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Aristotle · 1831

But the term "rational" added to it distinguishes us from them. We are rational, or the gods are; but the term "mortal" added to it distinguishes us from them. Those who further elaborate on differentia difference argue that it is not what separates things under the same genus, but rather what contributes to being, that is, into the "what it was to be" original: "τὸ τί ἦν εἶναι"; a technical term for essence, of which the thing is a part. For the ability to swim is naturally present in a man, even if it is a specific characteristic of man. We might say that of animals, some are naturally capable of swimming and others are not, thus separating man from others; but the ability to swim was one thing and a completion of the essence, not a part of it, but only an aptitude of it, because it is not a differentia in the way that those specifically called "specifying differences" are. Specifying differences would be those that make a different species, or those that are assumed into the "what it was to be." So much for differentia.
4 The proprium property is divided in four ways: that which belongs to a single species, even if not to all members, as healing or geometry does to man; that which belongs to every member of the species, even if not to it alone, as being two-footed does to man; that which belongs to one and all, but only at certain times, as greying in old age belongs to every man. The fourth is that in which belongs to one, and all, and always, as the ability to laugh does to man; for even if he does not laugh always, he is called capable of laughter by potentiality, not by the act of laughing always, but by his natural constitution; this is always innate to him, just as neighing is to the horse. These are called properties in the strict sense, because they convert; if something is a horse, it is capable of neighing, and if something is capable of neighing, it is a horse.
5 An accidens accident is that which comes and goes without the destruction of the subject. It is divided into two: the separable and the inseparable. The separable accidens is that which can be separated from the subject in thought, while being black happens inseparably to a crow or an Ethiopian, though it is conceivable that a crow could be white or an Ethiopian could lose his color without the destruction of the subject. They define it as follows: an accidens is that which can both belong and not belong to the same thing; whether it is a genus, a differentia, a species, or a property, it always exists by being in a subject.
6 Having defined all that was proposed—I mean the genus, species, differentia, property, and accidens—we must now state what commonalities exist among them and what properties. It is common to all that they are predicated of many, as has been said. But the genus is predicated of the species and individuals under it, and the differentia likewise; the species is predicated of the individuals under it, and the accidens of both species and individuals. For "animal" is predicated of both horse and ox, which are species, and of this horse and this ox, which are individuals. "Irrational" is predicated of horse and ox and of the particulars. The species, however, such as "man," is predicated only of the particulars. The property is predicated of the species, as it is a property derived from the individuals under it—for example, "capable of laughter" for man and the particulars—and "black" for the species of crows and the particulars, being an inseparable accidens. "Being moved" is predicated of man and horse, being a separable accidens, primarily of individuals, and secondarily of those things that encompass the individuals.
It is common to both genus and differentia that they are encompassing of species. For the differentia encompasses species, even if not all those that the genera do. For if "rational" does not encompass irrational things as "animal" does, it encompasses "man" or "god," which are species. Whatever the genus predicates as a genus, it also predicates of the species under it. Whatever the differentia predicates as a differentia, the species derived from it will also be predicated. For when "animal" is the genus, substance, ensouled, or sensory is predicated as a genus; but these are also predicated of all the species under "animal," down to the individuals. Of whatever differentia "rational" is, "using reason" is predicated as a differentia; this is not only predicated of the rational, but "using reason" will also be predicated of the species under the rational. It is common that when the genus or the differentia is removed, the things under them are also removed; just as when animal is not, neither horse nor man is, so when the rational is not, the animal that uses reason will not be. It is a property of the genus to be predicated of many, which the differentia, species, property, or accidens also are; for "animal" is predicated of man, horse, bird, and fish, while "four-footed" is predicated only of those having four feet, "man" only of individuals, and "neighing" only of the horse. Of the particulars, the accidens is similarly predicated of fewer. One must take the differences by which the genus is divided, not those that are constitutive of the essence, but the divisive ones. Furthermore, the genus contains the differentia potentially; "animal" contains the rational and the irrational; the differences do not contain the genera. Furthermore, genera are prior to the differences under them, which is why the removal of the genus results in the removal of the differences, but the removal of the differences does not result in the removal of the genus; even if all were removed, an ensouled, sensory substance might be conceived, which was the animal. Furthermore, the genus is in the "what it is," while the differentia is in the "what kind of thing it is," as has been said. Furthermore, there is one genus for each species—for man, it is "animal"—but there are several differences, such as rational, mortal, and capable of knowledge, by which he differs from other animals. And the genus is like matter, and the differentia is like form. So much for the commonalities and properties of the genus and the differentia.
Genus and species have in common, as has been said, being predicated of many; but let "species" be taken as species only, not as genus, in cases where the same thing is both species and genus. It is also common to them that they are prior to the things of which they are predicated, and that each is a kind of whole. But they differ in that the genus contains the species, and the species contains what the genus contains; for the genus is broader than the species. Furthermore, genera must be presupposed, which, when formed by specifying differences, constitute the species; hence, genera are prior by nature. They are removed along with the species, but are not removed by them; for if a species exists, the genus necessarily exists, but if a genus exists, it does not necessarily follow that a species exists. And genera are predicated synonymously of the species under them, but species are no longer predicated of the genera. Furthermore, genera exceed species in the extent of the species under them, while species exceed genera by their own proper differences. Furthermore, a species is known when it is a genus, and when a genus is the most specific.