Cladistics is just an inconsistent bubble resting on an erroneous axiom

Cladistics rests on the idea of “a single tree of life”.

A single tree of life is definitionally a set consisting of “the clade of all clades”.

The set “the clade of all clades” is definitionally the same kind of set as “the list of all lists”, in that they include the set itself as a member of itself (ie, the clade of all clades is also a clade, and the list of all lists is also a list).

The main problem with this kind of sets is how they can ever be completed, since the clade of all clades including this clade itself is yet another clade, and so on, just as the list of all lists including this list itself is yet another list, and so on. This property may not be immediately obvious concerning clades, but it’s just because we don’t consider the attributes of clades. We would see the same phenomenon concerning them if we did, instead of assuming that there must be a consistent “the tree of life”.

This kind of sets is thus infinetely regressive. This property is what the mathematician Henri Poincaret called “the vicious circle”. I bet cladists do not agree on that this circle is vicious, but it is no doubt the same circle. So, how can we (humans) disagree so fundamentally about infinitely regressive circles? Some of us (in this case cladists) believe that they contain the truth, whereas others (in this case non-cladists) consider them to be black holes in conceptualization. Well, the answer to this question may forever be hidden in the dark, but fact is that they indeed are vicious circles that do not contain the truth, because they are infinite. This fact turns the question into how cladists can believe that they contain the truth? The answer to this question is that it is because cladists assume as an axiom that classes are real and that they thus have to believe that they contain the truth to be consistent. Their only alternative is to discard their axiom, which they can’t.

Cladistics thus rests on the axiom that classes are real, leading to the idea of “a single tree of life”, which is the absent bottom of an infinitely regressive kind,  but can’t discard the idea because it can’t discard its axiom. Cladistics is thus just an inconsistent bubble resting on an erroneous axiom. As such, it will disappear like a fog in the morning with its proponents either just keeping quiet or, like Peter, denying three times that they have ever been cladists. An example is Kåre Bremer who claims that he does not deal with these issue any more. Cladists disappear like the fog in the morning. It was Willi Hennig, a remnant of the racistic nazi approach of the second world war, that clouded our learning history, but hopefully all remnants of the nazi approach will thus soon have disappeared. Classes are not, and can’t be, real, but are, instead, merely our subjective choice.