A dog is a kind of animal. But the species dog cannot be included in the genus animal–that is when we consider genus not as a mere classification but as a a way of understanding a particular nature in the Aristotelian sense. If we did include dog in the genus animal, every animal would have to be a dog, or the genus animal (which would then contain all the many specific animals) would simultaneously contain contradictory or opposite specifications.
Rather, the genus is more truly contained in the species. It is the particular which gives reality and designation to the species. It is the species which gives intelligible difference or specification to the genus.
Yet, the species does this, not by including something excluded from the genus, but by specifying something implicit in the genus. Similarly, the particular requires designate matter which constitutes not something excluded from the the species, but what is implicit or indeterminate in it.
Same & Other 