The concept “species” has two aspects: in time and over time, ie, type and lineage, corresponding to particle and wave, time and frequency, and pattern and process. Species in time are different types, whereas species over time are different lineages.
The problem with this fact is that the two aspects are orthogonal, ie, diametrically opposed, because it means that their relation is many-to-many, and thus that they have no single meeting point. There is thus no consistent fusion of them. Neither is anyone of them consistent on their own, since “lineages” is a type and “types” ultimately end in the contradiction called Russell’s paradox.
It means that the concept “species” either has to be partitioned into two orthogonally different kinds of species (ie, lineages and types) or fused into one kind of species using an orthogonal system of classification (like the Linnean system). There is no other consistent solution of this problem. Willi Hennig’s solution, today called cladistics, is simply fundamentally paradoxically contradictory.
The fact that the concept “species” has two aspects: in time and over time (corresponding to particle and wave, time and frequency, and pattern and process) does thus mean that we have to acknowledge either two different kinds of species, ie, types and lineages, or an orthogonal system of classification, like Linnean systematics. All other options are contradictory.