On the difference between phylogenetics and cladistics, and the error of cladistics

The error of cladistics is not that it assumes that species have orginated by a dichotomously branching process, but that it assumes that species (and thus also the species of species) are real, since this assumption is a paradox (which Bertrand Russell also demonstrated already in 1901, that is, before the origin of cladistics). This assumption does not phylogenetics do.

The scientific question concerning evolution is not how species have originated, as cladists appear to think, but how biological organisms have originated and diversified, as phylogeneticists think. Species are not concrete entities, as cladists appear to think, but an abstraction that phylogenetics uses together with the abstraction "genus" as an orthogonal conceptual tool to discuss the biological diversity. Cladists take the scientific phylogenetic discussion too literally, leading them into a typological perspective on reality which can be called inverse science, because it superficially looks like science but follows an orthogonally opposite line of logical reasoning, ie, resting on the axiom that abstract classes (like species) instead of concrete objects (like organisms) are real. This inverse science is also responsible for the disgusting race biology of the early 20th century.

On classification of dichotomously propagating (bifurcating) processes

Dichotomously propagating  (bifurcating) processes can't be classified unambiguously. This does not, however, only concern this kind of process, but moreover all kinds of processes (ie, processes in some generic sense). The reason is that kinds of processes actually are classes (of processes), and classification of classes is ultimately contradictory, since classification is orthogonal. 

It means that kinds of processes are inconsistent (ie, contradictory) entities, and thus that classification into such entities is infinitely recursive. There simply is no consistent solution to any such classification.

This fact may appear counter-intuitive to some of us, but this appearance is only due to that those of us are not aware of that typification is classification. Those of us simply classify (ie, typify) without being aware of that it is what they do. Also illustrating a dichotomously propagating (bifurcating) process with a line graph is typification, since such graphs is a class. Understanding such illustrations consistently is a science on its own (ie, graph theory in mathematics), see "Are node-based and stem-based clades equivalent? Insights from graph theory" by Jeremy Martin et al. 2011.