Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

Difference taken in common seems to be nothing other than a form that makes things differ, or insofar as it has the function of making them differ. Thus Porphyry says in the chapter “On Difference” that, universally, every difference, when added, makes something altered. From any form that makes things differ there therefore arises a twofold relation or order: one to the subject or thing it makes differ, and one to the term or extremes from which it makes it differ. Difference is a kind of separation and segregation, so it has a subject that it segregates and a term from which it separates.

Some relation must necessarily be understood in the very nature of difference, just as some relation to the agreeing and similar terms is understood in the nature of agreement, its opposite. The relation of difference to the subjects to which it belongs constitutes a difference predicable of them, and so leads to difference taken logically or predicatively. The relation of difference to the things from which it differs constitutes the nature of difference in its function of segregating and separating from another; this belongs to the quiddity of difference considered metaphysically, or taken in common.

Since difference is said to be a form that makes things differ, we must observe that differing, being diverse, diversity, and difference are distinct. Things are called diverse when they differ not through something added on, but through themselves, as things that are primarily diverse. Things are said to differ when they differ from another through something added on; thus they do not differ in their entirety, but agree in one respect and differ in another. Every difference therefore presupposes some agreement, while things with no agreement are primarily diverse, according to Aristotle, Metaphysics X, ch. 3,¹ and St. Thomas in his commentary there, lect. 4,² as well as Summa theologiae I, q. 3, art. 8, ad 3, and q. 90, art. 1, ad 3. The most general genera or categories are said to be primarily diverse, as are differences themselves, which do not properly differ but are principles of differing, and differ through themselves without agreeing in any univocal higher kind.

With these points established, THREE THINGS MUST BE EXPLAINED about the proposed division. First, whether the division is adequate. Second, what is divided and what the members of the division are. Third, whether the division is analogical or univocal.

On the first point: Nearly everyone agrees that the division is adequate, with very few exceptions. The reason is clear: it is made through members that exhaust and match the whole divided. For every form that makes things differ is either essential and intrinsic or accidental. If essential, it is maximally proper. If accidental, the accident is either separable or inseparable. If inseparable, it is a property and makes things differ in the proper sense. If separable, it is common to others as well and makes things differ in a common way. A common difference is so called because it is not so attached to one thing and proper to it that it cannot be found in another; or because we commonly grasp difference through sensible accidents, which are common, such as motion, color, and shape. A difference that is proper to an inseparable accident is so called not only with respect to a property flowing from the intrinsic and quidditative principles, but also with respect to an accident that inheres immovably, even if it does not flow from the principles of essence. Indeed, Porphyry uses such examples when explaining proper difference: “a scar from a wound,” he says, “the snubness of a nose,” and so on.

This readily resolves the question some raise about a proper attribute that makes things differ, yet does so neither essentially, since it is not an essential and constitutive difference, nor accidentally, since things with different attributes differ essentially. Likewise, individual differences in substance make one thing differ from another, but not essentially, since otherwise they would be specific differences; nor accidentally, since two individuals differ substantially. Therefore, they conclude, the division into essential and accidental is not adequate.

The reply to the first point is that a proper attribute formally makes things differ only properly, but virtually, or by inference, makes them differ most properly, as Cajetan rightly notes in this chapter “On Difference.” For it is an effect that follows upon the most proper difference, and an essential difference is rightly inferred from a difference through a proper attribute. Formally, however, it makes things differ only accidentally in the proper sense.

To the second point we say that among his examples of common difference Porphyry gives the difference between Socrates and Plato, which is an individual difference. St. Thomas also says in Metaphysics V, lect. 12:³ “Things that agree in species are distinguished only by accidental differences, as Socrates, who is white or just, and Plato, who is black or musical.” Nevertheless, although some common differences occur between two individuals, such as those St. Thomas assigns, we must not deny that individuals of a substance also differ through proper differences, since they differ inseparably. These are not proper differences that signify the proper attributes of a nature, because two individuals belong to the same nature and species, but proper differences in the sense of inseparable differences. They can indeed differ substantially and yet not essentially, but accidentally—not by predicamental accident, but by the accidental fifth predicable. For the intrinsic difference in these individuals is substantial, since it is the singularity of the first substance that constitutes a substantial individual. Although an individual difference divides substance, it does not divide it formally and essentially, but materially. And although this division takes place in substance, it depends on accidents, through whose connotation and relation matter is made designated; individuation is taken from this as from a principle. Hence an individual is also required as a collection of its properties, which are certainly accidents and cannot be found in another.

On the second difficulty: First, it is certain that the difference divided in this division is not the difference that is the third predicable. That is one of the members into which it is divided, namely the maximally proper difference, which alone is predicated in what-sort essentially. It also follows that what is divided is not a second intention belonging to any of the five predicables, whether the third, fourth, or fifth. The intention of the third predicable is the intention of differing essentially; the fourth and fifth concern the intention of differing accidentally. Therefore, none of these is the divided item that comprehends all the members of the division.

The difficulty, then, is whether what is divided in this division is something real or something of reason—some form or intention. This is the same as asking what this function of making things differ is. For, as Cajetan rightly notes in this chapter, difference in this division is not taken materially for the very form that makes things differ, but for the formal character or function of making them differ. Some call this the intention of difference, because just as the agreement of many in one is a certain notion or intention, so too is difference insofar as it is difference. But to avoid confusing logical intentions with metaphysical formal characters, we do not call it an intention; we call it the formal character or function of making things differ. It consists in a relation to the things from which separation or difference occurs, just as agreement, by contrast, consists in a relation to things that are similar or agree.

Some therefore think that this function of making things differ is something of reason. They rely on the following basis: differing presupposes agreement, since things that are distinguished in their entirety are diverse, not different. Agreement between two individuals or two species, however, is a relation of reason, since they agree in something common that is common only through reason. Therefore, actual difference too, which necessarily presupposes such agreement, cannot be a real relation, but only one of reason.

Some go further and add that common and proper difference, although it is produced through accidents distinct from the subject, is nevertheless something of reason. The accidents do not make things differ by reason of their genus, in which they agree, but by reason of their differences, which necessarily presuppose agreement in a genus. Therefore, the formal character of difference that arises through such accidents is also something of reason. For example, whiteness and blackness make Peter and Paul differ accidentally not through the very nature of color, which is the genus of white and black, but through their disgregative and aggregative differences. They therefore make things differ insofar as they presuppose generic agreement and are taken by the intellect precisely under the aspect of difference; all of this is something of reason.

Nevertheless, we must say that in real forms, which make things differ in reality, this formal character or function of making things differ is not merely an intention or relation of reason, but a true and real formal character. I do not see how anyone could doubt this unless they denied the existence of real relations of dissimilarity and diversity, and of similarity, agreement, or equality. Who would deny that two white things have in reality a real relation of similarity, whatever that relation may be, which they lose when one of the white things is lost? A relation of similarity is a real relation and formal character of agreement in real forms. Nor is there any contradiction in one and the same entity grounding a relation of similarity with respect to one thing and of dissimilarity with respect to another, as white grounds similarity with respect to white and dissimilarity with respect to black.

The basis is clear: the effect of a difference that makes things differ is real and grounds a real relation, if its term exists in reality. Therefore, it is not something of reason.

The antecedent is clear, because in reality there is distinction and separation between things that are not wholly diverse but retain some agreement and similarity. For example, Peter and Paul are really distinct and separate while retaining similarity in nature. Therefore, just as the agreement and similarity they retain are real, so too are the difference and distinction they have in reality, since one is really not the other. Real agreement and similarity can therefore be presupposed and real distinction or difference be posited. Although this difference and agreement occur according to different formal characters, some formal characters, such as real relations, are also found in reality. According to these, something is said to be formally similar to or in agreement with another, or dissimilar and diverse; and the proximate foundations of these relations are likewise found in reality.

From this we see how weak the opposing basis is. First, it fails by treating actual agreement between Peter and Paul, or between horse and human being, as something of reason, although they are similar in reality and agree by reason of their similarity, and similarity is a real relation. Those authors equivocate by failing to distinguish agreement from unity: Peter and Paul are one through reason, but they have agreement and similarity in reality. Second, although the formal character of difference presupposes agreement, it need not presuppose agreement by way of an actual relation or be founded on such a relation. It is enough that it presupposes fundamental agreement; once this is presupposed, the formal difference is exercised whether or not a relation of agreement is also exercised.

This explains what is divided in this division. The formal character or nature of making things differ is divided into the mode of making them differ essentially and accidentally; these are the immediately opposed members. Accidental difference is in turn divided into a mode of differing separably, which is common difference, and inseparably, which is proper difference. This also includes difference through a proper attribute: it is an accidental difference, although it infers or presupposes the essential difference from which it derives. Individual difference is also included, since individual difference must be either essential or accidental, these being immediately opposed members. Some reduce it to the essential because it is substantial, as we have already said; others reduce it to the accidental because it is material and depends on accidents that designate matter. Nevertheless, it is certain that it falls under one of these members, just as it is certain that it is an essential or nonessential difference. It cannot therefore be denied that this division is adequate, as some wrongly deny.

On the third controversy, or difficulty—whether this division is analogical or univocal—THERE ARE TWO OPINIONS. Some think that the division is univocal when taken according to the very function of making things differ, as appears in Magister Cabero, tractate 3, disputation 4, doubt 2, because this function is exercised univocally and simply by any difference, whether essential or accidental. But if difference is taken for the thing or form that makes things differ, the division is of accident into subjects, since the mode of making things differ is like an intention or notion that accrues to things rather than constituting them.

This is pressed further: if this division were analogical in any respect, it would be because one difference makes things differ essentially and another accidentally. But this is no obstacle. The minor premise is proved as follows. Even so, essential and accidental predicables agree univocally in the nature of a predicable as such. Likewise, accidental and essential agreement or similarity agree univocally in the nature of making things similar and under the same genus of relation. Therefore, essential and accidental difference likewise agree univocally.

Nevertheless, Thomists commonly defend the opposite view. See Cajetan and Soto in their commentaries on the chapter “On Difference,” and the Carmelite Course here, disputation 7, q. 1.

Without a doubt, the basis is stronger. For we can consider four things in difference itself. The first is the form that makes things differ; the second is the segregation or division that results from such a form making things differ; the third is the relation of difference or dissimilarity itself; the fourth is the nature of the third predicable. The first three belong to difference taken in the first intention, or physically; the fourth belongs to logical difference and the second intention.

If we attend to the first, it is clear that a form that constitutes or makes something differ essentially or accidentally is not univocal. An essential form constitutes the being of a thing simply, while an accidental form constitutes it in a qualified sense. It makes things differ in the same way that it constitutes them. Therefore, just as an essential and an accidental form do not agree univocally in constituting—one constituting simply and the other in a qualified sense—so too they do not agree univocally in making things differ.

If we consider the second, it is likewise clear that essential segregation or division is division simply, while accidental segregation or division is division in a qualified sense. For things that differ only accidentally and agree essentially differ in a qualified sense and agree simply. Therefore, the nature of making things differ does not belong to them simply, but only in a qualified sense. Whatever may be the case about whether some accidental differences make two things differ really and simply, as two individuals differ under the same species, it is clear that many accidental differences do not make things differ simply. They do not make something simply other and another, or one thing and another, even though the numerically same subject remains, as in the examples Porphyry gives, where the same thing differs from itself in different ways, such as Peter when healthy differing from himself when ill.

If we consider the third, namely the relation of difference, it will indeed be univocal in the category and genus of relation, whether it is the relation of an essential or an accidental difference. But here we are not speaking of a division of difference as a predicamental relation; we are speaking of it as the very effect of differing and the nature of making things differ, which occurs simply in essential difference and in a qualified sense in accidental difference.

Finally, if we attend to the fourth, it is much clearer that accidental and essential difference cannot agree univocally. For only essential difference constitutes the third predicable, which is predicated in what-sort essentially. The others do not constitute it, because they are predicated in what-sort accidentally. Therefore, they cannot agree univocally in the nature of constituting the third predicable.

The reply to the bases for the opposing view is this: To the first, we say that the function of making things differ is not found in the same way in essential and accidental difference, as we have shown. Essential difference removes identity, which is the opposite of difference simply; accidental difference removes identity only in a qualified sense, since it can be exercised in the same subject under a different state or accident.

To the second, we deny the minor premise. In proof, the reason is that there is a disparity between being predicated essentially or accidentally and making things differ. Predicability does not follow the thing itself as it exists in itself, but as it exists in the intellect. The intellect applies a predicate to a subject, whether the predicate is essential or accidental; predication consists in this application. It likewise abstracts one from many in the same way, whether they agree essentially or accidentally. Universality is founded on this unity abstracted from many. All five predicables have univocally in common that they are one in many, as we said above, q. 6,⁴ But making things differ is not an effect that belongs through the intellect; rather, it distinguishes things in reality and makes one differ from another, since we are speaking of it here metaphysically. A form that makes things differ essentially removes identity simply, which is in the essence; accidental difference does not remove it but leaves it intact.

As for what is brought forward about the relation of similarity and agreement, the reply is that the relation of similarity and agreement is univocal in the genus of predicamental relation, whether the agreement is accidental or essential, just as was said of the relation of difference. But the very character or form that makes things agree, considered precisely insofar as they agree, is not univocal in essential and accidental agreement with respect to the effect of producing unity or agreement simply, as was said of difference.