Article 7 — How numerical terms are predicated of the divine persons, whether positively or only negatively

The seventh point of inquiry is as to how numerical terms are predicated of the divine persons, whether positively or only negatively. (Parallel texts: ST I.30.3; In I Sent. 24.3; Quodlibet X, q. 1, a. 1.)

Obj. 1: And it would seem that they are predicated positively. For if they posit nothing in God, then one who speaks of three persons speaks of nothing that is in God. Therefore, also one who denies the three persons denies nothing about God that is in him. Therefore he would not be speaking against the truth, and thus he is not a heretic.

Obj. 2: According to Dionysius in On the Divine Names, things are predicated of God in three ways: negatively, eminently, and causally. (Pseudo-Dionysius, Mystical Theology 1 (PG 3:997–1002); The Divine Names 1.5–7 (PG 3:593–98).) Now in whichever of these three senses numerical terms are predicated in the divine, they must posit something. This is evident if they be predicated eminently or causally; and likewise even if they be predicated negatively. For as the same Dionysius says, we do not deny certain things of God as though he lacked them altogether but because they are not appropriate to him in the same mode as they are to us. (Pseudo-Dionysius, The Celestial Hierarchy 2 (PG 3:135–46); The Divine Names 4, 11 (PG 3:693–736, 947–56).) Therefore, in every way numerical terms must posit something.

Obj. 3: Whatsoever is predicated of God and creatures is predicated in a nobler way of God than of creatures. Now, numerical terms are predicated of creatures positively. Therefore, with much more reason are they predicated thus of God.

Obj. 4: The multitude and unity implied by the numerical terms when predicated of God are not only in the intellect; for thus there would not be three persons in God, save according to the intellect, which pertains to the heresy of Sabellius. Therefore, they must be something in God himself in reality, and consequently predicated of God positively.

Obj. 5: As the one is in the genus of quantity, so is the good in the genus of quality. Now, in God there is neither quantity nor quality nor any accident, and yet good is predicated of God not negatively but positively. Therefore, one is predicated of him in the same way, and consequently the multitude that the one constitutes.

Obj. 6: There are four first things that are called “beings”: namely, being, the one, the true, and the good. Now, three of these, namely, being, true, and good, are predicated of God positively. Therefore, so is one, and consequently so too multitude.

Obj. 7: Number and magnitude pertain to the two species of quantity, which are discrete and continuous quantity. Now, magnitude is predicated of God positively: great is our Lord and great is his power (Ps 146:5). Therefore, multitude and unity are also.

Obj. 8: Creatures bear a likeness to God inasmuch as a trace of divinity is apparent in them. Now, according to Augustine, every created thing holds a certain trace of the divine Trinity, inasmuch as it is something one, formed by a species, and having a certain order. (Augustine, On the Trinity 10.8, para. 11 (PL 42:979–80).) Therefore, a created thing is one according to its likeness to God. But “one” is predicated of a creature positively: and therefore of God also.

Obj. 9: If “one” be predicated of God in a privative sense, it follows that it removes something, and this can only be multitude. Now, it does not remove multitude, since if there be one person, it does not follow that there are not several. Therefore, “one” is not said of God by way of removal, and consequently neither is “multitude.”

Obj. 10: Privation constitutes nothing, whereas the one constitutes number. Therefore, the latter is not said privatively.

Obj. 11: There is no privation in God, since all privation is a defect. Now “one” is predicated of God. Therefore, it does not signify a privation.

Obj. 12: Augustine says that whatsoever is predicated of God is predicated either according to substance or according to relation. (Augustine, On the Trinity 5.5 (PL 42:913–14).) And Boethius also says that whatsoever things enter into the divine predication are changed into substance, outside the relative. (Boethius, On the Trinity 4 (PL 64:1252–53).) If, then, numerical terms are predicated of God, they must signify either substance or relation, and consequently must be predicated positively.

Obj. 13: “One” and “being” are convertible and seem to be synonymous. But “being” is predicated of God positively. Therefore, “one” is also, and consequently so is “multitude.”

Obj. 14: If “one” be predicated of God by way of removal, it must remove multitude as being opposite to it. But this cannot be the case, since a multitude is constituted from units, and one opposite is not constituted of its opposite. Therefore, “one” is not predicated of God by way of removal.

Obj. 15: If “one” indicate the removal of multitude, it follows that the one is opposed to multitude as privation is to possession. Now, possession is naturally prior to privation, and this is even the case according to its account, since privation cannot be defined except in reference to possession. Therefore, multitude will be prior to one both according to nature and according to account—which seems problematic.

Obj. 16: If “one” and “many” are predicated of God by way of removal, then one removes multitude and multitude removes oneness. But this cannot be admitted, since it would lead to a vicious circle of the one and the many such that the one is what is not many and the many are what are not one; and thereby nothing would be made known. Therefore, we must not say that “one” and “many” are said of God privatively.

Obj. 17: Since one and many are as measure and measured, it seems that they are opposed to each other relatively. Now, when terms are relatively opposite, both are predicated positively. Therefore, both “one” and “many” are predicated of God positively.

On the contrary (1), Dionysius says in On the Divine Names, that praised Unity and Trinity that is the divinity above all things is not the unity or trinity that is known by us or any other existing being. (Pseudo-Dionysius, The Divine Names 13.3 (PG 3:982).) Therefore, it seems that numerical terms are said of God by way of removal.

Furthermore (2), Augustine says: the poor human tongue sought how to express the Three, and it called them substances or persons: not intending to imply by these names that they are different, yet desirous to avoid saying that there is only one. (Augustine, On the Trinity 7.4, para. 9 (PL 42:941).) Hence, in speaking of God these numerical terms are employed more for the sake of removing than for the sake of asserting.

Furthermore (3), one and multitude, that is, number, are in the genus of quantity. Now, there is no quantity in God, seeing that quantity is an accident and a disposition of matter. Therefore, numerical terms assert nothing in God.

To this it will be replied (4) that although quantity according to the account of its genus or according to the account of accident cannot be in God, yet according to the account of a species a certain quantity can be predicated of God, just as a certain quality can be so predicated, such as knowledge or justice.

On the contrary, only those species of quality are taken into the divine predication that according to the account of their species indicate no imperfection, such as knowledge, justice, and equity, but not ignorance or whiteness. But every quantity according to the account of its own species indicates imperfection; for since what is a quantity is divisible, the species of quantity are distinguished according to diverse modes of division; for example, plurality is what is divisible into non-continuous parts, whereas a line is what is divisible according to one dimension, while surface according to two, and body according to three. Now, division is incompatible with the perfection of divine simplicity. Therefore, no quantity as to the account of its species can be predicated of God.

But it will be argued (5) that distinction according to the relations which makes the number of persons in the divine does not imply imperfection in God.

On the contrary, every division or distinction causes some sort of multitude. Now, not every multitude is the number that is a species of quantity, since multitude and one pervade all the genera. Hence, not any division or distinction suffices to constitute the number that is the species of quantity but only the division that is according to quantity, and such is not the distinction of relations.

But it will be objected (6) that every multitude is a species of quantity, and every division suffices to constitute a species of quantity.

On the contrary, given the presence of substance, quantity does not necessarily follow, since substance can exist without accident. Now, given substantial forms only, there follows distinction in substances. Therefore, not every distinction constitutes the multitude that is an accident and a species of quantity.

Furthermore (7), the discreteness that constitutes the number that is a species of quantity is opposed to the continuous. Now, discreteness is opposed to the continuous because it consists in division of the continuous. Therefore, only division of the continuous, which is impossible in God, causes the number that is a species of quantity; and thus, the number that is a species of quantity cannot be predicated of God.

Furthermore (8), every substance is said to be one. Either, then, it is one by its own essence or by something else. If by something else, since this again must be one, it must be one either by itself or by something else, and this again by something else. But this cannot go on to infinity. Hence we must stop somewhere. And it would be better, therefore, to stop at the beginning, such that substance is one through its very self. Therefore, unity is not something added to substance; and thus, it seems that it does not signify anything positively.

But it will be argued (9) that a substance is one not by itself but by accidental unity; and unity is one through itself; for the first things denominate themselves, just as goodness is good, truth is true, and likewise unity is one.

On the contrary, these denominate themselves because they are primary forms, for secondary forms do not denominate themselves; for example, whiteness is not white. Now, things which result from addition to others are not primary. Therefore, unity and goodness are not additional to substance.

Furthermore (10), according to the Philosopher, a thing is one insofar as it is undivided. (Aristotle, Metaphysics 5.6, 1016b3.) Now, to be undivided does not assert something but only removes something. Therefore, unity is predicated of God not positively but by way of removal, and consequently the same applies to multitude, which is composed of units.

I answer that about one and many, diverse things are found that have occasioned diverse opinions among philosophers. For it is found of the one that it is the principle of number and that it is convertible with being; and likewise it is found of the many that it pertains to a certain species of quantity, which is called number, and moreover that it pervades every genus, just as one does, which seems to be opposed to multitude.

Accordingly, some philosophers failed to distinguish between the one that is convertible with being and the one that is the principle of number, thinking that said in either way “one” does not add anything to substance; rather, said in either way “one” would signify the substance of a thing. From this it followed that number, which is composed of ones, is the substance of all things, following the opinion of Pythagoras and Plato.

On the other hand, others who failed to distinguish between one that is convertible with being and one that is the principle of number held the contrary opinion that in any sense one adds a certain accidental being to substance: and that in consequence all number is an accident pertaining to the genus of quantity. This was the opinion of Avicenna, which apparently was followed by all the teachers of old: for they did not understand by one and many anything else but something pertaining to discrete quantity.

There were others who, considering that there cannot be quantity of any kind in God, maintained that words signifying one or many do not assert something, when attributed to God, but only remove something. For they cannot assert but what they signify, namely, discrete quantity, and this can nowise be in God. Hence, according to them, one is predicated of God in order to remove the multitude of discrete quantity; and terms signifying plurality are said of God in order to remove that unity which is the principle of discrete quantity.

Apparently this was the view of the Master in Sentences I, distinction 24; (Peter Lombard, Sentences, bk. 1, d. 24 (PL 192:586–87).) and granted the root of this opinion—namely, that every multitude signifies a discrete quantity, and every one is the principle of such quantity—this opinion would seem of all of them the most reasonable. For Dionysius also says that in God negations are the most true, whereas affirmations are figurative. (Pseudo-Dionysius, The Celestial Hierarchy 2.3 (PG 3:142).) For we do not know what God is, but more what he is not, as Damascene says. (John Damascene, On the Orthodox Faith 1.4 (PG 94:797–800).)

Hence, Rabbi Moses says that whatever seems to be said affirmatively about God is more to be taken as removing something from him rather than as positing something. (Moses Maimonides, The Guide for the Perplexed 1.58.) Thus, we say that God is a living being in order to remove from him that mode of existing that the realities among us that are not alive have, not in order to assert that there is life in him; since “life” and all such terms are employed to denote certain forms and perfections of creatures which are far distant from God. And yet this is not altogether true, for as Dionysius says, wisdom and life and the like are not removed from God as though they were not in him, but because he has them in a more excellent way than the human intellect can conceive or words can signify; and from that divine perfection, created perfections come down in an imperfect likeness to it. (Pseudo-Dionysius, The Divine Names 11.6, 12 (PG 3:953–72).) Wherefore, things are said of God, according to Dionysius, not only through a mode of negation and through a mode of cause, but also through a mode of eminence. (Pseudo-Dionysius, Mystical Theology 1 (PG 3:997–1002); The Celestial Hierarchy 2 (PG 3:135–46); The Divine Names 1.4–2.8 (PG 3:589–646).)

But whatever the truth may be with regard to spiritual perfections, it is certain that material dispositions are altogether to be removed from God. Wherefore, since quantity is a disposition of matter, if numerical terms signify nothing but what is in the genus of quantity, it is necessary that they are not said of God except as removing what they signify, as the Master asserted. (Peter Lombard, Sentences, bk. 1, d. 24 (PL 192:586–87).) And although in his opinion unity removes multitude and multitude unity, this does not involve a vicious circle, because the unity and multitude removed from God are in the genus of quantity, neither of which can be said of God. Thus, the unity said of God, which removes multitude, is not removed, but that other unity, which cannot be said of God, is.

Some, however, through not understanding how affirmative expressions can be predicated of God for the purpose of removal, and not conceiving the one and the many except as included in the genus of discrete quantity—which they dared not ascribe to God—said that numerical terms are not predicated of God as expressions signifying any conceived reality, but as official expressions positing something in God, namely, a distinction according to the mode of syncategorematic distinction. All of this is clearly absurd, since nothing of the kind can be had from the signification of these terms.

Wherefore others, though holding that one and many are only in the genus of quantity, said that these terms denote something positive in God. For they say that it is not unfitting to ascribe some species of quantity to God, although the genus is removed from him, just as certain species of quality, as wisdom and justice, are also predicated of God, although there cannot be quality in God.

But as indicated above, (Q. 9, a. 7, obj. 5.) there is no comparison, for all the species of quantity from the account of their species hold imperfection, but not all the species of quality do. Moreover, quantity properly speaking is a disposition of matter; whence all the species of quantity are certain mathematical objects that cannot exist separated from sensible matter, except time and place, which are natural and are more connected to sensible matter. It is evident, then, that no species of quantity can belong in spiritual realities, except metaphorically. But, quality follows the form; hence, certain qualities are altogether immaterial and can be attributed to spiritual realities.

Accordingly, the above opinions were based on the supposition that the one which is convertible with being is the same thing as that which is the principle of number, and that there is no multitude but the number that is a species of quantity. Now, this is clearly false. For since division causes multitude and non-division unity, we must judge of one and many according to the account of the division.

Now, there is a certain division that altogether transcends the genus of quantity, and this is division through a formal opposition, which has nothing to do with quantity. Hence, the multitude resulting from such a division, and the one that excludes such a division, must be more universal and comprehensive than the genus of quantity.

However, there is a division according to quantity that does not transcend the genus of quantity. Wherefore, the multitude consequent on this division and the unit that lacks it are also in the genus of quantity. This one adds something accidental to the thing of which it is said, in that it measures it; otherwise the number constituted from the unit would not be some accident nor a species of some genus. But the one that is convertible with being adds nothing to being except the negation of division—not that it signifies non-division only, but substance along with non-division; for one is the same as a non-divided being. In like manner, the multitude that corresponds to the one adds nothing over and above the many realities except their distinction, which is viewed in the fact that one of them is not the other; and this they have not from anything added to them but from their own proper forms.

It is clear, then, that the one that is convertible with being posits being itself but adds nothing further except the negation of division. But the number corresponding to it adds to the things that are called many the fact that each of them is one and that each of them is not the other, in which consists the account of distinction. Accordingly, then, since one adds one negation over and above being, inasmuch as something is undivided in itself, multitude adds two negations, inasmuch as something is undivided in itself and distinct from another. This being divided is in fact one of them not being the other.

I say, then, that in speaking of God we do not predicate the one and many that pertain to the genus of quantity, but the one that is convertible with being and the multitude corresponding to it. Wherefore, “one” and “many” predicate in God the things of which they are said, but they add nothing besides distinction and non-distinction, which is to add negations, as explained above. Hence, we grant that, as regards what they add to the things of which they are predicated, they are taken of God by way of removal; but insofar as in their signification they include the things of which they are said, they are taken of God positively. We must now reply to the objections on both sides.

Reply Obj. 1: To speak of three persons in God is to indicate a distinction of persons; and to deny this is heresy. But this distinction adds nothing to the persons distinguished.

Reply Obj. 2: It is true that while we remove certain things from God, we understand at the same time that these things are predicated of God eminently and causally; yet some things are wholly denied of God and in no way predicated of him, for instance, “God is not a body.” In this way, according to the Master’s opinion, it might be said that numerical quantity is altogether denied of God; and in like manner, according to our own opinion, when we say, “the divine essence is one,” we altogether deny that God’s essence is divided.

Reply Obj. 3: In created things, numerical terms assert nothing in addition to the realities of which they are said, except insofar as they signify something that is in the genus of discrete quantity; in this way they are not predicated of God, and this pertains to his perfection.

Reply Obj. 4: It is true that the unity and multitude signified by numerical terms said of God are not purely in our understanding; rather, they are in God in reality. Yet it does not follow that they signify something positive outside the understanding of the things to which such terms are attributed.

Reply Obj. 5: The good that is in the genus of quality is not the good that is convertible with being. For the latter adds nothing real to being, whereas the good that is in the genus of quality adds some quality in respect of which a man is said to be good. And the same applies to the one, as already explained. Yet there is this difference, that good in either sense can be predicated of God, whereas the one cannot; for, as already explained, the accounts of quantity and quality are not the same.

Reply Obj. 6: Of these four primary things, being is first most of all; wherefore, it must be predicated positively, for negation or privation cannot be the first thing conceived by the intellect, since what is being denied or lacked is always of the understanding of a negation or privation. But the other three must add something that does not contract being; for if they contracted being, they would no longer be primary. Now, this is impossible unless that which they add were something only according to accounts. However, this is either a negation, which is added by one (as already stated); or a relation to something that is naturally apt to be referred universally to being, and this is either the intellect, to which the true bears a relation, or the appetite, to which the good bears a relation, for the good is what all things seek, as is said in Ethics 1. (Aristotle, Nicomachean Ethics 1.1, 1094a2.)

Reply Obj. 7: According to the Philosopher, we speak of many in two senses: in one way, absolutely, and then it is spoken of in opposition to the one; in another way, comparatively, as denoting a certain excess in relation to a smaller number, and then many is opposed to few. (Aristotle, Metaphysics 10.6, 1056b17–1057a17.) In like manner, great may be taken in two ways: first, absolutely, as indicating a continuous quantity that is called “magnitude”; second, comparatively, as indicating an excess in relation to a smaller quantity. “Magnitude” is not predicated of God in the first sense but in the second, and it indicates his eminence over all creatures.

Reply Obj. 8: The one that pertains to the vestige of God in created things is the one that is convertible with being. As we have already stated, this does assert something, namely, being, to which it adds nothing but a negation.

Reply Obj. 9: One opposite does not exclude the other except from the subject of which it is predicated. For supposing that Socrates is white, it does not follow that nothing is black but that he is not black. Wherefore, if the person of the Father is one, it follows that there are not several persons of the Father; however, it does not follow that there are not several persons in God.

Reply Obj. 10: The one does not constitute a number on the side of the privation but on the side whereby it posits being.

Reply Obj. 11: As is said in Metaphysics 5, privation may be taken in three ways. (Aristotle, Metaphysics 5.20, 1022b22–1023a8.)

First, properly speaking, when what is removed from something is what something is naturally apt to have and at the time it is naturally apt to have it; thus, to lack sight is a privation of sight in a man.

Second, commonly speaking, when what is removed from something it is not naturally apt to have, but its genus is. Thus, not having sight would be said to be a privation of sight in a mole.

Third, in the most common way, when what is removed from something is naturally apt to be had by anything else but not by it or by any other member of its genus. Thus, not having sight would be said to be the privation of sight in a plant.

This last kind of privation is a mean between a true privation and a simple negation, having something in common with both: with true privation in that it is a negation of something in some subject, such that it does not simply speaking belong to non-being; and with simple negation in that it does not require an aptitude in the subject. It is in this way that “one” is spoken of privatively, and in this sense it can be predicated of God, like other things that can be predicated of God in the same way, like invisible, unmeasurable, and so forth.

Reply Obj. 12: Numerical terms add nothing to God over and above that of which they are predicated. Hence, when they are predicated of essentials they signify the essence, and when they are predicated of personal properties they signify the relation.

Reply Obj. 13: “One” and “being” are convertible, according to their supposits; yet “one” adds, according to account, the privation of division; thus they are not synonymous, because synonyms are words which signify the same thing according to the same account.

Reply Obj. 14: “One” may be considered in two ways. First, as to what it posits, and in this way it constitutes a multitude; second, as to the negation that it adds above this, and in this way one is opposed to multitude privatively.

Reply Obj. 15: According to the Philosopher, multitude is prior to one according to sensation, just as the whole precedes its parts and the composite precedes the simple; but one precedes multitude naturally and according to account. (Aristotle, Metaphysics 10.1, 1052a34–b24.) But this does not seem sufficient in order that one be opposed to multitude privatively. For privation is posterior according to account, since within the understanding of privation is its opposite, whereby it is defined—unless perhaps this refers merely to the account of the term, insofar as this term “one” signifies privatively while “multitude” signifies positively; for we impose names according as we know realities. Wherefore, in order that something be signified by a name as a privation, it suffices that it be in any way whatsoever posterior in our knowledge, although this is not enough to make the thing itself privative, unless it is posterior in account.

It would be better, then, to say that division rather is the cause of multitude, and that it rather than multitude is prior according to concept; however, “one” is said privatively in relation to division (since it is undivided being), not in relation to multitude. Hence, division is prior to one, according to account, but multitude is posterior. This is proved as follows. The first thing that falls into the intellect is being; the second is a negation of being. From these two there follows, third, the understanding of division (since from the fact that we understand some being and we understand it is not this being, it follows within the understanding that it is divided from that); and it follows, fourth, that the intellect apprehends the account of the one, insofar as it understands that this being is not divided in itself; and fifth, the understanding of multitude follows, insofar as it understands this being is divided from the other and each of them is one in itself. For however many things are understood to be divided from one another, multitude is not understood unless each of the things divided be understood to be one. Wherefore, it is clear that there is no vicious circle in the definitions of one and multitude.

Reply Obj. 16: And this suffices for the reply to the sixteenth objection.

Reply Obj. 17: The one that is a principle of number is compared to multitude as the measure to the thing measured: and one in this sense adds something in a positive way to substance, as was stated.

Reply Sed Contra: After what we have said, the arguments on the other side present no difficulty to those who realize that they contain a certain amount of truth. We must, however, take notice of one point advanced in these objections, namely, that these primary things—namely, essence, unity, truth, and goodness—denominate themselves by account, inasmuch as one, true and good are consequent on being. Now, seeing that being is the first thing conceived in the intellect, it follows that whatever falls into the intellect is understood as a being, and consequently as one, true, and good. Wherefore, since the intellect apprehends essence, unity, truth, and goodness in the abstract, it follows that being and the other three concretes must be predicated of each of them. Thence it is that they denominate themselves, whereas things that are not convertible with being do not.