Biological systematists (and others) have long wondered what a "species" is. Well, I can tell them that a "species" is the opposite to an "object" (or "entity"). I can also tell them that the problem to find out what a "species" is, is that whereas an "object" has two different aspects: pattern and process, these two different aspects are in a species instead orthogonal properties. It means that a "species" is different from itself by having orthogonal properties (per definition).
This property of a "species" (ie, being different from itself by having orthogonal properties ) is difficult to understand, but Bertrand Russell (1901) gave the explanation by the paradox that became known as Russell's paradox. The explanation is simply that classification is inherently paradoxically contradictory by being orthogonal, and that species is the paradox itself.
A "species" is thus the opposite to an "object" (or "entity"), that is, a paradox. It is the paradox that emerges in the moment we distinguish "objects" of different "species". One of "objects" and "species" has to be a paradox, we can just choose which. (Whereof the approach for typologists, cladistics, chooses "objects". To a cladist the problem is thus not what a "species" is, but what an "object" is. A representative for a species, like the cladist Steve Farris for Homo sapiens, is not a representative for the species Homo sapiens, but the species Homo sapiens. As an object, he is a paradox, And, although this may be true for Steve Farris, it is not true for all representatives for all species).
