The assumption that dichotomously branching processes can be consistently classified into only clades (ie, the axiom of cladistics), is also an assumption that all such processes (ie, dichotomously branching processes) of all involved kinds of entities are congruent. If this assumption is sensible, then reality is insensible, since it means that present does not exist, and that process is impossible.
This inconsistency of the cladistic axiom may be difficult to understand, but the meaning of it isn't. It simply means that the cladistic classification, ie, into only clades, is inconsistent, ie, lacking a consistent solution.
It is thus possible to assume that dichotomously branching processes can be consistently classified into only clades, but it is not possible to make dichotomously branching processes consistently classifiable into only clades. It is possible to wish they were, but it is not possible to make them be. Wish is wish, and reality is reality.
Succumbing to cladistics is thus actually succumbing to a search for an illusion.
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