Single entities have two aspects: pattern and process. Pattern is the momentary aspect, that is, in time, whereas process is the temporary aspect, that is, over time. It means that it takes (at least) two consecutive patterns to make up one process, and that they, "pattern"and "process", thus are orthogonal, ie, diametrically opposed, or excluding a mutual 1-1 correspondance.
So-called "natural groups" (ie, the class, or the infinite type), that is, groups of entities that form super-entities by combining the the two aspects "class" and "historical unity", are the opposite to entities. It means that such "things" ARE two aspects at the same time, that is, that they conflate the two aspects "pattern" and "process". Such "natiral groups" thus both combine and conflate the two aspects "pattern" and "process",
This fact triggers the question: what, then, is the difference between "combining" and "conflating"? The answer depends on how one combines. If one combines by conflating, then the difference is none, that is, that there isn't any difference between them.
This fact explains the impossibility of "natural groups". Such groups have to conflate the two aspects "pattern" and "process", although these are two aspects of entities. Such groups are thus possible only if entities are impossible, and vice versa. Such groups and entities thus exclude each other.
The meaning of this fact may be difficult to understand, but it is simply that one of them is contradictory given that the other is unambiguous. This fact, in turn, means that the class "clade" (giving rise to cladistics) is practically contradictory per definition, since not both entities and natural groups of entities can be unambiguous at the same time. This fact makes applied cladistics non-sensical. The class "clade" simply can't make up a non-contradictory, ie, unambiguous, category (ie, finite class) per definition, since not both entities and natural groups of entities can make up categories at the same time.
Cladistics is thus inconsistent (actually consistently inconsistent) in an applied sense by including two categories that exclude each other. It means that cladistics rests on Russell's paradox. The only difference between science and cladistics is thus that cladistics believes that Russell's paradox can be found. Otherwise, they are totally parallell. Unfortunately, for cladistics, science is right and cladistics wrong.
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