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Entity (ie, the class of entities) and class (ie, the class of classes) are orthogonal (ie, diametrically opposed) in a finite sense, since all classes are members of the class of classes. Entity is thus a member of class, whereas class is the orthogonal class to entity.
It means that classification has to be divided into two levels (like in the Linnean system of classes in categories), because classification on a single level (like cladistics) is contradictory by attempting to fuse orthogonalities.
This does not mean that classification on a single level is impossible, on the contrary, such classification can be done in as many ways as the number of entities permit, but it means that every possible such classification is contradictory with respect to the properties of the entities. This, in turn, means that there isn’t any single most parsimonious such classification to be found, since it would mean that entity and class are not orthogonal, which they are. A single most parsimonious such classification (by cladists called The Tree of Life) is thus a definitional impossibility, that is, a pie in the sky.
Cladistics is thus the approach that attempts to solve the problem (problem for typologists like cladists, but actually a fact) that entity and class are orthogonal. It moreover appears to believe that it already has solved the problem (ie, fact) by simply denying it, when the truth is that it just has opened a route into a practical chase for this pie in the sky. It has also been successful, since a majority of biological systematists appear to be hooked on this bait today. A neutral observer has to conclude that biological systematists obviously have freaked out, but he will just be met with silence. There is no cladist out there today that is ready to defend cladistics in public, although there are lots of them chasing this pie in the sky, all of them getting paid for this vain chase by mecenates who do not understand better. In this sense, it is also a major fraud.
Can it get more absurd?
Another contribution to understanding of conceptualization http://menvall.wordpress.com/
Read more at Menvall’s Blog: change on different levels