Question Five: Is The Relation Of Origin
Question Five
IS THE RELATION OF ORIGIN
FORMALLY INFINITE?
5.1 The next question raised is about the intrinsic perfection of origin in the divine. It is whether the relation of origin* is formally infinite.!
Arguments Pro and Con Argument for the negative:
Everything formally infinite is a pure perfection,* for nothing can be more perfect than what is formally infinite. The relation of origin is not a pure perfection; therefore [it is not formally infinite].
5.2 Proof of the minor: One person has a relation of origin that another lacks. Therefore, were the relation of origin a pure perfection, one person would possess some pure perfection lacking in another, which is incongruous.
5-3 [For the affirmative] The opposing view is argued for in this fashion. Being is divided into finite and infinite before being divided into the ten categories.* Therefore any being, even if it does not come under some category, will be finite or infinite. The relation of origin is not finite; otherwise it would not be really identical with the divine essence, for the finite cannot be really the same as the infinite. Therefore, it is formally infinite.
Body of the Question 5.4 Three points need investigation here. First, the sense of the question; second, what is to be held; third, the solution of some doubts that occur.
ARTICGEE1
The Meaning of the Question 5-5 [Notion of the infinite] As for the first point, for the Philosopher, "The infinite is that whose quantity is such that no matter how much one removes from it, there is always more for the taking." The 'Cf. Duns Scotus, Ord. 1, d.13, 0.39 (v, 84-85); d.3, nn.1-107
(iu, 1-68).
QUESTION FIVE
reason is that the infinite in quantity, of which the Philosopher? speaks, can have being only potentially, if we take one after another.
For this reason, no matter how much is removed, what one takes will still be finite and will represent only a certain part of the infinite potential whole. More of it will always remain for the taking.
From this he infers that since the infinite in quantity has only being in the making or potentially, it does not fulfil the notion of a whole, for a whole has nothing outside itself. But there is always something outside this sort of infinite, that is, outside that which of itself has being in potency. It is never perfect, for the perfect lacks no perfection whereas this always lacks something.
5.6 For our purposes, let us change the notion of the potentially infinite in quantity, if possible, to that of quantitatively infinite in act. For just as it is necessary now that the quantity of the infinite should always grow by receiving one part after another, so we might imagine that all the parts that could be taken were taken at once or that they remained in existence simultaneously. If this could be done we would have in actuality an infinite quantity, because it would be as great in actuality as it was potentially. And all those parts which in infinite succession would be actualized and would have being one after the other would be conceived as actualized all at once. Such an infinite in act would indeed be a whole and in truth a perfect whole, since there would be nothing outside it, and it would be perfect, since it lacks nothing. What is more, nothing in the way of quantity could be added to it, for then it could be exceeded.
5.7 From this, we argue further: If we think of something among beings that is actually infinite in entity, we must think of it along the lines of the actual infinite quantity we imagined, namely as an infinite being that cannot be exceeded in entity by any other being. It will truly have the character of something whole and perfect. It will indeed be whole or complete. While something actually infinite in quantity would not be missing any of its parts or lacking any part of quantity, still each of its parts would lie outside the other and consequently the whole would be made up of imperfect elements.
A being infinite in entity, however, would not have any entity outside itself in this way. Neither would its totality depend upon elements which are themselves imperfect in entity, for it is in such a way that it has no extrinsic part; otherwise it would not be entirely
2 Aristotle, Physic. 1, c.6 (2077-9).
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whole. As for its being perfect, the situation is similar. Although something actually infinite in quantity would be perfect as to quantity, because as a whole it would lack no quantity, nevertheless each part of it would lack the quantity of the other parts. That is to say, an infinite of this sort would not be quantitatively perfect [as a whole] unless each of its parts were not imperfect. An infinite being, however, is perfect in such a way that neither it nor any of its parts is missing anything.
5.8 From the notion of the infinite in the Physics,* then, applied imaginatively to something actually infinite in quantity, were that possible, and applied further to something actually infinite in entity, where it is possible, we can form some sort of idea of how to conceive of a being intensively infinite* in perfection or power.
5.9 This enables us to describe a being infinite in entity as a being which lacks no entity in the way that one single being is able to possess it. The qualification "in the way, etc." is added because a single being cannot possess every entity whatsoever formally* and by a real identity. It can also be described in terms of how it exceeds any other finite being in this fashion. An infinite being is that which exceeds any finite being whatsoever not in some limited degree but in a measure beyond what is either defined or can be defined. Consider whiteness, for instance. It is exceeded triply by another entity, knowledge, or ten times by the intellective soul, or a hundredfold by the most perfect angel.1 No matter how high you go among be3 Ibid., c.6 (207a7-9).
+Scotus distinguishes between two radically different senses in which "quantity"
(or number) can be used to 'measure' differences between things. One is the strictly proper sense used by the mathematician or physicist (natural philosopher) which exists between what contemporary philosophers would call extensive or additive properties like weight, length, time intervals, electric current, etc. The other is analogous to that which holds between intensive or non-additive differences where these can be arranged serially. We can grade students, for instance, according to intelligence, mastery of a given subject matter, alertness, etc. Numbers can then be assigned to various groups. Thus two in the same percentile may be said to be equal, whereas those in different percentiles are said to be either better or worse than the others. Yet the "degree of difference" is not an exact mathematical one. As Scotus puts it, it is not constituted by some lesser entity to which something has been added, i.e., in the way the mathematician may add lengths, or angles, etc., according to fixed ratios.
For a modern analysis of this difference, see M. R. Cohen and E. Nagel, An Introduction to Logic and Scientific Method
(New York, 1934), pp.
QUESTION FIVE
ings, there will always be some finite measure according to which the highest exceeds the lowest. Not that there is any proportion or relative measure, properly speaking, as mathematicians use it, because the angel, being simpler, is not constituted by some lesser entity to which something has been added. It must rather be understood of the relative measure of perfection or power in the way that one species is superior to another. In this fashion, by contrast, the infinite exceeds the finite in entity beyond any relative measure or proportion that could be assigned.
5-10 [Infinity is not a property but an intrinsic mode of being] From this it follows that intensive infinity is not related to the being said to be infinite as a kind of attribute that accrues to it extrinsically. Neither should it be thought of as an attribute or property of being in the way "good" and "true" are. Indeed, intensive infinity expresses an intrinsic mode of that entity. It is so intrinsic that if we abstract from all its properties or quasi-properties, we have still not excluded infinity, but it remains integrally included in that one single entity itself.» Hence if we consider that entity most precisely, namely without any property, it will be true to say it has a measure of intrinsic excellence all its own which is not finite, since any limitation of degree is repugnant to it. Therefore it is infinite.
That which is infinite, considered most precisely, and not under the aspect of some attributable property such as wisdom or goodness, can also be aligned according to an essential order* with something it excels, but its superiority will not be measurable in any definite degree for then it would be finite. Therefore, the intrinsic mode of 293-97. What the threefold, tenfold, or hundredfold indicates in the example given is the relative position the thing in question holds in a scale or ladder of qualities. A classical example of such a scale is Friedrich Mohs'
"scale of hardness" used by mineralogists. It has ten degrees which range from talc, the softest, to diamond, the hardest. But the fact that topaz is eighth on the scale does not mean that properly speaking it is twice as hard as fluorite, which is fourth on the scale. What governs the relationship logically is that there is an objective transitive asymmetrical relationship that holds between the various members of the scale. Scotus, following
Aristotle's claim that "forms (or essences) are like numbers," believed that things could be classified in the sense that the higher in the scale has all the perfection of something lower in the scale, if not formally,* then virtually* or eminently.* 5 Cf. Duns Scotus, Ord.
1, d.8, nn.108-109
(IV, 202-203);
Iv, d.3, q.1, nn.go-33 (ed. Vivés xvi, 687-89).
Lil
GOD AND CREATURES
anything intensively infinite is infinity itself, which intrinsically expresses a being or essence which lacks nothing and which exceeds everything finite beyond any determinable degree.
5.11 Damascene® confirms this corollary when he says that the essence is an infinite and limitless sea of substance. Substance then, insofar as it represents what is absolutely first in the divine, he calls a sea, and as such it is infinite and boundless. But substance in this sense does not include [formally] either truth, goodness, or any other attributable property. Therefore, infinity as such is a mode of essence more intrinsic than any attribute it has.
5.12 [A relation cannot be infinite] Having examined the notion of infinite, let us turn to the question at issue, viz., Can a relation be formally infinite? Here the question is not whether the relation is really the same as something infinite. Common opinion is agreed that it is, for it is really the same as the essence.' Neither are we asking if the relation by identity* is that infinite [essence]. No, the question is this: Considered formally, that is, according to its own relational entity, is the relationship [of origin] intensively infinite and that in virtue of the relational entity's own infinity? In other words, is intensive infinity an intrinsic per se mode of the entity proper to this paternity—so intrinsic per se that the paternity is not just infinite by reason of something else with which it is really identical? Would this relational entity still be intensively infinite in itself even if one included no other identity than its own, indeed if one excluded anything other than the relational entity itself?
5.13 From this it is clear that the reply commonly given to the question is not to the point, namely, when they answer that the relation of origin is formally infinite, because the essence is infinite and this relation is the essence. For the question is not whether the relation is by identity some thing which is formally infinite, but whether the relation itself, according to the first mode of per se predication, is that thing whose per se intrinsic mode is infinity.
Hence the argument: "Divinity is infinite; paternity is divinity; therefore, etc." is not conclusive. The major is true according to formal predication,* whereas the minor is only true according to predication by identity.* Paternity is deity according to everyone, therefore no conclusion according to formal predication can be inferred.
For terms in the conclusion can have no greater identity than that * Damascene, De fide orth. 1, c.g: PG 94, 835; ed. Buytaert c.g, Pp. 49.
7 Cf. Duns Scotus, Ord. 1, d.g, nn.qiiff.
(1, 362ff.); d.8, nn.218-22 (IV, 274-77); U, d.1, q.4, nn.5ff. (ed. Vives xu, g8ff.).
QUESTION FIVE
which they have with the middle term in the premises.' That is why from one necessary and one contingent premise, only a contingent conclusion or contingent union of terms follows. But unless '"Paternity is infinite" is true according to formal predication, their thesis is not proved, as is obvious from what was explained above [in 5.6], for it would only follow that paternity through identity is a certain thing that is infinite.
5.14 But if you intended to infer something according to formal predication, and not merely that of identity, you would be switching from one form of predication to another, thus committing the fallacy of figure of speech. For you go from an essential qualification [quale quid] to "this something" [hoc aliquid], that is to say, the middle term which is an essential qualification is interpreted as being "this something." For like one who from a middle term that expresses an essential qualification infers a middle term that expresses ''this something," so here, by force of an inference according to formal predication, one intends to imply that "this something," which would not follow otherwise, actually does follow by virtue of the argument. The other premise [in 5.13], however, was only true in virtue of identity. The one switching from identity to formal predication, therefore, would seem to be interpreting both premises as instances of formal predication, whereas such is not the case because the minor can only be verified in terms of predication through identity.
5.15 One could say, in short, that this conclusion: "Paternity is infinite" [rather than 'Paternity is the infinite' is, properly speaking, untrue because the formal mode of expression is adjectival and signifies the form to be the form of that of which is asserted. Because of this characteristic, an adjective can only be predicated according to the mode of formal predication. Inferring this conclusion from the premises, then, would be a fallacy of figure of speech, for the reasons given above [in 5.14]. Therefore, if infinite is not simply asserted of paternity according to formal predication, the conclusion is false. If, therefore, the conclusion is interpreted to mean that there is a real identity of something infinite with paternity, then one ought to formulate the conclusion as "Paternity is something which is infinite.' But our question poses a special difficulty if we understand [the conclusion] in the other way, namely as if infinity were an intrinsic formal mode of paternity qua paternity.
8 Cf. supra, note 7, and Ord. 1, d.5,nn.17-24
(IV, 17-23).
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ARTIGEE!
Solution of the Question: Paternity is not Infinite 5.16 [Triple proof of the conclusion] As for the second article, I hold 'Paternity is not formally infinite," in the sense explained [in 5-12-15]. There are three reasons for this conclusion, the first is based on the unity of an infinite being; the second, on its communicability; the third, on its simplicity and incompossibility. For an intensively infinite being is something unique, incapable of being multiplied or replicated; it is not restricted but communicable; and it cannot be a component of something else. rea 1. The First Principal Reason 5.17 The first reason is formulated in this way: Several beings really distinct and formally infinite cannot exist. But there are several really distinct relations of origin. Therefore, they are not formally infinite intensively; neither is any single one of them infinite, because any reason for one being infinite would hold for the others as well.
5.18 [Three ways of proving the major] The major is proved first by seeing how several infinite things would have to be interrelated; second, by comparing the intensively infinite with the finite generally; third, by seeing how the intensively infinite is related to in-. tellect and will in particular.
5.19 [The first way] The first [of two proofs] is this: The infinite possesses all entity that can be had by any one thing. But it is possible for one supremely perfect being to have every pure perfection really and as identified with itself. Therefore the infinite has in itself really and by identity every pure perfection; but it does not have what is really distinct from it in this way; therefore, no pure perfection or something perfect can be really distinct from it. If there were another really distinct infinite, however, there would be pure
[8] perfection really distinct from it. Therefore, we have our major that there cannot be several really distinct infinites.
5-20 But it seems in this proof of the major, that the second proposition, viz., that a supremely perfect being can have every pure perfection by way of identity, needs corroboration. The evidence is this: Nothing is supremely perfect if it lacks some pure perfection, for no pure perfection is incompatible with any other pure perfection. If all pure perfections could not be possessed by the supremely perfect, this would be due to some mutual incompatibility
QUESTION FIVE
among them.* The underlying assumption here, that no pure perfection is incompatible with any other, is established from the very meaning of pure perfection. For according to Anselm, a pure perfection is something it is better for anything to have than to have what is not it, i.e., to have anything incompatible with it. (This will be explained in [5.31 of] article II in connection with the second principal argument.) Therefore, if two pure perfections, call them
A and B, were incompatible, A would be better in anything than non-A, namely anything incompatible with A, and hence it would be better than B which, by stipulation, is incompatible with A. By the same token, however, B would be better than A. Such circularity is impossible; otherwise one and the same thing would be less perfect than itself.
5.21 A second argument for the major using an intercomparison of several [infinites] could be this: When several things are equally good, the goodness of several exceeds that of one alone. Now if there are several infinite beings, each is equally good. Therefore those several good things exceed in goodness any one of them singly, and thus none of them would be infinite.
5.22 If you object that one could use this sort of argument to show God plus a creature exceeds the goodness of God alone, the objection is invalid. The goodness of one [the creature] does not equal or measure up to the goodness of the other [i.e., God] and thus is contained eminently* in that of the other. Hence, to take the two together does not augment or exceed the goodness [of God] in himself. But in our hypothetical case it is just the opposite, since one good is not completely contained in the other eminently, for this would run counter to the idea of the infinite.
5.23 [Second way] Comparing the infinite with the, finite geneo} erally, however one can argue [first] in this way: One infinite being suffices to ground the dependency of all finite beings, particularly if it bé the first being on which they depend. But it is impossible that several should each be the sufficient ground supporting the same dependent being in the same order of dependence. Therefore, there cannot be more than one infinite.'°
Proof of the major: Just as any form of dependency implies a note of imperfection, so it is a matter of perfection that something be the » Cf. Duns Scotus, Ord. 1, d.2, nn.377-87 (II, 344-49).
10 Ibid., m1, d.1, q.2, nn.g-5 (ed. Vivés xiv, 59-66); u, d.g, q.4, 0-3 (XH, 93); Iv, d.6, g.2, nn.2-3 (XVI, 543-44); 1, d.2, nn. 70-73 (i, 169-73).
LYS
GOD AND CREATURES
supporting term or ground on which something depends, not indeed in just any way, but first and foremost. But supreme perfection, which cannot be exceeded, exists in one intensively infinite being.
The major is also apparent from the fact that one unique essence actually supports sufficiently the full measure of the dependency of any dependent thing because it represents the first efficient cause as well as the exemplar and ultimate final cause of the dependent's being.
Proof of the minor, viz., There cannot be more than one primary sufficient ground that actually is supporting the same dependency.
For no term is actually supporting the dependence sufficiently if it can be eliminated and still leave the dependent being sufficiently supported, for otherwise something would depend on a support, which if written off, the dependent thing would lose nothing in the way of support and could continue to exist. But if two things were each supporting sufficiently the dependency in the same order, then if one were eliminated, the complete dependency on the other would continue. Thus the one eliminated actually gave no support.
The same argument would hold for the other, so that neither is supporting the dependent completely or else only one of them is.
Just as the first proof of the major then is based on the fact that . the infinite contains really and unitively all pure perfection, since all pure perfection can be possessed in this way by a single subject, so the present proof is grounded on the fact that the infinite contains the content of all limited perfection in an eminent fashion, and this suffices for it to support the full measure of any limited being's dependency. Thus these two proofs are based on what was said about the infinite in the first article [5.9], namely that it has all entity or every aspect thereof in the manner that a single subject can possess it, which for pure perfections is by identity and for limited perfection is by way of eminence.
[10] 5.24 A [second] proof based on the general comparison of finite and infinite can be put briefly as follows: The ascent in an essential order* or hierarchy always leads to unity and hence terminates with some single or unique thing.!? But the intensively infinite is absolutely the highest in the essential order. Therefore, it is a single unique thing.
5-25 [Third way] Third, the major is proved from the way the infinite is ordered to intellect and will in particular. It goes as follows:
11 Cf. ibid., 1; d.2, nn.64-73, 165-81 (11, 167-73, 226-36).
QUESTION FIVE
An infinite being is the primary object of an infinite intellect and also its beatific object. But the same infinite intellect cannot have more than one object that is both primary and beatific.
A similar argument could be made for the first or adequate beatific object of the will.!?
5.26 The first proposition can mean primary object in any of three senses and is true for all of them. Accordingly it contains three parts.
One of the primacies an object may have is called "primacy of adequation,"" namely when the power does not extend beyond this object. The colored or luminous is called the first object of sight in this sense.
Another meaning is "'primacy of virtue." Such would be that in virtue of which such an intellect knows or understands everything else. In this way light is the first object of sight.
{11] The third can be called "primacy of perfection." It obtains when the object as supreme contains in itself the perfection of all objects and has the power to perfect the intellect. Now the beatific object is that which quiets, satisfies, and perfects the intellect.
5.27 On this basis three major premises can be formulated.
The same intellect does not have several distinct adequate objects. It cannot know another object that lies outside the extension of its adequate object. Otherwise this adequate object would not really be adequate, since the intellective power in knowing equally well another distinct object would be going beyond it.
A power cannot have several first objects by a primacy of the second type, that of virtue, either. It is not possible for it to understand everything it understands, including B, by virtue of A, and at the same time to understand everything, including A, by virtue of B.
That A be the ground for understanding B, and B the ground for understanding A involves circularity, and such circularity is impossible.
Neither can the intellect find its supreme satisfaction in two equally distinct objects, for it does not come to rest and find complete happiness in any object which, if eliminated, it would be no less happy and at rest. But if one of the two were written off, the intellect would still be supremely satisfied, at rest and happy with the other. Therefore, it could not be perfected by the object eliminated, and by the same token neither could it be so by the second.
The three majors then are evident. The same intellect could not 12 Cf, ibid., 1, d.g, nn.171-74
(III, 105-107).
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have several equally distinct first objects, be the primacy that of adequation, of virtue, or of perfection in the way a beatific object is primary.
5.28 The minor, namely what is intensively and formally infinite is first object of the divine intellect in each of these three ways, is proved first in regard to the second type [that of virtue].
What is ground for being is also ground for knowing. Therefore, the infinite, which in itself contains the entity of everything eminently, also contains in itself all knowability eminently. But if anything contains virtually some object in this way, it is also that which moves the intellect to the knowledge of that object. Therefore, anything intensively infinite in this way will function as first object in regard to the divine intellect, and this by a primacy of virtue.
From this it follows that the intensively infinite is the first object by a primacy of adequation, for as we have shown elsewhere' in dealing with the divine intellect, this intellect does not have an adequate object common by way of abstraction from all the objects it knows, but rather one that is common to all per se objects by a community of virtue. Otherwise the divine intellect would be demeaned because it could be altered by a finite object. Therefore, that which is its first object virtually is also its first adequate object.
From this the third primacy also follows, viz., that of perfection which is characteristic of the beatific object. For in the most perfect of all objects, which contains in the highest all the perfection of every object, this intellective power is to the highest degree perfected, satisfied, and quieted, and so beatified.
5.29 Confirmation of the major and minor premises of this reason: Suppose there were two distinct infinites
A and B. The divine intellect will be able to understand them both; if not, that will be because one is not a being. Neither can be understood, however, except by a comprehensive act, since both are formally infinite. Now two distinct objects, each with its own infinity, cannot be grasped in just one comprehensive act, because a single object intensively infinite is what one infinite intellect is equal to. Therefore, since both A and B are infinite intensively, either both will never be understood, or, if they are, it will not be simultaneously, and thus there will be succession or mutation in the divine intellect.
2. The Second Principal Reason 5.30 The second main argument based on communicability is formulated in this way. Every pure perfection is communicable; *
18 Cf. ibid., prol., nn.197-201 (1, 133-36).
QUESTION FIVE
everything intensively infinite is a pure perfection. Therefore, [it is communicable]. No personal property, however, is communicable, since it is the formal ground for existing incommunicably [or as a person]. Therefore, no personal property is intensively infinite.
The [first] minor is evident, because nothing can be more perfect than what is intensively infinite.
5-31 Proof of the first major: From what one gathers of the mind of Anselm in the Monologion,!® a pure perfection is that which, in anything having it, it is better to have it than to have what is not it.
This rule needs two explanatory notes.
It does not mean "Better it than [not-it,] its contradictorily opposed negation," for in this sense everything positive would be a pure perfection, since anything positive is simply better than its contradictorily opposed negation. Here "what is not it" means rather
"anything whatsoever incompatible, also positively," so that the meaning is: a pure perfection is in anything better than whatever is incompatible with it.
Second, "in anything" does not refer to any nature but to any suppositum,* understood not insofar as it is the suppositum of such and such a nature, but taking it absolutely insofar as it is such a suppositum prescinding from any notion of the nature of which it is the suppositum. This is obvious, since for the gold considered as having the nature of gold or for a gold suppositum not-gold is not something it is better to be than gold. For there are some things for which the incompatible qua incompatible is not better, because it destroys a thing's entity. In fact, from this standpoint it is better for gold to be gold than to be anything incompatible with the nature of [14] gold. The meaning then is this: Pure perfection is such that in any suppositum, considered absolutely according to its essential meaning as a suppositum [i.e., as an individual independently existing substance], without specifying of what nature it is or what sort of suppositum it is, it is better to be this sort of thing than to be anything that is not this kind of thing.
5.32 From this the thesis follows that no pure perfection is formally incommunicable.
The implication holds, because what is formally incommunicable is also formally incompatible with any other subject, considering the latter as a suppositum, but not including its nature. Proof of this: What is repugnant to anything is not simply better for it than what is not such, for being repugnant, it would destroy the other.
14 Cf. ibid., 1, d.2, nn.g82-84 and the textus cancellatus (11, 346-48).
15 Anselm, Monolog. 15: PL 158, 162-63; ed. Schmitt 1, 28-29.
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But what is of itself incommunicable is repugnant to everything that also has the characteristic of being a suppositum, and hence is not better for it gua suppositum than what is not it. We have then this major: No pure perfection is formally incommunicable.
3. The Third Principal Reason 5-33 The third argument from incompossibility [cf. 5.16] goes [15] this way: Pure perfection must be really identical with whatever 1s compatible with it in the same suppositum, in the sense that if we take this and that abstractly, it is true to say in the abstract that this is that. But a relation of origin is not identical in this way with everything compatible with it in the same suppositum. Therefore
[it is not a pure perfection]. The minor is manifest for this proposition is not true: Active generation is active spiration.
5.34 The major is proved inductively and by argument.
It is established inductively in this way: There is nothing in the divine that is not the same thing as the divine essence and also the same as anything essential, so that considering such in the abstract, one can say simply "This is this." As regards the essence and essentials then, which are generally admitted to be formally infinite, the major is obvious. Each is identical with anything compatible or consistent with it in the same suppositum.
5.35 The major is also proved by this argument. Not only is the infinite not a composite but it is completely incapable of being a component of anything else, because a potential component is a potential part and hence can be exceeded, for the whole is greater than its part. The infinite, however, cannot be exceeded in any way.
Therefore, it is completely simple, uncomposed and unable to be a component of anything else. But if something compatible with it in the same suppositum were not the same thing as it, then the infinite would not be completely incapable of being a component, for then there would be in the suppositum some sort of composition, at least that of act and potency. Therefore, we have the first part of the major, viz., that the infinite must be really identical with whatever is compatible with it in the same suppositum.
5.36 Proof of the second part of the major, namely that it is so identical that predication in the abstract, such as 'This is this," is true. Since affirmative predication is true by reason of identity, every case of predicating the abstract of the abstract will be true if the ground of the identity is not destroyed by the abstraction.
Where abstraction eliminates the reason for the identity, however, the predication is not true.
QUESTION FIVE
[ 16 | Example: "Whiteness is color" is true, for though the terms are abstract, still the abstraction is only from a subject of a different nature, and that subject was not the precise ground for the identity of the terms. Even with the subject excluded, therefore, the basis for the identity of nature [of whiteness] with that [of color] remains. Whiteness and music, however, have only an accidental identity by reason of their subject; therefore, even though "The white individual is a musician" is true to the extent that the same subject is characterized by both accidents, nevertheless if you abstract from the subject which was the ground for the identity of the two descriptive terms, it is not true that '"Whiteness is music."'
It is clear then that predication in the abstract is true when the identity of the terms is such that the abstraction does not remove the reason for their identity. Now when one term is infinite, predication that abstracts from the suppositum does not destroy the ground for its identity with any perfection compatible with it in the same suppositum, and, therefore, because of the infinity, as was argued above [in 5.19-20], compatibility in the same suppositum is possible only where there is a true and perfect real identity. Therefore, whenever the term, in abstraction from the suppositum, retains the formal reason for its infinity, the basis for its identity with the other term is always present and consequently abstract predication, such as '""This is this,' remains true.
5-37 [Corollary about predication in the divine] This argument shows in general that in the divine, if it is not a case of predicating one opposite notional* term of another, certain predications are true not only in the concrete but also in the abstract, whereas certain others are true in the concrete but not in the abstract. We are not speaking of those predications not true in either way, namely those where the terms are opposed, for the Father is not the Son, nor is paternity sonship. Where the terms are not opposed, however, but are compatible in the same suppositum, at least in the concrete there is true predication, such as '""The Father is the one who spirates [the Holy Spirit] or "The Father is unbegotten," even though it is not true in the abstract that "Paternity is spiration."
Nevertheless the following predications are true: 'Deity is paternity" or 'Deity is spiration," but this is true only because divinity is formally infinite, not because paternity and spiration are. Because deity, in abstraction from the suppositum, still retains the note of infinity, the reason for its identity, understood simply [not formally], with paternity and with spiration, always remains, and therefore also the basis for true affirmative predication in the abstract.
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But when one abstracts 'paternity,' which is not formally infinite, from the suppositum, the reason for its identity with active spiration, which is not infinite either, is no longer there, since neither term, according to its proper notion, possesses infinity. Therefore, even though this is true: "The Father spirates," because both descriptive terms pertain to the same suppositum, nevertheless when one abstracts from this suppositum, since neither of these descriptive notions formally includes "infinite," the abstract predication
"Paternity is spiration"' is not true.*® 5.38 A converse argument of the same type is this: Whenever some essential feature is predicated of something essential, or something personal of something essential, or something essential of something personal, e.g., "Wisdom is paternity" or "Wisdom is spiration,' the proposition is true and vice versa.
For one term (in this case "wisdom '') is still infinite, abstracting from the suppositum; hence the ground for its identity with the other is retained despite the abstraction, and consequently also the truth of the affirmative predication.
5.39 This major, then, is evident, namely that the only predication by identity of one abstract of another that must be denied is that in which neither term is formally infinite, such as "Paternity is
Spiration."
5.40 As regards this major, however, some!' give a twofold explanation why in the divine certain predications in the abstract are denied. Although paternity and spiration are really identical, they differ conceptually, and this suffices to invalidate such predications.
But when one objects that such a distinction does not allow for the falsity of the proposition "Wisdom is goodness," they reply that just as the attribute "power" is not the attribute 'wisdom,' so also in the case at hand.
5.41 But this does not seem plausible. An attribute qua attribute expresses a second intention or asserts some conceptual relationship of the subject of which it is predicated. Hence one numbers attributes, and it is true to say that "goodness" and "'wisdom" are two attributes. In the sense then that they are subject to enumeration, which is in the conceptual order, it is not true to say ''This is this."
But this does not require one to deny the proposition: 'Wisdom is 16 Cf. Duns Scotus, Ord.
1, d.13
(vy, 65-124); ul, d.22, q-un., n.21
(ed.
Vives xIv, 777-78).
17 Thomas, Summa theol. 1, q.3, a.3, ad 1 (1, 16); q.28, a.3, ad 1-2 (1, 154); q.40, a.1, ad 1 (I, 202); Henry of Ghent, Quodl. v, q.1
(fol. 152P); Summa a.60, q.10 (u, fol. 172B-173H). ae
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goodness," where the conceptual aspect that allows them to be numbered is suppressed. By analogy, then, if we include only what is of the real order, "Paternity is spiration'" would be true if paternity and spiration were absolutely identical in reality, even though "The notion or property of paternity is the notion or property of spiration'' would not. For whatever those features be that are simply the same thing in God, they are predicated of each other, also in the abstract and in names of first imposition, but not when they are expressed by names of second imposition or those which designate some second intentional aspect. This is clear from the case of creatures. Although "Socrates is man" is true, this is not true: "That aspect of Socrates which is singularity is the aspect of man which is universality."
5.42 Another author's says, and seemingly with more reason, that the properties in the same person have some extramental difference that goes beyond a consideration of the intellect. This is enough for them to be disparate without being opposed [as paternity and sonship are]. That is why predicating one of the other in the abstract is not correct. The reason why such abstract predication is not true is that this extramental distinction stems from the fact that neither property is infinite. If this or that were infinite, such a distinction would not exist, and there would be nothing to impede predication in the abstract.
ARAAGCLE Itt Objections and Answers 5.43 [Four objections] As for the third article, four counterarguments are leveled at what has been said, the first of which is this.
[First objection] What is comprehensible only to an infinite intellect is formally infinite. This generation as generation is formally incomprehensible except to the divine intellect. Therefore [it is formally infinite]. The minor is proved from Isaiah'®: '""Who can describe his generation?' Commenting on this text in relation to the eternal generation of the Son, Jerome®? states: ""The Prophet says it is impossible to speak of it, etc.' What it is impossible to speak of is incomprehensible to a finite intellect. Ambrose*! also confirms this:
"How, I ask you, do you think the Son is begotten?"' And he goes on 18 William of Ware, Sent. 1, d.2, q.1.
19 Isaiah 53:8.
20 Jerome, Comment. in Evang. Math. 1, c.1: PL 26, 21; CCSL 77, 7.
21 Ambrose, De fide ad Grat. 1, c.10, n.64: PL 16, 543; CSEL 78, 28.
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to say: "It is impossible for me to know the secret of his generation.
The mind fails, the voice is silent, not only mine but that of the angels. It is beyond the Cherubim and Seraphim and transcends all understanding." He proves this from Paul to the Philippians*: "The peace of Christ which surpasses all understanding," arguing "Since the peace of Christ surpasses all understanding, would not such a generation as his surpass all understanding?"'
5-44 [Second objection] A second argument is this. Every action equal to its infinite principle and its infinite term is formally infinite.
In the divine, however, generation is an action equal to its infinite formal principle and its infinite term, for its source is the essence or infinite memory and it terminates first in the Son, who is infinite; also its formal term is the essence communicated or spoken knowledge, both of which are infinite. It is obvious the action is equal to its source and adequate for its term, because there can be but one action which stems from this principle and ends with this term.
Therefore [it is infinite].
5.45 [Third objection] The third argument is that the reason for subsisting is also the basis for having being in the most perfect way.
But the first person's relationship of origin is his basis for subsisting. Therefore, it is also the reason for his having being most perfectly, and hence the relationship of origin is infinite.
5-46 [Fourth objection] Furthermore, the divine intellect is formally infinite; otherwise it would not comprehend the infinite divine essence, yet it does so as intellect, a point proved in the first question [1.30-38]. But the divine intellect is only infinite because it is the same thing as the divine essence, which is infinite primarily. But paternity is also the same thing as the intellect. Therefore, for the same reason, paternity is formally infinite.
5.47 [Reply to the objections] Answer to the first [in 5.43]: When an intellect has an object that is first by virtual primacy, then it understands every other object in its hierarchical relationship to that first object. (This is evident from the reason given [in 5.25-28] when treating of intellect and will in article two of this question.
For example, when an intellect's first object is one of virtual primacy, then by means of that object it understands more immediately what is identical per se with that object than what is identified with it only incidentally or per accidens.) But the divine intellect has as its first object, by a primacy both of virtue and of adequation, the same, absolutely identical, thing, namely, the divine essence qua essence, as we said [in 5.47]. Therefore, there is nothing personal
22 Philippians 4:7.
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that is this intellect's primary object in this way. (Of course the personal relation is more proximate in this way to the intellect's first object than anything created. To the extent it is really identical with that object, the relation is closer to it in entity and hence also in knowability.) 5.48 As for the form of the argument, the major is true if understood in the sense that if the object is incomprehensible with its own incomprehensibility, it is also infinite with its own infinity. But then the minor is false, viz., that this generation as generation is incomprehensible, even though it could be given a true meaning per accidens either by reason of something concomitant with generation or, what is more to the point, by reason of the basis for understanding it. For generation is apt by nature to be understood primarily by means of the essence as first object both by the divine intellect and by that of the blessed, since the divine essence is the first object of both intellects. Now this basis for understanding the generation is indeed incomprehensible, and so the generation itself could be called incomprehensible causally or by virtue of its source [principiative}|. One could also say that it was incomprehensible concomitantly, i.e., as regards what it includes, for generation includes communication of the essence to a person, and this takes place by means of the essence itself or the person's nature. Now this communication includes the essence's infinity as a presupposition, for if the essence were not infinite, it could not be communicated in this fashion to several persons. Therefore, generation is incomprehensible as regards its presupposition, namely, communication of an essence that has to be infinite.
5.49 [Objection to this answer and its solution] These answers are challenged on the grounds that they ignore the force of what generation gua generation means. No matter what the principle be by which generation is understood or what its understanding or communication presupposes, the authorities cited [in 5.43] always seem to be saying that generation itself in its own right is incomprehensible and any intelligible whose intelligibility exceeds comprehension is infinite.
5.50 To this one could say that what is comprehensible to the finite intellect must be finite, whereas what is incomprehensible to it is non-finite. But from this it does not follow it is infinite. We shall say more about this [in 5.57] in answer to the initial argument. According to this negative interpretation of incomprehensible as something that cannot be comprehended, the major of the argument must be denied. For it to be true, "incomprehensible" would need
GOD AND CREATURES
to be interpreted quasi-contrarily, namely, as that whose virtual quantity extends beyond or exceeds everything comprehensible, which is not the way it is used here.
5-51 Reply to the second objection [in 5.44]: Equality, properly speaking, means that two things are equal in quantity, and in this sense no equality is involved here. In another sense, however, equality refers not to quantity but to proportion. In this sense, one thing is said to be equal to another if it is not disproportionate but supremely adequate. Equality in this sense is that which obtains between effect and cause where the effect is supremely adequate as an effect, even though it is not simply equal to the cause in quantity.
Also illumination, if it could be no greater, would be said to be what the sun is "equal to," even though illumination, as an equivocal effect,* could never equal the sun in quantity.
5.52 As for the form of the argument, the major would only be true of equality taken in the first sense, if such were there; but in that case the minor is false. It would be true of "equality" in the second sense provided this referred not to intension but extension, namely, insofar as this one principle of generation could not extend
[23] to any generation other than this. Consequently, there is no quantitative equality involved here or, properly speaking, even equality of intension, but only that of extension, and thus infinity in no way is included in what it is "equal to" [i.e., principle and term].
5-53 Reply to the third objection [in 5.45]: As we said at the end of the second article of the previous question [4.46], "to subsist'' is an equivocal term. In one sense it refers to being per se, and Augustine*® uses it in this way when he says: "Everything subsists in respect to itself; how much more God?" In another sense, it refers to "being incommunicably per se," insofar as communicable means not subsisting, as it were, but what is inhering, as it were, in a subsisting subject and has a quasi-mode of inherence. In the first sense, | concede ''to subsist'' formally implies most perfect being, and is only affrmed of the essence according to Augustine. In the second sense,
"to subsist'" presupposes, but does not formally include, perfect being. It only adds incommunicability to being per se in the first sense, and is thus a ground for subsisting in the sense of being incommunicably per se. The relation is this sort of thing. But the ground for having being incommunicably is not the ground for being most perfectly.
5-54 Reply to the last objection [in 5.46]: I admit the intellect is [24] 23 Augustine, De Trin. vu, c.4, n.g: PL 42, 942; CCSL 50, 260.
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formally infinite by an infinity all its own which is an intrinsic mode of its proper entity, namely intellectuality qua intellectuality. Paternity, however, is not infinite in this way, even though it is in some way really identical with the essence, as is the intellect.
5-55 Yo what is added about its infinity being due to identity with the essence, I answer: As we said in the first question [1.5-6], what is absolutely first in the divine is essence qua essence, which Damascene [in 5.11] says is a sea because it contains all divine perfections. The essence is infinite in itself, not only intensively but also
Virtually, as containing primarily and of itself everything intrinsic al to the divine. Now everything else contains other features by identity, but not all of them primarily, since it does not contain them in virtue of what it is but by reason of the divine essence, from which its infinity also derives. Therefore, the essence has infinity formally, properly, and primarily, because it contains it of itself. It is called a sea, since it contains every intrinsic entity insofar as it is possible to contain it formally in one single thing. Now from this first entity, and it is licit to speak in this way, emanate all other features in an orderly fashion. First, indeed, are the intrinsic essential features, expressing no relation to anything extrinsic or ad extra. Second, come the notional. [or personal properties]. Third and last, created or extrinsic things. Now everything emanating receives such perfection as it is consistently able to receive, and the quasi-efficient and _ primary source of what it gets is the infinity of the essence, although the formal cause or reason is the proper entity itself of what emanates. Therefore, essentials derive from the essence formal infinity, because the essence in its function as principle or foundation suffices to give them such quantity, or virtual quantity, or communicability as is not repugnant to them. To relate to another belongs to the personal relations, but not intensive infinity proper, for the relation is incapable of such quantity even as it is unable to be communicated. In the genre of formal principles there is also something basic. This one receives infinity and that not, because the first receives communicability whereas the second gets incommunicability, the reason being that this is this and that is that. For formal repugnance (like non-repugnance) is formally reduced in the first place to that basic feature said to have it. Finally, creatures receive finite entity from the essence, because only such entity pertains to them.
5.56 As for the form of the argument, therefore, I say that identity with the essence is not the only ground for possessing infinity formally, but it is the sufficient reason for possessing infinity in any-
GOD AND CREATURES
thing to which infinity is not repugnant formally. As was proved [in 4.17], infinity is formally repugnant to a personal relation, but not to anything essential. And if you ask why infinity is compatible with the latter and not with the former, one can reply by asking:
Why—as all admit—is incommunicability repugnant to one and not to the other? The answer is the same for both. It depends on the nature of the formal principle, namely on the fact that this is formally this and that is formally that. Because the essence, then, as the fundamental principle is one unlimited source from which many features emanate or proceed in orderly fashion, everything, in the first instant of its quasi-emanation or derivation, possesses its own proper entity. This has this sort and that has that sort. The ultimate reason why something is repugnant to one but not to another is to be found in the respective entity of each.
Reply to the Initial Argument [26] 5.57 To the argument [in 5.3] at the beginning I say: As was pointed out in the first article [5.9], infinity in entity expresses totality of entity, whereas finitude in its way expresses only partial entity, for every finite being as such is less than the infinite as such.
As Euclid says*#: "Every lesser number represents a part or parts of a greater number." This should not be taken to mean that this binary is a part of that ternary (for nothing like this occurs in the divine), but according to all the proportions observed to hold between quantities this binary number is related to that ternary number as a part or parts of a whole. For this binary is exceeded by another ternary of which it is a part. And that, I say, is what occurs here. As God is most simple, nothing created can be a part of him, but everything finite, since it is less than infinite entity, can be called a part, although not according to some definite measure, for it is exceeded infinitely. In this way every other being distinct from the infinite being is called "a being" by participation because it captures a part of that entity present there perfectly and totally.
Therefore, the point I wish to make is this: Everything finite, since it is less than the infinite, represents a part. Hence, to whatever it is repugnant to be a part or exceeded in reality by anything, it is also repugnant to be finite. Now to be a part of divinity in this special sense, or to be exceeded by divinity, is repugnant to pater- *4 Euclid, Elementa vu, def.4 (ed. Heiberg, in Bibliotheca Teubneriana,
1, Lipsiae, 1883, p. 199).
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nity, for paternity, because of the infinity of divinity with which it is compatible in the same suppositum, is, simply speaking, identical with it, and consequently in reality it can neither be exceeded, nor be a part, nor have any ground for being a part. Therefore it is neither finite nor infinite, as was proved [in 5.50], for as finite has the characteristic of a part in the manner just explained, so infinite has the character of a whole in this sense, namely, from the plenitude of its "virtual quantity" the infinite is measuring everything else as greater or lesser to the degree it approaches the whole or recedes from it. But neither does paternity have this mark of totality, for measurement according to certain degrees of perfections ends with something first in the order of measurement, which is the absolute essence. Therefore, I say briefly that paternity is neither formally infinite nor formally finite.
5.58 And when you insist that being divides immediately into finite and infinite, even before it splits up into the ten categories, I readily grant that finite and infinite are not further differentiations within some category. Indeed, any genus and being itself just prior to its differentiation into categories is specifically finite being. But finite and infinite are immediate divisions not of being but of ""quantified being." For just as finite and infinite, according to the Philosopher,®® correspond to quantity (which is true of "finite,'' "infinite," and '"'quantity" proper), so also, in an extended sense, finite and infinite as proper attributes [in disjunction] of being pertain precisely to a "quantified" being in the sense of having in itself some amount of perfection. But this sort of "quantity" pertains only to entity that can be "total" or "partial" in the hierarchy of essences. For one
"quantity" compared with another must immediately excel or be excelled and must have partial or total being, as we speak of "'partial" and "'total'' here. Paternity as paternity, however, can be neither a total nor a partial entity in this sense.
5.59 One could also say that virtual quantity, and therefore finitude and infinity, are characteristic only of a quidditative entity, namely, insofar as it is distinguished from a hypostatic entity. But this entity [ie paternity], though somehow quidditative in itself, nevertheless as such is purely hypostatic.
5.60 A third possible answer given is that virtual quantity pertains only to an absolute [or non-relative] entity. But these two last answers admit a dubious point about hypostatic entity and relative entity, namely that they have no virtual quantity.
25 Aristotle, Physic. 1, c.2 (185a33-b5).