in another of his works in which he stated: "Whoever would assert that any multitude is infinite, would not mean that it is a number, or that it belongs to the species of number. For number adds to multitude the idea of
measurement. Number is, indeed, multitude measured by one." (21) Hence it is certain that an infinite number is a contradiction in terms because every number bears a fixed relation to unity, and is the result of addition beginning from one, which is the principle of number. But the question is, whether an actually infinite and innumerable multitude, such as of grains of sand, is an impossibility. We have already discussed this question elsewhere.(22)
It is difficult for the peripatetic philosopher to give a negative reply to this question, because for him, as also for St. Thomas, there does not seem to be any repugnance in the idea that the world may have been created from eternity.(23) In this case there would have been no commencement of motion, for instance, of the sun; there would have been no first revolution of the sun, no first day, and there would be no difference between creation and preservation of things in existence. We find it difficult to imagine this yet there does not seem to be any re-pugnance in it according to St. Thomas. It would be like a footprint made in the sand from eternity by an eternal foot which would have a priority not of time but of causality as regards its imprint.
But if it were so, already the series of days antecedently would be actually infinite, just as the series of acts of immortal souls subsequently will be infinite. It is indeed true that past days, since they no longer exist, do not constitute an actually infinite multitude of actually existing parts. But in this hypothesis, there is nothing repugnant in the idea of God creating from eternity on any day whatever a grain of sand or an angel, and forever conserving these effects in being. In this case there would already be antecedently an actual infinite multitude of grains of sand, or of angels, although there could always be made an addition to these subsequently.
But these difficulties were not unknown to St. Thomas; in fact, he hints at them in the beginning of this article by remarking: (i) Number can be multiplied to infinity; nor is it impossible for a potentiality to be made actual; (2) the species of figures are infinite; thus the sides of a polygon can be multiplied to infinity; (3) if we suppose a multitude of things to exist, for instance, grains of sand, there can still be infinitely many others added to these.
This third difficulty finds its confirmation in the consideration of the non-repugnance of the world having been created freely from eternity, without a first day; for as was said, if on any day whatever, God had eternally created one grain of sand, and had afterward conserved all these grains in being, then the multitude of these grains would be actually infinite antecedently, and the multitude of these grains would be innumerable in a regressive series starting from the last created and going back to the earlier creations, because in this hypothesis there would not have been a first grain created, just as there would not have been a first day. But the days and years would have been from eternity, just as forever without end the intellectual and volitional acts of immortal souls are multiplied.
We shall see that it can be denied that St. Thomas took a definite stand in this difficult problem. Nevertheless the Thomists and many other Scholastics commonly deny the possibility of an actually infinite multitude of actually coexisting things. Many of them, however, grant that a multitude of past days could be actually infinite antecedently and innumerable, just as a multitude of intellectual acts of an immortal soul will be infinite subsequently, but these acts do not all exist at the same time.
Contrary to this among those who maintain the possibility of an actually infinite multitude of even coexisting things, must be named Scotus, and the nominalists Gregory of Arimini, Ockham, Gabriel Biel, as also Vasquez. The Jesuits of Coimbra University considered it to be a probable opinion that there is no repugnance in the idea of an actual infinite. Cardinal Toletus was of the same opinion.(24) Of modern philosophers, Descartes and Leibnitz admit the actual infinite. Likewise Spinoza admits in a pantheistic sense the infinity of all things, in existence, magnitude, and multitude. In more recent times this point has been the subject of great controversy, for instance, in France. Charles Renouvier keenly defended finiteness, and Milhaud defended the opposite thesis.(25)
We must first of all exclude arguments that have no probative force, before we consider the more cogent reasons advanced by St. Thomas.
It is quite astonishing that several authors did not even see the difficulty of the problem and said: Every multitude is divisible into two parts. But any part of it is finite. Therefore the whole multitude is finite. Those who assume that multitude is actually infinite antecedently, would reply: Certainly multitude can be divided into
two parts, one of them being finite both antecedently and subsequently, and the other being infinite antecedently. Others wish to prove the impossibility of an actually infinite multitude, because something could be added to and subtracted from it whereas nothing can be added to or subtracted from the infinite. It is easy to reply to this objection by saying that an actually infinite multitude requires merely that it have antecedently no beginning, and then something can be added to or subtracted from it subsequently, just as this could be done to the succession of days, if it were from eternity.
Finally, some unwarrantably assert that of two actually infinite multitudes, one cannot be greater than the other. But it would be so if the series of days were from eternity, because the series of hours would still be much greater.
We reply by distinguishing the antecedent: of two actually infinite multitudes one cannot be greater than the other, in their infinite aspect, this I concede; in their finite aspect, this I deny. Thus the series of hours would be greater in their finite aspect, so that there could be a series of days greater in their finite aspect by the addition of new days.
St. Thomas begins the argumentative part of this article by referring to the opinion of Avicenna and Algazel and then refuting it. He denies the possibility of an actually infinite multitude of coexisting things, and admits the possibility of a potentially infinite multitude.
The opinion of Avicenna and Algazel is this: An actually infinite multitude of things not essentially but accidentally subordinated, is possible. Examples of this are, if the generation of man actually depended on the man generating, and on the sun and on other agents actually exerting their influence in an infinite series; or if we take the case of a hammer moved by the hand, and by the will, and so on in an infinite series. In such cases there would be no supreme efficient cause, and hence no secondary causes which
' in their causation are dependent solely on the supreme cause.(26)
But according to Avicenna and Algazel, it is not repugnant to reason that there should be an infinite series of accidentally subordinated causes. This would be the case if the artificer were to make something with an infinite multitude of hammers, inasmuch as one after the other may be broken. This is accidental multitude, for it happens by accident, inasmuch as one hammer or mallet is broken and another is used.
It must be observed that St. Thomas admits this saying: "It is not impossible to proceed to accidental infinity as regards efficient
causes . . . as an artificer acts by means of many hammers accidentally, because one after the other may be broken." (27)
But St. Thomas denies that any particular consequence follows from this general assertion: namely, that now there would be an actually infinite multitude of coexisting things, for instance, of broken hammers or of immortal souls, granted that the series of generations is eternal. St. Thomas seems to see no repugnance in an actually infinite multitude of past things or of past days, which are no longer in existence, of generations of animals, for instance, which are now not in existence; but he denies this for the generation of men, because there would now be an actually infinite multitude (antecedently) of immortal souls.(28) He excludes the particular reason given by Avicenna, with the following remark: "One might say that the world was eternal, or at least some creature, as an angel, but not man. But we are considering the question in general, whether any creature can exist from eternity." (29) In like manner, in the reply to the first objection he says: "A day is reduced to act successively, and not all at once," so also a series of days.
The conclusion of St. Thomas is this: An actually infinite multitude of coexisting things, even accidentally connected is an impossibility.
Reasonable proofs are given which, however, according to the judgment of St. Thomas, do not appear to be incontestable.(30)
The counterargument is taken from the Scripture: "Thou hast ordained all things in measure, and number, and weight." (31) But this is said of those things that have been made, so that it leaves undecided the question of those things that can come into existence. The body of the article has two arguments; the first is derived from the determinate species of multitude, the other from the fixed intention of the Creator. The first argument is reduced to the following syllogism: Every kind of multitude must belong to some species of multitude. But no species of multitude is infinite; for the species of multitude are to be reckoned according to the species of numbers and any number whatever is finite, being multitude measured by one. Therefore no kind of multitude is infinite.
Doubt. Is this an incontestable argument? In answer we should note what St. Thomas wrote, following the statement of this proof as given by Aristotle. St. Thomas says: "It must be observed that
these arguments are probable, expressing the commonly accepted view; they are not, however, rigorously conclusive: because . . . if anyone were to assert that any multitude is infinite, this would not mean that it is a number or that it belongs to the species of number: for by number a multitude becomes measurable, as is stated in the tenth book of the Metaphysics, and therefore number is said to be a species of discrete quantity; but this is not the case with multitude which is of the nature of a transcendental." (32) Thus it is that things of the same species are numbered, and the multitude of angels, who are not of the same species, is not a number. However, it must be observed that St. Thomas wrote his commentary on the Physics in 1264, and the first part of the Theological Summa in 1265. In fact, in 1264 he wrote in another work: "It has not yet been proved that God cannot bring it about that there be actually infinite beings," (33) for instance, the creation from eternity on any day whatever (without there being a first day) a grain of sand, and the conservation in being of all these grains. Then this multitude would be antecedently infinite and innumerable.
Likewise St. Thomas wrote later on (1274) as follows: "To make something actually infinite, or to bring it about that infinites should exist actually and simultaneously, is not contrary to the absolute power of God, because it implies no contradiction; but if we consider the way God acts, it is not possible. For God acts through the intellect, and through the word, which assigns to all things their forms, and hence it must be that all things are formally made (that is, determined) by Him." (34)
This last consideration belongs to the discussion of the second argument. But on first inspection it does not appear to be incontestable. An adversary could say that a multitude of things accidentally connected (as grains of sand) is not necessarily in any determinate species, and in this it differs, for instance, from a plant or animal. Every plant must be in a certain genus and species, and the same is to be said of every animal, because its parts unite to form one natural and determinate whole. But it is not so evident that such is the case with a multitude of accidentally connected things; for it would have to be proved that an innumerable and actually infinite multitude of things antecedently and simultaneously existing is an impossibility. It is indeed evident that an infinite number is a contradiction in terms; but it is not so clear that such is the case with an actually infinite multitude, because, as St. Thomas says, "by number a multitude becomes measurable; for number is multitude measured by one." (35) Moreover, there is an infinite multitude of possible things.
St. Thomas says that "God can make something else better than each individual thing."(36) Why then could not God from eternity (that is, without any first day) have created every day an angel and always more perfect angels, and preserve them in being? Then the multitude of these would not be a certain number or measurable by number, but would be infinite antecedently. Hence the first argument does not appear to be incontestable; to consider it as absolutely certain would seem to be exaggerated realism. Moderate realism can indeed prove that every body, for instance, a mineral or a living being, which is essentially one as a natural whole, is in some species under some genus; but it does not conclusively prove anything like this of a multitude of simultaneously existing things that are accidentally connected.
The second,argument is derived from the clear intention of the
Creator, and is reduced to the following syllogism: Everything created is comprehended under some clear intention of the Creator - but multitude in nature is created therefore it is finite.
St. Thomas seems to propose this as a certain argument, for he wrote: "If we consider the way God acts, it is not possible. For God acts through the intellect and through the word, which assigns to all things their forms." (37)
What force has this argument? The work just quoted gives us the answer in these words: "To make something actually infinite is not contrary to the absolute power of God, because it implies no contradiction. But if we consider the way (assigning the forms) God acts, it is not possible." (38)
This is the same as saying that it is not intrinsically impossible according to God's merely absolute power, but that it is so if we consider God's power of ordaining all things in accordance with His divine wisdom, whether this power is ordinary or extraordinary. Thus it is shown farther on (39) that God could by His absolute power annihilate all creatures, immortal souls, the Blessed Virgin Mary, and the humanity of Christ, but this is not possible in accordance with God's power in ordaining all things (whether it is ordinary or extraordinary), for there can be no purpose or end in view in such annihilation, "since the power of God is conspicuously shown in His preserving all things in existence." (40) But it is not so clear that this argument applies as to the impossibility of an actually infinite multitude.
Is this argument as thus set forth incontestable? It is not quite certain that St. Thomas himself considered it an incontestable argument, for farther on he proposes the following objection: "Everything that works by intellect works from some starting point; but God acts by intellect; therefore His work has a starting point. The world, therefore, which is His effect, did not always exist" (41) He replies to this objection as follows: "This is the argument of Anaxagoras (Physics, Bk. III, chap. 4, no. 5, lect. 6 of St. Thomas). But it does not lead to a necessary conclusion, except as to that intellect which deliberates in order to find out what should be done, which is like motion. Such is the human intellect, but not the divine intellect." (42)
Moreover, this argument would have more force if it referred to any created thing whatever taken by itself, the parts of which unite to form one natural whole; for instance, if it referred to every plant or animal. But it has less force if it refers to a multitude of accidentally connected things; for if, every day from eternity, God had created the souls of men, any one of these would be determinate, and yet the multitude of these souls would be infinite antecedently. Nor it is easy to prove that God cannot so bring them into being and preserve them in being.
Finally, it must be observed that no serious consequence arises if we say with St. Thomas (43) that these arguments are not incontestable for no truth of great importance has its foundation
them. On the contrary, a very serious consequence would arise if
the proofs of God's existence depended on this conclusion. We have already seen (44) that the proofs of God's existence have not their foundation in the principle that it is impossible to proceed to infinity in a series of accidentally subordinated past causes, but in the principle that it is impossible to proceed to infinity in a series of essentially subordinated and actually existing causes. And this last process is impossible, not because an actually infinite multitude is impossible, but because secondary causes do not act unless they are premoved to act by the supreme Cause. If therefore the supreme Cause does not exist, or does not move others to act, then there are no secondary causes actually in motion and no effects. Therefore no serious consequence arises, if the aforesaid arguments of this article are not incontestable.
From the very fact that the arguments are not considered by St. Thomas to be incontestable,(45) this brings out more clearly the demonstrative validity required by him in a truly apodictic argument, in such arguments, for instance, as the proofs of God's existence.
Cajetan in his commentary is moderate in his statements. He writes: "It is sufficiently in agreement with the art of logic, so that it can be enunciated as a universal proposition, that every species of multitude is according to some species of number." (46) But when it is a question of an apodictic argument, he says more than "it is sufficiently in agreement with the art of logic."
At the end of the argumentative part of this article, St. Thomas says without any hesitation: "A potentially infinite multitude is possible," whether this be the continuous divisible to infinity, or the multitude to which something can always be added. From the replies to the objections evidently St. Thomas understands an actually infinite multitude as consisting of things simultaneously existing, so that it does not seem to be contrary to reason for a series of past days to be infinite antecedently.(47)
Thus the question of the divine infinity comes to an end. There is infinity of perfection, so that God is both in the highest degree determined, as pure Act, and unlimited, since He is the unreceived and self-subsistent Being, possessing in Himself all plenitude or perfection of being, just as whiteness that is not received in any other would have all the perfection of whiteness. Only God, who is not a body, is infinitely perfect. Hence also, if besides God there existed an infinite body or an actually infinite multitude either of angels or of bodies, none of these would be confused with God. It was therefore a great mistake for Spinoza to say that an actually infinite multitude is one of God's attributes. This would mean that God is a body, just as man is. But this has already been refuted .(48) It would follow, of course, from this that God is a composite of spirit and body; but every composite demands a cause, and in the final analysis a most simple cause, which is to being as A is to A, the self-subsisting Being without limitation of essence. "Things in themselves different (as spirit and body) cannot unite unless something causes them to unite," says St. Thomas (49) in treating of God's absolute simplicity, which would be destroyed in saying with Spinoza that infinite and divisible quantity is one of God's attributes. Thus not everything that is in God would be God, but a part of God.
All these things are contrary to reason if it is properly understood that God is the self-subsisting Being, who is (without any limitation of essence) not received in any other, incapable of this, and to whom there can be no superaddition of any accident, as are the finite modes of Spinoza, which would be successively produced from eternity.
From all that has been said we are assured that the supreme truth of the treatise on the one God is this: in God alone are essence and existence identica1.(50) It follows from this, as we have said, that God is absolutely simple and unchangeable and hence He is really and essentially distinct from the composite and changeable world. The infinity of God's intelligence, of His love, justice, mercy, power, follows from the infinity of the divine nature, because infinity is a mode of any of the divine attributes.
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.
21. Ibid., lect. 8.
22. God, His Existence and His Nature, 1, 77-80.
23. Summa theol., Ia, q.46, a.2 ad 7um.
24. In Iam, q.7, a.4.
25. Essai sur les conditions de la certitude logique, 177 f .
26. Summa theol., Ia, q.2, a.3.
27. Ibid. q.46, a.2 ad 7um.
28. Ibid. ad 8um.
30. Com. on Physics, Bk. III, chap. 5, lect. 8; also De aeternitate mundi, and
Quodl. 12, q.2, a work which he wrote near the end of his life.
31. Wis. 11: 21.
32. Com. on Physics, Bk. III, chap. 5, lect. 8.
33. De aeternitate mundi (the end).
34. Quodl., loc. cit.
35. Com. on Physics, loc. cit.
36. Summa theol., Ia, q. 25, a.6 ad 1um
37. Quodl., loc. cit.
39. Summa theol., Ila, q. 104, a.3 f.
40. Ibid., a.q ad 1um.
41. Ibid., q.46, a.2, obj. 3.
42. Ibid., ad 3um.
43. Com. on Physics, Bk. III, lect. 8.
44. Summa theol., Ia, q.2, a.2.
45. Ibid. See also De veritate, q.2, a.10, in which St. Thomas leaves the question
undecided. He speaks more forcibly in Quodl., loc. cit.
46. See a.4, no. 6.
47. Summa theol., la, q.46, a.2.
48. Ibid., q.3, a. 1.
49 Ibid., a.7.
50. Ibid., a.4.