Cladistics tries to both distinguish and confound shared ancestry and apomorphy at the same time

On the talk page for Wikipedia's definition of the term cladistics, E O Wiley begins by stating that:

"As it stands, this article confounds "cladistic" and Linnaean classification. What is being contrasted is not "cladistics versus Linnaean" but "Phylocode versus Linnaean."

Wiley is a little careless with words, but he appears to mean that the definition of cladistics confounds cladistic [classification] and Linnean classification by contrasting [the] PhyloCode versus Linnean classification instead of "cladistics versus Linnean".

Apart from his inconsistent (realistic) method of defining by either contrasting or equalizing, instead of circumscribing, this statement boils down to the term Linnean in his expression "cladistics versus Linnean". Wiley obviously distinguishes cladistic classification (ie, PhyloCode) from cladistics, but what is his corresponding distinction of Linnean classification from Linnean? What does he mean with Linnean (if not Linnean classification)?

This question redirects to what Wiley means with cladistics (if not cladistic classification). He does not clarify this point further, but it is addressed in the first post on the talk page titled "Definition of cladistics" in the second comment by "The Braz":

"Cladistic classifications are not based on shared ancestry, rather inferences of shared ancestry are based on cladistic classifications. I don't think this [difference] is semantic, I think it matters because one [ie, the former] approach is purely circular and the other [ie, the latter] is not."

To The Braz, cladistics does thus obviously mean "inferences of shared ancestry", and he points at that it must succeed cladistic classification to avoid pure circularity.

However, we can also note that Wiley and The Braz disagree in their meanings of cladistic classification. Wiley appears to mean that cladistic classification equals the PhyloCode, whereas The Braz clearly states that it is "the grouping of things according to shared apomorphy (synapomorphy)". Wiley thus means that cladistic classification is by ancestry, whereas The Braz means that it is by apomorphy. However, the fact that cladistics axiomatically assumes that every clade also is distinguishable by an apomorphy, these two meanings of cladistic classification are actually perfectly synonymous under this axiom (ie, that ancestry corresponds to both clade and apomorphy). Under this axiom, none of shared ancestry and apomorphy is thus based on the other, as The Braz axiomatically assumes, but are instead the same things.

However, if shared ancestry and apomorphy indeed are the same things, as cladistics thus axiomatically assumes, then the confounding of cladistic classification and Linnean classification that Wiley points at in his introductory statement is actually a corollary to the cladistic axiomatic synonymization of ancestry and apomorphy, ie, if ancestry indeed corresponds to both clade and apomorphy, then cladistic classification also equals Linnean classification.

We can thus understand that the confounding of cladistic classification and Linnean classification in the article about cladistics that Wiley points at in his introductory statement actually is a corollary of cladistics' axiom that ancestry corresponds to both clade and apomorphy. That is, this axiom actually means that there is no difference between cladistic classification and Linnean classification. This fact explains both the inconsistency of cladistics (in its founding axiom) and the rationale for Linnean classification at the same time.

It isn't easy to both distinguish and confound shared ancestry and apomorphy at the same time, as cladistics tries to do, especially not when they actually are orthogonal. This fact is the rationale for the orthogonal Linnean classification.

Cladistics is what you end up in if you conflate (confound) pattern with process, ie, object with class, that is, Russell's paradox.