The fundamental difference between Linnean and cladistic systematics (called cladification by Mayr) is that the Linnean systematics is an internally consistent system adapting to the fact that classification is internally ambiguous, whereas cladistic systematics is an internally inconsistent system only acknowledging internal inconsistency (i.e., ambiguity) and only over time.
The two systematics’ meet in the special case of a totally resolved system, i.e., a dichotomous system, which the Linnean systematics categorizes at every hierarchical level, but which cladistic systematics partitions into clades. This difference reflects the fundamental difference between them in that the Linnean systematics keeps all classes apart, also those following each other over time, whereas cladistic systematics confuse classes both in and over time in clades, “denying” the confusion in time by “denying” what it calls paraphyletic groups.
The difference between them does thus reside in how they handle distinguished classes: Linnean systematics keeps them apart, whereas cladistic systematics confuses them. Since the difference only concerns consecutive classes over time, it melts down to a difference between how to handle two consecutive distinguished classes: either keeping them apart or confusing them, Linnean systematics keeping them apart and cladistic systematics confusing them.
The two systematics are obviously contraries in that Linnean systematics acknowledges a distinction of classes, wheras cladistic systematics confuses the distinction. Cladistic systematics does thus confuse a distinction that Linnean systematics acknowledges. Cladistic systematics reverse Linnean systematics.
A choice between them does thus have to pose the question of where classes come from. If they come from reality, then cladistics is a perfectly valid “natural” approach, although being inconsistent (i.e., self-contradictory), but if classes come from our own minds, then the Linnean systematics is the rational approach to handle the difference between reality and our minds. So, the question is if there is any way to decide whether classes come from reality or our minds. The fact that classes are inherently ambiguous supports the alternative that they come from our minds, but it does not falsify the alternative that they come from reality. Reality may be inherently ambiguous. However, the assumption that classes come from reality (i.e., that reality is ambiguous) does also mean that time equals space in every moment, which is falsified by the fact that time is relative (to space). This fact does thus falsify the alternative that classes come from reality, leaving the Linnean systematics as the winner.
Facts (i.e., the fact that time is relative to space) do thus falsify cladistic systematics leaving Linnean systematics as the winner. The most interesting part in this evaluation of the two systematics is, however, that the statement that “reality is ambiguous” is ambiguous as an assumption but unambiguous as a conclusion. It means that it is doubly ambiguous as an assumption and ambiguous as a conclusion. This derivation does thus appear to support Rheticus’ (a disciple of Copernicus) statement that “we that seek the truth among things will always be torn between things and their appearance”. There appear to be no escape from the fact that reality is distinct from our minds. Cladistic systematics is an attempt to escape this fact, but it is merely a case of wishthinking, a hallucination. Clades do not exist, have not existed, will not exist, or cannot exist They are a dive into the nothing that characterizes non-existence.
(I welcome donations. One doesn’t get fat on revealing the cladistic hypocrisy).