Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

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.