Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

THE COMPARATIVE ACT of the intellect can be understood in two ways. First, as belonging to the intellect’s second and third operations, by which it joins one thing to another—composing, dividing, or reasoning by inference. Second, as belonging to its first operation, by which one thing is neither attributed to another nor derived from another, yet is known as ordered to another and not absolutely in itself; this is how relation itself is known through simple operation, when it is apprehended or defined. Thus, through cognition in the second operation something is attributed to a subject as a predicate. By such a comparative act, therefore, the nature itself can be predicated of its inferiors, to which it has a relation; and universality itself can also be predicated of the nature it denominates as a form, and consequently is predicated of it. By contrast, in comparison through the first operation, the attribution of predicate to subject is not considered. Rather, the nature is known as looking toward the term to which it is ordered. It may be known either in a signified and reflexive act, or, as it were, in an exercised act, by knowing the nature together with its order to its term. Note that this act is called comparative only because it looks toward the term to which it is ordered, which is properly the term of the comparison or relation—not because it looks toward the term from which it is abstracted. It is not compared to that term; it is separated from it.

AN ABSOLUTE ACT, by contrast with a comparative one, is an act that neither compares nor orders one thing to another, but knows the thing itself according to itself. One can be absolved from an order to another in two ways: purely negatively, by taking one thing while suppressing or omitting everything else to which it could have been ordered; or privatively, that is, positively, by taking one thing as separated from another while knowing both terms. Hence arise two kinds of abstraction, one negative and the other positive. Negative abstraction conceives one nature while omitting individuating conditions and taking a negative stance toward them. Positive abstraction separates a nature from conditions not by simply omitting and leaving aside individuals or individual differences, but by knowing both what it leaves aside and what it takes up, and consequently knowing the distinction between one and the other.

With these points established, and speaking of the universal known by the possible intellect, rather than merely represented in a species—as in the preceding article—there are TWO principal OPINIONS among the more authoritative writers. The first teaches that the universal is produced absolutely through an act of abstraction. The second teaches that it is produced through a comparative act, without distinguishing between the metaphysical and logical universal, or between comparison in simple apprehension and comparison in predication. Durandus taught the first, in I, distinction 3, question 5, no. 27, and II, distinction 3, question 7, no. 7; so did Toletus, On Universals, question 2, and others. The second is attributed to Scotus, I, distinction 3, question 1, solution to objection 1; to Soncinas, Metaphysics V, question 27, and Metaphysics X, question 15; and to others. See Araujo, Metaphysics III, question 3, article 5, and the Carmelite Course, disputation 3, On Universals, question 6.

Some who wished to reconcile these principal opinions said that the first is true of the metaphysical, absolute universal, and the second of the logical universal, which is relative. So Father Suárez, Metaphysical Disputations 6, section 6, no. 8. Martínez, however, On Universals, disputation 1, question 2, distinguishes universality as such from metaphysical and logical universality. He says that universality in itself is produced by abstraction insofar as abstraction gives it a precise unity. Metaphysical universality, he says, is produced by negative abstraction insofar as it leaves or omits the inferiors. Logical universality, meanwhile, is produced by positive abstraction, which he explains as follows: since this abstraction occurs by positively considering the inferiors themselves, the nature is understood as included in the inferiors yet conceptually distinct from them (for whatever is included is included not in itself but in another); it is also understood as separated from the differences of the inferiors. The universal is separated only from those differences, not from the inferiors themselves. We reported this opinion above, in the preceding question.

Finally, some have thought that a nature is made universal through a comparative act not of simple relation but of predication, which belongs to the second operation. Merinero attributes this view to certain Complutenses, On Universals, disputation 2, questions 2 and 3.

MY FIRST CONCLUSION: The metaphysical universal is produced by an absolute act that abstracts a nature from its inferiors, through both negative and positive abstraction. Thus both kinds of abstraction are absolute acts and do not serve formally to constitute the logical universal, which consists in a relation.

This conclusion is proved in two respects. First, that the act which sets the nature apart, whether positively or negatively, is absolute. Second, that the metaphysical universal results from both negative and positive precision.

THE FIRST POINT is proved as follows. An act is called absolute when it reaches its object without a reference or order to something as a term toward which it looks. But an act of precision does nothing but separate one thing from another as from a term a quo. Therefore, through such an act, something is not considered as ordered toward, and looking toward, a term ad quem; rather, it is considered as leaving that term aside. It is therefore incompatible with an act of abstraction, whose office is to remove and separate one thing from another, that it not be an absolute act: it does not compare or order to the other thing from which it separates. In sum, it is incompatible for an act to make something look toward a term both a quo and ad quem, since these two are opposed. But an act that sets apart and abstracts looks toward that from which it abstracts as a term a quo; therefore it cannot look toward it as a term ad quem. Comparison and order, however, are toward something, toward a term ad quem. Therefore, insofar as an act sets something apart, it is not comparative with respect to that from which it sets it apart: it regards that as a term a quo, and does not order it as a term ad quem.

THE SECOND POINT, which must be proved for this conclusion, is shown as follows: not only negative precision but also positive precision leaves the inferiors aside and separates the nature from them—the one through positive cognition, the other simply by omitting or not reaching them. Therefore both pertain only to the metaphysical universal.

The antecedent is clear from what has been said. The consequence is proved because the process concerns the same effect, namely the separation of the nature from the inferiors or from the differences outside which it is conceived. Therefore it regards these inferiors only as a term a quo. It does not yet posit in them the reference required for the logical universal, since that reference must be an order to being in, and being predicated of, many, as the very definition of a universal says. Therefore there must be an ordering that turns the nature toward the inferiors themselves as a term ad quem, since it tends toward them so as to be in them and be predicated of them. The reference by which the nature is merely turned away from the inferiors, or abstracted from them through positive cognition, is therefore insufficient. All of that belongs to the nature’s being stripped of its inferiors, in which state it is reached by the metaphysician; the logician reaches it in the state in which it is turned toward the inferiors so that it can be predicated of them, since predicability and an order of reason belong to logic.

YOU WILL SAY: This positive abstraction places the nature outside the differences, but not outside the inferiors themselves. For to be abstracted from the differences is one thing, since the nature lies outside their concept; to be abstracted from the inferiors is another, since the universal does not lie outside their essence. We do not properly say that animal is abstracted from man and horse, since it always remains in them, even conceptually, but that it is abstracted from something in man and horse, namely their differences. Thus, although this positive precision regards the differences as a term a quo, it does not regard the inferiors themselves as a term a quo or abstract from them; rather, it is included in them, and that suffices for saying that it regards them.

But the contrary is true: once the differences by which a nature is contracted and determined are removed, nothing remains in the inferiors in which it could remain included, or to which it could be compared as a term. In man, for example, there are only two constituents: animal as genus and rational as difference. So when abstraction removes animal from rational, what does it leave in the inferiors in which that animal could be included? It remains included only in animal itself, since man is destroyed when the difference is removed. Therefore, one cannot both set the nature apart from the differences and, by the same act, include it in the inferiors. Finally, an act that thus sets aside the differences either merely sets them aside or also reaches something else to which it refers the nature as a term. If the former, it does not compare or make the inferiors be regarded as a term ad quem; it merely removes the differences. If the latter, then the act’s office is not merely to abstract and remove the differences but also to compare the nature to the inferiors. Thus, insofar as it is positively abstractive, it still constitutes not the logical but the metaphysical universal. Insofar as it is comparative, it does what, in the opinion of the others, is done by a comparative act distinct from the act of precision. This opinion differs from theirs only in proposing that one act does what they assign to two: the abstractive act produces the metaphysical universal, and the comparative act the logical universal.

MY SECOND CONCLUSION: Unity and aptitude, which are the proximate foundation of universality, are said to belong to the nature through this act of precision even before the logical universal.

This follows from what has been said. That unity is not an essential predicate of the nature, since nature in itself is neither one nor many; it belongs to nature accidentally through the intellect, since it is a unity of reason. But precisely because the nature is set apart from its lower differences, whether positively or negatively, it is known through one concept. Therefore it is taken as one, since one concept terminates in one object. And in the nature thus taken as one there is nothing incompatible with its being made individual: there is no opposition, but rather conformity with those differences from which the intellect has taken it. Therefore it has aptitude for them—which is non-repugnance—and unity. How this unity constitutes the universal only fundamentally, and thus pertains to the metaphysical universal rather than to the universal considered as abstracting from the logical and metaphysical, was explained in the preceding question, article 5.

MY FINAL CONCLUSION: The logical, or relative, universal and its second intention are produced by a comparative act—not by way of composition or judgment, nor by way of inclusion in the inferiors, but by way of simple apprehension, through which the nature is known with an order and reference to the inferiors.

This conclusion is commonly taught by St. Thomas and his disciples, and is also accepted as common in the school of Scotus. See St. Thomas, Summa theologiae I, question 28, article 1, where he says that “sometimes the relation signified by things called ‘toward another’ exists only in the very apprehension of reason, which compares one thing with another.” In De potentia, question 7, article 11,¹ he says that a relation of reason is introduced by considering the order of what is understood to things outside, or by considering the order of understandings to one another. Finally, in Sentencia libri Perihermeneias I, lecture 10,² speaking specifically of the relation of universality, he says that the intellect attributes these relations “to the understood nature, insofar as it compares it to things outside the soul.” The same is found in Opusculum 48, treatise 1, chapter 2. ³ We should note that St. Thomas does not place this comparative act, by which the relation of universality is found, in the act of comparison by which something is attributed to another as a subject, but in the act by which it is ordered to something as a term. This is clear from the words cited, and especially from the cited passage in Summa theologiae I, reply to objection 1, where he says that “the proper notion of what is called ‘toward another’ is not taken through comparison with that in which the relation inheres, but through reference to another.”

From this we derive the BASIS for the conclusion stated. To find a relation through an act of the intellect, some comparison to a term is required—not a compositional comparison that attributes a predicate to a subject or makes something included in it. Therefore, the relation is simply an ordering to a term.

The major premise is clear: a relation is not something absolute, but something whose whole being is toward another. Therefore it must necessarily be apprehended precisely in what distinguishes it from the absolute. It differs from the absolute by comparison with another; therefore it requires a comparative act, that is, a comparison and ordering of the known nature to a term.

The minor premise is proved as follows. Comparison by composition and attribution either attributes the known nature to the inferiors or attributes the relation to the very known nature as a subject denominated by that relation.

The first is irrelevant, both because a compositional act can formally effect only the relation of predicate to subject, which is quite different from the relation of a universal to its inferiors, and because predicating a nature of its inferiors, as occurs in a proposition formed through an act of composition, merely makes the predicate actual. Therefore it presupposes what is predicable, since something is called predicable before it is called a predicate. Predicability is a property of universality or pertains to it. Therefore its relation precedes compositional comparison and formal composition, just as the relation of predicability precedes the relation of predicate as potency precedes act. The same reasoning proves that the universal does not consist in an act that produces inclusion, since this inclusion is either actual inclusion in the inferiors or merely aptitudinal. If the former, it is inclusion through actual predication or contradiction, which necessarily presupposes what is contractible and predicable, and thus the relation of predicability and contractibility. If the inclusion is aptitudinal, then the nature is only apt to be included, not actually included in the inferiors; and the aptitude to be included is the same as the aptitude to be contracted and predicated, since inclusion comes about through contraction. Therefore, before inclusion there is a logical universal: namely, the reference of an aptitude to be included.

If, however, one proposes the second, it is clear that attributing the relation to the very known nature as a subject denominated by it is not a formal consideration of the relation to its term, but of the relation to its subject, under the aspect of “in,” not “toward.” This consideration is common to every accident, even an absolute accident that has a subject; it is not proper to relation as relation. Consequently, it does not formally constitute the relation but presupposes it: it places it in the subject rather than ordering it to a term. It is therefore unnecessary, not only for the relation of universality but also for other second intentions, such as the relations of syllogism and proposition, to know the relation in a signified act and attribute it to the subject it denominates; that already presupposes a formed relation. It suffices for the extremes of the relation themselves to be known comparatively, one toward the other, in the very exercise of cognition—whether in forming a proposition, judgment, or syllogism, or in what pertains to the first apprehension. Through comparison itself these intentions are known as ordered and hence in the manner of a relation, even if they are not apprehended as an object known ut quod through a reflexive act, as we said in question 2, article 4.

THE ARGUMENTS ARE RESOLVED.

First, it is argued to prove that a comparative act is not necessary for formal universality: once the proximate foundation is posited, the relation immediately results; therefore it needs no act other than the one that posits the proximate foundation. But this foundation is posited before the comparative act, since it is unity and aptitude for being in many, which is obtained by the force of abstraction. Therefore universality, which is a relation, results from this act. For just as contraction alone suffices to make a nature singular, so abstraction suffices to make it actually universal.

The argument is confirmed: before the comparative act, the abstracted nature is actually denominated universal by that act; therefore it actually has the form of the universal, which is a relation. The consequence is clear, since a thing receives a denomination from its form alone, as the denomination is its formal effect. Therefore, if it is actually denominated universal, it actually has the form of universality. The antecedent is clear because, by the force of abstraction, before the comparative act the nature is not denominated singular, since it has been stripped of singular conditions; nor is it called merely nature in itself, since in itself it is neither one nor many, neither contracted nor abstracted. Therefore it is called universal.

THE REPLY is that in relations of reason a relation does not result merely from positing its foundation, because such a relation has being not by way of a result but through cognition. It is known only in order to its term, and that is what it means to be compared. Nor can abstraction be called a virtual comparison, since things that have being through cognition are not actually said to have being merely because they are virtually known; they have it only virtually and potentially. Since a relation is actually known only through a comparative act—it must be known in order to its term, to which it is compared or ordered—virtual comparison is only virtual cognition of the relation: the relation is not yet known as ordered to its term, but only as abstracted. Contraction produces the metaphysical singular, just as abstraction produces the metaphysical universal, not the logical universal, that is, the universal related to its superior.

In reply to the confirmation, we say that before the comparative act the nature is denominated metaphysically universal, not logically universal: proximately and fundamentally, not formally. Having the proximate foundation of universality is neither being singular, since the nature is stripped of individuals, nor taking the nature merely in itself, since this foundation is not an essential predicate of the nature. Rather, it is being metaphysically universal. Although this is not the form of universality with respect to universality as a second intention, it is the form with respect to the proximate foundation of that relation, which is founded on unity and aptitude for many. These are things of reason. Thus the name “universal” is indifferent between the foundation of universality and the relative form itself, just as God is denominated Lord from the power that is the foundation of the relation of lordship, and as one is denominated an index, teacher, or sign by designation and imposition ad placitum, not only by the relation of reason founded on that imposition and designation. Hence, if a universal existed on the side of things in the way Plato proposed, it would be a metaphysical universal considered in a precise unity; it would nevertheless ground a relation to the inferiors themselves—predicamental if the inferiors existed, or merely according to being said if they did not.

Second, it is argued to prove that a comparative act is required by way of inclusion—which some call positive abstraction—or by way of predication and composition. For the logical universal must consist in a reference of the abstracted nature to its inferiors; therefore the inferiors themselves must be known, since a reference cannot be known without its term. But the inferiors are constituted by inclusion of their superior. Therefore the logical universal necessarily requires inclusion in its inferiors; otherwise it would neither have nor regard them, since they are constituted through this inclusion.

The argument is confirmed. The comparative act either understands the nature to be in many by actually attributing and predicating it of them, or understands only that it is apt to be in them. If the first, this is predicative comparison, since the nature is not actually understood to be in many except by predicating it of many. If the second, an act of abstraction suffices to constitute this relation, since the relation is an aptitude for many. Therefore the act that suffices to posit the aptitude suffices to posit the relation of aptitude. But the aptitude is posited by the act of abstraction, which is virtually a comparison precisely because it leaves the nature apt for the inferiors themselves. For just as by its aptitude it is virtually in them, so it is virtually compared to them; and so on. According to those who hold that judgment consists only in attending to two extremes or concepts, it manifestly follows that this comparison occurs through an act of judgment, since comparison without attention to the extremes is impossible. But this premise is wholly false, for something can be conceived relatively even before any judgment, just as we know relations and define them through simple apprehension.

THE REPLY to the principal argument, which is the whole basis of Martínez’s position, is the solution given above, preceding question, article 5: the universal regards its inferiors not formally by inclusion, but rather by presupposing their exclusion and abstraction from them. Thus, although the inferiors in reality are constituted only by including the superior nature, formally, in the notion of an inferior, they are constituted not by inclusion but by subjection to the superior nature, while presupposing that in reality they include it. Thus, just as the superior, though identified with the inferior, is known as superior without it, so the inferior, though it includes and is identified with the superior, is regarded by the superior not through inclusion in it but through subjection to it. Hence, in the concept of the inferior insofar as it terminates the superior’s reference, the inferior’s inclusion is not expressed, although it has that inclusion in reality; only its inferiority and subjection are expressed.

If you object: Then the intention of genus cannot formally be given without the intention of species, nor species without the intention of individual, since these are correlatives. Thus the reference of genus cannot stand without its formal term, which is species, nor species without individual, which is the term of species.

The reply is that the argument proves that the intention of genus cannot formally be given without the species being known as subjectable, and likewise species without individual being known as subjectable; in this way they take on the character of the formal term of the relations of genus and species. Yet the intention of genus can be given without the intention of species being known as predicable, and the intention of species without the intention of individual being known as predicable of only one.

In reply to the confirmation, aptitude can be considered in two ways, negatively or positively. Negatively, it is mere non-repugnance to being in many; this is not known through a comparative act but follows from the absolute act of abstraction itself. Positively, it signifies an order to those for which it has aptitude. This order or relation is not formally found unless the aptitude itself is conceived with some comparison and order to its term. Therefore, the comparative act that formally constitutes the universal is not the act by which it is actually attributed to many, but the act by which it is conceived as apt to be in many—not aptitude taken as mere capacity or non-repugnance, which is something absolute, but aptitude taken as ordered and positively looking toward the many themselves. For this, it is not necessary that the relation itself be known as in a signified act, as a thing known ut quod. It suffices that some extreme be actually known as compared to another and in the manner of something relative; for in this very exercise the comparison and relation itself are known.

Finally, one might object to prove that abstraction does not make the nature metaphysically and fundamentally universal. Through abstraction, the nature is known only according to what belongs to it in its essence, with individuals removed. Therefore the nature does not become universal but is merely placed in a state of solitude, or considered in itself. Again: according to St. Thomas, the intellect knows a nature only as abstracted from individuals. Therefore precision itself cannot give universality, since universality belongs to the nature as known and consequently as abstracted; therefore precision, or cognition of the nature, comes before universality. Finally, universality is a relation in its being; therefore it is obtained only through the act by which the order and relation itself are apprehended. But the act of abstraction is absolute: it neither compares nor orders one thing to another.

THE REPLY is that all these arguments prove that universality formally as a relation is obtained only through a comparative act. Nevertheless, its foundation, which is the unity of precision and aptitude, is obtained precisely by the nature’s being known as abstracted in the manner of one. This does not presuppose a nature already known; precision itself makes it known. If it is not known in the manner of one, we are not speaking of this case or this precision, since such cognition abstracts not only from individuals but from every mode of unity, and leaves the nature in a state of pure solitude, considered in itself. But the abstraction that knows the nature in the manner of one makes the metaphysical universal. Perhaps it is impossible to conceive the nature in such a way that, from the very mode of understanding, it has neither unity nor plurality, although in itself, on the side of the thing known, it is neither one nor many by the force of its essential predicates. Whatever the case may be, at least the act that abstractively conceives the nature in the manner of one gives unity to the nature itself through the mode of knowing. Yet this act is not comparative but absolute, since it does not yet regard the inferiors as a term to which it is compared, but as a term from which it is separated.