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.

Having explained the character of difference as commonly understood and as it pertains to the metaphysician, we must now descend specifically to logical difference, which constitutes the third predicable and belongs only to difference in the strictest sense, which is essential. The other differences are not predicated essentially in answer to “what sort?” and do not constitute a predicable under the character of difference, but under the character of property or accident, to which accidental difference follows.

Porphyry gave FIVE DEFINITIONS of this difference, which is the third predicable. First: “Difference is that by which a species exceeds its genus.”¹ Second: “Difference is that which is predicated of many and of things differing in species, precisely as a ‘what sort?’”² Third: “Difference is that which by its own nature separates things that are under the same genus.”³ Fourth: “Difference is that by which individuals differ,”⁴ namely, in quiddity. Fifth: “Difference is that which not only separates things placed under the same genus, but contributes to the substance and account and is a part of that of which it is said to be the difference.”⁵

From these definitions we gather that three relations concur to constitute logical difference: namely, a relation to the genus, which difference contracts and to which it adds something; second, to the species, which it constitutes by contracting the genus and separating the species from the rest; third, to the inferiors of which it is predicated as a “what sort?” These are the very inferiors of the species, for it is predicated as a “what sort?” only of them. Since the definition that says difference is predicated of many, etc., explains more fully the character of a predicable and universal, we commonly use it in explaining the third predicable. These definitions do not concern individual differences, because they are not universals but individual differences, and therefore do not pertain to the third predicable, which is universal. Although an individual difference can be conceived in general as such, it is still not predicated essentially as a “what sort?”, because it is individual and presupposes the whole constituted nature.

Accordingly, DIFFICULTIES arise concerning these three relations that concur in the character of the third predicable, and they are to be examined in this and the following articles. Regarding the relation to inferiors, the difficulty is how the definition of the third predicable says that it is predicated of many differing in species, which belongs only to subordinate difference, and not of things differing in number, which belongs to atomic difference. Regarding the relation to the species, the difficulty is whether difference is universal with respect to the species it constitutes or with respect to the inferiors contained under the species. Regarding the relation to the genus, the difficulty is whether differences are contained under a genus, so that lower differences are contained under higher differences. We will resolve the first difficulty in this article, the second in the next, and the third in the last.

Concerning the first point, which explains the phrase “of many differing in species,” a common difficulty arises: why is this phrase placed in the general definition of difference, which includes both atomic and subordinate difference, when being predicated of many things differing in species belongs only to subordinate differences? One cannot say that Porphyry, Aristotle, and the other ancients were ignorant of or denied atomic differences. They were not ignorant of definitions and atomic species, since so many are defined in the sciences; how, then, could they have been ignorant of atomic differences, without which specific quiddities are neither constituted nor understood?

Indeed, Aristotle explicitly inquires how a definition should be given through genus and difference, and what the ultimate difference is, as is clear in Posterior Analytics II⁶, lect. 13 in St. Thomas⁷, lect. 14⁸, and lect. 15 at the end⁹, as well as Metaphysics VII¹⁰, lect. 12¹¹, and Metaphysics VIII¹², lect. 2¹³. Why, then, in the definition by which Porphyry explained difference as the third predicable, did he treat only of difference predicated of many things differing in species, which is subordinate difference? I think this question is not as important as the anxiety it causes some, especially since Porphyry did not omit an explanation of atomic difference in his other definitions of difference. For example, he says, “Difference is that by which a species exceeds its genus,” “that by which individuals differ,” and “that which separates things contained under the same genus,” and so on; these fit atomic difference very well.

Cajetan, commenting on Porphyry's chapter 3, thought that this definition could be adapted to atomic differences by explaining it not positively, but through non-repugnance, or negatively: namely, that it is not repugnant to difference itself to be predicated of many things differing in species. Thus it is not repugnant to quantity, by the very character of quantity, to be divided infinitely in a syncategorematic sense; yet it is repugnant to natural quantity—that is, quantity as subject to the form of a natural thing—because that form and natural thing would be destroyed if it were divided into such tiny parts. Similarly, it is not repugnant to atomic differences in themselves to be predicated of many things differing in species, although it is repugnant by reason of the atomic species they constitute. This can be understood further if we consider that any difference, insofar as it is a predicable predicated as a “what sort?” of many, has no other many or other inferiors than those its species has that is constituted by that difference. Hence, of itself, it does not state that it is predicated of many differing in species or number; it is determined to this by reason of what it constitutes. If the quiddity it constitutes is an atomic species with inferiors differing only in number, the difference that constitutes such a species will have the same inferiors. If what it constitutes is a subordinate species with distinct atomic species as inferiors, the difference will be predicated of those same things differing in species. Still, if the species constituted through the difference has no more inferiors distinguished in species, but only in number, it will be repugnant to the difference—not by reason of the difference itself, but by reason of the species constituted by it, which does not provide it with further inferiors.

Even so, Cajetan's explanation seems to me to need further softening. Adhering to Porphyry's own wording, I say that the words themselves must be carefully attended to. He said that difference is “that which is predicated of many and of things differing in species as a ‘what sort?’” I stress that Porphyry did not say “that which is predicated of many things differing in species,” but “of many and of things differing in species.” Why did he insert the word “and” unless to distinguish predication of many absolutely from predication of things differing in species? Thus, in the phrase “of many,” he included all predicable differences, whether atomic or subordinate. In the addition “and of things differing in species,” he specifically indicated subordinate differences, as if to say: difference is that which is predicated as a “what sort?” of many, even if those many differ in species. Thus the word “and” is equivalent to “also.” This was necessary to explain fully the nature of difference insofar as it is predicated as a “what sort?” Difference is predicated as a “what sort?” because it is predicated by way of actuality and determining form, for this pertains to the mode of qualification. It was therefore necessary to explain that even generic, or subordinate, differences are predicated as a “what sort?” although they may seem to have the character not of act but rather of potency with respect to their species; they are still predicated as a “what sort?” because they are predicated by reason of the generic form they signify. Accordingly, Porphyry's meaning is: “Difference is that which is predicated of many as a ‘what sort?’, even if those many differ in species.” This is the force of the word “and” inserted in the definition when he says “of many and of things differing in species”—that is, “also” of things differing in species.

Understood in this way, Cajetan's view, which many distinguished authors follow, has nothing harsh or difficult in it, but is highly subtle and especially suited to Porphyry's meaning.

Others say more simply and not implausibly that Porphyry defined only subordinate differences because they are more common and better known, while atomic differences are numerous and scarcely known. Once subordinate differences are defined, atomic differences are virtually defined by replacing “differing in species” with “differing in number.” This is especially so because Porphyry included atomic species in his other definitions of difference, as we noted above. Finally, this seems a sufficient reason for omitting atomic differences: they are explained in the definitions of species, with which they are convertible. Thus, just as in the treatise on the predicables he does not deal with the definition but with the species itself that can be defined, so too he does not deal with atomic difference, which is convertible with the definition and proper to it; he does, however, treat subordinate difference, because it constitutes a genus, which is not convertible with the definition of a species.

I omit the solution of others, who say that in the definition “of many differing in species” we should understand “of many differing in species” not from one another, but from others from whom they are specifically distinguished. On that account this definition also applies to atomic differences. For example, “rational” is predicated of Peter and Paul insofar as they differ in species not from one another, but from horse and ox, from which “rational” specifically distinguishes Peter and Paul. This solution, however, seems forced. For many are not said absolutely to differ in species unless they differ in species from one another, not from others. Otherwise one could also say they differ generically, because just as Peter and Paul differ in species from others from whom they are distinguished specifically, so they differ generically from those from whom they are distinguished in genus. Thus we meet a similar absurdity: why did Porphyry place only “of many differing in species” in the definition of difference and not add “of many differing in genus,” according to this explanation?

BUT YOU WILL OBJECT against the first solution: It is absurd to give a definition solely by something that stands to another in a non-repugnant way. First, a definition should explain the character of the thing defined positively, not merely by non-repugnance. Second, otherwise it could be defined through terms repugnant to it, as if a human being were defined as an irrational animal, because although “irrational” is repugnant to a human being insofar as human, it is not repugnant to it insofar as animal. One lowest species could likewise be defined through another, since although they are repugnant to one another according to their specific character, they are not repugnant according to their common and generic character. Therefore it is similarly absurd to define difference through what is not repugnant to it, including both atomic and subordinate difference, merely because being subordinate is not repugnant to difference in general.

This is confirmed because if the phrase “of many” signifies both many differing in species and many differing in number, why, when Porphyry defined species, did he explicitly say “of many differing in number,” but when he defines specific difference, does he not say so, but only “of many”? Also, predication of many belongs to all predicables; therefore this phrase does not specifically explain the third predicable.

The reply is that this argument does not militate against our explanation, because we have shown, in accordance with Porphyry's text, that the phrase “differing in species” belongs only to subordinate differences, while the phrase “of many,” taken absolutely, includes both atomic and subordinate differences, which are predicated of many things distinct either in number or in species. The phrase “and of things differing in species” is added to show how being predicated as a “what sort?” also belongs to generic differences. In Cajetan's strict sense, however, it is said that a definition of a species through the non-repugnance of something opposed to it is defective when such an opposite is truly found in that species, as is clear from the examples given. But when some nature or species is not repugnant of itself to something, while whether it in fact has it or is impeded from having it depends on something extrinsic, it is not defective to define it through non-repugnance. Thus quantity is defined as divisible to infinity, although this is repugnant to natural quantity. Since difference, property, and accident, which are predicated as a “what sort?”, have no other inferiors than those their subjects permit them to have, which they constitute or affect, it is necessary to understand their being predicated of many differing in species or number permissively, or as non-repugnant, insofar as concerns them in themselves. This holds even though it is repugnant to a difference as affected and bound to the atomic species it constitutes, just as it is repugnant to quantity as it exists in a natural subject to be divided to infinity. Hence in this solution it must be said that atomic and subordinate difference are not species of difference as such, nor is difference itself a genus of them. Rather, the difference between atomic and subordinate arises in difference from the thing it constitutes. If it constitutes a generic nature, it will be subordinate and predicated of many things differing in species; if it constitutes a specific nature, it will be predicated only of things differing in number.

But if you ask: If difference stands permissively toward either case, namely, being predicated of many differing in species or in number, why did Porphyry mention only things differing in species?

The reply is that when something is defined by non-repugnance and permission, the greater and more principal case should always be stated, because if it is not repugnant to the thing in the more principal case, this more strongly supports its being non-repugnant in the less principal case. Thus quantity is better defined by saying it is not repugnant to it to be divided to infinity than by saying it is not repugnant to it to be divided in the opposite way.

To the confirmation, it is said that the phrase “of many” does not mean only many differing in number, but absolutely many differing either in number or in species. It would be incongruous to say this of the second predicable, because the second predicable is predicated only of things differing in number. The third, however, admits both: it is predicated of many differing in number and of many differing in species, according to the species it constitutes.

To the other part of the confirmation, it is said that being predicated of many is common to every predicable, but being predicated of many as a “what sort?” is proper to the third predicable alone. This can then be divided into being predicated of many distinct in number or in species. Porphyry did not posit only the first phrase, but also added the second.

Regarding the final phrase, “as a ‘what sort?’,” note two things. First, when one says “as a ‘what sort?’,” the word “what” means essentially or quidditatively, not substantively. For that phrase “what” signifies both: on the part of the thing signified, an essential and quidditative character; on the part of the mode, its standing substantively and not adjectivally, as we explained in the question on Genus¹⁴.

Second, just as in natural things form or act is related to matter as to potentiality from which it is educed, and to the whole constituted from matter and form, so too difference first regards genus as potential, which it actualizes and from whose potency it is educed—not by physical eduction, as form is from matter, but by metaphysical eduction, as a determinate and actualizing character is educed from an indeterminate, confused, and actualizable one. It then regards species as a kind of whole constituted and formed by the difference itself. Hence difference stands as a “what sort?” with respect to genus, because it determines its confusion and potentiality. With respect to species, however, it is not called a “what sort?” because it determines the species' potentiality, but because it is a constitutive part of it, more actual and more determinate. You will find this teaching in St. Thomas, Summa theologiae I, q. 50, art. 4, ad 1, and On Created Spiritual Things, art. 8, ad 9¹⁵. From this it is clear that difference must always be more perfect than its genus, as act is more perfect than potency, the determinate than the indeterminate, and quality than what is qualified.

Since difference is convertible with the species it constitutes, and is predicated of individuals through the species, while species is universal, and since difference is said of the species equally and convertibly, it must be universal just as the species is. THE DIFFICULTY, however, is whether it is formally universal because it regards the species, or because of its formal relation to the individuals of that species.

There may also be a doubt concerning the inferiors of difference itself: which things are directly and per se inferiors of difference? For some are inferiors immediately under the difference itself, while others are immediately under the species and mediately under the difference. For example, “rational” can be predicated of Peter and Paul as inferiors of “human being”; it can also be predicated of this and that rational thing as inferiors immediately under it.

WE THEREFORE INQUIRE with respect to which inferiors difference is constituted as the third predicable.

I ANSWER AND SAY, FIRST: Difference is not formally a logical universal by its relation to the species, but to inferiors, although it concomitantly has an order to the species as a universal with which it is convertible.

THE REASON is clear, because the formality of universality is taken from the order to its correlative. The correlative of a universal formally is its inferiors: for a universal is related to many as a superior and as something contractible to inferiors. It is clear, however, that the difference of a species is neither superior to nor contractible by that species, since it is equal to it. Therefore it cannot be formally universal with respect to the species or be superior to it.

This is confirmed because something is universal and superior with respect to another when, upon being communicated to that other, it is contracted by it; and something is contracted to another when through contraction it loses universality and abstraction. But by being communicated to a species, difference does not become singular or lose its universality; rather, it preserves it. Therefore with respect to the species it is neither contractible nor superior. Hence one cannot say that it is predicated of the species as a superior universal, for it is not predicated of it as something higher, but as an equal of an equal. This equality therefore presupposes universality concomitantly, as the second part of the conclusion says; it does not formally constitute universality. For example, someone is not formally called a king because he is equal to the king; rather, because he has a kingdom and rules others, he is equal to the king.

IF IT IS SAID that difference is not formally universal by its order to the species because the species is not an inferior, but that it is universal radically, because by regarding the species and being convertible with it, it consequently regards the individuals contained under the species.

THE OBJECTION IS: The root of universality is the same as the foundation of universality, which is unity abstracted from many and an aptitude for many. But unity abstracted from many and an aptitude for them do not have their root in a relation to the species, because this relation is one of convertibility and equality, not superiority to those many things. Therefore difference is not radically universal because it regards the species, but because it is abstracted from and apt for those many things, which are its inferiors.

I SAY, SECOND: As the third predicable, difference does not regard this and that difference as its inferiors—for example, rational and this or that rational thing—but the inferiors contained under the species it constitutes. For example, rational regards Peter and Paul as its inferiors.

THE REASON is clear, because the predicability of the third predicable is “in answer to what sort.” Therefore only those things should be constituted as its inferiors with respect to which difference functions as a superior and as “in answer to what sort,” and can be predicated as “in answer to what sort.” But it does not function in this way with respect to this and that difference, although it does with respect to the individuals of the species. For when I say “this rational thing is rational,” the predication is not “in answer to what sort,” since no difference of this rational thing is predicated of it; rather, its whole and complete nature, whatever it may be, complete or incomplete, is predicated. Therefore this does not predicate a quality of it, but its quiddity, although it is not per se a genus or species, as we said above in the question on genus¹, since it is not contracted by other differences, which would entail an infinite regress. With respect to the inferiors of its species, however, difference is predicated as the account that qualifies their nature and functions as a superior. Therefore these are the inferiors of difference insofar as it is the third predicable.

THE ARGUMENTS ARE RESOLVED.

First it is argued against the first conclusion: “A human being is rational” is a predication of the third predicable; therefore, with respect to human being there is a universality of predicability just as there is predicability. But human being is not conceived there as an individual, but as a species.

The antecedent is certain, because this predication cannot pertain to any other predicable than the third.

This is confirmed because the third predicable has the species as its immediate correlative and through the species regards the individual contained under it; therefore it is called universal more by its order to the species than by its order to the individual.

The consequence is proved because a relation is more denominated by its order to an immediate correlative than by its order to a mediate one. The antecedent is proved because the third predicable formally, insofar as it is such, regards its correlative as “in answer to what sort,” but it does not immediately regard individuals, only the nature of individuals, which is the species; otherwise it would not be an essential quality if it did not immediately qualify the essence. Therefore its immediate correlative is the species itself, or the constituted essence; for that is an immediate correlative which is immediately constituted and qualified by difference.

THE ANSWER IS that the predication “A human being is rational” belongs to the third predicable in a material and metaphysical sense, not formally and logically. For what is predicated of human being is the reality that is the third predicable, but not under the formality and relation of the third predicable or third universal; thus it is more a third predicate than a third predicable. Nevertheless, it concomitantly retains there the universality of the third predicable, which it exercises not with respect to the species but with respect to individuals. This is like genus when it is predicated of an individual, as “Peter is an animal”: there it retains the account of genus, though it is not genus by its order to that individual, but by its order to the species. And when a proper attribute is predicated of specific nature, as “A human being is capable of laughter,” it does not exercise the account of a universal, although it predicates a nature receptive of the fourth predicable by its order to individuals.

To the confirmation, the antecedent is denied. As for its proof, the species is said to be immediately constituted by difference, and in the account of what is constituted it immediately regards difference as a metaphysical difference, not in the account of a universal or logical difference; in that latter account, its immediate correlative is its inferiors. But because difference regards them as predicable “in answer to what sort,” the order to the specific nature as constituted in this way by difference must be presupposed, so that it grounds predicability “in answer to what sort.” It is no contradiction for difference to have one relation to the species as constituted and another as a universal with respect to inferiors. Just as difference regards genus as contracting it and as comparing with it to constitute a species, so it regards the thing constituted by the relation of a constituent; that relation is nevertheless one of reason, because genus, difference, and species are not really distinct. The relation of difference to its inferiors as “in answer to what sort” is a relation of superior to inferiors, which nevertheless presupposes its relation to the species as constituted.

Second it is argued: Difference as the third predicable regards the species and individuals by the same relation or intention; but this relation, insofar as it touches individuals, is universal; therefore it is universal also insofar as it touches the species.

The consequence is clear, and the minor was granted above. The major is proved: First, in regarding the species, difference regards all things contained under it, since whatever is said universally is said of everything contained under it. Again, difference is predicated of the species and individuals under the same concept and predication; therefore it is under the same intention and relation.

This is confirmed because difference is predicated of the species equally and convertibly with it; therefore it is universal, since a species, being universal in itself, can be equaled only by a universal.

THE ANSWER IS: The antecedent is distinguished. If taken as the relation of difference as constituent to the species as constituted, difference regards the species and individuals by the same relation, because it constitutes the same thing in individuals as in the species, namely, nature. But if taken as the relation of difference as a universal and predicable formally and logically, it regards individuals and the species by different relations: it regards individuals as superior and the species as equal.

As for the proof, in regarding the species, difference also regards the individuals under the account of constitution by the same relation, but under the account of superiority and equality by different relations, although one is connected with the other. Thus its predication of individuals is universal, but its predication of the species is not.

To the confirmation, it is said that by being equal to the species difference does indeed have universality, but not with respect to the species to which it is equal; rather, it is universal with respect to individuals, to which it is not equal but superior.

It is certain, assuming that metaphysical grades are distinguished only by reason, as we determined above,¹ that the reality which is a difference and which is a genus are not really and materially distinct from one another, and consequently that the generic difference is not distinct from the specific difference in the same subject. But THE DIFFICULTY IS whether, according to formal predication, a higher and generic difference stands to a lower one in such a way that it is predicated of it and included in it as a predicate constitutive of it.

The resolution is negative, and is more common among the doctors. On this question see Sanchez here, book 3, q. 28; Cabero, treatise 3, disputation 4, doubt 3; and the Carmelite Course, disputation 7, q. 4. This is drawn from St. Thomas in Metaphysics III, lecture 8, section He objects to the present point,² and in Against the Gentiles I, chapter 17, because a genus cannot be predicated of a difference: a difference does not participate in a genus, as is said in Topics IV.³ For then the genus would be included in the differences and would become analogical, as we shall prove in the treatise on Analogy.⁴ The same reasoning applies to a generic difference, because it constitutes a genus and is a quidditative part of it.

The point is further explained. In contracting a genus, a specific difference also contracts the generic difference itself, from which the quiddity of the genus is constituted. But a difference that contracts a genus is outside the concept of the genus; therefore it is also outside the concept of the generic difference, since it contracts that difference by contracting the genus.

The minor premise is proved from the Philosopher, Metaphysics III,⁵ and St. Thomas there, lecture 8,⁶ because if a genus were included in differences, it could not be included in them as a contractible part, but only as the whole and complete difference. For a difference, being simple, is not composed of genus and difference, nor of something contractible and something contracting; otherwise there would be a process to infinity. If a difference consisted of genus and difference, then the difference by which it is constituted would in turn consist of genus and difference, and one would ask again about that other difference, since the same reasoning would apply to it. Therefore, if a genus or generic difference is included in a specific difference, it is not included as a contractible, generic part; rather, since the difference itself is simple and without parts, it will be the whole difference. The genus would thus be analogical, partly the same—insofar as the species agree in it—and partly diverse, insofar as it signifies the entire difference by which the species differ from one another. Similarly, if a generic difference is included in a specific difference not as a part (for a difference, being simple, lacks parts), the generic difference would be the whole and complete specific difference. It would follow that one lowest species differed from another by that very generic difference, with nothing else added; this is impossible. For in that case the same difference would constitute the genus insofar as it is a generic difference, and divide the genus because it would be wholly and completely the specific difference.

THE ARGUMENTS ARE ANSWERED.

First, an objection is made from Aristotle, who in Metaphysics VII, text 43,⁷ lecture 12 in St. Thomas,⁸ says that common differences are divided into other differences, as having feet, which is a difference of certain animals, is divided into having split feet and unsplit feet. Indeed, he says of the difference of split-footedness that a higher difference is predicated of it; for it is true to say that splitting of the feet is a kind of footedness. Therefore higher differences are predicated of lower ones. Again, at the end of Metaphysics X, text 23,⁹ lecture 9,¹⁰ St. Thomas shows that in genera under which contraries are found, intermediate differences are composed of contrary differences. Our foundation would then collapse—the claim that generic differences are not included in specific differences, because they are not composite.

This is confirmed by the familiar syllogism: Every human being is sensitive; every human being is rational; therefore some rational being is sensitive. It is in a valid figure, namely Darapti, and the premises are true; therefore so is the conclusion.

If you say that the conclusion does not entail that the rational is sensitive formally, but materially or identically.

On the contrary: first, that predication is formal: “The rational is sensitive,” just like the predications in the premises. Second, one can make the syllogism by adding the word “formally”: Every human being is formally rational; therefore some rational being is formally sensitive.

THE REPLY to Aristotle’s first passage is that common differences are divided into other differences not formally but materially—that is, not by reason of themselves, but by reason of the genus constituted by higher differences. For a genus cannot be divided by lower differences unless the very differences constituting the genus are also divided. Aristotle said instead that the higher differences themselves are divided, rather than the genus constituted by them, to show which differences belong to a genus per se and which belong to it accidentally. When a genus is divided by lower differences because, by its own intrinsic constituent difference, that genus is in potency to them, it is divided by differences per se and not accidentally. For example, by its very notion of being two-footed, a two-footed animal is in potency to having split or unsplit feet; therefore it is divided per se into these differences. But when a genus is in potency to inferiors not by reason of its own constitutive difference but from some other source, that division is not by differences per se but accidentally—for example, if a two-footed animal is divided into white and black. From this, however, one cannot conclude that those common differences are formally predicated of the lower differences. Rather, they are divided by them, not predicated of them. And because they are divided by them, what is divided is the genus as constituted by that difference, together with the difference itself. This is the plain explanation of that text given there by St. Thomas, lecture 12 cited above,¹¹ where he says that “in this way the difference ‘having feet’ is to be divided: among animals of this kind, one has split feet, another unsplit feet.” Here not only the notion of two-footedness, or the difference of having feet, but the animal itself is divided. Thus, when it is said that splitting is a kind of footedness, St. Thomas says, “this is the same as being contained under ‘having feet’”;¹² and so it is contained under footedness as differences are contained under the genus of which the generic difference is a part.

The reply to the second authority from Metaphysics X is similar: the intermediate differences there are not differences that are the third predicable, but opposed species under the same genus—not opposed as extreme contraries, but as intermediates. Such species are called intermediate differences because they differ or are opposed not as contraries at the extremes, but as intermediate contraries.

In reply to the confirmation, there is no difficulty in the first syllogism: the inferred conclusion “The rational is sensitive” is verified identically, not formally. Nor must a conclusion inferred from premises verified in the formal sense also be true in the formal sense; it suffices that it be true in the identical sense, as often happens in the third figure. For example: “All milk is white; all milk is sweet; therefore something sweet is white”; “This man runs; this man is just; therefore the just man runs.” These conclusions are true only in the identical sense. In the second syllogism, where the word “formally” is added, the reference plainly shifts because that word is applied differently. In the premises it makes the predication formal. In the conclusion, however, the extremes are verified identically, so that word “formally” has no place there. For a syllogism to be valid, it suffices that if the antecedent is true, the consequent also be true; it is not required that they be verified in the same sense and relation. The antecedent can be true according to formal predication, and the consequent according to identical predication, as we have seen. The reason is that the word “formally” must always be understood relatively and under some reference: what is formal with respect to one thing may not be formal with respect to another. Therefore the reference under which it is formal must remain unchanged whenever the word “formally” is added. A human being is formally rational and sensitive because he receives these predicates as formal attributes; but “the rational is sensitive” is verified only through identification in the same subject. They therefore cannot be verified under the same formal aspect; if “formally” is added, its reference shifts.

But if you object: This syllogism is valid in Celarent—“No rational being is formally sensitive; every human being is formally rational; therefore no human being is sensitive.” Here there is no shift in reference, and yet, even if “formally” is removed from the conclusion, it is false; therefore the proposed solution is insufficient.

The reply is that the reference shifts in the same way because of the word “formally,” which always gives a sense that is not absolute but qualified by some restriction, dependence, or relation—namely, insofar as the extremes fall under that formality and relation. What is not joined or in agreement under one formality and relation may nevertheless agree under another. Hence one cannot infer from a negation under one relation a negation under another relation, or an absolute negation. Thus, from the fact that the rational, formally—that is, under the concept and formality of rationality—is in no way sensitive, one cannot infer that, under the concept and formality of a human being, a human being, who is identical with the rational, is not sensitive. This variation of formal aspects and references must be carefully observed in many other subject matters. For example, this does not follow: “Given a precept, Christ here and now can act and not act, because he acts freely; and if he did not act, he would sin; therefore he can sin and not sin.” I say that it does not follow, because he can refrain from acting under the aspect and formality of action, as required for freedom, but not under the formality and concept of sin, as though sinning were part of the nature of freedom.

Finally, an argument is made: A lower specific difference has some common and higher predicates; for example, rational is living and is a substance, etc. Therefore it has something common to it as a genus and higher predicate; therefore such a generic difference or genus can be predicated of a lower difference.

It is confirmed that the concept of a difference admits some composition, since it has something potential, as a created thing, whereas only pure act is altogether simple. Therefore it can be resolved into a common or generic concept and a specific or differential one. But that higher concept is a subordinate difference, since a lower difference has a nature and operation subordinate to the generic difference. For example, neighing in a horse is a kind of sensitive operation, and is consequently subordinate to the common sensitive, which is the generic difference of animal.

THE REPLY is that those higher predicates belong to a difference not in a formal and direct line, but reductively and according to a certain relation or connotation. For the rational is called a substance or living, not because it is in itself a substance or living thing, but because the form from which it is taken is a principle of substance, of living things, or of another grade. A form is not that which something is, but that by which something is; just as matter and form are substances as principles of substance, or incomplete substances. Differences likewise are something incomplete in their own category. Thus it is not the complete higher notion, nor generic differences themselves, that are predicated of them, but the incomplete notion of that category—for example, substance insofar as it abstracts from the complete and incomplete—which is included transcendentally in everything that pertains to and is reduced to that category.

In reply to the confirmation, a difference is not composed of these things but is composed with them, since it is a part or functions as a part. A part is not simple like pure act, with the simplicity of perfection, but with the simplicity of negation—that is, it is not fully perfect. The simplicity of negation has more potentiality, because the part can be composed with something else by which it is perfected. Yet it is not composed by being resolved into several concepts of which it consists, except perhaps analogically, because being is included in all things, even in differences. Nor is a lower difference formally and directly subordinate to a higher one as to a genus, though it presupposes it, just as it presupposes the genus constituted by it. Thus: “Neighing is a principle of sensitive operation”—I distinguish: if “sensitive” is taken suppositively and materially, I concede; if formally and directly, I deny. That is, the sensitive is presupposed for something to be neighing, but neighing is not formally the sensitive.