Ever since the dawn of Biological systematics, it has discussed what a "species" is. This fundamental problem appears to concern how we shall specify a consistent and unambiguous kind of group of organsisms, but does actually concern how we shall overcome the fact that such a kind of group is a definitional contradiction. Such a kind of group consists of both single species and single organisms at the same time, and is thus consistent only if species equal organisms, which are not groups, but single organisms. The problem is thus not how we shall specify a consistent and unambiguous kind of group of organsisms, but that we can't.
Rather than asking the question what a species is, we thus ought to ask the question why we can't specify what a "species" is, which is answered by the conclusion above. This answer does not, however, suffice to those biological systematists that ask the question what a species is. It does not even qualify as an alternative among the possible answers to their question. "Nothing" is not an acceptable answer to them.
Carl von Linné partly overcame this problem by constructing an orthogonal system of classification wherein species is consistent in relation to genera, and genera is consistent in relation to species. This system did not solve the fundamental problem that reality is distinct from our conceptualization of it, ie, that the relation between the two can't be unambiguous, but only the problem of consistency.
A later approach in biological systematics called Cladistics instead "solved" this problem by simply asuming as an axiom that we indeed can specify what species are, in the form of a single true tree of life. This solution did not, however, actually solve the problem, but merely transfered it into finding the single true tree of life, which, thus, is a definitional impossibility. Such thing is simply impossible per definition. Another approach in biological systematics called Evolutionary taxonomy adopted Linné's system and was thus at least consistent, although ambiguous.
However, in a fundamental battle in biological systematics in the 1980-ies, biological systematists downvoted Evolutionary systematics in favor for Cladistics. The outcome of this battle tilted biological systematics up-side-down from being a scientific discipline into being a belief in a single true tree of life. It simply expelled scientific thinking from biological systematics. (This was the time I entered biological systematics (in the beginning of the 90-ies). Unfortunately, I was thus expelled from biological systematics in the moment I paid for entering it. I didn't get in before I was out. Not yielding for a belief in a single true tree of life effectively excluded me from getting any position at any academy. This belief was the ticket of entrance to positions. Since then, I have been referred to expressing my protests against this belief to media that is not governed by cladists, also excluding Wikipedia (which is governed by cladists)). Today, biological systematics is thus dominated by Cladistics, although Cladistics is paradoxically contradictory. You can thus get a position at any academy if you search for a paradox, but not if you say that Cladistics is a search for a paradox. Paranoia is acceptable, but not stating that it is a paranoia.
Ultimately, cladistics is doomed to eternal splitting (like the species it believes in are), on the contrary to Linnean systematics, because a house can only stand firmly on a consistent ground, like Linnean systematics. Belief in eternal splitting does, of course, lead to eternal splitting.
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