Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

Because the universal, as was said in art. 1, is defined as what is one in many, or apt to be in many, it is necessary to explain how unity belongs to it and how aptitude to be in many belongs to it. In this article we shall treat unity, and in the next, aptitude.

Two things, then, must be noted for the present difficulty: First, what we understand by the term “formal unity.” Second, wherein lies the point of difficulty and controversy between the school of St. Thomas and that of Scotus concerning the distinction of this formal unity from individual unity according to the nature of the thing.

Generally speaking, unity formally signifies an absence of division, and denotes something positive on the side of entity and something negative on the formal side, which it adds to entity, as may be gathered from St. Thomas, Ia, q. 9, art. 2, ad 2; and in I, dist. 19, q. 4, art. 1, ad 2¹, and dist. 24, q. 1, art. 3². Hence a different mode of unity usually results from a different way of denying division. For there to result, however, not merely a different mode of unity but an absolutely different unity, not only must the mode of denying division vary, but the very nature of the positive entity must also be made different, since absolute diversity of unity produces multitude: for several unities are a multitude. Where there is no multitude, however, there is no absolutely different unity, although there may be a different respect in which division is denied. For multitude is composed not of negations but of entities as regards the positive element included in unity, as St. Thomas teaches in the cited place, q. 11 of the First Part.

When, therefore, we here distinguish in the same thing formal, individual, and universal unity, and formal unity is in turn distinguished into generic and specific, we are not distinguishing several unities absolutely and on the side of positive entity, as though they constituted some multitude; we are distinguishing only different respects in which division is denied.

For when formal principles, which constitute quiddity, and material principles, which pertain to individuation, concur in some thing, if the formal principles are undivided—that is, division does not occur according to the formal principles—then the respect of lacking division, insofar as it is on the side of such principles, is called formal unity. This can still vary according to variation in the formal principles, for some formal principles are generic and others specific. If the lack of division is according to generic principles alone, it is called generic formal unity; if the lack of division is according to specific principles, it is called specific formal unity.

When, however, there is a lack of division not only on the side of formal principles but also on the side of material principles, which pertain to individuation, then that unity is numerical or individual. And since quiddity and individuation concur together in one individual, it is not incompatible for formal unity also to be found conjoined with the unity of individuation. But if it is separated by the intellect from all individuation, and that formal unity then remains as abstracted, it is called universal unity or unity of abstraction.

Second, we must note that the point of controversy and difficulty between the school of St. Thomas and that of Scotus in this matter does not consist in formal unity's being found in the thing so distinct from singular unity that it either exists separated from it (for that would be to posit Plato's Ideas), or is positively found common to numerical unities—for Scotus never said this. His view consists only in two claims:

First, that there is found on the part of the thing a true and proper unity accompanying the nature considered in itself, which is neither numerical nor universal, but less than numerical, because it is not undivided to the same degree as numerical unity. Hence this unity, since it belongs to nature considered in itself, is found in every state. In the state of abstraction it remains conjoined with universal unity; in the state of singularity it remains conjoined with numerical unity. Nevertheless, it is a true and proper unity even when considered in itself, and not merely by reason of the numerical unity or abstraction conjoined to it. Rather, in each individual there is numerical unity and, in addition, formal unity; and in each universal there is that same formal unity together with unity of abstraction.

Second, this formal unity, which belongs to nature in itself, can be called universal negatively, that is, non-singular, because of itself that nature, and consequently its unity, is neither singular nor positively universal, as St. Thomas also holds in ch. 4 of On Being and Essence³. For the nature's quiddity-predicates and proper attributes, one of which is unity, belong to it only in that state. See Scotus, II, dist. 3, q. 1, § But against and § To the question.

This formal unity is said to belong by the nature of the thing because it follows upon the principles of the nature in itself, and not through the intellect's contribution.

Some, however, wrongly interpreting Scotus, said that this unity belongs to nature in the state of isolation and in itself in such a way that it does not descend to individuals nor occur in them, but that, once that state of isolation is excluded, this unity vanishes. Others, by contrast, wished this formal unity to be found in singulars in such a way that it retains there something of universality, at least imperfectly and incipiently, insofar as it exists actually in many, though not according to an aptitude by which it can be predicated of many. On this, see the Coimbra commentators, q. 4, On the Universal, art. 3.

NEVERTHELESS, FOR THE RESOLUTION I SAY FIRST: No unity belongs to nature in itself that is positively and absolutely a unity less than numerical unity, and that is found on the part of the thing conjoined with numerical unity; rather, only negative formal unity belongs to it, that is, a negation of division according to formal principles.

Thus, in the thing there is found the agreement and likeness of one nature with another in quiddity-predicates, which the intellect takes up under the aspect of unity; and consequently, in each nature there is found a negation of division according to formal principles. Nearly the whole equivocation in this matter lies here: it is thought that the negation of division occurs only through true and positive unity, although it can also occur through agreement alone. For things that agree are not divided by virtue of the principles according to which they agree. This is taken from Cajetan, ch. 4 of On Being and Essence, q. 6. There⁴ St. Thomas himself teaches this, saying that nature in itself is neither one nor many. “If it is asked,” he says, “whether this nature can be called one or many, neither should be granted, because either is outside the concept of humanity, and either can accrue to it. For if plurality were of its nature, it could never be one, although it is one insofar as it is in Socrates. Likewise, if unity were included in its understanding and nature, then the nature of Socrates and Plato would be one and the same and could not be multiplied in many.” So St. Thomas.

From his words is taken the BASIS of this conclusion: Positive unity is absolutely and simply unity when it not only denies division on one side, but leaves the subject or entity undivided on every side and determinately reduced to unity. For if it leaves room on some side for division or plurality, it is one only in a qualified respect, not simply. To remove unity simply, it suffices that division or plurality has not been removed on some side. But nature considered in itself does not have division removed on every side, nor does it remove all principles of plurality. Therefore it does not have positive and simple formal unity.

The minor premise is proved: nature considered in itself is indifferent to plurality or unity and claims determinately neither for itself, as St. Thomas's reasoning proves. For if it had plurality, it could never be one; and if it had unity, it could never be multiplied, because what belongs to nature under that state belongs to it essentially: it is the only state in which quiddity-predicates are considered, and whatever belongs there belongs quidditatively. Therefore, in that state nature is indifferent to being determinately one or determinately many, since by its quiddity it is incompatible with neither. Therefore it does not yet have a state in which it removes and is incompatible with every principle of multiplication and division; therefore it does not yet have positive unity.

Nor is it an objection that it has a negation of division according to formal principles, because this proves only that it has negative unity. For this reason St. Thomas says in Opusculum 42, ch. 7⁵, that “in nature itself, taken absolutely, there is a certain unity, since its definition is one.” This unity is not simple and positive unity, but unity as regards the negation of division according to formal principles, which pertain only to the definition. But concerning positive and simple unity, St. Thomas adds there what he had said in the cited place of On Being and Essence: “no unity, nor even plurality, belongs to the understanding of nature taken absolutely, because either can accrue to it.” This is further shown because that negation of division according to formal principles affects nature considered in itself in such a way that, when nature is multiplied in the state of individuation, the negation itself is also multiplied and does not remain one in all individuals. This is a sign that it did not make nature one simply, since the negation of formal division is found there in such a way that there is still indifference as to whether that very negation is multiplied or remains one. But how can a negation of indivision that is itself not yet one make nature simply one? Nature therefore does not have every kind of unity on the side of the subject until such a nature is found in some state, either of singularity or of universality.

I SAY SECOND: Although nature in itself is negatively common, and the negation of formal division that belongs to it is also negatively common, that is, non-singular, nevertheless this unity, whether positively or negatively common, is never found absolutely and actually in the thing outside the intellect.

THE REASON FOR THE CONCLUSION IS that, by the very fact that nature is posited outside the intellect, it takes on the state of singularity, since nature cannot be found without singularity; otherwise a Platonic nature would be posited outside the intellect. But when singularity is posited, not only is positive commonality removed, which nature acquires in the intellect (this Scotus too admits), but negative commonality is removed as well. First, because one negation does not remain in those singularized natures. For just as the specific nature itself is multiplied, so too is the negation of formal indivision that accompanies nature. Second, because to be negatively common is not to be divided in many. But once singularity is posited, it remains divided in many, since nature is truly and positively multiplied; this is to have the opposite of that negation by which it is negatively common, namely, not divided. Therefore it does not remain negatively common—just as, once light is posited, the air does not remain negatively dark, because the very illumination expels the absence of light.

YOU WILL SAY: That singular nature outside the intellect still does not have that multiplication of itself, but from the added state of singularity. Therefore, in itself, that nature always remains negatively common, and formal unity belongs to it as negatively common, insofar as it is of itself, notwithstanding the multiplication.

We answer that it does not suffice for a nature not to have some form or accidental predicate of itself in order to say simply that it does not have it, when in fact it belongs to it absolutely, even if it does not belong to it through what is proper and intrinsic to it. For whiteness does not belong to man through what is proper to him, nor luminosity to air; yet when a man is white and air is illuminated, we cannot say that he or it is absolutely not such, on the ground that it does not have this intrinsically. So, although nature in itself is not multiplied and divided, and consequently is negatively common, that is, non-singular, nevertheless, if it is actually singularized and multiplied, it no longer remains negatively common, although by what is proper to it it is neither common nor singular—and this is always the case for it. Thus it must never be granted absolutely that nature in itself is negatively common in the thing; rather, it does not have singularity and multiplication in the thing through what is proper and essential to it—and this is true—although absolutely it does have them. For a thing to be denominated negatively common in the thing, it does not suffice that it not be singular of itself, where “of itself” pertains to its mode of not being; it must lack singularity itself.

BUT YOU WILL OBJECT, because St. Thomas says in ch. 4 of On Being and Essence⁶ that nature in itself is what is predicated of individuals; but this is proper to universality. Therefore nature in itself is universal.

We answer that, as Cajetan rightly observes there in the third doubt, in nature there is a difference between the thing that is predicated and the condition or state by which it is predicated. The thing that is predicated is nature in itself, for its quiddity is communicated to its inferiors. But the condition or state by which it is communicated is superiority; this does not belong to nature in itself. That it is the thing predicated of singulars is what belongs to nature in itself; St. Thomas says no more than this.

I SAY, FINALLY: Once the intellect has abstracted from singulars, nature and its formal unity have the character of determinate and positive unity, insofar as it is made a unity common to many—which is unity of abstraction—and, in like manner, when contracted to singulars it is made one by numerical unity. Hence formal unity is never found simply and positively unless it is unity of universality or singularity.

This conclusion is established by what has been said. Concerning this unity, St. Thomas says in the cited Opusculum 42, ch. 7⁷, that “there is another unity of nature, which it has from the intellect, in which all supposits agree.” He therefore holds that the nature to which formal unity belongs from the intellect receives determinate unity of reason. Likewise, in Opusculum 55⁸ St. Thomas says that “that nature which is universal insofar as it is in the soul is one in number,” that is, it is conceived under the aspect of positive unity, as though it were numerically one. And in Opusculum 29⁹ he says that “unity of reason remains to nature in its communication”; therefore it is not a unity on the part of the thing.

AND THE REASON is clear: nature conceived in this way represents only that in which all inferiors agree, as though it were one nature separated from them all. But if this nature existed on the part of the thing as it is conceived—just as Plato said it did—it would have positive unity on the part of the thing. Therefore it has that unity in the intellect, since it is conceived under unity. This unity is attributed to the nature known, although it has its foundation in the thing itself, because the inferiors resemble and agree in some one aspect. Nevertheless, that common aspect is made one “insofar as it has a uniform character in relation to all the individuals outside the soul,”¹⁰ and by reason of this uniformity “many men are one man,”¹¹ as St. Thomas says. Hence this concept, being thus uniform, does not represent all individuals immediately and formally; rather, it directly represents one aspect in which they agree, and represents the inferiors themselves materially and mediately, insofar as they are those to which that aspect belongs and in which it is multiplied, the unity of abstraction having been dissolved.

From this you must not mistakenly infer that some explain the unity of the universal as nothing other than the essence of many, or the many themselves conceived in relation to some common operation, attribute, or accident. This is not true. For if the unity of common nature were nothing other than several things ordered to one operation, I ask: how are that operation, accident, or attribute one? If they are one only through likeness, they are just as much many as the things of which they are attributes, for things or natures too are alike. But if on account of this likeness the intellect takes the operation or attribute as one, why does it not do the same with nature itself, which has that same likeness?

THE ARGUMENTS ARE ANSWERED.

First, it is argued by the common argument: Peter and Paul are not formally distinct on the part of the thing as Peter is distinct from a horse; therefore they are formally one on the part of the thing. This is not numerical unity, because they are not one in numerical unity but distinct. Therefore there is on the part of the thing a formal unity distinct from numerical unity.

It is confirmed: as many ways as one of a pair of opposites is said, so many ways is the other said. But there is a formal distinction on the part of the thing, different from numerical distinction, just as man and horse are formally or specifically distinct in the thing. Therefore there is also in the thing a formal unity distinct from numerical unity.

WE ANSWER that the argument proves Peter and Paul have formal unity on the part of the thing fundamentally and as regards negative unity, but not formally and according to positive unity. We call agreement or likeness fundamental unity, for this is found on the part of the thing, since Peter and Paul are alike in nature. But this agreement is not unity, since agreement rather presupposes distinction between the terms. Likewise, when we say that there is a formal negative unity, we do not mean that the same negation is in two individuals, since their subjects are different and consequently there are two negations; rather, each negation has one effect, namely that the nature is not divided according to formal principles. In the same way, two individuals of different species are less one than individuals of the same species—that is, they agree and resemble one another less—not that either is more or less one by a real and positive unity.

To the confirmation we answer similarly: it proves that just as there is a formal distinction in the thing, so there is a formal unity in the thing. But in the thing it is always conjoined with numerical unity, not apart from it. It suffices, however, that there be in the thing a negative or fundamental unity, which is only agreement and likeness, for this too is opposed to formal division.

Second, it is argued: Nature in itself, as distinguished from individuation, is a true entity; therefore it has a true and formal unity, which is a property of being. Agreement or likeness does not suffice, since a property of being is not agreement or likeness but unity. Therefore unity belongs to nature in itself. It is clear that numerical unity does not belong to it; therefore formal or specific unity does.

It is confirmed: likeness and agreement themselves are relations founded upon unity, not upon the unity of agreement and likeness, for then agreement would be founded upon agreement. Therefore they are founded upon true and proper unity. Not numerical unity, since this is not found between Peter and Paul; therefore they are founded upon formal unity.

WE ANSWER that unity is found in nature in the same way as nature itself is found. For if nature is considered without any determinate state, but only according to its essential principles, it is not considered as having unity determinately and positively, but only negatively, that is, it is not different according to those formal principles. In the thing, however, because it has a singular state, it also has determinate positive unity—not a unity by which several singularized natures are said to be one, but one by which each nature has its own unity, and, in the specific and formal aspect, agreement and a negation of division according to those same formal principles.

But if you insist: In nature in itself there is positive entity, and there is a negation of division with respect to formal principles; therefore there is full and perfect unity, since this consists in nothing other than entity together with a negation of division.

We answer that in such a nature there is not a negation of division absolutely and determinately, such that the negation of division is by the positing of unity—for in this way it is called an absolute negation of division—but only under that reduplication, “insofar as it is according to the formal principles”: that is, it is not divided on that side, although it does not yet positively have unity. And because this leaves it indifferent to having plurality or unity absolutely and according to material principles, it does not remain perfectly and simply one, but only negatively, that is, under the reduplication just described. In this way some unity, at least negative unity, always follows upon being in whatever state.

To the confirmation we answer that likeness and agreement, as relations, are founded upon agreement and likeness as their foundation. Thus agreement is not founded upon agreement, but the relation of agreement is founded upon unity itself, that is, upon the very uniformity of the agreement, which is the foundation of such a relation. It is not founded upon unity simply, for this is rather incompatible with agreement, which is a conformity of many.

Third, it is argued: Formal unity is that by which something is said to be formally one, or one in species. But an individual without another's company is not said to be one in species; for we do not admit that Peter is one in species unless we add “Peter together with Paul or Francis.” Therefore formal unity is not multiplied in each individual, but makes several individuals one with one another. Hence St. Thomas, IIIa, q. 2, art. 5, ad 2, says that human nature does not have the character of a species insofar as it is in one individual, but insofar as it is abstracted from every individual or insofar as it is in all. Therefore St. Thomas holds that the unity of the species is found in all individuals, and not in each separately.

WE ANSWER: I distinguish the minor: An individual without another's company is not said to be one in species with respect to likeness and agreement, I grant; with respect to indivision and specific unity, I deny. For the nature that is in one individual, even insofar as it is in that individual, has a negation of specific division according to formal principles. But without the company of another individual it does not have agreement and likeness with another individual. Thus the formal unity found in each individual is said to make several individuals one with one another because it makes them agree in one thing, or have likeness and agreement in nature.

To the passage of St. Thomas we answer that human nature has the character of a species insofar as it is in all individuals in the way in which the universal is said to be in many: either fundamentally, because one nature is abstracted from many, in which it is found one not through identity and unity simply, but through agreement and likeness; or because it is in many through predication and aptitude to be in them. But this it has through the intellect, and not in the thing through a unity common to many.

Finally, it is argued: Nature in the state of isolation has everything required for it to be free of singularity, since it is neither contracted nor determined nor, in itself, incommunicable. Therefore in itself it is communicable, not singular and contractible; therefore the unity it has is a unity common to many.

WE ANSWER that, once that reduplication “in itself” is posited, one cannot infer from a negative to an affirmative by changing the predicate from finite to infinite; nor can one infer from the absolute negation of one to the positing of the other. Thus this inference is invalid: Nature in itself is neither singular nor determined nor incommunicable; therefore in itself it is communicable or universal, etc. For in itself it is neither one nor the other, but capable of either. It would be a contradiction, however, to say: Man in itself is not communicable; man in itself is communicable. But the second proposition is false, while the first negative proposition is true; from the removal of one, the positing of the other follows, provided the same reduplication or reference of the particle “in itself” is preserved throughout. Nevertheless, affirmative statements must never be made determinately of that nature in itself, so as to say that it is communicable or that in itself it is incommunicable; rather, the negative is always true: in itself and essentially, it is neither one nor the other.