The approach called cladistics in biological systematics rests on the notion of "clades". This kind of "thing" is, however, confusing. The fundamental problem is that if "clade" (in indefinite form), analogous to "human", means both the class clade, analogous to the class human, and a single clade, analogous to a single human, then every single clade must consist of ONLY clades, and there must also be NEITHER anything else than clades NOR any clades at all, contrary to "human". "Clades" does thus, obviously, exclude everything, including itself. Accepting it does in practice mean denying everything, including itself.
What, then, is the reason for this confusion? Well, the reason is that "clade" is the opposite to "object". "Clade" is thus not a kind of "object", but actually the opposite to "object". It means that we have to think up-side-down and in-side-out when we discuss "clades". Thus,
- whereas there are different kinds of objects, there are different clades of kinds.
- whereas "object" is ambiguous between pattern and process, "clade" is instead contradictory between pattern and process.
- whereas objects are classified, classes are cladified.
- whereas objects are different from classes, clades are classes.
- whereas objects exclude clades, clades exclude objects.
"Clade" is simply using the ultimate conclusion if one starts with objects as axiom, that is, Russell's paradox, as axiom, thus landing in the opposite to object as ultimate conclusion (wherein the conclusion equals the axiom). It is a play with words landing in a paradox (i.e., Russell's paradox) as both axiom and conclusion.
The confusing property of "clade" does thus reside in that it turns assumption (actually axiom) and conclusion up-side-down and in-side-out. However, it is not the turning up-side-down and in-side-out itself that is confusing - it might just as well have been a normal development in science, a so-called "paradigm shift - but instead the fact that "clade" is a paradox, since it means that the axiom can't be real. Not even if all biological systematists would agree on this axiom could it be real, because it is contradictory, i.e., a paradox. "Clades" simply can't be real because they are contradictory, i.e., a paradox. The confusing property of "clade" is thus that it is contradictory (i.e., a paradox) and thus can't be used as an axiom because they are far from self-evident (as axioms ought to be). A contradiction may, of course, be self-evident to some of us, but not without contradiction.
The answer to the question "Is "clade" a class or an entity?" is thus "both". It is both a class and an entity. The problem is that class and entity are contradictory. The only difference between cladists and non-cladists is thus that cladists interpret this "both" erroneously as a confirmation (i.e., it is both at the same time), whereas non-cladists interpret it correctly as a contradiction (i.e., it is neither). This difference sends cladists on a vain search of a contradiction they call "clade", which currently seems to occupy a large part of the "research" in biological systematics. This search is thus correctly diagnosed as a mental desease - paranoia.
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