Commentaria in Summam contra Gentiles, Liber I

Since it has been shown that God is one, Saint Thomas next shows that this one God is infinite ¹. Concerning this he does two things: first, he declares what sort of infinity it is and how it belongs to God; second, he proves his intended point ².

I. As to the first, he posits a twofold distinction. The first is this. Since the infinite follows upon quantity, and quantity is twofold, namely corporeal and spiritual, the infinite is twofold: one kind according to corporeal quantity, another according to spiritual quantity. Now although spiritual magnitude is considered with respect to two things—namely with respect to power, and with respect to the goodness and completeness of nature (for something is said to be more or less white according to the degree to which its whiteness is completed in it; and from the magnitude of actions and deeds the magnitude of a power is assessed)—yet because the magnitude of a power follows the magnitude of nature and perfection, since in virtue of being in act something is active, and therefore the measure of its power's magnitude is the degree to which something is completed in its act, spiritual things are accordingly said to be great absolutely according to the measure of their perfection; as in Augustine, De Trinitate VI, chapter 8: "In things that are not great by bulk, to be greater is the same as to be better." And thus they will be said to be absolutely infinite according to the measure of their perfection.

The second is this. "Infinite" is said in two ways: privatively, and negatively.

When, therefore, God is said to be infinite, we do not speak of the infinity of bodily quantity, for He is not infinite in multitude, since He is one, nor in continuous quantity, since He is not a body; but of the infinity of spiritual quantity, or of perfection. — Likewise, "infinite" is not taken privatively: for something is said to be privatively infinite from the fact that it is naturally apt to have a limit and this is withdrawn from it, on account of which it is imperfect; but imperfection does not befit God. Rather He is said to be infinite negatively: because He is supremely perfect, and there is no term or limit of His perfection.

It must be noted that "infinite" is said privatively on account of the removal of a form, for privation signifies the negation of a form that ought to be present; and therefore the term that is excluded by such infinity has the character of a form, from which a finite thing has the completion of its measure. Because it lacks such a term due to itself—which is to be infinite privatively—it lacks its perfection and form. And for this reason such an infinity, which is also called in the First Part, q. VII³ an infinity holding on the side of matter, is imperfect.

Now, the infinite in a negative sense is said of spiritual things on account of the removal of that which receives and of matter limiting the form to some degree of its perfection: for the amplitude of a form is limited by matter and by what receives it. And because a form not limited to any one of its degrees, but possessing all its perfection, is more perfect than if it were limited to some particular degree, therefore such an infinity—which is called infinite as holding itself wholly on the side of the form⁴—is most perfect: either simply, if it be simply infinite; or within its genus, if it be infinite in its genus.

For this reason, wishing to show how God is infinite without imperfection, that is, negatively infinite, Saint Thomas says that there is no terminus of his perfection, but he is supremely perfect; that is, his perfection is not limited to any degree of perfection, such that he would have one perfection and not another, but he possesses every perfection and every mode of perfection in himself eminently.

II. As to the second⁵, the conclusion is proved. First: God is not in a genus, but contains the perfections of all genera, as was shown above. Therefore He is infinite. — The consequence is proved: because everything finite is determined by its nature to the account of some genus.

Note that, since the categories explain all the general modes of being of finite being, nothing can have the character of finite being unless it belongs to some categorial genus. And therefore St. Thomas says that everything finite, by its nature, pertains to the character of some genus, because it must be contained under some categorial genus.

Second. God is an act existing in no way in another: since he is neither a form in matter, nor does his esse inhere in any form or nature, but he subsists. Therefore he is infinite. — The consequence is proved. Because act existing in nothing is in no way limited, just as, conversely, every act inhering in another is limited by that in which it is: as, if whiteness existed of itself, it would not be limited, but would have whatever belongs to the perfection of whiteness.

III. Concerning this proposition, "Every act inhering in another receives its termination from that in which it is," a doubt is raised. For, as Scotus argues, I Sent., d. II, q. 1⁶, every finite essence is finite in itself, prior to any comparison of it with another essence. Therefore the form is not terminated and limited by that which receives it.

Similarly, against this line of reasoning, he argues, first, as follows: Form is limited by matter; therefore a form that is not by nature meant to exist in matter is infinite. For it would follow that an angel, which is separate from matter and from what is receptive, would be infinite.

Second, because the fallacy of the consequent is committed. For just as it does not follow, as we find in Physics III⁷: A body is finite in relation to a body; therefore, if it is not finite in relation to a body, it is infinite—for then the outermost heaven would be infinite—so too it does not follow: A form is finite through matter; therefore, if it is separate from matter, it is infinite.

2. For the clarification of this, we must first consider that, since we can consider two things in a form—namely, the specific nature and the esse owed to that nature—when we say that the form is limited by matter, we do not understand this of the form with respect to its specific essence: for by its own proper difference it is limited to this species and to this grade of being, not by matter. Rather, we understand it of the form with respect to its mode of esse.

It must be known, secondly, that just as a form receptive in another is limited to a determinate degree of being and to a determinate species, so it has a determinate esse in the nature of its being simply: for such an esse is owed to whiteness insofar as it is whiteness that no other is owed to it. Yet nevertheless this esse owed to such a nature possesses a certain breadth of being, according as what is receptive of the form can be disposed in various ways, and the form itself can be received in diverse subjects. Hence with respect to this esse it can be limited: namely, so that it does not have the whole and perfect esse owed to its nature, but only some numerical grade of it. The form is therefore limited by matter: because, since each thing is received in another according to the mode of the receiver—that is, according to that mode by which the recipient is naturally apt to receive it—it is necessary that a form received in another be limited according to the capacity of the recipient; that is, so that it does not have the esse owed to it in that perfect manner in which it could have it, but only according to the disposition and capacity of the recipient. But if a form were separate from every recipient, it would have no limitation in the esse owed to it, but would have its esse in the most perfect manner according to the condition of its nature—not limited to any grade of being within its breadth, but possessing its whole esse, containing all the grades according to which it could be in its recipient, unitedly and perfectionally.

From which it follows that, if the nature itself, considered in itself, does not signify some determinate grade of being, and if it is separated from everything receptive, it will be simply infinite in respect of the perfection of esse, as limited in no way: just as, because esse considered in itself does not signify some determinate grade of being, but includes indistinctly every perfection of being, if it subsists of itself, it will be simply infinite, as determined to no grade of being simply speaking. But if the nature itself does signify some determinate grade of being, then, separated from everything receptive, it will not be simply infinite, since by its own ratio and quiddity it assigns to itself some determinate grade of being: rather it will be infinite in a qualified sense, that is, in its genus or in its species, insofar as it possesses every perfection of being owed to its nature. But those who attack St. Thomas are deceived, because they take the infinity of a form after the manner of the material and quantitative infinite, and of that which has its perfection from an end; whereas a form is called infinite for no other reason than that it is not contracted to some grade of its nature, but is able to belong to every grade possible to it.

It must be considered further that, when we say the receptive subject limits the form, we do not understand this as though matter produced something in the form in the manner of an efficient cause; but rather because the form, by the very fact that it is received in a receptive subject, acquires limitation according to the exigency of that subject. Thus it is the receptive subject that limits the form in the manner of a material cause, not in the manner of an efficient cause.

3. These suppositions being granted, the answer to Scotus's first argument is that a finite form is finite in itself and not by reference to something else, formally and essentially, as determined to some degree of being; yet it is not materially finite, as limited to some degree of esse within the breadth of its esse, except by reason of the matter in which it is received. It is of this finitude that Saint Thomas speaks.

To the second it is said that the angel is infinite in genus and in a certain respect, as is clear from what has been said; but not simply, because from its own definition it signifies a nature holding a determinate degree among beings.

To the third it is said that inherent esse and finite esse are convertible; likewise separate esse and infinite esse.

And because in convertible propositions one can argue from the destruction of the antecedent to the destruction of the consequent, therefore in them the fallacy of the consequent is not committed by arguing thus, but the argument is valid: If it is inherent, it is finite; therefore, if it is not inherent, it is not finite, in the manner in which it has been explained.

Against the instance concerning body, it is said that it is not to the point. For a finite body does not receive its limitation from the fact that it is terminated to another body; rather, it happens to it, insofar as it is finite, that there is another body to which it is terminated. But a form receives its material and individual termination from the very subject receiving it, and to it, insofar as it is so terminated, there belongs per se in that subject the esse of its species. Hence "body is finite" and "body is terminated to another body" are not convertible, just as "a form is in another" and "a form is finite in its species" are not.

IV. Third. Prime matter, which is pure potency, is infinite in its potentiality. Therefore God, who is pure act, is infinite in his actuality. — The consequence is proved: because potency is said with respect to act, just as in each thing act cannot be exceeded by potency, so neither can it be exceeded simply.

Concerning that proposition, "Potency cannot exceed act in any given thing," a doubt is raised. Matter which is under the form of fire is also in potency to the form of water. Therefore potency in fire exceeds act.

It is answered that we can speak in two ways of a potency with respect to some act: in one way materially, namely with respect to that to which the notion of potency belongs; in another way formally, namely insofar as it is a potency directed toward this act. If it is taken in the first way, then it is not unfitting for a potency to exceed the act it has, as the argument proves. If, however, in the second way, then a potency cannot exceed the act it is directed toward. For a potency for the form of fire signifies an ordination to the form of fire. But it is impossible that a potency for fire, as receptive of the form of fire, be receptive of another form. For even if the matter of fire is receptive of the form of water, it is not receptive of it as a potency for the form of fire, but as a potency for the form of water: for a potency for the form of fire signifies an ordination only to the form of fire, if it is taken formally. Therefore the proposition of St. Thomas is understood formally: not however materially, as the objection proceeded.

V. Fourth. God is pure act without any admixture of potency. Therefore he is infinite. — The consequence is proved: because the less act is mixed with potency, the more perfect it is; and that which has potency admixed has a limit to its perfection, whereas that which does not have it has no limit of perfection.

Note that an act which is in potency to another act—which here is said to have potency mixed in with it—of necessity lacks some perfection: for, if it lacked no perfection, it would not be in potency to it; nothing is in potency to what it already has. And therefore it is not universally perfect, but possesses one perfection in such a way that it does not possess another: and this is to have a limit to its perfection. But an act into which no potency is mixed lacks no perfection in itself, but is subsistent esse itself: for everything that is not esse is by its nature in potency to it, as to something outside the quiddity of the thing. Hence it has no limit to its perfection, but is universally perfect.

VI. Fifth. If the esse of anything is finite, it must be limited either by some cause of it or by its receiver⁸, because esse in itself is infinite, as being participable by infinitely many things and in infinitely many ways. But the esse of God has no cause and no receiver, since God is his own esse. Therefore it is not finite.

Note that, although Saint Thomas touches upon two modes of limitation, namely from the productive cause and from the receptive subject, yet one follows of necessity from the other. For if something is received in a subject, it must be produced by some cause, since nothing produces itself from non-being to being. Likewise, if it has a productive cause, there must be some receptive subject for it: because esse, as we showed above⁹ is not finite and determinate except because it is the esse of this thing, either in act or in aptitude and proportion.

VII. Sixth. Nothing better and more perfect than God can be thought. Therefore He is infinite. — The antecedent is proved: something is the more perfect in respect of a given perfection, the better and more fully it participates that perfection. But nothing can be participated more fully than by being such through its own essence, as God is goodness itself and esse itself. Therefore, etc.

But that consequence seems not to hold: Nothing more perfect than God can be thought, Therefore He is infinite. Rather it follows rather: Therefore He is finite; for the infinite is that of which, in those taking its quantity, there is always something further to take¹⁰.

It is answered that the consequence is good, and necessary, and holds proportionally with respect to infinite quantity. For although the infinite is such in itself that, any finite quantity of it being taken, something always remains to be taken, nevertheless nothing greater in quantity than the infinite can be thought, in the way in which it is infinite. And if something can be thought greater than it by some quantity, that thing is not infinite but finite, since it can be exceeded. In a similar way, the infinite according to perfection is such that, any finite mode in it being taken according to the consideration of our intellect, another mode always remains to be taken. Yet nothing more perfect than it can be thought. Indeed, if something else more perfect can be thought, that thing is of finite perfection, as being able to be exceeded by what is more perfect.

VIII. Seventh. Our intellect, in understanding, is extended to infinity. This is shown by this sign: because, given any finite quantity whatsoever, it can conceive a greater one to infinity. Therefore there must be some infinite intelligible nature, which must be the greatest of things. — The consequence is proved. Because otherwise this ordination of the intellect to infinity would be in vain.

But that argument does not seem to conclude, for two reasons. First, because the intellect can conceive many false and impossible things.

Second, because the intellect is not ordered to apprehend any infinite intelligible, although it has an inclination to understand or to conceive something greater than any given finite thing, dividedly, to infinity.

To make this evident, it must be known that this ordination of the intellect to the infinite is nothing other than the power of the intellect for thinking of an infinite thing. That such a power is given to the intellect is proven by this sign: whatever finite thing it conceives, it conceives something greater without limit, as if driven by the very nature of the intellect toward the inquiry into some infinite intelligible. For this reason, the inquiry of the intellect does not rest until it has arrived at the infinite intelligible.

To the first point, then, it is said that, although the intellect sometimes conceives impossibilities, it nevertheless has an inclination toward the infinite intelligible. And therefore, unless that were to be found, this natural inclination would have been given to it in vain.

Similarly, to the second, the antecedent is denied. Indeed, from the mode of thinking to infinity it is persuaded that it has an inclination toward arriving at some infinite intelligible.

Yet I take that argument to be persuasive, not demonstrative.

IX. Eighth. Our intellect cannot think of anything greater than God. Therefore it is infinite. — The consequence is evident, because of any finite thing the intellect can think of something greater. — The antecedent is proved, because an effect cannot extend beyond its cause. But the intellect is an effect of God.

It must be known that, since an effect is a kind of likeness of its cause, it cannot be the cause of something of greater power, as was shown above¹¹. But this must be understood proportionally, according to the mode of the effect. For some effects receive from their cause the power to produce other things according to natural being; others, however, according to conceivable being, not according to natural being, as is the case with the speculative intellect. Therefore, just as an effect cannot, by the power it receives from its cause, produce an effect in the being of nature more perfect than its cause, so neither can the intellect produce in conceivable being anything more excellent than its cause. Which is to say: one cannot think of anything more excellent than its cause. If, therefore, God is the cause of our intellect, it follows that nothing greater or more perfect than God can be thought.

X. Ninth ¹² The power of God is infinite. Therefore His essence. — The antecedent is proved: because He moves through infinite time. — But the consequent is proved: because power names the principle of action, and each thing acts through its form, which is its essence or a part of its essence.

If it is said that this argument presupposes the eternity of motion, which theologians do not posit: — it is said that it does indeed proceed from the eternity of the world, and yet the infinity of power is confirmed even more strongly if the eternity of the world is not posited. For an agent is so much the more powerful in acting as it reduces to act a power more remote from act: just as greater power is needed to heat water than air. But what is not at all is infinitely distant from act. Therefore, if the world was made after it was not at all, the power of its maker is infinite.

Although this argument is not drawn from the eternity of the world, it nevertheless holds even for those who posit the eternity of the world: for they posit that God, eternal, is the cause of the everlasting world, just as a foot would have been the cause of a footprint from eternity if it had been impressed in the dust from eternity. For whether the world was produced from eternity or in time, there is nothing in reality that is not produced by God. And it is thus produced with no matter presupposed. From this the argument is formed differently. The proportion of an active power is taken according to the proportion of a passive potency to act: for the more a passive potency is understood or preexists as extended away from act, the greater the power by which it is brought into act. Therefore, since a finite power requires some potency of matter, that which requires no matter is infinite.

2. Concerning that proposition, "Each thing acts through its own form, which is the essence or a part of the essence," it must be noted that it is understood of the first formal principle, not of the proximate one. For, as Saint Thomas says in the First Part, q. 77, a. 1 ¹³, in creatures substance is not the proximate principle of action, but the accidental form, which has the character of a power.

Likewise, when it is said that "virtue names the principle of action," it is taken indistinctly, as the extension is made to the first and to the proximate principle. For in creatures, virtue, insofar as it names the proximate principle, is not the substance of the thing but an accident accompanying the substance of the thing; but insofar as it names the first principle, it is substance. Yet because in God the first formal principle and the proximate one are not distinguished, since His virtue and His operation are His substance, therefore in Him it is universally true that the virtue of God is His essence.

XI. Against the first form of argument, by which it is proved that God's power is infinite because He produced the world from no pre-existing potency ¹⁴, Scotus, IV Sent., d. 1, q. 1 ¹⁵ denies the minor premise. For when the extremes are immediate, their distance is precisely as great as the greater of the two extremes: just as, if the highest possible creature were to be produced, there would still be an infinite distance between it and God, because God is infinite while that creature would be finite. But the distance between the affirmation and negation of the being and non-being of a created thing is immediate. And a created act is not infinite but finite. Therefore the distance between them is not infinite but finite.

To the second form ¹⁶ he says that, although the distance of no power to act bears no proportion to the distance that belongs to some power to act, it does not follow from this that the power which can extend over the former is disproportionate to the power which can extend over the latter. For one positive thing is not disproportionate to another positive thing except on account of infinity in the other. But in those distances there is no proportion because the one did not have any quantity by which it could be proportioned, since it is the distance of non-being from being.

XII. In response to these points, and in confirmation of the argument of St. Thomas, it must be known from his doctrine in IV Sent., d. 5, q. 1, a. 3 ¹⁷ that there is a twofold infinite distance. One is infinite simply, namely when the distance is infinite on the side of both extremes; and this is when each extreme is infinite. Another is infinite in a certain respect: and this is when the distance is infinite on the side of only one extreme. For since a thing is as distant from one of two opposites as it approaches the other, if something approaches the opposite extreme so as to possess it infinitely, it must be infinitely distant from the other; but if it participates in the opposite finitely, it will be only finitely distant from the other. Therefore between being and non-being there is no distance infinite simply unless that being be infinite. And because no created being is infinite, therefore the distance of a created being from non-being is not infinite simply. Indeed, it is finite on the side of the being itself: because a being more perfect than this created being is more distant from non-being than this being is. Yet on the side of non-being the distance itself is infinite: because nothing is more distant from anything than non-being. Hence the distance of non-being altogether from being is not proportional to the distance of any being from another; otherwise there could be a distance of one being from another greater than the distance of non-being altogether, according to the manner of Aristotle's argument in Physics IV and VIII ¹⁸. Therefore between being and non-being there is a distance infinite in a certain respect.

It must be known, secondly, that this distance, infinite in a certain respect, namely on the side of non-being alone, requires an infinite power, since active power is proportioned to the distance of potency from act: proportioned, I say, in this manner, that as the proportion of one distance from act to another distance, so is the proportion of the active powers to one another; because, as Saint Thomas says here, each agent is the more powerful, and exceeds another agent, the more it reduces a potency more remote from act to act. But the distance of non-being altogether from being has no proportion to the distance that is between two beings: otherwise there would be found some distance of being to being equal to the distance of non-being from being. Therefore the power that operates altogether from non-being has no proportion to the power that operates from a presupposed being. Therefore it is infinite. — The consequence is evident. Because such an active potency is called disproportionate because it exceeds every finite potency: just as that distance which is between being and non-being is called disproportionate to every distance that is between beings, because it is greater than every distance that is between beings. But a potency exceeding every finite potency is infinite.

2. Thus, then, it is clear that the argument of St. Thomas is efficacious, and that Scotus's solution is not sufficient. Whence, to the first objection, it is said that indeed on the side of created being that distance is not infinite, as the argument proves. It is nevertheless infinite on the side of non-being, as we have said: since nothing can be more distant from being than to be altogether non-being. And this infinity of distance argues an infinity of power: since powers are proportioned to the elongations of potencies from act.

The response to the second form of the argument is also null. For it denies this consequence: These distances are disproportionate; therefore also the powers—although we have shown that it is necessary, because such as the proportion of these distances is, such is the proportion of the powers themselves; for the more one distance exceeds another, the more one power exceeds another, since a greater distance requires a greater power.

3. But this can still be proved from the line of reasoning by which Aristotle, Physics IV, text 72, ¹⁹ proves that motion made in a vacuum has no proportion to motion made in a plenum. For if an active power acting with absolutely no presupposed potency is proportioned to one which acts from presupposed matter, notwithstanding the improportion of the distances, let it be granted, for example, that it is twice as great. Then I take another power which acts from matter twice as indisposed as the matter from which the other power acts. Therefore it will itself be twice as great as that one. But in the same proportion the power acting from absolutely no presupposed matter was related to it. Therefore the power producing from some matter is equal to the power acting from [no] presupposed matter. But this is unacceptable, because experience makes it clear that the more something is removed from act, the greater the power it requires. Therefore, etc.

It must be noted, however, concerning that proposition of St. Thomas—"The greater the passive potency that preexists or is preunderstood, the more it is brought to completion in act by a greater active power"—that a passive potency can be understood to be greater in two ways: in one way, because it is more remote from act; in another way, because it is more disposed to receive act, in the manner in which we say that wood or air has a greater potency for a statue than water. In the first way, potency is said to be simply greater potency, namely because it has less of act. In the second way, it is said to be greater in relation to act, because it is more capacious of act and more disposed toward it. The proposition of St. Thomas, therefore, is understood of the greater potency in the first way, not in the second: for it is more difficult to make a statue from water, and it requires greater power, than to make one from wood or copper.

XIII. Tenth. The duration of God is infinite; therefore God himself is infinite. — The consequence is proved. For a thing endures the longer the more efficacious its cause is. If, then, the duration of God is infinite, since he has no cause but himself, he himself will be infinite.

It must be noted that, when it is said that God has no cause other than himself, this is not said as though he himself produced his own esse—for that is impossible—but because his substance is for himself the reason of being, and there is no need to posit any other productive cause of him.

2. Concerning this proposition, that each thing is the more enduring the more efficacious its cause is, a doubt arises. For it seems to be contradicted by what Saint Thomas said above, chapter XX. For there he held that, because immutable esse has no extension of quantity, therefore the infinite duration of that esse does not require infinite power, since it makes no difference whether by that power something endures for an infinite or a finite time. Therefore greater endurance in immutable esse does not require a greater and more efficacious power. The opposite of this is said here.

To this it is said first, that there is no contradiction in the words of St. Thomas. For here he speaks of the power of the efficient cause of duration: such a power is indeed infinite if it cause infinite duration. But above he was speaking of the power of the formal cause of a thing's esse, which need not be infinite if it cause perpetual esse. This is clear from the teaching of St. Thomas in Metaphysics XII, lecture 6, and in the Questions on the Soul, article 14, ad 4.

It is said second, that the reason for this diversity is because esse is compared to form as that which follows from it per se. But the fact that something which follows per se from a thing is always inherent in it does not argue for its infinity: just as the fact that duality is always even does not argue for its being infinite. To an efficient cause, however, esse is compared as an effect produced by its power. Now the effect of an efficient cause, all else being equal, is the more durable the more efficacious the power of the agent was. For we see that heat in water is the more durable the stronger the power of the fire by which it was introduced. Hence, although duration of time is related to substantial esse only accidentally, it is nevertheless related to the very power of the agent essentially, as a condition of its effect.

It is said thirdly that, just as a thing is more enduring whose efficient cause is more efficacious in acting, so, if some thing lacks an efficient cause on account of its own perfection, it will be the more perfect in itself the more enduring it is: because its endurance does not come from another, but only from the perfection of its own nature. Therefore St. Thomas rightly infers that, because God's endurance is infinite, and he himself is the cause of his own endurance negatively (that is, he does not have his endurance from another, but he himself is his own infinite duration), his power and perfection are infinite.

It is confirmed lastly by the authority of the Psalmist. — Also by the authority of the ancient philosophers, who, compelled by truth itself, posited that the first principle is infinite: although they erred in holding that this first principle is a body.