ARTICLE VII

ARE NUMERAL TERMS PREDICATED OF THE DIVINE PERSONS?

Sum. Th. I, Q. xxx, A. 3

THE seventh point of inquiry is as to how numeral terms are predicated of the divine Persons, whether positively or only negatively: and it would seem that they are predicated positively.

             1. If they signify nothing positive in God, then by affirming three Persons we do not speak of something that is in God. Therefore by denying three Persons one would not deny anything that is in God: and consequently one would not say that which is untrue nor would one be a heretic.

             2. According to Dionysius (Div. Nom.) things are predicated of God in three ways: negatively, eminently and causally. Now in whichever of these three senses numeral terms are predicated of God they must needs have a positive signification. This is evident if they be predicated eminently or causally: and likewise if they be predicated negatively. For as the same Dionysius says (Coel. Hier. ii; Div. Nom. iv, xi) we do not deny things of God as though he lacked them altogether, but because they are not appropriate to him in the same way as they are to us. Therefore in any way numeral terms must have a positive meaning as applied to God.

             3. Whatsoever is predicated of God and creatures is affirmed in a more eminent sense of God than of creatures. Now numeral terms are predicated of creatures positively. Therefore with much more reason are they thus predicated of God.

             4. Plurality and unity as implied by the numeral terms when predicated of God are not mere mental concepts, for thus there would not be three Persons in God save logically, which belongs to the heresy of Sabellius. Therefore they must be something really in God, and consequently predicated of him positively.

             5. As unity is in the genus of quantity, so is good in the genus of quality. Now in God there is neither quantity nor quality nor any accident, and yet goodness is predicated of God not negatively but positively. Therefore unity is predicated of him in the same way, and consequently plurality which is based on unity.

             6. There are four transcendentals, namely being, unity, truth and goodness. Now three of these, to wit being, truth and goodness, are predicated of God positively. Therefore unity is also and consequently plurality.

             7. Number and magnitude are two species of quantity, namely discrete and continuous quantity. Now magnitude is predicated of God positively (Ps. cxlvi, 5): Great is our Lord and great is his power. Therefore multitude and unity are also.

             8. Creatures are like God inasmuch as they bear a trace of the Godhead. Now according to Augustine (De Trin. vi, 10) every creature bears a trace of the divine Trinity, inasmuch as it is one particular thing, informed by a species, and has a certain order. Therefore the creature is one in its likeness to God. Now one is predicated of a creature positively: and therefore of God also.

             9. If one be predicated of God in a privative sense, it follows that it removes something, and this can only be plurality. Now it does not remove plurality, since if there be one Person it does not follow that there are not more. Therefore one is not said of God by way of remotion: and consequently neither is number.

             10. Privation constitutes nothing: whereas unity constitutes number. Therefore the latter is not predicated in a privative sense.

             11. There is no privation in God, since all privation is a defect. Now one is predicated of God. Therefore it does not denote a privation.

             12. Augustine says (De Trin. v, 5) that whatsoever is predicated of God indicates either substance or relation. And Boethius (De Trin. iv) says that whatsoever is predicated of God refers to the substance except relative terms. If then numeral terms are predicated of God they must denote either the substance or a relation, and consequently must be predicated positively.

             13. One and being are convertible terms and are apparently synonymous. Now being is predicated of God positively. Therefore one is also and consequently number.

             14. If one be predicated of God by way of remotion, it must remove number as being contrary thereto. But this cannot be the case, since number is constituted by units: and one contrary is not made up of the other. Therefore one is not predicated of God by way of remotion.

             15. If one indicate the removal of number, it follows that one is opposed to number as privation to habit. Now habit is naturally prior to privation: as well as logically, since privation cannot be defined except in reference to habit. Therefore number will precede unity both naturally and logically: which is apparently absurd.

             16. If one and number are predicated of God by way of remotion, then one removes number and number removes unity. But this cannot be admitted, since it would lead to a vicious circle, namely that unity is where there is not number, and number where there is not unity, and we should be none the wiser. Therefore we must not say that one and number are said of God privatively.

             17. Since one and many are as measure and measured it would seem that they are opposed to each other relatively. Now when terms are relatively opposite both are predicated positively. Therefore both unity and number are predicated of God positively.

             1. On the contrary, Dionysius says (Div. Nom. iv, 13): That Unity with Trinity in which we worship the supreme Godhead is not the same unity or trinity with which we or any other living being are acquainted. Therefore seemingly numeral terms are predicated of God by way of remotion.

             2. Augustine says (De Trin. viii, 4): The poor human tongue sought how to express the Three, and it called them substances or persons: not intending to imply that they are different, yet desirous to avoid saying that there is only one. Hence in speaking of God these numeral terms are employed negatively rather than positively.

             3. One and many, i.e. 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 numeral terms indicate nothing positive in God.

             4. To this it will be replied that although quantity as to its generic nature or considered as an accident cannot be in God, yet in its specific nature a certain kind of quantity may be predicated of God, even as a certain kind of quality such as knowledge or justice.

             On the contrary only those species of quality can be predicated of God which in their specific nature contain no imperfection, such as knowledge, justice, equity, but not ignorance or whiteness. But all quantity by its specific nature implies imperfection: because since a thing that has quantity is divisible, the various species of quantity are distinguished according to various kinds of division: thus plurality is quantity divisible into non-continuous parts: a line is quantity divisible as to one dimension: while a surface is divisible as to two, and a body as to three. Now division is incompatible with the perfection of divine simplicity. Therefore no quantity as to its specific nature can be predicated of God.

             5. But it will be argued that distinction according to the relations which causes the number of Persons in God, does not imply perfection in him.

             On the contrary every division or distinction causes plurality of some kind. Now not every kind of plurality is that number which is a species of quantity, inasmuch as many and one pervade all the genera. Hence not any division or distinction suffices to set up number which is a species of quantity, but only quantitative division, and such is not relative division.

             6. But it will be objected that every plurality is a species of quantity, and every division suffices to cause a species of quantity.

             On the contrary given substance, quantity does not necessarily follow, inasmuch as substance can be without accident. Now given substantial forms only, there follows distinction in substances. Therefore not every distinction causes number, which is an accident and a species of quantity.

             7. Discreteness that causes number which is a species of quantity is opposed to continuity. Now discreteness is opposed to continuity because it consists in division of the continuous. Therefore only division of the continuous, which division is impossible in God, causes number that is a species of quantity: so that such a number cannot be predicated of God.

             8. Every substance is one. Either then it is one by its essence, or by something else. If by something else, since this again must be one, it must be one either of itself or by something else, and this again by something else. But this cannot go on indefinitely: and hence we must stop somewhere. And it were better to stop at the beginning, so that substance be one of itself. Therefore unity is not something added to substance: and thus seemingly it does not signify anything positively.

             9. But it will be argued that a substance is one not by itself but by accidental unity: and unity is one essentially, since the primary notions are named after themselves: thus goodness is good, truth is true and likewise unity is one. --On the contrary these are named after themselves because they are primary forms; whereas second forms are not named after themselves: thus whiteness is not white. Now things which result from addition to others are not primary. Therefore unity and goodness are not additional to substance.

             10. According to the Philosopher (Metaph. v) a thing is one in so far as it is undivided. Now to be undivided is nothing positive but only removes something. Therefore unity is predicated of God not positively but negatively: and the same applies to number which is composed of units.

             I answer that about unity and number there are various points which have given rise to various opinions among philosophers. As regards unity it is to be observed that it is the principle of number and that it is convertible with being: and as regards plurality it belongs to a species of quantity called number; moreover, it pervades all the genera like unity, which apparently is opposed to number.

             Accordingly some philosophers failed to distinguish between unity which is convertible with being, and unity which is the principle of number, and thought that in neither sense does unity add anything to substance, and that in either sense it denotes the substance of a thing. From this it followed that number which is composed of unities is the substance of all things: and this was the opinion of Pythagoras and Plato.

             On the other hand others who failed to distinguish between unity that is convertible with being and unity that is the principle of number held the contrary opinion that in any sense unity 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: and apparently all the teachers of old followed him: 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 have no positive signification when attributed to God, but only remove something from him. For they cannot ascribe to him save what they signify, to wit discrete quantity, and this can nowise be in God. Hence according to these one is predicated of God in order to remove the plurality 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 (I., D. xxiv): and granted the principle on which his opinion is based, namely that all multitude signifies discrete quantity, and all unity is the principle of such quantity, this opinion would seem of all the most reasonable. For Dionysius (Coel. Hier. ii) says that we are nearer the truth when we speak of God in the negative, and that all our affirmations about him are figurative. For we know not what God is, but rather what he is not, as Damascene says (De Fid. Orth. i, 4). Hence Rabbi Moses says that whatever we affirm about God is to be taken as removing something from him rather than as placing something in him. Thus we say that God is a living being in order to remove from him that mode of being which inanimate beings have, and not in order to ascribe life to 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 (Div. Nom. xii) 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 higher degree than mind can conceive or words express: and from that divine perfection created perfections come down in an imperfect likeness to it. Wherefore things are said of God according to Dionysius (Myst. Theol. i: Coel. Hier. ii: Div. Nom. ii) not only negatively and causally but also eminently. Still 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 numeral terms signify nothing outside the genus of quantity it follows that they are not to be said of God except as removing what they signify, according to the Master's opinion (loc. cit.), and although in his opinion unity removes plurality and plurality unity, this does not involve a vicious circle, because the unity and plurality removed from God are in the genus of quantity, neither of which can be ascribed to God. So that the unity ascribed to God which removes plurality is not removed, but that other unity which cannot be said of God.

             Some, however, through not understanding how affirmative expressions can be predicated of God for the purpose of negation, and not conceiving unity and plurality except as included in the genus of discrete quantity, which they dared not ascribe to God, said that numeral terms are not predicated of God as though they expressed an idea with an objective reality, but as official expressions positing something in God, namely a kind of syncategorematic distinction, all of which is clearly absurd, since nothing of the kind can be had from the meaning of these terms.

             Wherefore others, though holding that unity and multitude are only in the genus of quantity, said that these terms denote something positive in God. They say in effect that it is not unreasonable to ascribe some kind of quantity to God, although the genus is not to be attributed to him: even as certain species of quality, as wisdom and justice are predicated of God, although there cannot be quality in God. But as indicated in an objection (5) there is no comparison: because all the species of quantity from their specific nature are imperfect, but not all the species of quality. Moreover quantity properly speaking is a disposition of matter: so that all the species of quantity are mathematical entities which cannot exist apart from sensible matter, except time and place which are natural entities and which are better described as adjuncts of sensible matter. It is evident then that no species of quantity can be attributed to spiritual things otherwise than metaphorically. Whereas quality follows the form, wherefore certain qualities are altogether immaterial and can be ascribed to spiritual things. Accordingly the above opinions were based on the supposition that the one which is convertible with being is the same with that which is the principle of number, and that there is no plurality but number that is a species of quantity. Now this is clearly false. For since division causes plurality and indivision unity, we must judge of one and many according to the various kinds of division. Now there is a kind of division which altogether transcends the genus of quantity, and this is division according to formal opposition which has nothing to do with quantity. Hence the plurality resulting from such a division, and the unity which excludes such a division, must needs be more universal and comprehensive than the genus of quantity. Again there is a division of quantity which does not transcend the genus of quantity. Wherefore the plurality consequent to this division and the unity which excludes it are in the genus of quantity. This latter unity is an accidental addition to the thing of which it is predicated, in that it measures it: otherwise the number arising from this unity would not be an accident nor the species of a genus. Whereas the unity that is convertible with being, adds nothing to being except the negation of division, not that it signifies indivision only, but substance with indivision: for one is the same as individual being. In like manner the plurality that corresponds to this unity adds nothing to the many things except distinction, which consists in each one not being the other: and this they have not from anything added to them but from their proper forms. It is clear then that one which is convertible with being, posits being but adds nothing except the negation of division. And the number corresponding to it adds this to the things described as many, that each of them is one, and that each of them is not the other, wherein is the essence of distinction. Accordingly then, while oneadds to being one negation inasmuch as a thing is undivided in itself; plurality adds two negations, inasmuch as a certain thing is undivided in itself, and distinct from another; i.e. one of them is not the other.

             I say then that in speaking of God we do not predicate the unity and plurality which belong to the genus of quantity, but one that is convertible with being and the corresponding plurality. Wherefore one and many predicate in God that which they signify: but they add nothing besides distinction and indistinction, which is the same as 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 attributed to God by way of removal; but in so far as in their signification they include the things of which they are said they are predicated of God positively. We must now reply to the objections on both sides.

             Reply to the First Objection. 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 distinct Persons.

             Reply to the Second Objection. 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: but some things are denied of God absolutely and in no way predicated of him; as for instance, God is not a body. In this way according to the Master's opinion it might be said that numeral 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 to the Third Objection. In created things numeral terms posit nothing in addition to the things to which they are affixed, except in so far as they signify something in the genus of discrete quantity: in this way they are not predicated of God, and this pertains to his perfection.

             Reply to the Fourth Objection. It is true that the unity and plurality signified by numeral terms predicated of God are not purely subjective but are really in God: and yet it does not follow that they signify something positive besides the things to which they are attributed.

             Reply to the Fifth Objection. The good that is a kind of quality is not the good that is convertible with being. The latter adds nothing real to being, whereas the former adds a quality in respect of which a man is said to be good. The same applies to unity, as already explained; yet there is this difference that good in either sense can be predicated of God, whereas unity cannot: because as already explained the comparison between quantity and quality fails.

             Reply to the Sixth Objection. Of these primary notions being is the first, wherefore it must be predicated positively: because negation or privation cannot be the first thing conceived by the intellect, since we cannot understand a negation or privation unless we first understand what is denied or lacking. But the other three must add something that is not a contraction of being: for if they contracted being they would no longer be primary notions. Now this is impossible unless that which they add were purely logical, and this is either a negation which is added by unity as already stated, or relation or something which by its very nature is universally referable 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 (Ethic. i, 1).

             Reply to the Seventh Objection. According to the Philosopher (Metaph. x) we speak of a number of things in two senses: first absolutely, and then number is the opposite of one: secondly comparatively, as denoting excess in relation to a smaller number, and then number is opposed to a few. In like manner magnitude may be taken in two ways: first absolutely, in the sense of a continuous quantity which is called a magnitude: secondly comparatively, as denoting excess in relation to a smaller quantity. In the first sense magnitude is not predicated of God but in the second, and denotes his eminence over all creatures.

             Reply to the Eighth Objection. The unity that pertains to the trace of God in his creatures is the one that is convertible with being. As we have already stated this posits something, namely being, to which it adds nothing but a negation.

             Reply to the Ninth Objection. 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, but not that there are not more than one Person in God.

             Reply to the Tenth Objection. One is not a constituent of a number, on the side of privation, but inasmuch as it posits being.

             Reply to the Eleventh Objection. Privation may be taken in three ways (Metaph. v, text. 27). First strictly, when a thing lacks that which by nature it should have, and when by nature it should have it: thus to lack sight is in a man privation of sight. Secondly in an extended sense, when a thing lacks that which is due not to its specific but to its generic nature: thus lack of sight may be called a privation of sight in a mole. Thirdly in a very broad sense, when a thing lacks that which may be naturally due to anything else but not to it, nor to any other member of its genus: thus lack of sight may be called a privation in a plant. This last kind of privation is a mean between real privation and simple negation, and has something in common with both. With real privation in that it is the negation of something in a subject, so that it cannot be predicated simply of nonbeing: and with simple negation, in that it does not require aptitude in the subject. It is in this way that one denotes privation, and in this sense it can be predicated of God, like other things that can be predicated of God in the same way, as, for instance, invisible, immense and so forth.

             Reply to the Twelfth Objection. Numerical terms add nothing to God besides the subject 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 relations.

             Reply to the Thirteenth Objection. One and being are convertible as to their supposits: yet one adds logically the privation of division and thus they are not synonymous, because synonyms are words which signify the same thing from the same point of view.

             Reply to the Fourteenth Objection. One may be considered in two ways. First as to what it posits, and thus it is a constituent of number: secondly as to the negation which it adds, and thus it is opposed to number privatively.

             Reply to the Fifteenth Objection. According to the Philosopher (Metaph. x), number precedes unity objectively, as the whole precedes its parts and the composite precedes the simple: but unity precedes number naturally and logically. But this seemingly is not sufficient in order that unity be opposed to number privatively. For privation logically is an afterthought, since in order to understand a privation we must first understand its opposite whence its definition is taken: unless perhaps this refer, merely to the definition of the term, in so far as one has a privative signification, while number has a positive meaning: since we name things according as we know them. Wherefore in order that a term have a privative signification it suffices that the thing signified come in any way whatsoever to our knowledge as an afterthought: although this is not enough to make the thing itself privative, unless it come afterwards logically. It would be better then to say that division is the cause of number and precedes it logically; and that one since it is undivided being is predicated privatively in relation to division, but not in relation to multitude. Hence division logically precedes being but number follows it: and this is proved as follows. The first object of the intellect is being; the second is the negation of being. From these two there follows thirdly the understanding of distinction (since from the fact that we understand that this thing is and that it is not that thing we realize that these two are distinct): and it follows fourthly that the intellect apprehends the idea of unity, in that it understands that this thing is not divided in itself; and fifthly the intellect apprehends number, in that it understands this as distinct from that and each as one in itself. For however much things are conceived as distinct from one another, there is no idea of number unless each be conceived as one. Wherefore there is not a vicious circle in the definitions of unity and number. And this suffices for the Reply to the Sixteenth Objection.

             Reply to the Seventeenth Objection. The one which is a principle of number is compared to many as measure to the thing measured: and unity in this sense adds something positive to substance, as stated in the Article.

             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 notions, essence, unity, truth and goodness denominate themselves inasmuch as one, true and good are consequent to being. Now seeing that being is the first object of the intellect, it follows that every other object of the intellect is conceived as a being, and therefore 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 them. Thus it is that they denominate themselves, whereas things that are not convertible with being, do not.