Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

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.