Cladistics is paradoxically contradictory
The fact that cladistics rests on the axiom that classes, instead of objects (or entities), are real, ie, that cladistics is subjective instead of objective, and the corollaries of this fact, requires an explanation.
The cladistic acknowledgement of classes (instead of objects) is not explicit, but implicit in that cladistics ”only acknowledges” continuity. The explanation is that continuity actually is synonymous with class in that it is a kind of class per definition and that it thus is indistinguishable from class, ie, is included in class (see fig below). Every continuity is thus also a class, but not every class is a continuity. This definitional relation is the same as that between humans and primates, ie, every human is a primate, but not every primate is a human.
However, this particular case (ie, continuity and class) of this definitional relation is a little bit more complicated than the others. There is only one additional kind of class, namely infinite class (ie, abstract type), since continuity equals finite class (or category) per definition. It means that classes (in a generic sense) are both finite and infinite, and, since these have a 1-1 correspondance between reality and the abstract per definition, that they can be consistently “acknowledged” (ie, break even) only if they are of the same number and also are identical, which they can’t be, since finite is orthogonal to infinite, meaning that each of them is either N-1 or N+1 of the other per definition. Instead, their orthogonal relation means that they are paradoxically contradictory (which Russell’s paradox also reveals). It means that the cladistic acknowledgement of continuity actually is a paradoxically contradictory acknowledgement of classes (ie, acknowledgement of a paradox) in the form of the class clade.
Cladists thus think that they acknowledge continuity (and at the same time objects) envisioned as “clades”, when they actually acknowledge classes instead of objects leading to the paradoxically contradictory class clade. The other side of this paradoxically contradictory “acknowledgement” is thus the rest of the classes (ie, the non-continuities), that is, those classes that cladists say they don’t acknowledge, which they call “paraphyletic groups”. However (read carefully now, because this is a description of the cladistic bridge from objectivity to subjectivity), cladists actually also acknowledge ”paraphyletic groups” simply by distinguishing this class (ie, paraphyletic groups). Cladists actually acknowledge them just as much as they acknowledge clades. A more correct word for what they do with paraphyletic groups is that they dislike them (instead of like them).
At this point, the cladistic bridge has taken us (triangulated us) via a paradoxically contradictory distinction (ie, of clades and paraphyletic groups) to the question of whether we like or dislike the two classes of the distinction. The problem is, however, (passing the bridge from cladistic subjectivity back to objectivity again) not whether we like or dislike the classes of the distinction, but rather that the distinction is paradoxically contradictory. Fact is that classes simply can’t be partitioned consistently into continuity (ie, clades) and discontinuity (ie, paraphyletic groups), since finite can’t equal infinite. The cladistic question whether we like or dislike clades and paraphyletic groups is thus simply irrelevant, since we can’t find them (without contradiction) anyway. Instead, such clades (ie, holophyletic groups) and paraphyletic groups are actually two orthogonal aspects of monophyletic groups, so that every monophyletic group is both holo- and paraphyletic, just as every single object is both process and pattern. Holo- and paraphyletic groups are just two different ways of looking at monophyletic groups.
The cladistic denial of paraphyletic groups and search for only clades (ie, holophyletic groups) is thus just as insensible as a search for only process would be and also just as vain (ie, a search for the running point). It is simply impossible to get rid of any of them since they are just two aspects of the same things (ie, monophyletic groups). The cladistic belief that it is possible to get rid of paraphyletic groups is merely a corollary to an acknowledgement of classes, instead of objects, which is paradoxically contradictory (as also Russell’s paradox shows). Cladistics is thus actually The Paradoxically Contradictory Approach (ie, acknowledging only paradoxes). Congratulations Willi Hennig!
Another contribution to understanding of conceptualization http://menvall.wordpress.com/
2012-08-31 14:13:46
Source: http://menvall.wordpress.com/2012/08/31/cladistics-is-paradoxically-contradictory/
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