I really like the way this guy writes. I have been trying for years, off and on, in a totally unguided manner, to grasp the meanings of the terms used in Aristotelian-Thomistic philosophy, by reading this book and that, hoping my mind would eventually piece things together. But certain authors are able to state things in a way that sinks in right away (another one being Edward Feser).
Here are a couple of excerpts by George Hayward Joyce, S.J., having to do with how we define species:
When it is said that the notes expressed by the species are those which make the thing what it is, we must not be supposed to signify that these concepts give us some peculiar insight into the inner constitution of class-natures. It is only in the case of mathematical figures, as e.g. of the triangle or circle, by reason of their extreme simplicity, that our minds can represent the actual constitutive principle of their object. Here indeed our concepts are adequate (Ch. II, 3). In regard to natural classes all we can do is to form concepts representing certain characteristic notes that distinguish one class from another. We must be content that our concepts shall be clear.
George Hayward Joyce, S.J., Principles of Logic, London: Longmans 1916, p. 123.
[I]n the real order the genus and the differentia are not two different parts of the nature. We cannot in the real order separate between a triangle and its equiangularity. It is the mind alone which can distinguish the differentiating form from the indeterminate generic nature, and can view the triangle and its form as equiangular or isosceles, as distinct. Thus there is a great difference between the essence of a thing in the real order, and the logical essence of which we are here treating. In the real order the parts which make the thing to be what it is are real parts. Socrates is a man because he possesses a human soul and body. The parts of the logical essence on the other hand are not real parts but conceptual parts — the incompletely determined genus and the determining differentia.
Id., p. 126.
One insight that I get from these excerpts is the distinction between the real order and the logical order. The real order is what’s really out there, things as they are in themselves. The logical order is how we conceive of the things in the real order: how we distinguish between them and make sense of them in our minds.
When defining a species, we don’t have to grasp the inner essence of the thing in its fullness. Only God could do that in any case. And we don’t have to give an exhaustive list of every one of its attributes, which would be an interminably long list; and which, again, if it were to be truly exhaustive, only God could do. No, all we need to define the essence or nature of a species, is to list the attributes which distinguish it from other species: A group of attributes it possesses, of which no other species possesses every one.
Thus we define “man” as “rational animal”, not because it exhausts everything there is to say about man’s nature, but because it suffices to distinguish man from every other known being. Obviously, of man as he is in himself, i.e. in the real order, there is much more that could be said.
When defining mathematical figures, we are able to grasp and define their essential features exhaustively, “by reason of their extreme simplicity”. Thus, a triangle is an enclosed plane figure with three straight sides, and that’s pretty much all there is to say about it. But “in regard to natural classes”, because the natural, God-created world and everything in it is so frigging incredibly awesome and complex, “all we can do is to form concepts representing certain characteristic notes that distinguish one class from another.”