Is not cladistics rather paradoxical?

The British philosopher, logician, mathematician and historian Bertrand Russell showed 1901 that naive set theory leads to paradox.

The German entomologist Willi Hennig asserted (claimed) 1955 that only clades (ie, historical sets) are "natural" groups and that there is a single clade of clades (ie, historical set of all historical sets, or a true tree of life) to be found.

Since Russell's paradox no doubt is true, Hennig must thus assert (claim) that paradoxes can be found.

"Finding" a paradox can only mean finding a solution of the paradox. Russell's paradox is stated as:

According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R qualifies as a member of itself, it would contradict its own definition as a set containing all sets that are not members of themselves. On the other hand, if it is not a member of itself, it qualifies as a member of itself by the same definition (slightly modified from Wikipedia).

The paradox thus means that R (ie, the set of all sets that are not members of themselves), corresponding to Hennig's "historical set of all historical sets (that are not members of themselves)" is inconsistent.

So, did Hennig find a consistent solution of this paradox? No, he merely asserted (claimed) that only such paradoxes (ie, sets) are "natural" groups and that there is a single solution to them.

Hennig's assertion (claim) gave rise to the new branch of biological systematics called cladistics and looking for the solution to Russell's paradox.

This leads unsought to the question: is not this new branch (ie, cladistics) rather paradoxical?