Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

Speaking of relation in its full breadth, as it comprehends transcendental and categorial relation, relation according to being said and according to being, I find no one who has absolutely denied every relation. For even the ancient philosophers did not deny relations according to being said, as is clear from the text of the chapter “On Relation,” although Aristotle there asserted against them a categorial relation that differs altogether from absolute being.¹

Speaking, then, of relations in the present question insofar as they are distinguished from every absolute entity—a feature that belongs only to relations according to being—some have held that they are nothing other than extrinsic denominations or something of reason. This view is usually attributed to the Nominalists and to those who do not distinguish real relations from their foundation. The latter, however, speak in a very different sense, as we shall see below when treating the difficulty. Finally, others think that relations belong to things only according to objective being and are merely intentional affections by which we compare one thing with another. Hence they constitute relations not in respect but in comparison; in the thing, however, all relations are according to being said, because a relative thing is nothing other than an absolute thing known by comparison with another. They claim that this is Aristotle's opinion in this chapter, “On Relation,” and in Metaphysics 5, chapter 15². Others cite St. Thomas, 1. 2. q. 7. art. 2. ad 1., where he teaches that a relative thing is denominated not only from what is in it, but also from what is extrinsically adjacent to it.

To begin with this last view, it can in no way be ascribed to the Philosopher, since in the chapter “On Relation” he manifestly rejects the definition of the ancients, who defined only relatives according to being said, because from their definition it followed that substance too is relative, as is any being that is said with dependence and comparison to another. Aristotle, however, in defining relatives says that “they are those whose whole being is toward another.” But in the opinion of those who posit only relations according to being said, the whole being of relatives is not toward another, since the being they have in reality is absolute; they have a relation only because they are known comparatively with another. Therefore Aristotle's definition—those whose whole being is toward another—does not apply to such relative things. Aristotle would have corrected the definition of the ancients to no purpose if he himself had ever posited relations according to being said; for the ancients did not deny them, nor that they are known comparatively with another. Cajetan therefore rightly noted in his commentary on this chapter “On Relation” that, in this definition, the Philosopher defined relation according to the nature it has, not according to how it is known or spoken of. Thus he said “they are toward something,” not “they are said to be toward something”; in the definition of the ancients, however, it was said “they are said to be toward something.” Therefore the Philosopher posited real relations distinct from relations according to being said.

There can be no doubt whatever about the mind of St. Thomas, since he expressly refutes those who said that relation is not a thing in nature but something of reason. See 1. p. q. 13. art. 7.; q. 28. art. 2.; q. 39. art. 1.; Contra Gentiles 2, chapter 12; q. 7. De Potentia, arts. 8 and 9³; and q. 8. De Potentia, art. 2⁴. In a thousand other places as well, but especially in these, he clearly affirms that relation is something real and an inhering accident.

THE BASIS IS THIS: Relations according to being said have absolute being and are not wholly toward another; relations of reason exist only in the intellect that apprehends them, from which they have objective being. But in reality, even when no intellect considers them, there are some things whose only being is toward another. Therefore there are real relations that are not according to being said, and so they can constitute a category separate from absolute things.

The antecedent is proved as follows: even when no intellect considers them, there are found in reality things to which no absolute being can be assigned. For example, order is found, as in an ordered army or an ordered universe; likeness, dependence, paternity, and other similar things are found, and these cannot be explained by any absolute being; their whole being is toward another. A sign of this is that when the term does not exist, likeness or paternity ceases. But if their being were something absolute, it would not cease solely from the absence of a term. To deny that these things are given in reality, with no intellect forming or fabricating them, is to deny what even the most unlearned people know is given in reality.

St. Thomas often uses this argument, and he indicates another in To Hannibald, book 1, dist. 26, q. 2, art. 1⁵, drawn from the divine relations, which are given on the part of the thing insofar as they are really distinct from one another; otherwise, the relative persons would not be really distinct, which would be heretical. They are distinct only insofar as they are pure relations according to being. For if they were distinct in something other than a pure relation, absolutes too would be divided in God, not only relatives. Therefore real relations are given in God, although, because of the supreme simplicity of the divine nature, they are identified with the substance. Why, then, would it be impossible for such relations to exist in created things, where they are neither substances nor infinite?

Finally, how does the intellect form pure respects if it has only absolute things, or relations according to being said, after the likeness of which it might form them? Relations formed by the intellect would therefore be mere fabrications, since there are no pure and true relations in reality after the likeness of which they could be formed.

Nor can one say that these relations are indeed given in reality, but by way of extrinsic denomination, not as an intrinsic form. The contrary is clear, because every extrinsic denomination comes from some real form existing in another subject, as being seen or known comes from cognition existing in the knower. Therefore, if relation is an extrinsic denomination, it comes from some form existing in another subject. That form, then, is either in itself a relation or an absolute entity. If it is a relation, an intrinsic relative form is already given, and thus, just as it is given in that subject, it can be given in another. But if it is an absolute form that nevertheless informs extrinsically, how can a relative denomination proceed from it? For no relative formal effect, either intrinsic or extrinsic, emanates from an absolute form. For example, being seen in a wall is not a denomination of relation but of termination, although we conceive it by way of relation; in reality, however, there is no relation.

Finally, this opinion will have great difficulty explaining how the relative persons in divine things are really constituted and distinct if they are extrinsic denominations, and from what absolute form such denominations proceed. But if there are no extrinsic denominations in God, but rather intrinsic forms, even though they are substantial and identified with the divine substance, why should we say that such a kind of relative being is impossible in creatures, even if it is not identified with substance, when created things have a stronger foundation for such relation, since they are more dependent on and ordered or subordinated to another?

THE ARGUMENTS ARE ANSWERED.

You will object first: Relation posits nothing real in a subject beyond the extrinsic denomination of coexisting extremes. For it is not apparent how this mode, called relation and distinguished from the other absolute forms, comes to a thing without an intrinsic change in it, if it is an intrinsic mode; nor how it is newly caused merely by the position of a term, at any distance whatsoever. For example, if something white is produced in India while I am in Spain, a relation results from that term, so distant; it is not now produced by the agent that produced whiteness here, because that agent often has already ceased to act when the relation results, and therefore cannot act then.

Second, the multitude of relations in the same subject seems to increase without limit, in relation to everything that is like or equal to it, that acts on it, that is acted upon by it, and so on. This seems especially so because one relation can also be the foundation of others, since two relations are no less alike than two absolute things; thus the number of relations would increase without limit.

Finally, there seems to be no need to multiply these relative entities and distinguish them from absolutes. For as soon as two white things are posited, they will be alike without any other entity or mode; and as soon as someone has begotten, he will be a father without any addition of entity. Since, then, there is no experience of these relations, and the other reasoning by which their existence is proved is sufficiently preserved by the mere positing of the two extremes, there seems to be no solid basis for proving that these relations are intrinsic forms. Hence St. Thomas, in opusculum 48, treatise On Relation, chapter 3⁶, says that relation differs from its foundation only by reason of the extrinsic term. And in the place cited above, from 1. 2. q. 7. art. 2. ad 1., he teaches that a relative is denominated not only from what is in it, but also from what is extrinsically adjacent to it.

To the first, it is answered that relation comes to a subject without any change that terminates directly and immediately in the relation, but not without a change that terminates in it mediately and indirectly. Just as risibility flows from the same action by which a man is produced, so, when something white is produced, likeness to another existing white thing is produced. But if that other thing does not exist, by the force of the generation of the white thing that likeness and every other relation remain as it were virtually, so that the relation may result once its term is posited. Hence distance neither contributes to nor prevents this, since these relations do not depend on local position: a son is a son of his father in the same way whether the father is distant or near. Nor is relation in the other extreme produced by the term itself when it is posited through some emission of power. Rather, the position of the term is a condition for the relation to result from the previously posited foundation by the force of the first generation, through which it was placed in the nature of things as apt to regard any term of such a foundation. Thus, although the generator has already ceased, it remains in its power insofar as it leaves a sufficient foundation for the relation to result, just as a heavy thing retains the power to move downward when an obstacle is removed, even though its generator is gone.

When an objection is made that Aristotle often teaches that relation is not the term of a change, the answer is that it is not the term of a physical change per se and directly; the Philosopher does not, however, deny that it is the term of a change accidentally, that is, through another thing and secondarily. Hence St. Thomas, in Physics 5, lect. 3⁷, expressly teaches that a real change occurs in real relations, namely, some new determination by which what was in the foundation is made explicit in actuality. And in Metaphysics 11, lect. 12⁸, he says “that in relation there is motion only accidentally.”

To the second, it is answered that there is nothing unreasonable in these relations being multiplied whenever their foundations and terms are multiplied. In particular, according to St. Thomas the number of relations is much smaller, because he holds that one relation numerically can be referred to numerically diverse terms, in 3. p. q. 35. art. 5. St. Thomas altogether denies that one relation is founded on another, as we shall show more fully below. See q. 7. De Potentia, art. 9, ad 2⁹, and 1. p. q. 42. art. 1. ad 4.

To the third, it is said that there is no less need to posit this genus of relative entity than the genus of quantity or quality. For, because we see the effects of quantity and quality in things, we infer that such forms exist. Likewise, because we see this effect given in the nature of things—namely, that some things are ordered and have a relation to others, as likeness, paternity, order, and so on—and because in these the effect of regarding another is not mixed with an absolute character, but their whole being consists in relation, we rightly infer that this genus of relative entity exists, just as we infer absolute entities from absolute effects. Nor is more experience required here than for the other accidental forms, whose effects we indeed experience, but not their distinction from substance. If God were to leave two white things without a resulting relation, they would remain alike fundamentally, but not formally.

As for the passages of St. Thomas: To the first, from opusculum 48¹⁰, it is answered that the sense is that relation differs from its term by reason of its termination; he does not deny that relation is intrinsically a form, which St. Thomas affirms so often. Specifically, he teaches in q. 7. De Potentia, art. 9, ad 7¹¹, that it is an inhering accident. In the second passage, from 1. 2., St. Thomas teaches only that relation takes its denomination not only from what is in it, that is, insofar as it inheres, but also from what is extrinsically adjacent, that is, from the term or its order toward that term. This does not remove, but presupposes, that it inheres; this is his explanation in the cited place in De Potentia and in 1. p. q. 28. art. 2.

To understand predicamental relation, one must distinguish it both from a relation of reason and from a transcendental relation, which is also commonly called a relation according to saying.

For this to be better understood, the common doctrine MUST BE PRESUPPOSED: in this kind of being called relation, three things must concur, namely subject, foundation, and term. The subject, common to every accident, is that which is informed and denominated by the relation. A foundation is required as the rationale and cause from which these relations receive their entity and being. A term is that toward which this respect tends and in which it comes to rest. Although a cause is required for every entity and form, a foundation is said to be required especially for relation: other forms require only a cause in order to be produced and exist, whereas relation, on account of its minimal entity and because by its own concept it is toward another, requires a foundation not only in order to exist but also in order to be capable of existing—that is, to be a real entity. Thus St. Thomas says in 1. ad Annibaldum dist. 30. quaest. unica art. 1.¹, “that relation is nothing other than the bearing of one thing toward another; hence, according to its proper rationale, it does not have it that it be something in that of which it is said, but sometimes it has this from the cause of the bearing.” He says nearly the same in 1. dist. 26. q. 2. art. 1.² and 1. p. q. 28. art. 1., where he says that “those things called relatives signify, according to their proper rationale, only a respect toward another. This respect is sometimes in the nature of things, as when certain things are ordered to one another by their nature.” This is so because relation, on account of its minimal entity, does not depend precisely on a subject as other absolute forms do, but stands as a third entity consisting in and resulting from the coordination of two extremes. Therefore, to be in the nature of things it must depend on a foundation that coordinates it with a term, and not merely on a subject and a productive cause.

From this it will not be difficult to distinguish relations according to saying from those according to being, and real relations from relations of reason. Relatives ACCORDING TO BEING and ACCORDING TO SAYING are distinguished by their very exercise: in relatives according to being, the whole rationale or exercise is to regard, and so they are said to regard the term precisely as term. But the exercise or rationale of a relation according to saying is not simply to regard the term; it is to exercise something else from which a relation follows. Hence St. Thomas rightly said in 2. dist. 1. q. 1. art. 5. ad 8. first listed³ that these relatives imply a foundation and a relation, whereas relatives according to being signify only a relation. For relatives according to saying stand toward the term more by founding a relation than by actually regarding it; consequently, they regard it not under the rationale of a pure term but under another rationale, such as that of cause, effect, object, or something similar. Therefore, according to St. Thomas, a relation according to saying is always distinguished from a relation according to being in this respect: the principal signification of a relation according to saying is not the relation but something else, from which a relation follows. When the principal signification of something is the relation itself and not something absolute, it is a relation according to being, as is clear from 1. p. q. 13. art. 7., 1. dist. 30. q. 1. art. 2.⁴, and opusc. 48. tract. de praedicamento Ad aliquid cap. 1.⁵, where he teaches this plainly.

It is also clear from this that a transcendental relation, which is no different from a relation according to saying, does not signify a relation as its principal signification, but something absolute from which some relation follows or can follow. For if it did not signify something absolute, it would not be transcendental—that is, ranging across different genera—but would belong to only one category. Thus a transcendental relation is not a form accruing to a subject or absolute thing; it is imbibed in it, while connoting something extrinsic on which it depends or about which it concerns itself, as matter is related to form, a head to what is headed, and a creature to God. Thus transcendental relation coincides with relation according to saying. Some wrongly distinguish a remainder, dividing being into transcendental and predicamental, since the transcendental relation is in the absolute entity itself and does not differ from its being; hence its whole being is not toward another, as is required for a relation according to being. Whether transcendental relation implies some imperfection and dependence and must therefore be excluded from God is a question for metaphysicians and theologians.

REAL RELATIONS AND RELATIONS OF REASON, a division found only within relation according to being, are distinguished by the absence of some condition required for real relations. St. Thomas requires five conditions in opusc. 48. tract. de Relativis cap. 1.⁶: two on the part of the subject, two on the part of the term, and one on the part of the related things. On the part of the subject, the subject must be a real being and have a real foundation or rationale for founding. On the part of the term, the term must be some real thing that really exists, and, second, it must be really distinct from the other extreme. On the part of the related things, they must be of the same order; for this reason there is no real relation between God and a creature, nor between a measure and what is measured, if they are of different orders. This doctrine agrees with what he teaches in 1. dist. 26. q. 2. art. 1.⁷ and 1. p. q. 28. art. 1. Formally and principally, however, the whole difference between a real relation and one of reason comes down to this: a real relation has a real foundation together with the term’s coexistence, whereas a relation of reason lacks a foundation, as is gathered from St. Thomas in 1. ad Annibaldum dist. 30. quaest. unica art. 1.⁸

WITH THESE POINTS PRESUPPOSED, I STATE BY WAY OF RESOLUTION: For a relation to be predicamental, it must have the conditions by which it is distinguished from a relation of reason and from a transcendental relation, or relation according to saying. Hence a predicamental relation is defined as a real form whose whole being is toward another.

By the first phrase it is distinguished from a relation of reason, which is not a real form; by the second, from a transcendental relation and from anything absolute, whose whole being is not toward another, since it is also something absolute in itself.

Three conditions of a predicamental relation are gathered: first, that it be a relation according to being; second, that it be real, which includes all the conditions required for a real relation; third, that it be finite. Scotus adds a fourth condition: that it be a relation accruing intrinsically—that is, one that arises immediately, without any change, once the foundation and term are posited. He assigns relations accruing extrinsically to the six last categories: once their foundation and term are posited, they do not result immediately and as it were from within, but require some extrinsic change in order to result. But in q. 19., when treating the six last categories, we shall show that these are not relations accruing extrinsically.

The first condition of predicamental relation therefore excludes all relations according to saying, or transcendental relations; the second excludes all relations of reason; the third excludes all divine relations, which are banished from the category because they are pure acts.

BUT YOU WILL ASK about that condition of real and predicamental relation, namely that the extremes be really distinct: is it required that they be distinct only on the side of the things or extremes materially, or also on the side of the rationale for founding, so that the proximate foundation too is really distinct?

The answer is that there is a difference here between the school of St. Thomas and that of Scotus. In 1. dist. 31. quaest. unica Scotus requires only a distinction between the things that are the extremes, not between the rationales for founding. St. Thomas requires both, as is clear in 1. p. q. 42. art. 1., where he denies that there is a real relation of likeness and equality among the divine persons because the foundation is the same in all the persons, namely the divine essence, by reason of which they are alike; the same would hold if one whiteness were posited in two stones. The reason is taken from Cajetan there and other interpreters: in these relatives the material extremes are related because the very rationales for founding are related. For because whitenesses are alike, white things are alike. Conversely, if whitenesses are not alike because there is only one whiteness, the white things themselves cannot be alike in whiteness; rather, they are the same, since there is only one and the same whiteness. If, however, they are alike in something else, they are not alike in the very formal rationale of being white. It is enough to have indicated this difficulty; it belongs more properly to theologians and metaphysicians.

THE ARGUMENTS ARE RESOLVED.

First, an argument is made from that well-known but difficult passage of St. Thomas, 1. p. q. 28. art. 1., where he says that only among things that are relative are some found according to reality and others according to reason. These words have seemed difficult to many. For either St. Thomas is speaking of predicamental relation, or of relation insofar as it abstracts from real and relation of reason. If in the first way, it is false that relations of reason are found in predicamental relation, or we falsely said that predicamental relation must be real. If in the second way, it is true that both are found in relation so abstracted, namely real relation and relation of reason; but it is false that this is found only in relation. For something can also be fictively conceived in substance, which would be called a substance of reason, such as a chimera, a goat-stag, and the like; and in quantity there is imaginary space, with similar cases in the other genera. Therefore something of reason is not found only in relation. Cajetan’s reply there increases the difficulty: relation has this peculiarly, that being in reason is not a diminishing condition, but that relation which is of reason is a true relation. For it is clear that if it were a true relation, it would truly make the subject be referred, not fictively, and thus not through apprehension but really.

This difficulty gave many occasion to understand St. Thomas perversely or to philosophize less well about relation. Some think that real relation is divided into two concepts: the concept of an accident, which they call in, and the respect, which they call ad; the first is real, the second is of reason or abstracts from real and relation of reason. Others think that St. Thomas only meant that something can be devised by reason after the pattern of a predicamental relation. Still others think that he speaks of relation insofar as it abstracts from real and relation of reason.

But the first group excludes true reality from the category of relation if what is proper to that category—namely, the respect and rationale of ad—is not made real. The second group says nothing peculiar to relation, as St. Thomas presents it, since beings of reason can also be formed in the likeness of other genera, for example after the pattern of substance and quantity, and so on.

Therefore the third interpretation is entirely true in one respect: St. Thomas speaks of relation in its full breadth, insofar as it abstracts from real and relation of reason. For the holy Doctor did not say that some things according to reason are found in the category Ad aliquid; he said absolutely “among those things that are toward something,” to show that he was not speaking of relation as determinately a genus, but absolutely and in itself. Some who read the holy Doctor less attentively ought to have noticed this. Thus St. Thomas speaks of relation under the most formal concept ad and means that, insofar as it is considered toward a term, it has positive standing and is not determinately a real form, but allows that it be a real being or a being of reason, even though predicamental and founded ad is real. St. Thomas therefore did not mean to specify which relation is real or which is of reason, but from which side relation can be real or of reason: namely, from the side on which it is toward a term. Although it can have reality there, it does not have it from there. The holy Doctor expressed this in 1. ad Annibaldum dist. 26. q. 2. art. 1.⁹, saying “that relation can be considered in two ways: in one way, with regard to that to which it is said, from which it has the rationale of relation; in this respect it does not have it that it posits something, although neither does it have it from this that it is nothing. For some respects are something according to reality, while others are nothing. In another way, with regard to that in which it is, and thus when it has it in a subject, it inheres really.” So St. Thomas.

We say that this is peculiar to relation and is not found in the other genera because in the other genera their proper and most formal rationale cannot be understood positively without also being understood entitatively: their positive rationale is only toward themselves and absolute, and so it is not understood positively unless also entitatively, since what is toward itself is entity. Relation alone has being as a being and toward a being; insofar as it is toward a being, it stands positively, yet it does not thereby have real entity. Rather, reality comes to relation from elsewhere, namely from the foundation; its positive rationale ad comes from elsewhere, namely from the term. From the term it has being not as a being but toward a being, although that ad is truly real when it is founded.

That something can therefore be considered positively, even if not really entitatively, is proper to relation. This alone is what Cajetan wished to say in the cited place when he says that a relation of reason is a true relation, not with the truth of an entity and an informing form, but with the truth of an objective and positive tending toward a term. Nor did Cajetan say that in predicamental relation the ad itself is something of reason; he expressly says that it is truly made real.

When it is objected that other genera too can in this way be called something of reason—for example, a chimera would be a substance of reason, imaginary space a quantity of reason, and so on—we reply that, as was said above in q. 12. art. 1., that after whose pattern a being of reason is formed is not called a being of reason. A being of reason is formed after the pattern of a real being; rather, that non-real thing which is conceived after the pattern of a real being is called a being of reason. There is therefore no substance of reason or quantity of reason: although some non-being is conceived after the pattern of substance, for example a chimera, and something after the pattern of quantity, for example imaginary space, neither substance itself nor some rationale of substance is conceived by reason and formed in being after the pattern of another real being. Hence the negation or non-being of a chimera, and the non-being of imaginary space, is called a being of reason. But this is a being of reason called a negation; it is not a substance of reason, since substance itself is not conceived as a being of reason after the pattern of something real. Rather, negations or non-beings are conceived after the pattern of substance and quantity. In relatives, however, not only is some non-being conceived after the pattern of relation; the relation itself, on the side of its respect ad, when it does not exist in reality, is also conceived or formed after the pattern of real relation. Thus it is what is formed in being, not merely that after whose pattern it is formed; for this reason there is a relation of reason, but no substance of reason.

Second, an argument is made: The highest genus of this category is a true real relation, yet it has no term distinct from itself that it regards. Therefore we falsely said that this is required for a real predicamental relation.

The minor premise is proved as follows. That term is either something relative or something absolute. It is not absolute, because, as we shall say below¹⁰, the formal term of a relation is not something absolute but relative. Besides, that absolute thing cannot be something real existing in an individual; for a relation in general cannot regard some determinate individual as its term, since then all relations would regard it. If it is something abstracted from individuals, it cannot terminate a real relation, since it is not given in reality. If it is something relative, it is either equal to that relation or inferior to it. If equal, there will be two genera of relations. If inferior, it will be regarded by relation in general as that of which relation is predicated, not as that toward which it is terminated per se as a relation, but as a universal.

THE ANSWER IS that relation in general does not regard a term in act and in exercise; it is conceived only as the rationale and quiddity of relation itself and as a higher grade by which lower relations are constituted to regard—not as what it actually regards, since it has that through its inferiors. In the same way, first substance, taken vaguely and in general, is that by which one underlies accidents, not that which actually underlies them. The reason is that relation taken generically is not the concept of relation as opposed, but as uniting by reason of the natures of relation. Thus relatives and correlatives agree in it; they are not opposed in it. Relation is exercised toward a term only under relative opposition. Accordingly, relation conceived under a generic concept casts off the state of opposition and explains only the concept in which all relations agree, not the exercise of regarding a term, though it is the rationale for regarding one in its inferiors. Even on the view that the term of relation is something absolute, the term cannot be taken in general as something one: according to that view, the term of relation is found in every genus, and one term cannot be made from all the genera to be regarded by relation as such. A determinate term, however, is not regarded, since the relation is generic.

Third, an argument is made: Transcendental relations too have their whole being toward another: the whole essence of matter is toward form, and the whole essence of habit and act is toward an object, since from it they receive their whole specific nature. Conversely, predicamental relation does not have its whole being toward another, since it is also an inhering accident and thus has being in a subject, not toward a subject.

It is confirmed that transcendental relation also depends on its term, just like relation according to being. Therefore there is no reason why a transcendental relation can terminate at something nonexistent, but a predicamental relation cannot.

THE ANSWER IS that transcendental relation is not primarily and per se toward another as predicamental relation is. Although its whole species and essence is taken from another or depends on another, it is not toward another in the way matter depends on form and act on an object as on causes from which they receive being and specification. It follows from this that they regard that thing as a term. But being primarily and per se toward another as toward a term is proper to predicamental relation. Hence it is said to regard a term as a pure term—that is, only as toward another, not as from another, about another, or in some other causal way, as transcendental relation does. The claim that predicamental relation is in a subject does not prevent its whole being from being toward another: its whole being, I mean, its proper and distinctive being, by which it differs from the other absolute genera, while presupposing the common rationale of accident, namely being in something. By reason of this common rationale it does not have being toward another, but neither does that exclude it.

In answer to the confirmation, we reply that transcendental relation is not primarily and per se toward another, as has been said, but from another or about another, as dependence or causality or something similar. This can sometimes be preserved not through what actually is, but through what can belong to it or what it requires to belong to it. Predicamental relation, however, because its whole being is toward another, arises only from the positing of the extremes. Hence, if one of them is absent, it is absent.

In dividing predicamental relation, we can consider a TWOFOLD LINE OF DIVISION: the first according to the accidental conditions of relation, the second according to its species and essential differences.

In the first way, relation is divided in two stages: First, into mutual and non-mutual relations; second, mutual relation is divided into a relation of equiparance and one of disquiparance. A mutual relation obtains when, on the side of each extreme, there is reciprocally a relation of the same order or entity: that is, if it is a real relation, it is real on the side of each extreme; if it is a relation of reason, both are relations of reason. For example, father and son are related to one another. It is not enough that they be reciprocally convertible, since non-mutual relations too are convertible: one regards, and the other is regarded. Conversely, a non-mutual relation obtains when a true and proper relation is present in only one extreme, as in a creature’s relation to God or knowledge’s relation to what is knowable. A relation of equiparance is a mutual relation of the same account or denomination, as the relation of likeness and the relation of equality denominate both extremes as alike or equal. A relation of disquiparance has a different denomination in each extreme: a father is said in relation to a son, not to a father, and a master in relation to a servant, not to another master. These divisions are called accidental because the account of mutual and non-mutual, equiparance and disquiparance, is not taken directly according to foundations and terms, but follows relation according to the manner in which it touches such a term and foundation, from which the species of relation is taken.

In the second way, relation is divided into essential species according to the foundations of relations, to which different formal terms must also correspond. The Philosopher proposed three foundations by which relation is divided in general in Metaphysics V, chapter 15¹, lecture 17 according to St. Thomas². The first foundation is according to unity and number, on which are founded relations of likeness and unlikeness, agreement and disagreement, and so on. The second foundation is according to action and passion, as with all effects and causes. The third is according to measure and what is measured, as powers are measured by their objects, by which they are specified.

St. Thomas gathers the SUFFICIENCY of this division in the cited place. To understand it, one must observe that although every absolute category can be the subject of a relation, as receiving it materially and being denominated by it, it cannot have the character of a foundation unless it has the character of ordering one thing to another. Hence, as St. Thomas says, through substance and quality according to their proper concepts something is ordered only to itself, not to another, except accidentally: insofar as a quality, substantial form, or matter has the character of an active or passive power, or insofar as some account of quantity is considered in them, that is, unity or identity, or number.³ Therefore only those things will be foundations of relations that introduce an account of ordering one thing to another. Whatever is ordered to another is ordered either according to being, according to operation or power, or according to proportion, number, and agreement. If according to being, it is the foundation of measure and what is measured, since things are measured when they receive being and specification from another. If according to operation and power, it is the foundation according to action and passion. If according to proportion and agreement—which the Philosopher calls according to quantity, that is, unity or number—it is the foundation of unity and diversity, agreement and disagreement. No other account is given that makes one thing apt for and orders it to another, which is not reducible to these.

Many questions are commonly disputed concerning these foundations, and they pertain to metaphysics. But since the character of predicamental relation cannot be perfectly understood without at least some knowledge of them, at least a few must be considered. They will be reduced to THREE DIFFICULTIES: First, whether real relations themselves can found other relations. Second, whether all three of these foundations truly found predicamental relations, or only relations so called. Third, whether relations of the second kind have action and passion themselves as their immediate foundation, or active and passive power. In explaining these difficulties, the proper account and nature of such foundations will also be explained incidentally.

FIRST DIFFICULTY.

Concerning the first difficulty, there is disagreement between the school of St. Thomas and Scotus. SCOTUS thinks that another predicamental relation can also be founded upon a relation. His principal reason is that there is no basis for saying that all other natures, whether substantial or accidental, which agree and differ among themselves, found a relation of identity and agreement, while two relations—for example, two paternities or two filiations—cannot do so, since they truly have agreement with one another and disagreement from others. But the claim that relations are relative forms in themselves, and therefore seem not to need other relations in order to be alike or unlike, is futile: paternity, for example, is a form of referring in the character of father, not in the character of alike or unlike; therefore it will need other relative forms in order to be alike or unlike.

And this is confirmed because, according to Euclid, proportionality is defined as the likeness of two proportions.⁴ Therefore another relation, that of likeness, is founded upon proportions, which are relations.

Nevertheless, St. Thomas expressly maintains the opposite in Summa theologiae I, q. 42, a. 1, ad 4, and many authors commonly follow him. THE REASON IS that an infinite regress in relations would follow. For if paternity, for example, founds a relation of likeness to another paternity, it will also found a relation of unlikeness to a filiation or to another relation. In turn, that relation of unlikeness will found another relation of likeness to a similar species of relation, and the relation of likeness will found unlikeness to another species. Thus, by alternating, likeness will found unlikeness to another, and unlikeness to what is alike, without end. But the existence of infinitely many relations is objectionable both for the general reason against positing an actual infinite, which we shall discuss in Physics III⁵, and for the special reason that there can be no infinite regress in causes with respect to effects, since an infinite cannot be traversed either by motion or by causality. There would be no assignable last effect if infinitely many causalities and effects preceded it. But the foundations of relations are causes or principles from which they result; therefore there is no infinite regress among them.

A DOUBLE SOLUTION is commonly offered to this argument. The first admits an infinite regress in relations, just as the division of a continuum into unassignable parts is infinite. Others stop the regress among relations that are related according to the same account: for example, two paternities found a relation of identity, yet the relation of identity thus founded does not found another relation of likeness and identity, but by itself regards every identity.

But the first solution admits an infinite regress in causes, which the Philosopher rejects in Metaphysics II⁶, and this is evident in itself: if infinitely many concurrences or causalities are required for one effect, the last effect can never be identified, because the last concurrence cannot be designated. Moreover, although it may be debated whether an actual infinite is possible by absolute power, naturally no one doubts that it cannot exist, as is proved in Physics III.⁷ Therefore there is no infinite regress in the causation of relations. The example of the division of a continuum is irrelevant, because that infinity is not an infinity of actually divided parts, but of a quantity divisible potentially and syncategorematically; whereas in our case the relations are actually infinite.

The second solution, however, is excluded by the reason given above. We do not say that only a relation of likeness is founded upon one relation—which would indeed have likeness to others through itself and not through a superadded relation—but we also say that one relation founds a relation of unlikeness, just as it founds one of likeness. Alternating in this way yields an infinite regress, since we found unlikeness upon a relation of likeness and likeness upon a relation of unlikeness. Reversing them again, we always find a new relation and an infinite regress. This solution does not eliminate that result, since it speaks only of a relation of one account.

TO THE OPPOSING REASON, the reply is that relations of the same species do indeed have likeness and agreement in a quasi-transcendental way, not as predicamental relations, so that the infinite regress described above does not follow. We can investigate the reason for this a priori from the weakness of relation: it has such minimal entity that it does not suffice to found a real relation. For every foundation must be more perfect than that which is founded, just as one accident cannot underlie another by sustaining it, as we said in q. 15⁸, because it does not possess the perfection of a mode of being. Thus, since all relations are equal in their relative mode of being, one cannot be the foundation of another.

The reply to the confirmation is to admit Euclid’s definition of proportionality. But it remains for Scotus to prove that this likeness or equality of proportions is a distinct relation founded upon the relations of the proportions; it is enough that this equality be transcendental.

SECOND DIFFICULTY.

Regarding the second point, some have said that RELATIONS OF THE FIRST AND THIRD KINDS are not predicamental. Some think they are relations of reason, because the foundation of relations of the first kind presupposes something of reason, namely a formal or essential unity common to many; otherwise they could not be founded upon unity.

Others think they are transcendental, because unity and number, upon which these relations are founded, are something transcendental and are found in every category. There is no reason, they say, to restrict the relation of unity and number to quantitative number alone, since a relation of likeness and difference is also found among angels.

Finally, others exclude RELATIONS OF THE FIRST KIND from the category of relation, because they think they are extrinsic denominations: first, otherwise the multitude of relative entities would multiply immeasurably, since there are almost infinitely many combinations of agreement and disagreement; second, because paternity and filiation in divine things do not found real relations of likeness and diversity, and therefore these are not real relations in themselves; third, because coexistence or distance expresses an extrinsic denomination, as the character of right-handness in a column does. Therefore diversity and likeness will likewise be extrinsic denominations.

Some exclude RELATIONS OF THE THIRD KIND from the category of relation, relegating them to transcendental relations. For it seems superfluous to posit both a predicamental and a transcendental relation of knowledge to what is knowable, such as the relation that remains in knowledge when what is knowable has been destroyed. Others think these are extrinsic denominations: although knowledge founds a predicamental relation to what is knowable, they say, that is not a relation of this third kind but of the first or second. In this third kind, however, Aristotle does not enumerate the relation of knowledge to what is knowable or of what is measured to its measure, but the reverse: that of what is knowable to knowledge and of the measure to what is measured, as is clear in Metaphysics V, ch. 15⁹; but a measure is not a real relation.

NEVERTHELESS, with the common opinion, one must assert that both kinds of relations, the first and the third, are predicamental, as is commonly held with Aristotle, St. Thomas, and Scotus.

THE SOLE REASON is that all the requirements for predicamental relation are present in these relations no less than in relations of the second kind. For in them there are real correlatives that are really distinct: namely, those between which there is likeness or diversity, measuring and measure. An existing term is also present, as I now assume; for if the term’s existence is lacking, the relation perishes, as it does in relations of the second kind. There is likewise a real foundation: in relations of the third kind, dependence for specification upon an object, as in relations of the second kind, the effect’s dependence upon a cause. This foundation is distinct from the relation itself of the second kind, because, as St. Thomas rightly notes in Metaphysics V, lecture 17¹⁰, the foundation of the third kind is commensuration to the specifying object, not proportion or unity as in the first, or action and efficiency as in the second. Likewise, in relations of the first kind the foundation is something real—not some common unity existing in many things, but agreement or conformity, such as exists in distinct subjects: in reality Peter and Paul agree, while Peter and a horse disagree. Therefore the character of predicamental relation is no less present in these than in the second kind.

YOU WILL SAY: In relations of the first kind, no foundation distinct from the subject is found—namely, unity or agreement—as action is distinct from power in relations of the second kind. But first, this is false of the relation of accidental likeness. Next, in essential likeness, why is it required that the foundation be distinct from the subject? Only a real distinction between the extremes of the relations is required. Why is a distinction between the subject and the foundation necessary? And if it is permitted to argue from divine to created things, there one finds a foundation—for example, the generative power, indistinct from the Father—which nevertheless founds a real relation.

NOR IS IT AN OBJECTION that transcendental relations are sometimes found in these cases, as between knowledge and what is knowable, and sometimes between similar extremes. First, if this were an objection, relations of the second kind would also have to be set aside, because there is a transcendental relation between effect and cause, as of a creature to God: the effect regards God not only under the character of a pure term but under the character of a cause. Next, in relations of likeness and diversity we see that when the term is destroyed, the relation of likeness ceases. Therefore it was not merely a transcendental relation, since that does not perish when its term perishes; it is predicamental. This is much clearer in the relation of accidental likeness, which is founded upon something superadded and does not transcend it.

TO THE OPPOSING ARGUMENTS: To the first, against relations of the first kind, the reply is that these relations are not said to be founded upon unity insofar as unity means indivision, since relation rather requires divided and distinct extremes; rather, they are founded upon unity insofar as it means agreement and conformity, which is present in several subjects. One should not, therefore, expect a formal unity produced by reason and positively undivided.

To the second, it is said that the foundation of this relation ranges materially across all the categories, but formally it is always one, namely agreement or unity, wherever it is found in a category or predicamental class. The same argument proceeds against relations of the second kind. For action and passion, cause and effect, are also found in different categories: all effects are effects of God, and many things are also causes, at least material or formal ones.

To the third, the reply is that this multitude of relations does not frighten us at all into denying that such relations exist; however great it is, it is finite. Besides, according to St. Thomas’s opinion that one relation can terminate in several numerically distinct terms, the multitude of relations is quite moderate. We say that there is another account concerning relations because, as stated above, real relations are not founded upon other relations. It does not follow from this, however, that there cannot be a real relation of likeness or diversity in created absolute things. As for coexistence and distance, I say that nothing prevents them from being real relations, like likeness and difference. Right and left are not analogous: they are found really only in an animal, which has a heart or other organs from which its right side draws strength and power. This is not found in a column, which is called right by denomination from its being placed beside an animal.

Regarding the objections against relations of the third kind: To the first part, the reply is that predicamental relation is not superfluous even if a transcendental relation is posited; indeed, a predicamental relation is often founded upon a transcendental one, as the effect’s relation to its cause. The transcendental relation also serves a purpose, because even when the term is removed and destroyed, the transcendental order remains, though the predicamental one does not.

To the second part, the reply is that the Philosopher’s meaning is gathered from the text, where he first posited a relation on the side of what is measurable to its measure, saying¹¹: “Other relatives are related as the measurable to the measure.” Then he adds an example, “as what is knowable to knowledge, what is sensible to sense,” to show that these relations are not mutual. This was expressed more clearly by explaining those extremes on whose side the relation is absent: they are denominated by the other extreme, in which true relations are found, not extrinsic denominations.

St. Thomas explains why relations of this third kind are not mutual in Summa theologiae I, q. 13, a. 7, and De potentia, q. 7, a. 10¹²: the extremes are not of the same order; rather, one depends on and is subordinated to the other, and not conversely. One is the measure and the other what is measured; one perfects and the other is perfected. But what perfects, as such, does not depend on what is perfected; the converse is true. Hence they are not ordered to one another mutually, but only one is ordered to the other. Thus God is outside the order of the creature, the sensible outside sense, and the intelligible outside intellect, because all these act or specify without being changed. They are therefore outside the order—that is, outside the change of their correlatives—so that they neither depend upon nor are related to one another mutually.

THIRD DIFFICULTY.

Concerning the third point, AUTHORS dispute the matter, some of them quite anxiously. To me, however, it does not seem so important. All agree that action is required at least as a condition, and that the proximate and radical principle of action is also required. But Scotus, in Sentences IV, dist. 6, q. 10, and Metaphysics V, ch. 14, says that since the action passes away while the relation endures, action cannot be the foundation of the relation: when the foundation is removed, the relation that inheres in it or is identified with it collapses. Therefore action is required for founding the relation in a way, as a condition, in its coming-to-be, but not for preserving it in being as its foundation.

Others, such as Father Suárez, Metaphysical Disputations 47, sect. 12, no. 5, in order to provide better for the relation’s preservation, say that it is founded neither upon action nor upon proximate power, but upon radical power—that is, upon the substance itself. For a father has the relation of paternity in actuality not only after the action has passed away, but even if the power to beget is lost; therefore this relation cannot be founded upon proximate power. If that were its foundation, as soon as it was destroyed the relation would cease to exist; for when the foundation is removed, the relation does not remain. This argument is forceful according to the opinion of those who distinguish proximate powers from radical ones. They are compelled to say that if the relation is founded upon a power and the relation does not remain when its foundation passes away, then, if the relation of action is founded upon the proximate power, it does not remain when that proximate power is destroyed. Hence, if it remains, it must be founded upon radical power. But Scotus, who does not distinguish proximate powers from radical ones, consequently does not admit that proximate power is removed unless the substance is destroyed, although its operation can be prevented if the organ on which the power depends is destroyed.

NEVERTHELESS, the opinion of St. Thomas holds that these relations of the second kind are founded upon action and passion as their proper foundation, not merely as a required condition. For this is required generally of every relation: as St. Thomas says, a new relation cannot really arise in anything except through motion, which is terminated mediately at the relation itself and immediately at the foundation or term.¹³ We do not doubt that some relations are founded immediately upon active power itself, as the heat-producing power regards what can be heated. This relation precedes the action, since it is not to the effect but to the producible object, insofar as the object belongs to that power; and so it is more properly reduced to a relation of the third kind, because it is by way of commensuration, as can be gathered from St. Thomas, Metaphysics V, lecture 17.¹⁴

Speaking of a relation of the second kind, since it is not to what can be produced but to what has been produced, or to the effect, St. Thomas always teaches that it is founded upon action and passion, as is clear in Summa theologiae I, q. 28, a. 4; Opusculum 48, treatise On Relation, ch. 4¹⁵; and Summa contra Gentiles IV, ch. 24. But he speaks more explicitly and better in Sentences III, dist. 8, q. 1, a. 5¹⁶, where, after saying that these relations are founded upon action and passion, he adds: “One must also consider that some relations arise not from acts insofar as they are in act, but rather insofar as they have been, as someone is called a father after an effect has followed from the action; and such relations are founded upon that which is left in the agent by the action, whether a disposition, a habit, some right or power, or anything else of this kind.” From these words it is clear that actions are said to found relations not insofar as they are in the process of coming-to-be, but insofar as they are in the state of having-been-made. Accordingly, on the side of the effect they leave its production, while on the side of the cause they leave some determination toward the past effect, whether by a habit, disposition, right, or something similar. That such a determination or change is present in the cause even after the action has passed is manifest: after the action has passed and the effect has been produced, a created cause regards that effect differently than it regarded it before. Previously it regarded it as producible by itself; after producing it, it no longer regards it as producible by itself, whether this is due to something extrinsic or intrinsic, since a created cause cannot reproduce numerically the same effect. Therefore that relation, or transcendental order, to the effect that was previously possible for it but is no longer possible for it, is changed. This is because it regards the effect as already made. Thus some determination, change, or ordering toward the produced effect is left in the cause, by reason of which it is ordered to that effect as something made and no longer as something possible. This is not so in God, who can reproduce an effect even after producing it. We therefore see how the relation is founded after the action has passed: not upon bare power, but upon power determined by the action, even after the action itself has passed. Thus it is truly founded upon the action, not as it is in the process of coming-to-be, but insofar as its determination remains in the cause.

HENCE, TO THE OPPOSING ARGUMENT, the reply is that when the foundation is removed, the relation is removed. But the foundation of this relation is not the radical or proximate principle taken nakedly; for in that way it signifies only the relation of one able to act, not of an agent. For one is not called a father because he can beget, but because he has begotten. Hence these relations of the second kind must have the action itself as their specifying foundation, not merely as a required condition, and not merely have power as their foundation. For the species of these relations is according to acting, not according to being able to act. That from which specification is taken functions as a foundation, not as a condition. Yet the relation is not founded upon the action insofar as it briefly endures in act, but insofar as it leaves its determination in the power, both proximate and radical. This determination is not removed as long as the radical principle endures, even if the action passes away or the proximate power is destroyed.

TWO THINGS MUST BE EXPLAINED for an exact resolution of this difficulty: first, whether a relation is really distinct from its foundation; second, what sort of distinction it is, whether real as one thing from another or as a mode from a thing. We are speaking only of categorical relations, because transcendental relations are not something distinct from an absolute thing, but are truly absolute entities. They do not have a special category, but range across all categories; by their transcendence they are immersed in the absolute thing itself rather than distinguished from it.

On this difficulty the AUTHORS are divided. At one extreme, some think relations are not really distinguished from their foundations, but only by reason; this opinion is usually attributed to the Nominalists, against whom we argued in article 1. Some who admit categorical relations against the Nominalists nevertheless follow them in holding that relations are distinguished from their foundations only by reason. So Father Suárez, Metaphysics, disputation 47, section 2. At the other extreme, others distinguish all categorical relations really from their foundations, as the Thomists commonly do, although some distinguish a relation from its foundation as one thing from another, and others only as a mode. There is also a third, intermediate opinion, which distinguishes some relations from their foundations and not others. Some relations can exist without their foundations, such as paternity, likeness, and the like. These are really distinguished from their foundations. Other relations cannot exist without their foundations, as a creature cannot exist without its relation to God; these, they say, are not distinguished from their foundations. So the followers of Scotus commonly hold; see Father Merinero here. These relations, which cannot exist without their foundations, are not distinguished from transcendental relations. If any categorical relations are founded on such transcendental relations, they are thereby conceived as distinct from the transcendental relations.

THEREFORE, FOR THE RESOLUTION, I SAY FIRST: Every categorical relation is really distinguished from its remote foundation, which is its subject.

This conclusion is drawn from many passages of St. Thomas. In Summa theologiae I, q. 28, art. 2, ad 2, he says “that what is found in a creature beyond what is contained in the signification of the name of a relation is another thing, whereas in God there is no other thing.” Relations, however, are clearly founded on something absolute. Therefore, if what is found beyond the signification of the relative name is another thing than the relation, consequently the foundation is another thing than the relation. Again, in Against the Gentiles IV, chapter 14, replying to objection 9, he says that “in us relations have dependent being, because their being is other than the being of substance; hence they have their own mode of being according to their own character, as happens with other accidents.” He teaches the same in Metaphysics XII, text 19, lect. 4¹. He likewise teaches that relation is an inhering accident in On Power, q. 7, art. 9, ad 7², and q. 8, art. 2³.

THE BASIS IS the supposition, established in article 1, that relations are not extrinsic denominations but give an intrinsic formal effect. We see that this formal effect can be removed while the subject remains undestroyed. Therefore the form itself, which provides that effect, is also removed, while the subject is not removed. Therefore relations are really distinguished from their subjects by some real distinction. Whenever one thing is really removed from another, they are really distinct, because separation itself is the clearest proof of distinction.

The antecedent is self-evident: if one white thing is really similar to another white thing and the latter becomes black, it loses its likeness. Similarly, a man is not a father before he begets a child, but is a father afterwards. Therefore this relation is sometimes found in the subject and sometimes not, while the subject is not destroyed.

YOU WILL SAY that the reality of the relation is not destroyed even if its formal effect ceases, because its reality remains while the foundation stands, just as it arises in the foundation without any real change when the terminus is posited.

But the contrary is true. The formality that is destroyed or posited when a relation is destroyed is either something real or nothing. If it is nothing real, then no reality of the relation is destroyed when the terminus is destroyed. Consequently, when the terminus is destroyed, not only does the relation's reality remain, but so does the real formality it had before, and therefore its primary formal effect remains. For no form can be understood to be posited in a subject without its own primary and proper formal effect. Thus, if the whole reality and formality remains in the thing, its whole formal effect remains. If, however, the formality that is destroyed is something real, then it is either extrinsic and informing, in which case one falls into the Nominalists' opinion, refuted in article 1, or it is intrinsic and informing, in which case it is really distinct from its foundation or subject.

YOU WILL SAY AGAIN that when the terminus is directly destroyed, the formal effect of that entity insofar as it is relative is impeded, although the entity itself is not destroyed. For example, when a hypostatic union is posited in a soul, the soul is made incapable of receiving the formal effect of grace in the character of adoption, while the whole reality of grace remains with respect to its other effects. So the whole reality of a relation remains, but because a required condition—the coexistence of the terminus—is lacking, the subject is made incapable of its formal effect.

But the contrary is true, because a condition sufficient to make a subject incapable of a primary formal effect is sufficient to expel the form entirely from the subject. Where there is no primary effect, the form is not communicated primarily and immediately to the subject; thus the form is not in the subject, at least in the connatural manner. I am not now discussing whether grace or intellection could exist in a stone as a sustained quality without giving its own specific formal effect. If that happened, it would not occur connaturally, nor could it happen naturally, just as a subject naturally remains without the formal effect of a relation. In the example given, however, adoptive filiation is a secondary effect of grace consequent upon its primary effect, which is participation in divine being, on which filiation is founded. If someone says that the form which is a relation is an absolute entity in its entitative being but relative secondarily, and that this effect is impeded in that entity when the terminus is destroyed, this either falls into the Nominalists' opinion that denies relations, since all entities would be absolute and nothing purely relative would exist, or it confuses categorical relations with transcendental ones and must deny Aristotle's definition: the whole being of a relation is toward another. On this account, however, its whole being would be primarily absolute and only secondarily toward another or relative. St. Thomas said this of transcendental relations, as we saw above in article 2.

Therefore, since a categorical relation is one of the ten categories, if it has no real distinction from the others, it is not a distinct category, since a category consists only of real natures and, consequently, a distinct category consists of natures really distinct, not different by reason alone.

Furthermore, if a categorical relation is really distinct from its subject, it is distinct from the subject even if it is inseparable from it because its terminus cannot cease to exist. That inseparability does not prevent it from being a categorical relation and therefore of the same nature as other categorical relations. But the nature of such relations requires that they be really distinguished from their subject. Therefore this is found in all of them.

I SAY SECOND: With respect to its proximate foundation, it seems more probable, following St. Thomas, that a relation is not distinguished from it as one thing from another, but as a mode. Nevertheless, through this foundation, with which the relation is identified, it is not incompatible for the relation to be really distinguished from the subject, if that foundation is really distinguished from that subject.

That a relation is only a mode can be proved with some force from St. Thomas's common statement that among all genera relation has the least and weakest being, as he says in Against the Gentiles IV, chapter 14, ad 9, and Metaphysics XII, text 19, lect. 4⁴. It is clear that some genera are only modes and not realities, such as where, position, and the like. Therefore, if relation has the weakest being among all genera, it must be less than those that are modes; thus relation itself will not be a reality, since it would then be more perfect than those genera.

The argument is pressed further because relations can be founded on where, position, and other modes—for example, likeness or unlikeness, effect or cause, and so on. In that case, relation will not be a reality but a mode, since its foundation is a mode; an entity founded on another cannot be more perfect than its foundation. If, then, one relation is only a mode, all the other relations will also be modes, since they have the same quiddity and genus and consequently the same kind of entity. Things that directly and per se belong to the same genus cannot be so related that one is a thing and another a mode.

Nevertheless, different passages of St. Thomas and different Thomist opinions are found on this point. In Summa theologiae I, q. 28, art. 2, ad 2, he says that “what is found in a creature beyond what is contained under the signification of the relative name is another thing.” But in opusc. 48, treatise On Relation⁵, he says that the relation of likeness is not another thing than whiteness. In Sentences I, dist. 33, q. 1, art. 1⁶, he says that relation, as an accident, makes a composition with its subject. But in On Power, q. 8, art. 2⁷, he says that what is attributed to another as proceeding from it into something else does not make a composition with it, as action does not compose with the agent. In Against the Gentiles II, chapter 12, final argument, he says that if real relations came to exist really in God, God would be changed per se or per accidens. But in Physics V, lect. 3⁸, he says that when something begins to be equal to another, nothing new comes to it, and that I am equal to another only through a change in the terminus.

Since this variety of passages is found, to reconcile them we use the distinction stated above: a relation is compared either with its foundation or with its subject, which is also called its remote foundation. Compared with the foundation, it is distinguished from it only modally; compared with the subject, however, it is distinguished from the subject in the same way as the foundation with which it is identified. For example, degrees of intensity and the character of extension in habits are distinguished from a quality only modally, but from the substance or subject of the quality they are distinguished in the same way as the quality itself, with which they are identified.

This explains how a relation can be founded even on any modes whatever, which would not be possible if relation in itself were a reality distinct from its foundation. It also follows that a relation is said to result without physical change when its terminus is posited, as St. Thomas often asserts according to Aristotle's thought, especially in Physics V, lect. 3⁹, and Sentences I, dist. 26, q. 2, art. 1, ad 3¹⁰, where he says that a relation ceases without any change taking place in the thing itself that is related. This is understood to happen without physical or entitative change, solely through the result of a new mode. St. Thomas does not deny this, but clearly posits it in the cited passage from Physics V, saying that the root of a relation, which is in something, is newly determined when a relation to this or that thing is posited, even though nothing new comes to it.

The passages of St. Thomas that speak of a real distinction as one thing from another do not concern a relation with respect to its foundation, but a relation referred back to its subject. Thus he either speaks expressly about the subject when he says that a relation has a being other than its subject, as in Sentences I, dist. 20, q. 1, art. 1¹¹, and dist. 33, q. 1, art. 1¹²; or he speaks of that which is said relatively, which is certainly the subject, as in Summa theologiae I, q. 28, art. 2, at the beginning of the solution to ad 2: “As,” he says, “in created things, in that which is said relatively, one finds not only a respect, etc.” It is less of an objection that in Sentences I, dist. 2, q. 1, art. 5, ad 2¹³, he teaches that “thing” is transcendental and therefore applies commonly to absolutes and relatives. There he takes “thing” transcendentally, as common to entity and mode. And when he says that relation makes a composition with its subject, this is understood through the foundation, which is distinguished from the subject: in this way it makes a real composition with the subject and a modal one with the foundation.

We say these things to preserve the explicit passage of St. Thomas in opusc. 48, chapter 2, On Relation¹⁴, where he expressly states that relation is not a thing distinct from its foundation. Nor should we deny this work to be by St. Thomas, whose authority we invoke so often.¹⁵

Nevertheless, YOU WILL STILL OBJECT AGAINST THE FIRST CONCLUSION: If a relation is really distinguished from its foundation, God could impede it from resulting when the foundation and terminus are posited, because things really distinct can be separated or impeded. Yet it is unintelligible for two white things to exist and not be similar, precisely because they are of the same nature. Second, if a relation is distinct from its foundation, there is no reason why there should not be per se motion toward it, since every entity, even a modal one, is capable of motion, as are where, position, and so on. Yet the Philosopher denies that there is per se motion toward relation in Physics V, chapter 2¹⁶. Third, the relation of double to half in the number four with respect to two must belong to the whole number four; but if it is something distinct from its foundations, one real accident or mode will be in several subjects. Finally, there will be infinitely many relations, because in every continuum there are infinitely many proportional parts, each of which has its own relation to another; it is unreasonable to multiply so many distinct entities.

To the first, the reply is that, even if the relation were impeded, those two white things would remain alike fundamentally, though not formally. The relation serves to make things formally, not fundamentally, be called related. Or, second, not everything really distinct from another is always separable from it, if it is a thing, or can be impeded from resulting, if it is a mode. According to St. Thomas, matter cannot be separated from every form, nor bounded quantity from every figure.

To the second, the reply is that per se motion cannot be posited for every real entity. Some result is sufficient, as with proper attributes, which are not produced per se but result from the production of substance. A relation, however, is an entity that follows from a foundation and terminus. The modes cited in the argument are not something that follows from another, but are producible per se; therefore they terminate change per se, not merely through a new result, as a relation does. On this see St. Thomas, Physics V, lect. 3¹⁷.

To the third, the reply is that the relation of double or proportion found in four will be subjectively only in the final unit, although it presupposes the other units, as we said about number in the preceding question¹⁸; for this relation entirely follows the character of number itself. If number is not a being per se but only a multitude, then the relation of a greater number to a lesser, or conversely, is not one simple relation; rather, each subject has its own relation, insofar as it is a part composing that multitude and is comparatively in excess over the parts of the other number. It is like several people pulling a ship: in each person there is not simply a relation of “puller,” but one of contributing to the pulling and thus constituting the traction.

To the final objection, the reply is that, according to St. Thomas's opinion that one relation can regard several termini distinct only in number, the argument presents no difficulty, because one part can regard infinitely many others through a single relation. The truth, however, is that those indesignable parts are not actually infinite but potentially infinite, because they can be divided infinitely in a syncategorematic sense. Therefore, it is not necessary that there be actually infinitely many relations, but only potentially so. On this see more fully Physics III¹⁹.

To explain the point of the difficulty, it is certain that the term of a relation, taken denominatively, is something absolute. For example, a father does not regard filiation as the term denominated; he is not the father of filiation, but of the substance generated by him. Nor is Peter similar to the relation in Paul; rather, he is dissimilar to it, since it is of another genus. He is similar instead to the individual human being who is Paul. The DOUBT, then, concerns the formal character by which something is denominated the term of a relation: what is it formally to be a term of a relation?

ALL VIEWS REDUCE TO THREE OPINIONS. The first, at one extreme, says that all relations, whether mutual or non-mutual, terminate in something absolute. They generally take the character of terminating to mean the denominated thing or what grounds the termination. Thus a son terminates because he is generated, not because he is directed toward his father. Following Scotus in Sentences I, dist. 30, q. 2, his disciples teach this, as do Father Suárez, Metaphysical Disputations 47, section 16, Vázquez, Summa theologiae I, disp. 159, chapter 6, and others.

The second opinion, at the other extreme, says that all relations, whether mutual or non-mutual, terminate in something relative. It takes the character of terminating to mean the very formality of termination, not its foundation. A son does not terminate because he is toward himself, but because he is toward his father or something belonging to his father. This is the more common opinion among Thomists; see Cajetan, Summa theologiae I, q. 13, art. 7, and there Bañez, Zumel, and Nazarius, as well as Araujo, Metaphysics V, q. 5, art. 7, and others.

Finally, others distinguish between mutual and non-mutual relations, saying that mutual relations terminate in something relative, but non-mutual relations in something absolute, because on the other side there is no relation. Nor does an extrinsic denomination from the relation in the other extreme suffice, since this follows the termination itself: from the actual termination of a relation it results that a thing is called its term. This is Ferrariensis, Against the Gentiles II, chapter 2, whom others follow.

NEVERTHELESS, FOR THE RESOLUTION I SAY FIRST: The formal character of the relative term, insofar as it is a term, cannot be something wholly absolute and directed to itself.

There are two REASONS. First, a term, insofar as it is a term, is formally the term of something; nothing terminates except something else. Therefore the term of a relation is something relative. If it is a categorical relation, its term is purely terminating—that is, it has nothing other than terminating, or being opposed to the relation and belonging to it insofar as it regards something. In this it differs from the foundation, which must give being to the relation by inherence, in which respect it shares the being of an absolute accident. The term, however, does not give being to the relation, but the opposition of termination. Therefore the formality of the term is not something absolute.

The second reason is that, as is clear from St. Thomas, To Annibald, Sentences I, dist. 30, single question, art. 1, ad 3¹, a term cannot be understood except under an opposed relation. In Against the Gentiles II, chapter 11, he says that “something cannot be understood to be said relatively to another unless, conversely, that other is said relatively to it.” The reason is that a relation as such has opposition, no less than contrariety or privation; it has opposition only to its term. Therefore the term, insofar as it is a term, is relatively opposed to it. Just as a relation cannot be understood except as having opposition to a term, neither can the term be formally understood except as opposed; but that opposition is relative. Therefore insofar as it is a term, it is something relative.

BUT THE OPPONENTS SAY that there is a twofold opposition among relatives: one terminating, the other relative. Terminating opposition consists only in this, that the extremes are distinct and one regards while the other is regarded. In this way they are opposed because they cannot coexist in the same thing; for there is no relation of a thing to itself. Relative opposition, however, consists in one relation regarding another, not as its term, but as founded on and opposed to itself by means of the term.

Moreover, if that terminating opposition consists only in the extremes being distinct and unable to coexist in one thing, it is common to every opposition, whether contrary, privative, or relative. It remains, then, to explain what species of opposition this terminating opposition is. For there are only four species of opposition, as is clear from the chapter on Opposites²: contradictory, privative, contrary, and relative. This is neither contradictory nor privative, since both extremes are positive. It is not contrary, because the extremes are not under the same genus, given that the term is said to be something absolute, which is not in the same genus or category as relation. Nor is it relative, as they themselves say, since they distinguish relative opposition from terminating opposition. Therefore it is no species at all.

Again, relative opposition cannot consist in two concomitant relations extending from one extreme to the other and conversely, but in their being opposed—that is, in the extremes mutually terminating and referring to one another. Either, then, one relation terminates formally in the other or in its material aspect. If the first, we have our conclusion: a relation terminates in something relative. If the second, this relative opposition coincides with terminating opposition, since it is directed to the absolute term itself. Therefore terminating and relative opposition are distinguished to no purpose; there is only relative opposition.

I SAY SECOND: It seems more probable that in relations of the third order there is no formally correlative term, but only a proximate fundamental term.

This is the third opinion mentioned above.

It seems to follow from St. Thomas, who often teaches that the opposition in the terms of these relations is understood together by the intellect, not in the thing, as is clear in Summa theologiae I, q. 13, art. 7, especially ad 2. In To Annibald, Sentences I, dist. 30, art. 1, ad 3³, he says “that to every relation another relation is opposed, which is sometimes in the thing to which the relation terminates, and sometimes only in the intellect—not as in what is related, but as in one understanding something under a relation.” It is clear, then, from St. Thomas that a term signifies opposition as relative, and yet this relation is not always in the terminating thing, but in the intellect; consequently, there is no term formally in the thing. This is plainly inferred from the preceding conclusion, because the formal character of a term consists in opposition to its correlative. This opposition, however, is not found formally on the side of the other extreme, because it has no real relation and consequently no relative opposition. Therefore, it is not formally a term in the thing.

That it is a term fundamentally and proximately is proved because it is denominated extrinsically as such by the relation existing at the other extreme. Thus God is called Lord by the relation of servitude existing in the creature, and according to St. Thomas, Summa theologiae III, q. 35, art. 5, and Sentences III, dist. 8⁴, Christ is called the Virgin's son because of the relation of maternity existing in the Virgin. See Sentences I, dist. 40, q. 1, art. 1, ad 2⁵, where he says: “Among relatives, something is sometimes denominated by what is in it, as a father by fatherhood, which is in him; sometimes it is denominated by what is only in the other, as among those in which the relation is real in one and only according to reason in the other.” All this is grounded in Aristotle's statement in Metaphysics V, text 20⁶, often repeated by St. Thomas: the measurable and the knowable are said of something because something is said with reference to it, as something is called knowable because there is knowledge of it. Once this denomination is made, the concept of the opposed relation, which includes the formality of the term, can be founded proximately on it.

I SAY THIRD: In mutual relations, the formal term is not the mutual relation itself insofar as it is mutual—that is, as being of the same character as the other—but insofar as it is opposed, for opposition formally constitutes the term. But because in relations opposition is not another relation added on, as St. Thomas teaches in Summa theologiae I, q. 42, art. 1, ad 4, and as we proved in the preceding article, one relation is said absolutely to terminate in another insofar as they are correlatives of one another.

The REASON follows from what has been said: the formal character of a term must be understood under an opposed relation and as opposed to the relation. Therefore it is not the relation of the term insofar as it is mutual, but insofar as it is opposed; nor is it the relation merely accompanying the other and of the same character, but as correlation and one against the other. In this way it terminates the other and is opposed to it. Thus, in mutual relations, neither relation, insofar as it is similar and mutual, or of the same character, is formally a term; rather, it is a term insofar as it is opposed and grounds correlation, not insofar as it is a relation, although the same relation is a correlation.

THE ARGUMENTS ARE ANSWERED.

First you will object: In non-mutual relations a formal term exists in the thing, while no relation exists there; therefore they do not terminate formally in something relative.

The major premise is clear, because that relation does not remain unterminated in the thing; otherwise it would not remain a relation. How could it formally regard something unless that regard rested in and terminated in something? If an action exists in the thing, it must terminate in something in the thing. The minor premise is clear, since it is a non-mutual relation.

And if one says that the relation intrinsically in one term denominates the other extrinsically, we said above against this that this denomination results from the relation's having terminated; therefore it does not constitute the term but presupposes it.

THE REPLY is to deny the minor premise. To its proof it is said that the relation does not remain unterminated, because it regards a term that is proximately a term fundamentally, and the relation rests there as at its ultimate point, though not as at an opposed point. The character of the ultimate point in a term is one thing, and the character of the opposed point is another. The ultimate point is common to every term, whether in the genus of substance, as subsistence, or in the genus of quantity, as a point. But the character of a term as formally the term of a relation is that it is relatively opposed to it. Therefore in non-mutual relations the formality of the term is lacking as an opposed and relative term, not as an ultimate point, because the relation rests there and does not pass to another correlative. The case of action is not similar, because its term's formality is being produced, not being opposed. The formality of a relative term is not only being ultimate, but being ultimate in a certain way, namely, as relatively opposed.

To the final reply it is said that this denomination results from the relation's terminating in the extreme itself, but it does not terminate formally as an opposed extreme; it terminates as an ultimate point, and extrinsically as an opposed point.

Second it is argued: A relation results from the positing of a foundation and a term; therefore it cannot have an opposed relation as its term.

The antecedent is a common axiom. The consequence is proved because relatives are simultaneous by nature, so one does not presuppose the other; but it does presuppose its term. Therefore the term is not an opposed relation.

This is confirmed because either a relation terminates in something relative because relation as such, or because it is mutual. Not because it is relation as such, for then this would also occur in non-mutual relations. Not because it is mutual, since even if there were no relation at the other extreme, it could still be the term of a relation—for example, if there were fatherhood but no resulting relation, as St. Thomas holds in Summa theologiae III, q. 35, art. 5: the Blessed Virgin has a real relation of maternity to her Son, yet there is no real relation of sonship in the Son toward her. Also, something white does not terminate a relation of likeness because it has a relation, but because it is white; it agrees with another white thing in whiteness. Therefore the relation terminates in whiteness, not in likeness. Such a relation, then, is concomitant in mutual relations; it is not formally the term.

THE REPLY is that a relation results from the positing of a foundation and a term—not a term formally as opposed, but as the thing grounding that opposition and having the character of an ultimate point. For the term as opposed and correlative is simultaneous by nature with its relation. The relation does not depend on the term as that from which it proceeds, but as that to which it is directed: it does not receive being from the term as it does from its foundation, but is directed to it, and thus receives opposition from it. It is therefore enough for the term to precede not as an opposed point, but as an ultimate point.

To the confirmation it is said that a relation does not terminate in something relative merely because it is a relation or merely because it is mutual, but because it is opposed. Hence it does not follow that a non-mutual relation formally terminates in something relative, because there is no term formally in the character of a term there, as we said. The same should be said of the relation of maternity in the Blessed Virgin according to St. Thomas. Similarly, something white terminates a relation of likeness fundamentally because it is white, and formally because it is relatively opposed. Thus neither does the relation itself, insofar as it is mutual, terminate the relation, as we said, but insofar as it is opposed; and insofar as it is so opposed, it is simultaneous by nature as terminating and opposed.

Third it is argued: One relative is defined by its term, as is clear, and cannot be defined formally by its correlative; therefore the term is not constituted formally by the relation.

The minor premise is proved, first because relatives are simultaneous in cognition; therefore a relation cannot be defined by its correlative, since everything defined is defined through something better known, and consequently prior in cognition, not simultaneous. Also, it would follow that there is a circle in the definition of relatives: a relative is defined by its term—for example, a father by a son—and again the son, which is the formal term, is defined by the father, which is its formal term. Therefore there is a circle in the definition of relatives. Since we can put the definition in place of the thing defined, if we say that a father is one who is toward a son, and again that a son is one who is toward a father, we could say that a father is one who is toward one who is toward a father; thus the father as defined would enter into his own definition. A circle in definitions is always defective, because a definition must be given through better-known things; but those things are called better known than the thing defined when their cognition does not depend on the thing defined. If a circle is admitted, then, what defines is not better known than the thing defined, since its cognition depends on it.

THE REPLY is to deny the minor premise. To the first proof, it is said that correlatives are simultaneous in cognition formally insofar as they are opposed. In this respect, however, they do not enter the definition of a relative as better known, but as equally known, because they do not stand as that on which the relation depends as a principle—that is the foundation—but as that to which it is directed as a pure term. For relatives are simultaneous by nature, and therefore neither, formally taken, has causality with respect to the other, although one is essentially directed to it as that to which it is opposed, not as that from which it is derived, as we will explain further in the next article. Nor must everything that enters a definition be better known than the thing defined by priority of cognition; it is enough that it be required for explaining the thing defined, even if it is simultaneous with it in cognition and by nature. It is enough for a definition that all its defining elements together be better known than the thing defined, not that each be better known separately, as we said in Summulae, q. 4, art. 2. This is especially so because a relation is not defined by its term as its cause, but as directed to its term, as we will say in the next article.

To the second proof, concerning a circle in the definition, it is said that no formal circle is committed, because relation and term stand to one another in different kinds of cause. It is not objectionable for two mutually opposed things to be placed in one another's definitions, because they are not placed there under the same character and formality. Thus, because causes are causes in relation to one another, their definitions must include one another. But because this occurs under a different relation, it is not considered formally circular: one does not include the other along the same line and in the same genus. Only a formal circle is defective, not a material one, as we will show in the books of the Posterior Analytics⁷.

As for the claim that the thing defined is placed in the definition, it is said that the definition “A father is what is toward that which is toward a father” involves two definitions, namely, of father and of son: father insofar as he terminates in son, and son insofar as he terminates in father. Thus the father is not placed in his own definition, but in the definition of the son involved there.

This difficulty depends on two other general difficulties: specification from extrinsic principles, for example from objects, and the individuation of accidents by subjects; these are to be treated elsewhere.¹

As to the first, for now WE ASSUME the more common opinion: that powers and acts can be specified by their objects, as St. Thomas proves in 1. p. q. 77. art. 3. They are specified by objects taken not materially but formally, that is, insofar as they pertain to the formality and order of the thing being specified. We will speak about this at greater length in the books On the Soul.²

Accordingly, since a relation depends on its foundation and term as on a principle and an end—the reasons for which objects are said to specify, as St. Thomas teaches in 1. 2. q. 1. art. 3.—we must consider how it derives its species from them. Here we do not take the term materially or the foundation remotely. For it is clear that several relations terminate materially at the same term: in one man, for example, the relation of father, the relation of likeness, and relations of cause or effect, among hundreds of others, terminate; likewise, several relations can be founded in the same subject, or remote foundation.

WE INQUIRE, then, into two matters concerning specific unity and diversity: First, whether they are taken from the foundation alone or also from the term; second, if they are taken from both, how each contributes to specification. As for numerical unity, the only question is whether it is taken from the unity or plurality of terms, or from the unity of the subject, even if the terms are numerically many.

On the first question, it seems on one side that a relative cannot be specified by its term. First, correlatives are simultaneous in nature; therefore one does not stand as prior to the other, and hence neither as specifying it, since the specifying factor is prior to what it specifies, as its cause. Second, the term is opposed to the relation; but a species is not taken from its opposite, since that would yield an opposite species. Third, the term is a pure terminus with respect to the relation, and so does not specify it: what is a pure terminus exercises no causality but is simply regarded, whereas specifying is a kind of causing. Finally, in a son there is only one relation to his father and mother, as St. Thomas teaches in 3. p. q. 35. art. 5.; for there is only one birth in him, and therefore one filiation, which follows that birth. Yet it terminates at terms that differ in species, namely paternity and maternity, which are different relations, just as the foundations for generation are altogether different. Therefore the specific unity of a relation is compatible with terms that differ in species, and thus is not taken from them.

Conversely, that the term alone specifies is proved as follows. First, by a general consideration: everything that is toward another is specified by that toward which it is, as are habits and acts. A relation, whose whole being is toward another, should all the more be specified by it, and hence so should its whole quiddity and species. Second, the same foundation can serve different relations: the same whiteness is the foundation of likeness to snow and unlikeness to a crow; the same quality in an inferior cause is the foundation of its relation to its effect and to a superior cause; and the same sign provides the foundation of its relation to a cognitive power and to what is signified. Therefore relations are distinguished by their terms, not by their foundations.

NEVERTHELESS, IT MUST BE SAID that both contribute to the specification of a relation, and neither excludes the other. The relation receives specification from its foundation as from a cause and specifying principle, but from its term not as from a cause of specification, rather as from that which completes and terminates the account of specification.

Hence Albert rightly said,³ as Master Soto reports in q. 1. On Relation, ad 8., that one relative is not defined by another but with reference to another: “by” indicates a cause, while “to” indicates an order. St. Thomas generally takes the specification of a relation from its foundations, because he says that a relation is real by virtue of its foundation. This is clear in 1. dist. 26. q. 2. art. 2. ad 4.,⁴ where he says: “Since a relation has natural being only because it has a foundation in a thing, it is placed in a genus on that account. Hence the essential differences of relations are taken according to the differences of other beings, as is clear from the Philosopher in 5. Metaph., where he says that some are founded on quantity, others on action, and so on. Accordingly, the order of relations is also according to the order of the things in which they are founded.” This, then, is why in many places St. Thomas takes the specific account of relations from their foundations: in 3. p. q. 35. art. 5., Quodlib. 1. art. 2.,⁵ and Quodlib. 9. art. 4.,⁶ Opusc. 2. cap. 212.,⁷ and in 3. dist. 8. q. 1. art. 5.,⁸ where, in reply to objection 4, he also distinguishes motion from relation: “Every motion is something in reality, but not every relation is. Therefore, although the relations of a relation are multiplied by its terms, it does not follow that relations are multiplied in reality, as motions are multiplied in reality by the diversity of their terms.” In that passage the Angelic Doctor always traces the reality of relations back to their foundations, and, given the foundation, to their terms, though not to the terms alone, as in the case of motion. The same can be drawn from St. Thomas’s general rule in 1. 2. q. 54. art. 2., where he says “that all things said relatively are distinguished according to the distinction of the things to which they are said.” Therefore relations too derive their specification from their terms. He states this also in 1. p. q. 32. art. 2., where he says “that two relations are not specifically different if one relation corresponds to them from the opposite side”; we will examine that passage below.

The reason for these positions follows from what has been said: the whole reality of a relation comes from the foundation according to its order toward the term, since, as its definition says, the whole being of a relation is toward another. Since it essentially requires both, foundation and term, its specification should not be taken from one alone, to the exclusion of the other.

THE SECOND PART of the conclusion, concerning how these two contribute to specification, should not be understood as their contributing only partially, with the foundation supplying one part of the specification and the term another. Rather, each supplies the whole specification in a different kind of cause. Some explain this by saying that the foundation contributes initiatively and the term completively. Others say that the foundation contributes in the genus of efficient cause and the term in the genus of extrinsic formal cause. Still others say that the foundation specifies by virtually containing beforehand the term to which it is proportioned, so that the diversity of foundations is referred back to a diversity in the formality of the terms.

Still, a distinction must be made. The term is either taken most formally as an opposed term, or fundamentally, from the side of the absolute thing that grounds this account of terminating. In the first way, the term contributes to specification purely by terminating, not by causing it, because in this way it is a pure term and is simultaneous in nature and cognition with the relation. Therefore, taken in this way, it is not a specifying cause, since a cause is not simultaneous in nature with its effect, but prior to it. If considered in the second way, it functions as an extrinsic formal cause and specifies in the manner of an object. In this way, a single account of specifying a relation arises from the foundation and the term, insofar as the foundation contains the term within itself in proportion and virtually. For a foundation is not toward such a term unless it is such a foundation, and conversely. Thus, insofar as they are proportioned to one another, they make up one account of specifying a relation, which requires both such a foundation and a term corresponding to it.

From this you can also gather what the formal term is in its role as a specifying factor. Although different relations specifically can terminate at the same material term, they cannot terminate at the same term formally. The formal specifying account in the term is taken according to its correspondence and adequate proportion to its foundation. For example, white constitutes the formal term of a relation of likeness insofar as it corresponds to agreement and identity; of unlikeness insofar as it corresponds to disagreement; and of paternity or filiation insofar as it corresponds to generation, and so in other cases. Thus, just as the foundation is considered under the ultimate account by which it grounds, so the term is considered under the proportion and correspondence by which it terminates.

We said “which corresponds completely or adequately,” because one total term can correspond to relations that differ specifically, as the relation of paternity and the relation of maternity correspond to filiation. For filiation is caused by those two modes of generation, paternal and maternal, but proceeds by one birth. St. Thomas teaches this in 3. p. q. 35. art. 5. ad 3. Yet he seems to say the contrary in 1. p. q. 32. art. 2., where he says “that two relations are not specifically different if one relation corresponds to them from the opposite side.” Those who think that both father and mother contribute actively do not escape this difficulty. For even if both contribute actively, they do so in different ways, sufficient to ground the different relations of paternity and maternity, just as the sun and a human being both contribute actively to generation, but in different ways that ground different relations of cause. Therefore the reply is that one total term, or correlative, can correspond to two partial relations, but not to two total relations. Father and mother, and several causes of the same order contributing to the same effect, are diverse in a quasi-partial way; together they constitute one complete cause and one total term, even though there are several partial ones. In the first passage, from 3. p., St. Thomas is speaking of several partial relations on one side, to which only one adequate relation can correspond on the other side. In the second passage, from 1. p., he is speaking of different relations that correspond adequately and completely.

TO THE ARGUMENTS FOR THE OPPOSITE OPINIONS: To the first, it is answered that although the term is simultaneous with its correlative, specification depends on it, not as on a principle that causes specification, but as on that which terminates and completes it. Thus all the priority of the specifying cause belongs to the foundation. The relation is not specified by the term, but with reference to it.

To the second, it is answered that specification can be taken from a term opposed by relative opposition, as from that which terminates and completes, not as from that which causes it. For relative opposition is the least of all oppositions: it does not remove the other extreme but posits or presupposes it, and thus the specification of the relation can be ordered toward it.

To the third, it is answered that a pure term, under the formality of a term, can specify by terminating and completing, not by causing; it specifies as that to which, not that by which.

The answer to the last argument is clear from what has been said.

TO THE ARGUMENTS FOR THE SECOND OPINION: The first has already been answered: terms specify by purely terminating, while foundations specify by causing. Thus the whole being of a relation is toward the term as that which purely terminates it.

To the second, it is said that the same foundation cannot serve proximately and formally for relations that differ in species. For example, whiteness, under the formality of agreement, grounds likeness; under the formality of disagreement, it grounds unlikeness. Likewise, in the other examples cited, if they are different relations (a question I am not disputing), there are also different proximate and formal foundations.

As to the second difficulty involved in this article, concerning the numerical distinction and unity of a relation, it depends on the famous question whether accidents are individuated by their subject, such that two accidents differing only numerically cannot be in the same subject. This need not be treated here. We need only explain whether one relation can extend to and concern several terms, each of which sufficiently terminates it, as one father has several sons. This seems impossible. First, the same effect cannot depend on several total causes of the same order and account. But each son is a sufficient and total term of paternity, since the relation is specified sufficiently and totally by him; therefore the same relation cannot depend on a subsequent son. Also, a new generation occurs with respect to a new son, and therefore there is a new relation, which is identified with the generation. Nor can the relation be extended anew, since this extension would be a new increase and addition to the relation, not part of it; but a relation has no parts, and so it would be a new relation. Finally, a relation is an indivisible and simple mode. Therefore, if one son dies while another remains, the relation to one persists and that to the other ceases; the same entity would thus persist and not persist, since it is simple.

THE ANGELIC DOCTOR HOLDS THE OPPOSITE OPINION in 3. p. q. 35. art. 5., Quodlib. 1. art. 2.,⁹ and Quodlib. 9. art. 4.¹⁰ AND ST. THOMAS PROVES IT not only from the general account of accidents, which cannot be multiplied numerically in the same subject, but also from the special case of relations: the cause or foundation is numerically the same. For example, in a relation of equality, the same quantity is related to all quantities of the same extension—a single cubit is equal in the same quantity to every cubit; likewise, the same generative power is related to all sons, though modified by different actions. Also, to avoid an infinite multiplication of relations: in one subject there are infinitely many proportions among parts, yet in one teacher teaching many there are not many acts of teaching, but one; and in one dominion and one king there are not as many dominions and relations as there are subjects, since many can be taught and ruled by the same action. Finally, a son is related to his father and mother by one relation, and several people drawing a ship are related to it by one relation. Therefore one relation can likewise reach all the terms of its species as inadequate to its extension, although each suffices for its existence; and so, although this relation numerically regards this particular term, it does not regard it adequately, but also regards all the others in which the formality of such a term is present.

TO THE OPPOSING ARGUMENTS it is answered: To the first, we say that one effect cannot depend formally on several total and adequate causes. If, however, the causes are several only materially, the effect can indeed depend on them, insofar as they agree in one mode of causing or terminating. Thus, if ten people suffice to pull a stone, twenty can do so as well; they are more numerous only materially, but formally agree in one account of causing. Likewise, the relation of a father is sufficiently terminated by one son; yet if there are several, it is also terminated by them, insofar as they agree in the same account of terminating one generative power modified by different actions. For this relation is founded on that power as thus modified, as we said from St. Thomas in article 3.

Finally, this is explained by different examples. We see that when one effect has been produced by one sufficient cause, and another sufficient cause comes along, it does not produce the effect anew, but engages with it in a new way. For example, alteration produces a quality, while intensification, which comes about anew, does not produce it but applies and reaches it in a new way, although it would be sufficient to produce the quality. Likewise, although transubstantiation in the Eucharist is sufficient to produce the substance of Christ’s body, because it finds that substance already produced, it does not produce it anew but applies it in a new way. So although one son sufficiently terminates the relation of a father, if a new son comes along after the relation has been produced, he does not terminate a new relation but extends the same relation as pertaining to him. For St. Thomas’s opinion that there is only one existence in the whole composite, a more fitting example is in 3. p. q. 17. art. 2.: if, when the whole exists, one part is missing—say, a hand or foot—and it comes along later, a new existence is not produced in it; rather, the existence of the whole is applied to it as something pertaining to the whole. We say the same about the simple habit of science extending to several conclusions without the addition of a new habit, and about an intensified quality taking root without the addition of a new quality.

To the second, it is said that although a new generation is posited with respect to a new son, because it takes place at a different time and from different matter (otherwise several sons could indeed be born by the same generation), nevertheless the relation is not identified with the action, nor founded on it, except insofar as it determines the generative power, as we said above; and this power is one. Thus, just as when several sons are born in the same delivery, the father’s relation can only be one, because it is founded on the same action, so too when they are produced by several actions. It is incidental that several actions or one action of the same power modify it toward a relation of the same account. This extension of the relation to different terms does not occur by adding a new relation, but by unfolding the pre-existing one, insofar as it of itself regards all terms proceeding from the same foundation. It is unfolded in act when an action either grounds or at least in fact posits a new term, as St. Thomas explains in 5. Phys. lect. 3.¹¹ concerning the resulting of a relation upon the term’s being posited from the root of its foundation, where it was already present beforehand. For a relation to be emitted anew from its foundation, or for one already emitted to be unfolded or applied to that new term as pertaining to it, is intrinsic to the relation itself: namely, to tend and be determined in act toward that to which it tended virtually of itself, and which was absent only because the term did not exist. This helps explain how the species of an angel can represent a new object without any change in its representation, an object that did not exist before and now begins to exist.

To the third, it is answered that a relation is simple in entity but multiple in its terminating, which is to be divisible relatively while indivisible entitatively. Therefore, when one of the terms materially present there perishes, the relation perishes as to its application and extension to that term, but not simply or in itself. Something similar is found in the simple habit of science, which extends to new conclusions and can lose one conclusion without failing as to the others or entitatively in itself; likewise in the existence of the whole communicated to its different parts, and in one angelic species reaching some objects that exist but not those that do not. All these matters will be examined in their proper places.

These properties pose a difficulty because in relatives the relation depends on its term, and likewise one relative is defined through another. Therefore priority, rather than simultaneity, seems to obtain, since wherever there is dependence, there is priority of nature.

To resolve this difficulty, WE MUST PRESUPPOSE what Master Soto notes in the chapter “On the Relative,” concerning text 5, and in the chapter “On the Modes of Being Simultaneous”: two conditions are required for things to be simultaneous. First, neither is the cause of the other. Second, they entail one another. For if one is the cause of the other, they are not simultaneous; one is prior to the other. And insofar as they are simultaneous, one cannot stand without the other, and thus they mutually entail one another. Likewise, being simultaneous in cognition, according to the Philosopher in the chapter “On the Relative”¹ and St. Thomas in opusculum 48, treatise on Relation, chapter 5², consists in this: whoever cognizes one must necessarily cognize the other, because the being of one relative is wholly directed to the other. This does not require one to be defined through the other as through a cause, but as directed to the other as a term; thus the term does not specify causatively, but purely as a terminus, as we said above.³

I SAY, THEREFORE, FIRST: The first property is understood of relatives formally, insofar as they are relatives and as they exercise the act of referring, as Cajetan notes on this chapter on Relation and St. Thomas indicates in 1. p. q. 13. art. 7. ad 6., where he says: “To know whether relatives are or are not simultaneous by nature, one must consider not the order of the things of which they are said, but the significations of the relatives themselves. For if one includes the other in its account, and conversely, then they are simultaneous by nature, as double and half, father and son.” Thus there need not be simultaneity in the very things that ground the relation. Indeed, relation is often grounded in cause and effect, and in that respect the father is prior to the son in causing, but simultaneous in referring.

THE REASON IS that in the very account of referring and the formality of the relative, they have no causality, since one relation does not cause another; each is caused by its own foundation. They do, however, have connection, since one cannot exist without the other; therefore they are simultaneous by nature.

BUT YOU WILL SAY: One relative specifies another, since it is its term. But what specifies is prior to what is specified, since it is its cause; therefore they are not simultaneous. Second, in relatives of the third kind, there is only a relation of reason, since they are not mutually relative. But a relation of reason is not simultaneous with its correlative, since it depends on cognition, not merely on foundation and term. Therefore this property does not belong in the fourth mode to every categorial relation. Finally, relations of reason are also simultaneous, as genus and species are; therefore this property belongs to things other than categorial relatives.

To the first point, the answer is that the term, as formally opposed and correlative, does not specify the relation first and per se; rather, the relation is specified with respect to the term, not from it, as we said above.⁴ The foundation concurs as what specifies by way of principle and cause, but with an order to the term, in which the specification is completed and terminated.

To the second point, the answer is that this property is found in non-mutual relations only proximately and fundamentally, because the term is not found there formally as opposed and correlative, as we said above; rather, one extreme receives an extrinsic denomination from the relation of the other to it, and is said to terminate it proximately and fundamentally, not formally. In this way the term is simultaneous by nature with the relation that is toward it. Hence the knowable is not simultaneous with knowledge by reason of a transcendental relation, since in that respect it is the specifying object and cause, nor by reason of a relation of reason, which is posterior; it is simultaneous by reason of the proximate foundation that terminates it, by reason of which it is taken as terminating the categorial relation in the way that it can. Thus the rule of St. Thomas stated above is entirely true: to determine whether relatives are simultaneous by nature, one must attend to their significations. If the knowable is considered as the object of knowledge, it does not include the relation of knowledge in its account and is not simultaneous with it by nature, because in this way it is signified according to the transcendental relation of knowledge. But if it is considered not as an object, but as terminating the categorial relation of knowledge, at least proximately and fundamentally, then it is signified as correlative, at least extrinsically, and consequently as simultaneous by nature.

To the final point, it is said that relations of reason are not simultaneous by nature because they do not have being, but are only cognized; therefore they are no more simultaneous by nature than the cognitions from which they result.

I SAY, SECOND: The other property, namely that relatives are simultaneous in cognition, is understood of relatives formally, according to the exercise of referring—not according to the things that are materially relative, nor insofar as a relation is considered as informing, but as referring.

THE REASON for this conclusion is that what is material and foundational in a relation can be cognized as prior to its term, since it can be its cause, specifying factor, or object. Thus, although it cannot be defined without the term, it is not simultaneous in cognition, because it is rather the cause of cognizing and explaining the term, since it is what defines. Only relatives insofar as they are correlatively related and exercise opposition are simultaneous, because their respect and their pure terms have connection and not causality. If the relation itself is considered in the force of a form and in the signified act—that is, as exercising the function of informing a subject, not the function of referring to a term—then it need not be simultaneous in cognition with its correlative, because in this way it takes on the mode of an inhering thing, which is common to relative and absolute things. In that respect it need not be cognized simultaneously with its term or correlative, but only when it is cognized according to what is proper to a relative, namely, its exercise of referring. Thus, when in divine things we conceive the relation of paternity as subsisting and constituting a person, we need not conceive it as terminating in the Son, but as subsisting as the Son's principle.

From this it follows, first, that relatives are simultaneous in cognition both as to quiddity and as to existence. As to quiddity, because the proper and quidditative account of a relative is “toward another,” and consequently by its essential principles it calls for connection with another, not causality but termination, which is to be simultaneous. As to existence, because a relative cannot exist in reality without a term and correlative; for a real relation calls for a really existing term, as has often been said.

It follows, second, that although the foundation is sometimes included in the definition of relatives, as when one says “A father is one who has begotten someone similar in nature,” their simultaneity in cognition does not come from their foundations, in which there is sometimes priority and dependence; rather, it comes from correlative opposition, even if this is not always explicitly stated, nor intrinsically and formally present in all cases, as in non-mutual relatives.

ORDER OF THE CATEGORY OF RELATION.

The highest genus is real relation according to being. It is divided into three immediate genera: first, what is founded on quantity or proportion; second, what is founded on action and passion; third, what is founded on measure.

The first genus is divided into relations of equality and inequality, similarity and dissimilarity, agreement and diversity, and proportion, as in double, subdouble, and so forth; all these are atomic species.

The second genus is divided into relations of cause and effect, action and motion or change, proximity and recession, insofar as these depend on motion. Each can be divided into various species according to the various accounts of cause and effect: for example, one relation is that of an efficient, material, or formal cause, and so on; another relation is founded on the motion of generation or alteration, or on the action of creation, and so on.

The third genus is divided into relation to a measure, which is either an object or a model or prototype. Relation to an object is divided into relation of a power, habit, or act. Each of these is divided into various species according as it is an active or passive, cognitive or appetitive power; and the cognitive kind is divided into various species, such as relation to what is visible, audible, intelligible, and so forth. Similarly, models can ground diverse relations of species, according to the different ways in which they are called models and exemplars.