Thomas Aquinas
The Quodlibetal Questions

Article 4: Whether an angel is in a place through [its] operation alone.

We proceed to the first point as follows: (1) It seems that an angel is not in a place according to its operation alone. For being is prior to operating. Therefore, being in a place is prior to operating in a place. But the posterior is not the cause of the prior. Therefore to operate in a place is not the cause why an angel is in a place.

(2) Moreover, two angels can operate in one place. If therefore an angel were in a place only through [its] operation, it would follow that several angels would be together in one place, which is held to be impossible.

But on the contrary: The more noble does not depend on the more ignoble. But the essence of an angel is more noble than a corporeal place. Therefore, it does not depend on a corporeal place.

I reply: It is to be said that how an angel exists in a place can be viewed from the way in which a body exists in a place. For a body is in a place by touching the place. Now a body’s touch occurs through dimensive quantity, which is not found in an angel since it is incorporeal. Rather its place is a virtual quantity in it. Therefore, just as a body is in a place through the touch of dimensive quantity, so an angel is in a place through the touch of power. But if someone wants to call the touch of power an “operation”, because of the fact that to operate is the proper effect of a power, [then] it may be said that an angel is in a place through [its] operation—​yet in such a way that by ‘operation’ not only is motion understood but any unifying (unitio) by which it unites itself to a body by its own power by presiding over it, containing it, or in whatever other way.

To the first [objection] therefore it is to be said that nothing prevents something from being absolutely prior that is not prior with respect to [a certain] “this”. For instance, a subject body is prior to a surface absolutely, but not with respect to the fact that it is colored. And likewise body is absolutely prior to touch. Nevertheless [a body] exists in a place through the touch of dimensive quantity. And likewise an angel [is in a place] through the touch of power.

To the second [objection] it is to be said that if something is moved perfectly by one mover, it is not consistent that it be moved immediately by another [mover] simultaneously. Hence the reasoning is valid more in opposition to this [objection] than in favor of it.

Article 5: Whether an angel can be moved from one extreme to the other without traversing the middle.

We proceed to the second point as follows: (1) It seems that an angel cannot be moved from one extreme to the other unless it traverse the middle. For everything that is moved, is in a state of being moved before it is in a state of having been moved, as is proved in Physics VI.¹ But if an angel is moved from one extreme to the other, for instance from a to b, [then] when it is at b it is in a state of having been moved. Therefore, it was in a state of being moved before. But not when it was at a, because then it was not yet moved. Therefore, when it is at c, which is in the middle between a and b. And so it has to traverse the middle.

(2) Moreover, if an angel is moved from a to b without its traversing the middle, it will have to be corrupted in a, and be created again in b. But this is impossible, because then it would not be the same angel. Therefore, it has to traverse the middle.

But to the contrary: Everything that traverses a middle has to traverse [a distance] equal to or less than itself before [it traverses a distance] greater [than itself], as is said in Physics VI,² and as is apparent to sensation. But there can be no space smaller than an angel, which is indivisible. Therefore, it must traverse an equal [distance], which is an indivisible and point-like (punctualis) place. But there are an infinite [number] of points between any two boundaries of motion. If therefore it were necessary that an angel in its motion traverse the middle, it would have to traverse an infinite [number of points], which is impossible.

I reply: It is to be said that an angel, if it wishes, can be moved from one extreme to the other without traversing the middle. And if it wishes, it can traverse all the middle [regions]. The reason for this is because a body is in a place as contained by it. And therefore in moving it has to follow the condition of [its] place, so that namely it traverses the middle [regions] before it arrives at the extreme of the place. But since an angel is in a place by the touch of power, it is not put under a place as contained by it. Rather it contains³ the place, [and] is dominant (supereminens) in the place by its power. Hence it does not have the necessity of following the conditions of place in its motion. Rather the fact that it applies itself by the touch of power to this place and that—​and, if it wishes, without the middle—​is subordinate to its will, just as the intellect too can be applied to understanding one extreme—​for instance, to white—​and afterwards to black, indifferently either thinking or not thinking about the intermediary colors, although a body [that is] subjected to color cannot be moved from white to black except through the middle.

To the first [objection] therefore, it is to be said that the statement of the Philosopher and its proof have their place in continuous motion. But the motion of an angel does not have to be continuous. Rather the succession of the aforesaid applications is itself called its motion, just as also the succession of thoughts or affections is called the “motion” of a spiritual creature, according to Augustine in his literal commentary on Genesis.

To the second [objection], it is to be said that this does not happen through the corruption of the angel or a new creation, but because its power dominates the place.

With respect to what was objected to the contrary, it is to be said that an angel is not in a place by measurement (commensurationem), but rather by the application of its power to the place, which [application] can be to a divisible or an indivisible place indifferently. Hence [the angel] can be moved continuously, like something existing in a divisible place, continuously cutting off the space. But insofar as it is in an indivisible place, its motion cannot be continuous or traverse all the middle [regions].

Article 21: Whether a glorious body can exist with another body in the same place.

We proceed to the first point as follows: (1) It seems that a glorious body can naturally exist with another body in the same place. For if it is prevented from existing with another body in the same place, [that] is either because of [its] thickness (grossitiem) or fleshiness or else because of [its] dimensions. But [it is] not because of [its] thickness or fleshiness, because a glorious body is spiritual according to the Apostle, 1 Corinthians 15. Likewise, [it is] not because of [its] dimensions. For, since things that touch are those the extremities of which are together, it is necessary [when bodies touch] that a point of one natural body be together with a point of another, and a line with a line and a surface with a surface and, by the same reasoning therefore, a body with a body. Therefore, a glorious body is not prevented from naturally existing together with another body in the same place.

(2) Moreover, the Commentator says in Book VIII of the Physics, text 82 of the commentary, that the parts of air and water enter into (subintrant) one another in part, because of the fact that in part they are of a spiritual nature. But glorious bodies will be altogether spiritual, as has been said already. Therefore, they will be able to enter into another body entirely, and likewise to be with them [in the same place].

But on the contrary: Glorification does not take away nature. But in its present state the human body cannot naturally exist together with another body in the same place. Therefore, neither will the glorified [body be able to do this] later on.

I reply: It is to be said that clearly in its present state the human body cannot exist with another body in the same place. If therefore the glorious body is naturally able to exist with another body in the same place because of some property (proprietatem) imparted [to it], that property takes away that because of which the human body in its present state is prevented from existing with another body in the same place. Therefore, we must consider what it is that prevents this.

Now some people say that this [preventing factor] is thickness or a certain fleshiness that is taken away by a gift of glory that they call “subtlety”. But this is not intelligible. For what this kind of fleshiness or thickness is is not to be found. For it is not some quality, because there can be no quality such that, when it is removed, a body can exist with another body in the same place. Likewise, it cannot be a form or matter, which are the parts of the essence. For then the whole essence of the human body would not remain with glory, which is heretical.

And therefore it is to be said that this preventing [factor] is nothing other than the dimensions under which the corporeal matter stands. For it is necessary that, in whatever genus, that which exists by itself is a cause. Now distinction according to site (situm) primarily and by itself pertains to dimensive quantity, which is defined to be quantity having position. Hence also the parts in a subject have a distinction according to site from the fact that they are subject to a dimension. And just as the distinction of diverse parts of one body is according to the diverse parts of one place through dimensions, so [too] because of diverse dimensions diverse bodies are distinguished according to diverse places. For an actual division of corporeal matter makes two bodies, while a potential divisibility [makes] two parts of one body. Thus too the Philosopher says in Physics IV⁴ that, just as water or air that enters into a wooden cube has to cease (cedat) from [being] water or air, so it would have to be that separated dimensions ceased if a vacuum were posited.

Since therefore glory does not take away the dimensions of a body, I say that a glorious body cannot naturally exist with another body in the same place because of some property imparted [to it].

To the first [objection], therefore, it is to be said that the human body in its present state is prevented from existing with another body in the same place, as was said, not because of a fleshiness or thickness that is taken away by glory. (For the Apostle opposes spirituality to the animality according to which the body needs sustenance, as Augustine says, but he does not oppose it to thickness or fleshiness.) Rather it is impeded because of dimensions. Now the reasoning that was raised in objection to the contrary is included by the Philosopher among sophistical reasonings in Physics IV. For place is not attributed (debetur) to a point or a line or a surface, but to a body. Hence it does not follow, if the ends (termini) of bodies that touch one another are together, that because of this several bodies can exist in the same place.

To the second [objection] it is to be said that, as the Commentator explains in the same place, the “entering into” (subintractio) occurs through condensation, and they are said to have spiritual power (virtutem) because of their being rarefied (raritatem). Now it would be erroneous to say that glorious bodies are spiritual in the sense that they are like air and the winds, as is clear from Gregory, Book XIX of the Moralia.

Article 22: Whether a glorious body can in any way exist together in the same place with another body.

We proceed to the second point as follows: (1) It seems that a glorious body can in no way exist together with another body in the same place. For as one body is to one place, so two bodies [are] to two places. Therefore, commuting [the proportion] (commutatim), as one body is to two places, so two bodies [are] to one place. But one body can in no way exist in two places. Therefore, neither [can] two bodies [exist] in one place.

(2) Moreover, if two bodies exist in one place, take the two points at the two extremes of the place. It follows therefore that between these two points there will be two straight lines through the two bodies existing in the same place, which is impossible. Therefore, it is impossible for two bodies to exist in the same place.

But to the contrary, there is the fact that Christ entered in to his disciples while the entrances where closed, as John 20 has it. This cannot be unless his body were together in the same place with the body of the doors. Therefore a glorious body can exist with another body in the same place.

In reply: It is to be said that for two bodies to exist in the same place is prevented by [their] dimensions, as was just said, because corporeal matter is divided according to dimensions. But dimensions are distinguished according to situation (situm). Now God, who is the first cause of all things, can conserve an effect in being without [its] proximate causes. Hence, just as he conserves the accidents without [their] subject in the case of the sacrament of the altar, so he can conserve the distinction of corporeal matter, and of the dimensions in it, without a diversity of situation.

Therefore, it can happen by a miracle that two bodies exist in the same place. Hence it is attributed to the body of Christ by the saints that it issued forth from the closed womb of the Virgin, and that it entered by divine power (virtutem) when the entrances were closed. And likewise, I say that the glorious body, which will be likened (configuratum) to the body of the splendor (claritatis) of Christ, will be able to exist with another body in the same place, not because of some created power imparted [to it], but by the help of the divine power alone, which performs this, just as the body of Peter cured the sick by its shadow, but with the help of the divine power that did the miracles.

To the first [objection] therefore, it is to be said that one should use a commuted proportion as follows: As the first is to the second—​for instance, two to three—​so the third [is] to the fourth. Therefore, commuting [the proportion], as the first is to the third, so too the second [is] to the fourth—​that is, three to six. And the reasoning ought to proceed in accordance with this. As one body is to one place, so two bodies [are] to two places. Therefore, as one [body is] to two bodies, so one place [is] to two places.

And so it does not follow that if one body cannot exist in two places, two bodies cannot exist in one place. For it implies a contradiction for one body to exist locally in two places, because it belongs to the notion of a place that it is the boundary of what is in that place (locati). But a boundary is that outside of which there is nothing of the thing. Hence nothing of what is in a place can exist in an exterior place. If it is posited to exist in two places, it follows that it is outside its own place, and so it follows that it is in a place and not in a place. Neither is the case of the body of Christ an objection, because [the body of Christ] is not in the sacrament of the altar locally, but rather by conversion.

To the second [objection] it is to be said that for two straight mathematical lines to exist between⁵ two points is impossible, because no other reason for the distinction can be understood in them except from [their] situation. But for two natural lines to exist between⁶ two points is impossible by nature, to be sure, but possible by a miracle. For there remains another reason for the distinction in the two lines, from the diversity of the subject bodies, which are conserved by the divine power even though the diversity of [their] situation has been removed.

Article 1: Whether God can bring it about that matter exists without form.

We proceed thus to the first point. It seems that God can bring it about that matter exists without form. For just as matter, according to its being, depends on form, so an accident [depends] on a subject. But God can bring it about that an accident exists without a subject, as is clear in the sacrament of the altar. Therefore, he can bring it about that matter exists without form.

But to the contrary: God cannot make contradictories exist together. But for matter to exist without form implies a contradiction, insofar as the being of matter implies (importat) an act, which is a form. Therefore, God cannot bring it about that matter exists without form.

I reply: It is to be said that the active strength (virtus) of any thing whatever is to be assessed according to the mode of its essence, insofar as anything whatever acts to the extent that it is actually a being. Hence if in something there is found a form or nature [that is] not limited or contracted, its strength will extend itself to all the acts or effects that belong to that nature. For instance, if it were understood that there existed a heat subsisting by itself or in some subject that received [heat] according to all its power (posse), it would follow that [that subsisting heat or that subject] would have the strength to produce all the acts and effects of heat. But if some subject did not receive heat according to all its power, but rather with some contraction and limitation, it would not have an active strength with respect to all the acts or effects of heat.

Now since God is subsisting being itself, it is clear that the nature of being belongs to God infinitely, without any limitation or contraction. Hence, his active strength extends itself infinitely to all being and to all that which can have the aspect (rationem) of being. Therefore, that alone can be excluded from the divine power (potentia) which is inconsistent with the notion (rationi) of being—​and this not because of a defect in the divine power, but rather because it cannot be a being, and so cannot be brought about.

Now a non-being that simultaneously and in the same respect exists is inconsistent with the notion of being. Hence. it cannot be brought about by God that something exist and not exist at once. Neither can anything that includes a contradiction [be brought about by God]. But for matter to exist in act without form is like that. For everything that actually exists either is itself an act or else is a power participating an act. But actually to exist is inconsistent with the notion of matter, which according to its proper notion is a being in potency. It remains therefore that [matter] cannot exist in act except to the extent that it participates an act. But the act participated by matter is nothing other than form. Hence it is the same thing to say that matter exists in act and [to say] that matter has a form.

Therefore, to say that matter exists in act without form is to say that contradictories exist at once. Hence it cannot be brought about by God.

Therefore, with respect to what was objected to the contrary, it is to be said that an accident, according to its being, depends on a subject as on a cause that sustains it. And because God can produce all the acts of secondary causes without those secondary causes, he can conserve an accident in being without a subject. But matter, according to its actual being, depends on form to the extent that form is the very act of [matter]. Hence the case is not similar.

Article 2: Whether God can make the same body exist locally in two places at once.

We proceed to the second point as follows. It seems that God can make one body exist locally in two places at once. For it is more difficult that this substance be changed into that substance than that this accident be changed into that accident. But in the case of the sacrament of the altar, from the fact that the substance of the bread, while its dimensions remain according to which it is commensurate with a place, is converted by the power of God into the substance of the body of Christ, it follows that the same body of Christ is not locally in two places at once according to the measurement (commensurationem) of its own dimensions, but rather sacramentally. Therefore, he can bring it about that the dimension of this body is converted into the dimension of another body. And thus the same body will exist locally in two places at once.

But to the contrary: Every two places are distinguished from one another in accordance with some contrariety of place. These are up and down, before and behind, right and left. But God cannot bring it about that two contraries exist at once. For this implies a contradiction. Therefore, God cannot bring it about that the same body exist locally in two places at once.

I reply: It is to be said that for some body to exist locally in some place is nothing else than for the body to be circumscribed and comprehended by the place according to the measurement of its own dimensions. Now what is comprehended by some place exists in that place in such a way that nothing of it exists outside that place. Hence to posit that it exists locally in this place and yet exists in another place is to posit that contradictories exist at once. Hence, in accordance with the premises, this cannot be brought about by God.

Therefore, with respect to what was objected to the contrary it is to be said that it is more difficult for this accident to be changed into that accident than for this substance to be changed into that substance, both because the two substances come together in the material subject that is an essential part of either substance, and [also] because a substance has individuation through itself while an accident is not individuable through itself but through [its] subject. Hence it cannot agree with [the notion of an accident] that this accident be converted into that accident. Nevertheless, given that this dimension were converted into that dimension, it does not follow that the same body would exist in two places at once, but only in one. For just as after the substance of the bread is converted into the substance of the body of Christ, there are then not two substances there but only one, so too if this dimension of this body is converted into that dimension of another body, there will not then be two dimensions but only one. And so it would not be measured by diverse places, but only by one.

Article 4: Whether God can reduce something to nothing.

We proceed to the first point as follows. It seems that God is able to reduce something to nothing. For there is an equal distance between non-being and being and between being and non-being. But God can make something from nothing. Therefore, God can make nothing from something.

But on the contrary: God cannot be a defective cause. But a cause that makes [something] tend to non-being is a defective cause. Therefore, God cannot reduce something to nothing.

I reply: It is to be said that we can speak of the power of God in two ways: in one way absolutely, by considering his power; in another way, considering it in relation (in ordine) to his wisdom or foreknowledge. Therefore, speaking absolutely about the power of God, in that way God can reduce the whole of creation to nothing. The reason for this is because a creature is not only produced in being by the action of God, but is also conserved in being through the action of God, according to what [was said] to the Hebrews 1:3, “Carrying all things by the word of his power”. Hence Augustine says in Book IV of his literal commentary on Genesis that “the power of God, if at some time it ceased from ruling the things that were created, their species would also cease at the same time and every nature would perish”.

Now just as God acts by his own will for the production of things, and not by a necessity of nature, so too for their conservation. And therefore he can withdraw his action from the conserving of things, and by that fact all things would fall away.

But if we are speaking of the power of God in relation to his wisdom and foreknowledge, in that way it cannot happen that a thing is reduced to nothing, because the divine wisdom does not contain this. For “God created, so that all things might be”, as is said in Wisdom 1:14, not so that they pass away into nothing.

The first [objection] therefore we concede, to the extent that it deals with absolute power.

With respect to the second [preliminary argument], it is to be said that something can be the cause of some defect in two ways: in one way, from its proper intention, as when something that takes light away causes shadows. And in this way that which causes a defect does not have to be a defective cause. Now in this way God can be the cause of some defect or blinding or hardening, or even of annihilation, if he wanted. In another way something can be a cause of a defect beyond [its] intention. And in this way the cause of a defect is always defective, because from the defect of the agent it happens that it does not induce perfection in its effect. And in this way God can in no way be the cause of a defect or of a tending to non-being.

Article 5: Whether God can restore numerically the same thing that was reduced to nothing.

With respect to the second point, we proceed as follows: (1) It seems that God cannot restore numerically the same thing that was reduced to nothing. For the Philosopher says in De generatione II⁷ that things the substance of which is corrupted are not repeated the same in number. But the substance of things that are reduced to nothing is corrupted. Therefore, they cannot be repeated the same in number.

(2) But to the contrary, there is what Augustine says in On the City of God IV⁸: “If human flesh had perished in all respects, and nothing of its matter remained in any hiding-place, could not the Omnipotent restore it if he wished?” But when no matter remains of the thing corrupted, that which is corrupted is reduced to nothing. Therefore, God can restore the same in number that which was reduced to nothing.

(3) Moreover, difference is the cause of number, as Damascene says. But nothing does not make any difference, for there are no species and differences of non-being, according to the Philosopher. Therefore, what is restored by God can be one and the same in number, even though it had been reduced to nothing.

I reply: It is to be said that among things that can be reduced to nothing, a certain difference must be observed. For there are some things the unity of which has a continuity of duration in its [very] notion, as is clear in the case of motion and time. And therefore the interruption of such things is indirectly contrary to their unity according to number. Now things that imply a contradiction are not contained among the number of things possible to God, because they are lacking in the notion of being. And therefore, if [things] of this sort are reduced to nothing, God cannot restore them the same in number. For this would be for contradictories to be true together, namely if an interrupted motion were one thing.

But there are other things the unity of which does not have in its notion a continuity of duration, like the unity of permanent things, unless [it is] by accident insofar as the subject of their being is motion. For then both are such things measured by time, and their being is one and continuous according to the unity and continuity of time. And because an acting nature cannot produce these things without motion, hence it is that a natural agent cannot restore them the same in number, if they had been reduced to nothing or if they had been corrupted according to substance. But God can restore such things, and without motion, since it is in his power that he produce effects without intermediary causes. And therefore he can restore them the same in number, even though they had lapsed into nothing.

Hence the reply to the first and second [objections] is clear.

To the third [objection], it is to be said that nothing is not a difference of any being, if by the fact that something is reduced to nothing the continuation of its being is interrupted, which pertains to the unity of a motion and of the things that follow on motion.

Article 1: Whether the aforesaid [number] six is the creator.

We proceed to the first point as follows: (1) It seems that the aforesaid [number] six is the creator. For when every creature is taken away, perfection does not remain except in the creator. But when every creature made in the works of the six days is removed, there remains the perfection in the number six.⁹ Hence Augustine says in Book IV of his literal commentary on Genesis,¹⁰ “And so, if these did not exist,” namely, the works of the six days, “it would be perfect,” namely, [the number] six; “now unless [the number six] were perfect, these [works of the six days] would not be made perfect in accordance with it.” Therefore, the number six is the creator.

(2) But it was said that Augustine is speaking about six with respect to the idea of six that is in the divine mind. To the contrary: Just as, when all creatures are taken away, there remains the perfection in the idea of the number six, so there remains the idea of a stone in the divine mind. Therefore, the number six would not have any preeminence over a stone in this respect. But this seems to be contrary to Augustine’s intention.

(3) Moreover, that which is more permanent than every creature is not created, but rather the creator. Now the number six is more permanent than heaven and earth, which nevertheless seem to be the most permanent creatures. Hence, Augustine says in Book IV of his literal commentary on Genesis,¹¹ “It is easier to cross over heaven and earth, which are made according to the number six, than to be able to bring it about that the number six is not the sum (compleatur) of its [aliquot] parts. Therefore, [the number] six is not a creature but rather the creator.

But on the contrary: The perfection of a creature does not consist of parts. Neither is there anything in it that has parts. But, as Augustine says in the same book,¹² “We find that the number six is perfect by reason of the fact that it is the sum of its [aliquot] parts.” Therefore, the number six is not the creator, but rather a creature.

I reply: It is to be said that, according to Avicenna in his Metaphysics, there are three ways of considering any nature. First, insofar as it is considered according to the being it has in singulars. For instance, the being of “stone” in this stone and that stone. But there is another way of considering a nature, according to its intelligible being. For instance, the nature of a stone is considered insofar as it is in the intellect. The third way of considering a nature, however, is absolute, insofar as it abstracts from either being. According to this way of considering it, the nature of a stone, or of anything else, is considered with respect to only those things that belong to such a nature by itself.

Now of these three ways of considering [a nature], two always maintain uniformly the same order [with respect to one another]. For the absolute consideration of some nature is prior to its consideration according to the being it has in singulars. But the third way of considering the nature, which is according to the being it has in the intellect, does not always stand in the same order with respect to the other ways of considering [the nature]. For the consideration of a nature according to the being it has in the intellect that takes it from things is subsequent to the other ways of considering it. It is by this kind of order that the knowable precedes the knowledge [of it], and the sensible the sensation [of it], and so too the mover [precedes] the moved and the cause the caused. But the consideration of a nature according to the being it has in the intellect that causes the thing precedes the other two ways of considering it. For when the intellect of the artisan contrives some form of an artificial object, the nature or form of the artificial object, considered in itself, is posterior to the intellect of the artisan. And consequently the sensible box [made by the artisan], which has such a form or such a species, [is] also [posterior to the intellect of the artisan].

Now just as the intellect of the artisan is to the artificial object, so too the divine intellect is to all creatures. Hence the first way of considering any nature whatever is according as it is in the divine intellect. But the second way of considering any nature is absolutely. The third [way of considering it is] according as it has being in the things themselves, or in the angelic mind. The fourth [is] according to the being it has in our intellect. And therefore Dionysius says in On the Divine Names, Ch. 12, while he is assigning this order, that the first among all things is God, the “substantificator” of things. But afterwards [come] the gifts of God, which are shown to creatures, considered both universally and particularly, like Beauty by itself, [and] Life by itself, that is, the very nature of life, which he says is a gift coming from God. Then [come] the participants in [those gifts], considered universally and particularly. These are the things in which the nature has being.

In [all] these cases, therefore, that which is prior is always the reason for the posterior. When the posterior is taken away, the prior remains, but not the other way around. Hence it is that that which belongs to a nature according to its absolute consideration is the reason why it belongs to some nature according to the being it has in singulars, and not conversely. For Socrates is rational because man is rational, and not the other way around. Hence, given that Socrates and Plato did not exist, still rationality would belong to human nature. Likewise too, the divine intellect is the reason for the nature considered absolutely and in singulars. And the nature absolutely considered and in singulars is the reason for the human understanding [of it], and in a certain way the measure of it.

Therefore, Augustine’s remarks about six can be understood in two ways. In one way, so that by the number six there is understood the nature of six absolutely, to which perfection belong primarily and by itself. This [nature] is the reason for the perfection of the things that participate in six. Hence when all the things that are perfected by six are taken away, perfection still belongs to the nature six. And in this way ‘six’ names a created nature.

In another way six can be understood according to the being it has in the divine intellect. In this way its perfection is the reason for the perfection found in creatures established in accordance with [the number] six. If these also were taken away, perfection would remain in the aforesaid [number] six.

Now in this way six will not be a creature, but rather the reason of the creature in the creator, which is the idea of six, and is in reality the same thing as the divine essence, differing only by reason.

To the first [objection] therefore it is to be said that when all the creatures that were made during the six days are taken away, it is not said that perfection remains in the number six as though the number six had some being in the nature of things even though no creature existed. Rather [it is] because when every created being is taken away, the absolute consideration of the nature “six” remains, insofar as it abstracts from every kind of being. And it is in this way that perfection is attributed to it, just as if all individual men were taken away, still rationality would remain attributable to human nature.

To the second [objection] it is to be said that just as among created things there are some more common and some more contracted, so too the reasons of the more common things in God extend to more things, but [the reasons of] the less common things [extend] to fewer. Now because unity and multitude are common to all created things, therefore also the ideal reason of number extends to all creatures. Hence Boethius says at the beginning of his Arithmetica, “All things whatever that are constituted from the primordial nature of things seem to be formed by the species of numbers.” For this was the principal thing in the mind of the [their] constitutor. Now the exemplar or idea of a stone does not extend to all creatures. And therefore, if “six” is taken for the idea of six in this sense, still six will be more eminent than a stone, that is than the idea of a stone, namely, insofar as it extends to more things.

Again, perfection belongs to six according to the nature of six, but [it does] not [belong in this way] to a stone.

To the third [objection] it is to be said that it is not Augustine’s intention to say that even if other creatures cross heaven and earth, “six” would remain according to some created being, but rather that [even] if all creatures lacked being, still the nature of six, which belongs to its perfection, would remain, insofar as it abstracts from every being of this kind, just as also human nature will remain such that rationality will belong to it.

But as for what was objected to the contrary, it is to be said that although in God there cannot be anything having parts, nevertheless the reason of a thing that has parts can be in him. And so there is in him the reason of [the number] six constituted from [its] parts, and [also] the reason of its parts.

Article 1: Whether God can make infinites actually exist.

With respect to the first point, it was asked whether God can make infinites actually exist. And it seems not. For God can make something greater than all that which he makes, because the work is not equal to the power, as Hugh of Saint Victor says. But there cannot be anything greater than an infinite in act. Therefore, it cannot be that he should make an infinite in act.

But on the contrary: God can make more than man can say or think, according to the [remark] in Luke 1:37, “For God every word shall not be impossible.” But man can say “to be an infinite in act”, and even think [it], since certain philosophers have posited it, as is clear in Physics III.¹³ Therefore, God can make an infinite in act.

I reply: It is to be said that when it is said that God cannot make something, this is not because of a defect of the divine power but rather because of an incompossibility that is involved in what is made. Now this can happen in two ways. [It can happen] in one way, because it is inconsistent with what is made insofar as it is made. For instance, we say that God cannot make some creature that conserves itself in being, because from the fact that some thing is posited to have a superior, it is also posited to need a conservator, since the cause of a thing’s¹⁴ being is the same as what conserves the thing in being.

[The incompossibility mentioned above can also happen] in another way, because it is inconsistent with this thing made insofar as it is this thing made. For instance, if we say that God cannot make a horse be rational. For to be rational, although it is not inconsistent with what is made insofar as it is a made, nevertheless this thing made—​namely, being rational—​is inconsistent with every horse insofar as it is a horse, in the definition of which ‘irrational’ occurs.

Now some people say that God cannot make an infinite exist in act, because for an infinite to exist is inconsistent with what is made insofar as it is made. For it is against the [very] notion of a creature that it should equal the creator, which one would have to posit if there were some infinite creature. For the infinite is not greater than the infinite.

But that does not seem a reasonable thing to say. For nothing prevents that which is infinite in one way from being surpassed by that which is infinite in several ways. For instance, if there existed some body infinite according to length but finite in breadth, it would be less than a body infinite in length and breadth. Now, given that God made some body actually infinite, that body to be sure would be infinite in dimensive quantity, but it would of necessity have the bounded nature of a species and would be limited by the very fact that it would be a natural thing. Hence it would not be equal to God, whose being and essence are infinite in all ways.

But other people said that to be in some way infinite in act is not inconsistent with what is made insofar as it is made, or with this thing made insofar as it is this thing made, which is a being in act. But in some way it is inconsistent with being in act to be infinite. And this is the opinion of Algazel. For he distinguishes two kinds of infinite, namely, the infinite in itself (per se) and the infinite by accident. This distinction can be understood as follows. Since the infinite is principally found in quantity, as is said in Physics I,¹⁵ if the quantity in which the infinite consists has such a multitude [that] each part of it depends on another and has a fixed [position in the] order, so that each part of that multitude is required in itself, then the infinite in such a quantity is said to be infinite in itself. For instance, this is clear in the case where a stick is moved by a hand, the hand by the muscles and nerves, which are moved by the soul. If this went on to infinity, so that namely the soul is moved by another and so on to infinity, or else the stick moved something else and so on to infinity, the multitude of these movers and things moved will be an infinite in itself.

But if the quantity in which the infinite consists results from several things that have the same [position in the] order, and [any given] number of them is not required except by accident, then there will be an infinite by accident. For instance, if some smithy makes a knife, for the construction of which he needs many hammers because of the fact that one is broken after another, and one [hammer] takes the place of the other in succession and holds the [place in the] order that the other one did—​if such a multitude [of hammers] should grow to infinity, it would be called an infinite by accident and not in itself. For the infinite multitude of hammers is accidental to the smithy’s work, since it could equally have been fulfilled by one hammer as by infinitely many, if [the one] had held out.

They say therefore that an infinite in itself is inconsistent with what it is to exist in act, insofar as in the case of things that in themselves have an order the last one must be fulfilled, except through a comparison in some way with all the prior things.¹⁶ And so for the construction of one thing an ordered influx of infinite things will be required, if there is something infinite in itself. And so it could never be completed, since one cannot traverse infinites.

But an infinite by accident, according to them, is not inconsistent with what it is to exist in act, since one part of the multitude does not depend on the other. Hence, in accordance with this, nothing prevents there existing an infinite in act. For instance, Algazel says in his Metaphysics that the rational souls of dead men are infinite in act, insofar as he maintains that the generation of men has existed from eternity and that souls remain after the death of the bodies. According to this opinion, God could make infinites, or an infinite in act, even if an infinite in act is not found in nature.

But to the contrary, the Commentator says on Metaphysics V¹⁷ that neither an infinite in itself nor an infinite by accident can exist in act. An infinite by accident, however, is found in potency, but not an infinite in itself. And so, according to him, to be infinite is altogether inconsistent with what it is to exist in act.

And this [view] seems to be the truer. For there cannot actually exist in reality something unspecified, related indifferently to the diverse species. For although the intellect conceives animal not specified by a rational or irrational difference, nevertheless there cannot actually exist an animal that it not rational or irrational. Thus according to the Philosopher, there is nothing in a genus that is not in some species of [the genus]. Now every quantity is specified by a certain boundary of the quantity—​for instance, the species¹⁸ of multitude are two and three and so on, and the species of magnitude are two cubits and three cubits and so on—​or by some determinate measure. Hence it is impossible so to find some quantity in act that it is not limited by its own boundaries. Now since the infinite belongs to quantity, and it is called infinite by the taking away of the boundary, it will be impossible for there to exist an infinite in act. Because of this the Philosopher says in Physics III¹⁹ that the infinite is like matter not yet specified but existing under a privation, and that it belongs more to the notion of a part and a content than to [the notion] of a whole and a container.

Therefore, just as God cannot make a horse rational, so he cannot make an infinite being actually exist.

Hence we grant the first [objection], because it concludes [something] true, although it does not conclude it correctly, insofar as if God is assumed to make something [that is] infinite in one way, still he can make something infinite in another order. For instance, if he were able to make infinite lions. For there is nothing greater than the infinite in the order in which it is infinite. But in another order nothing prevents there being something else greater than the infinite. For instance, the even numbers are infinite, and yet the even numbers and the odd ones taken together are more than the even numbers.

With respect to what was objected to the contrary, it is to be said that not only what is uttered is called the word of the understanding, but [also] what is conceived by the mind. Now what is inconsistent with itself cannot be conceived by the mind, because no one can understand contradictories to be true together, as is proved in Metaphysics IV. Hence, since being infinite is inconsistent with what it is to exist actually, this [phrase ‘infinite in act’, as in the objection] is not a “word”. Hence an infinite in act does not exist.²⁰ And therefore it does not follow that it is possible for God. But the philosophers who maintained that an infinite exists in act did not know what they were saying (propriam vocem ignoraverunt).

Article 2: Whether God can make contradictories be true together and infinites exist in act together.²¹

To the first point therefore, it is to be said that no [he cannot make contradictories be true together]. And this does not involve an imperfection in the power of God. Rather [it is] because it does not have the aspect (rationem) of the possible. For every active power produces an effect like itself. Now everything that acts acts insofar as it is a being in act. Therefore, the effect of an agent is a being in act. Therefore, whatever is inconsistent with what it is to exist in act is inconsistent with an active power. Which would be the case if contradictories existed together.

To the second point, it is to be said that for there actually to exist something infinite could be [regarded as] suspect at first glance because it would be impossible. For it would follow that it would be equal to God. But this does not follow. For that which is infinite in one way is not equal to that which is infinite in all ways. For granted that there existed a fire infinite in magnitude, it will not be equal to God, because although it is a fire infinite in quantity, nevertheless it is something finite in species. Now God is infinite in all ways.

Therefore, when it is asked whether it is possible for God to make something infinite in act, it is to be said that [it is] not. For there are two ways in which, through the understanding, something is inconsistent with an active power: in one way, because it is inconsistent with its power; in the other way, because it is inconsistent with the manner in which it acts. In the first way it is not inconsistent with the absolute power of God, because it does not imply a contradiction. But if the manner in which God acts were considered, it is not possible. For God acts through his intellect and through the Word, which is formative of all things. Hence, all the things he brings about (agit) must be formed. Now the infinite is taken like matter without form. For the infinite pertains to the side of matter. If therefore God brought this about, it would follow that the work of God would be unformed. And that is inconsistent with that through which he acts and the manner of [his] acting. For he brings all things about through his Word, by which all things are formed.