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Aristotle · 1831

Since it is necessary, Chrysaorius, for the teaching of Aristotle’s categories to know what a genus is, what a difference is, what a species is, what a property is, and what an accident is; and since this theory is useful for the rendering of definitions and, in general, for matters regarding division and demonstration, I shall attempt, by providing a brief overview in the manner of an introduction, to go through what the ancients have said, avoiding deeper questions and aiming moderately for the simpler ones. I shall omit speaking about whether genera and species exist in nature or reside only in simple concepts, whether they are corporeal or incorporeal, and whether they are separate or exist within and around sensible things; for such a matter is very deep and requires a greater examination. I shall attempt to show you now how the ancients—and especially those of the Peripatetic school—reasoned about these matters logically.
It must be noted that neither genus nor species is used in a single sense. A genus is said to be a collection of certain things having a relation to one thing and to each other; according to this meaning, the "race" genos genus/race/kin of the Heracleidae is spoken of as coming from a single source—namely, Heracles—and from the multitude of those having a kinship to one another originating from him, and distinguished by this separation from other races. Again, a genus is spoken of in another way as the starting point of each person's generation, whether from the parent or from the place in which one was born; thus we say that Orestes has his lineage from Tantalus, and Hyllus from Heracles; or again, that Pindar is Theban by lineage, and Plato is Athenian. The homeland is a starting point of each one's generation, just as the father is. This meaning appears to be straightforward; for the descendants of Heracles are called Heracleidae, and the descendants of Cecrops are called Cecropidae, as are their close relatives. A third way that is called a genus is the starting point of each one's generation, not referring to the multitude of those from one source (like the Heracleidae), but rather the source itself, by which we define and separate them from others, calling the whole collection the "genus of the Heracleidae." Another way a genus is spoken of is that under which a species is placed, perhaps said by analogy to the others; for the genus is a kind of starting point for those things under it, and it seems to contain the whole multitude under itself. Since "genus" is used in three ways, the discourse among philosophers concerns the third. Defining this, they have stated that a genus is that which is predicated of many things that differ in species, in the category of "what it is," such as "animal." For of the things predicated, some are said of only one thing (these are the individuals, such as Socrates, or this, or that), while others are said of many, such as genera, species, differences, properties, and...
...accidents, generally but not specifically to one thing. A genus is, for example, "animal"; a species is, for example, "human"; a difference is, for example, "rational"; a property is, for example, "capable of laughter"; an accident is, for example, "white," "black," or "sitting." Genera differ from things predicated of only one thing in that they are predicated of many. They differ from species in that, even if species are predicated of many, they are not predicated of things differing in species, but only in number. For "human," being a species, is predicated of Socrates and Plato, who do not differ from each other in species but in number. But "animal," being a genus, is predicated of human, ox, and horse, which differ from each other in species, and not merely in number. A genus differs from a property in that a property is predicated of only one species (or those under the species), such as "capable of laughter," which belongs to humans alone; but a genus is not predicated of one species, but of many that differ in species. A genus differs from a difference and common accidents in that, even if differences or common accidents are predicated of many things that differ in species, they are not predicated in the "what it is," but in the "what kind of thing it is." For when someone asks "what is that of which these are predicated?", we answer with the genus; but when the question is "what kind of thing is it?", it is not the genus that is predicated, but rather a quality. When asked "what kind of thing is a human?", we say "rational"; when asked "what kind of thing is a raven?", we say "black." "Rational" is a difference, and "black" is an accident. But when asked "what is a human?", we answer "an animal"; and "animal" is the genus to "human." Thus, the fact that a genus is said of many things distinguishes it from individuals predicated of only one thing; the fact that it is said of things differing in species distinguishes it from species or properties. The fact that it is predicated in the "what it is" separates it from differences and common accidents, which are predicated not in the "what it is," but in the "what kind of thing it is" or "in what state it is." Therefore, the definition of genus provided contains nothing superfluous nor lacking. The term "species" is used in reference to the form of each thing, as it is said, "the first species worthy of tyranny." "Species" is also used for that which is placed under the provided genus, as we are accustomed to say that "human" is the species of "animal" (animal being the genus), that "white" is the species of "color," and that "triangle" is the species of "shape." Since we mentioned "species" when providing the definition of genus—saying that it is predicated of many things differing in species in the category of "what it is"—and we also say that the species is that which is placed under the provided genus, one must know that since a genus is a genus of something and a species is a species of something, it is necessary to use both in each other's accounts. Thus, they define species in this way: a species is that which is ordered under the genus, to which the genus...
(*) Addition by A: To Phoenix the student, Plutarch the Lycopolite: Christ our God, work with us.