You saw in Extension and Comprehension that terms nest inside one another, and in Definition by Genus and Difference that a definition names a wider class and then narrows it. Logic names the two ends of that relation.
Key idea
A genus is a wider class that is divided into narrower classes; each narrower class is a species of that genus. The same class can be a species of one genus and a genus of other species.
Why it works
Genus and species name a relation between two classes, like "parent" and "child". Nobody is a parent all by themselves; you are a parent of someone. In the same way, "polygon" is a species when we compare it with "shape" (every polygon is a shape, not every shape is a polygon), and a genus when we compare it with "triangle". Only the comparison decides.
Worked example
Worked example: One class, two roles
How is "mammals" related to "animals" and to "dogs"?
- Compare mammals with animals: every mammal is an animal, but some animals (birds, fish) are not mammals. So mammals is the narrower class: a species of animals.
- Compare mammals with dogs: every dog is a mammal, but not every mammal is a dog. So mammals is the wider class: a genus of dogs.
Answer: a species of animals and a genus of dogs
Porphyry drew these nested classes as a tree, now called the Tree of Porphyry: substance at the top, then body, living body, animal, and rational animal (human being) near the bottom. A class with no wider class above it is a highest genus; a class that is not divided any further is a lowest species. Everything between is both a genus and a species.
Common mistake
Using the biology ranks. In biology, "genus" and "species" are fixed levels (Canis is a genus, Canis familiaris a species). In logic they are relative: any wider class is a genus of any narrower class inside it, at any level. Check by asking "wider or narrower than what?"