The problem with the notion of “species” is that there are two kinds of them: one in time consisting of similar organisms, and another over time consisting of lineages, because these two kinds are orthogonal, ie, diametrically opposed, and that these kinds thereby are ambiguous concerning defining properties.
Biologists (and others) have tried to fuse these two kinds of species consistently forever, but not until Linné did they succeed, and then it was in the form of an orthogonal system – “species” was defined in terms of “genus” and “genus” was defined in terms of “species”.
Recently (in the 1950-ies), however, the Nazi biologist Willi Hennig once again tried to fuse them by calling lineages of species “natural groups” (an approach later called cladistics). This conceptual confusion is so entangled that it is difficult to tangle out. The fundamental problem is that there are two orthogonal kinds pf species, which Hennig bypasses by talking about lineages of species. However, if we understand that every entanglement (ie, complication) at the same time is a simplification, we can understand that Hennig actually says that species are lineages, which thus is only partially true (ie, over time, not in time). If it had been totally true, then the concept “species” itself had not been a species.
Instead, species are consistent only in the context of an orthogonal system of classification, like Linnean systematics. Otherwise, is is ambiguous between the descent and the type that an orthogonal system combines consistently.