What is a paraphyletic group?

Cladistics (actually Willi Hennig) invented the notion of paraphyletic group by inventing the notion of clade, but hasn’t been able to define any of them yet. However, whereas the notion of clade appears intuitively obvious, ie, “a single continuity”, the notion of paraphyletic group instead appears totally incomprehensible. ie, “a part of a continuity”. What on earth can a part of a continuity be? So, what is a paraphyletic group?

As can be seen in the intuitive definitions, the answer hinges on the definition of continuity. If we assume as an axiom that there are continuities, and if we accept the corollary axiom that there are differently inclusive continuities (ie, continuities consisting of continuities, like lineages consisting of organisms), then there are also whole continuities and parts of continuities (whereof paraphyletic groups thus are parts of continuities).

However, the notion of “parts of continuities” and ”whole continuities” is a relative staircase wherein every “whole continuity” on one level also is a “part of a continuity” on a more inclusive level, meaning that every clade on one level also is a paraphyletic group on a more inclusive level. At this point in reasoning, cladists protest, instead claiming that a clade on one level also can be a clade on a more inclusive level. This protest is, however, due to that they exclude paraphyletic groups consisting of a single continuity from paraphyletic groups consisting of more than one continuity. They simply do not consider a single continuity to be a group of continuities.

It means that a paraphyletic group is a group of continuities consisting of more than a single continuity, in difference from a clade, which is a single continuity. This difference does, however, contradict the axiom we assumed above, ie, that every continuity is a group of continuities, because this axiom means that there simply isn’t any single continuity, but just continuities that consist of other continuities. The difference that cladistics rests on is thus actually a difference between axiom and claim, ie, a contradiction between axiom and claim.

The difference between a paraphyletic group and a clade is thus actually a contradiction between a definition and its axiom, ie, a mind ghost. Cladists think that they have nailed continuity by this contradiction when they actually have created two mind ghosts: clades and paraphyletic groups, whereof they are presently trying to get rid of one, that is, paraphyletic groups, when they ought to be going to therapy to get rid of both of them.

(Does this reasoning surprise anyone?)