Philosophy
The conflict between phylogenetic and traditional nomenclature reflects differing views of the metaphysics of taxa. For the advocates of phylogenetic nomenclature, a taxon is an individual, an entity that gains and loses attributes as time passes. Just as a person does not become somebody else when his or her properties change through maturation, senility, or more radical changes like amnesia, the loss of a limb, or a change in sex, so a taxon remains the same entity whatever characteristics are gained or lost.
For any individual, there has to be something that connects its temporal stages in virtue of which it remains the same thing. For a person, the spatiotemporal continuity of the body provides the relevant connection; from infancy to old age, the body traces a continuous path through the world and it is this path, rather than any characteristics of the individual, that connects the baby and the octogenarian. For a taxon, if characteristics are not relevant, it can only be ancestral relations that connect the Devonian Rhyniognatha hirsti with the modern monarch butterfly as representatives, separated by 400 million years, of the taxon Insecta.
If ancestry is sufficient for the continuity of a taxon, however, then all descendants of a taxon member will also be included in the taxon, so all bona fide taxa are monophyletic; the names of paraphyletic groups do not merit formal recognition. As "Pelycosauria" refers to a paraphyletic group that includes some Permian tetrapods but not their extant descendants, it cannot be admitted as a valid taxon name.
To the adherent of traditional nomenclature, on the other hand, taxa are sets or classes. Unlike individuals, they are constituted by similarities, characteristics shared among their members. Monophlyletic groups are particularly worthy of attention and naming primarily because they often share properties of interest. Since many paraphyletic groups also share such properties, plesiomorphies in their case, providing them with names is also conducive to productive research. Such naming is strongly defended by some scientists; in a 2005 letter to the editors of the journal Taxon, 150 biologists from around the world joined in defense of paraphyletic taxa. For Darwin, they pointed out, evolution involved descent and modification, not just descent. Taxa, for them, are sets of organisms united by similarity; when the similarity is too weak, descendants are not in all of their ancestors' taxa.
Read more about this topic: Phylogenetic Nomenclature
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