Biological systematics: organisms being placed into a rigid ranked hierarchy of taxa or not being “slotted” into a rank in an overall hierarchy of taxa?

In today’s cladist discussions one often meet the argument that:

“Linnaean taxonomy demands that all organisms be placed neatly into a rigid, ranked, hierarchy of taxa, such that one individual kind of organism must belong in one of each of the categories: species, genus, family, order, class, phylum and kingdom, whereas since clades can be nested at any level, they do not have to be neatly slotted into a rank in an overall hierarchy”. 

The argument is ambiguous by discussing two different kinds of things: organisms and clades. What an organism is, is not in doubt, but what a clade is, is in doubt. Clade does actually include the groups we call paraphyletic groups, although cladists “deny” that they do. The problem with clades (i.e., clade) is thus not whether they “have to be neatly slotted into a rank” , but that the concept is ambiguous. If it hadn’t been, we would have organized organisms into clades long ago. The problem is that any classification of reality (also cladification) “slots” reality. And the problem with cladification is that it “slots” reality inconsistently and empirically erroneously, which the Linnean system doesn’t. Cladists make the discussion appear as if we have the choice of “slotting” reality or not “slotting” reality, when we just have the choice of “slotting” reality consistently or inconsistently. In this choice, the Linnean system is a consistent “slotting”, whereas cladism is an inconsistent (and empirically erroneous) “slotting”.

I guess the fundamental problem for biological systematics is that there isn’t an unambiguous “slotting” to be found at all per definition, since every concept contains at least two contrary concepts per definition. There thus isn’t any final biological systematization (i.e., “slotting”) to be found per definition, independently of whether it uses the consistent Linnean system or the inconsistent cladification. This is a tough fact to face for any scientific branch. A definitional lack of end turns it into a matter of reaching consensus, which pheneticists tried, but evoke the contrary. Seeking and reaching consensus is not the hallmark of biological systematics.