Isagoge: Chapter 2:5 — Of the Nature of Genus and Species

In this paragraph, Porphyry takes a great while to explain how comprehension and extension vary as you go up and down the chain of genera, species, and individuals. I’m not going to take it apart; you can read it for yourself. I’ll summarize at the end.

Genus then, and species, being each of them explained as to what it is, since also genus is one, but species many, (for there is always a division of genus into many species,) genus indeed is always predicated of species, and all superior of inferior, but species is neither predicated of its proximate genus, nor of those superior, since it does not reciprocate. For it is necessary that either equals should be predicated of equals, as neighing of a horse, or that the greater should be predicated of the less, as animal of man, but the less no longer of the greater, for you can no longer say that animal is man, as you can say that man is animal. Of those things however whereof species is predicated, that genus of the species will also be necessarily predicated, also that genus of the genus up to the most generic; for if it is true to say that Socrates is a man, but man an animal, and animal substance, it is also true to say that Socrates is animal and substance. At least, since the superior are always predicated of the inferior, species indeed will always be predicated of the individual, but the genus both of the species and of the individual, but the most generic both of the genus or the genera, (if the media and subaltern be many,) and of the species, and of the individual. For the most generic is predicated of all the genera, species, and individuals under it, but the genus which is prior to the most specific (species), is predicated of all the most specific species and individuals; but what is species alone of all the individuals (of it), but the individual of one particular alone.14 Now, an individual is called Socrates, this white thing, this man who approaches the son of Sophroniscus, if Socrates alone is his son, and such things are called individuals, because each consists of properties of which the combination can never be the same in any other, for the properties of Socrates can never be the same in any other particular person; the properties of man indeed, (I mean of him as common,) may be the same in many, or rather in all particular men, so far as they are men. Wherefore the individual is comprehended in the species, but the species by the genus, for genus is a certain whole, but the individual is a part, and species |618 both a whole and a part; part indeed of something else, but a whole not of another, but in other things, for the whole is in its parts. Concerning genus then, and species, we have shown what is the most generic, and the most specific, also what the same things are genera and species, what also are individuals, and in how many ways genus and species are taken.

In short, the species is predicated of every individual in the species; the genus is predicated of every species within it, and so on up the chain. Thus, Socrates is a man, an animal, a body, and a substance.

It’s tempting to think of genera and species as mathematical sets: a species is the set of all individuals in the species, a genus is the set of all individuals in the species, and so forth, and indeed this is the way modern logic encourages us to think. But to do so is to confuse genera and species with their extensions: remember that the extension of a genus or species is precisely the individuals of which the genus or species is predicated. But genera do not contain individuals; they contain species. And in addition to extension, each genus and species has a comprehension, that is, a meaning. The extension of the species Man is all men precisely because all men are rational animals. Individual men belong to the species because they fit the defining criteria; a species is not an arbitrary set of individuals.

Given that, we can say that every genus has a wider extension than any species within it, and every species has a more precise–indeed, more specific–comprehension than its genus.

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