On classification and the cladistic idea of a "true tree of life"

1,a Classification of objects (ie, entities, like you, me, a cell and a mitochondrion) is ambiguous, because every object can be assigned to at least two classes of objects.

1.b Classification of classes of objects (like classes of biological organisms, eg, humans, cells and mitochondria) is contradictory, because every object of a class is contradictory between at least two classes of objects.

2,a Classification of classes of classes of objects (like Linnean genera) is ambiguous, because every class of class of objects can be assigned to at least two classes of classes of objects.

2.b Classification of classes of classes of classes of objects (like the different Linnean genera) is contradictory, because every class of class of class of objects is contradictory between at least two classes of classes of objects.

3a Classification of classes of classes of classes of classes of objects (like Linnean families) is ambiguous, because every class of class of class of objects can be assigned to at least two classes of classes of objects.

3.b Classification of classes of classes of classes of classes of objects (like the different Linnean genera) is contradictory, because every class of class of class of class of objects is contradictory between at least two classes of classes of classes of objects.

And so on ...

In this scheme, we can see that there are two principally different components of classification: objects and classes. We can also see that each of these components occurs at every second level of a classification into more inclusive classes (ie, objects in 1.a, 2.a and 3.a, and classes in 1.b, 2.b and 3.b), and that objects consistently are ambiguous between their classes, whereas classes consistently are contradictory between their classes, and that the classes of objects are the same as the classes of the classes (ie, 1.a and 1.b, 2.a and 2.b and 3.a and 3.b). This fact is just a consequence of the two facts that every object can be assigned to at least two classes, and that every class is contradictory between at least two classes, whereof "can be assigned to" ultimately equals "is contradictory between", because the relation between object and class is orthogonal. The relation between object and class is simply both ambiguous and contradictory at the same time.

The scheme thus paints the practical picture of the orthogonality of classification. This orthogonality means that classification itself neither can be "true" nor can contain the "truth", because it is fundamentally orthogonally circular. Its output totally depends on its input. There is a saying that "shit in", "shit out", but in this case it is rather "anything in", "the same thing out", but always contradictory. Every particular solution simply points at another solution. Consistency (ie, not pointing to another solution) can only be found using an orthogonal system of classification (like the Linnean systematics), consistently keeping objects and classes apart.

The question whether this means that there isn't a single true tree of life (to be found) has the answer that it depends on whether this hypothetical tree is orthogonally consistent or not. If it isn't, then there isn't, whereas if it is, then there is. If the classes that every object "can be assigned to" actually equals the classes that every object "is contradictory between", then there is indeed a true tree of life, but if thy don't, then there is not a true tree of life. The existence of a true tree of life does thus depend on the actual history of life: if the history of all included classes are congruent, then there is a true tree of life, but if they aren't, then there isn't. The probability that there isn't is, however, vastly larger than the probability that there is. A true tree of life actually requires a multiple of two entities, which have a totally symmetrical origin, and wherein all properties also are totally consistently distributed. The probability of such a tree is almost zero.

The probability that there is a single true tree of life is thus almost zero. Moreover, if there indeed should be one, then our fundamental partitioning of reality into objects and classes, and thus the foundation for this tree, should be wrong. If cladistics should be right, then all of us, including the cladists, thus should be wrong.

Cladistics is thus a huge problem for science. How do we get rid of it? How can we explain that it is impossible, ie, a vain serch to define the indefinable, as Darwin called it?