On the consistency of phylogenetics

If we model evolution as a “tree of life” consisting of “species”, then this model contains sets of organisms called “species”, and a set of these sets. However, as sets can’t contain sets (see Russell’s paradox), the set of species is correctly called a “family” of sets (see set theory).

So, what’s the difference between the consistent “family of sets” and the inconsistent “set of sets”? Well, the difference is that a family of sets can be any collection of sets except “the set of all sets that do not include themselves”, because it is this particular set that distinguishes sets of sets from families of sets by being (paradoxically) contradictory.

It means that we can model evolution as a “tree of life” consisting of “species” consistently (ie, without paradoxical contradiction) only if we do not assume that there is a single “true” tree of life, because this assumption equalizes “families” of sets with “sets” and does thereby enter Russell’s paradox.

We can thus model evolution as a “tree of life” consisting of “species” consistently as long as we do not assume that there is a single true tree of life. It means that phylogenetics is consistent as long as it does not assume that there is a single true tree of life (ie, that phylogenetics is consistent as long as it does not slide into cladistics, that is, stays as evolutionary systematics).

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