Both Linnean systematics (including evolutionary taxonomy) and cladistics (ie, cladification, or classification into only clades) are classifications of dichotomously branching processes. The difference between them is that Linnean systematics incorporates the orthogonality between pattern and process consistently, whereas cladistics doesn’t. It means that Linnean systematics is ambiguous with respect to the classified process, whereas cladistics is self-contradictory. Linnean systematics thus offers several different consistent classifications of a single dichotomously branching process, whereas cladistics offers ONLY contradictory classifications.
This fact may come as a surprise some of us given that there are single “true” such processes. The problem is, however, that there isn’t any such process for ALL objects of any kind, because kinds are artificial (ie, our inventions) and are also ultimately paradoxically contradictory (see Russell’s paradox). Assuming that there is a single such process (like a true tree of life) for a single kind of objects (like biological species) is thus self-contradictory (actually an infinite recursion), how obviously true it may seem. The problem with this assumption is thus not that processes aren’t true, but that kinds aren’t “true”.
The difference between Linnean systematists and cladists is thus that Linnean systematists keep process and pattern consistently apart, whereas cladists confuse them. This difference leads Linnean systematists into a pragmatic compromise between pattern and process, and cladists into an extremist infinite recursion between pattern and process. The truth we all seek is hidden in the intersection between them, that is, in Russell’s paradox, also called the class “clade”. This fact may appear mysterious, but does just tell us that truth is relative, ie, a matter of gray scale rather than of black and white. The paradox is due to that a gray scale, ie, a relation, lacks an unambiguous middle. Relations are simply ambiguous per definition.
The difference between Linnean systematists and cladists is thus that Linnean systematists accept that relations are ambiguous, but cladists don’t. Cladists instead raise the irrational claim that relations aren’t ambiguous.