Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

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.