I don't know about that. I think that the current version of the Linnean taxonomy system is possibly arbitrary in an absolute sense.
Linnaean taxonomy arbitrarily puts species into genera, classes, etc. For example, whether or not chimps belong in the Homo or Pan genus is an arbitrary distinction. It was also an arbitrary decision to put all mammals into one class instead of multiple classes. There is only one non-arbitrary classification in biology which is at the species level. Cladistics solves these problems by rooting species by shared characteristics within a phylogeny.
This is made even more obvious if you think about the history of life. At one point in history, there was only one species of mammal. If we had to categorize life at that point in history with the Linnaean system then this one species of mammal would comprise a single genus within the class Reptilia. So how does a genus become a class within Linnaean taxonomy? Well, it can't. The arbitrary nature of Linnaean taxonomy has a tough time organizing evolving populations over time.
Start with the class Mammalia. Pick two orders within that class, say rodents and primates. Do all the families within one order (e.g. the mouse family and the mole rat family in the rodent order) show the same degree of difference as all the families within the other order (e.g. the great ape family and and the lesser ape, i.e. gibbon family in the primate order)? Would that imply an absolute classification system?
Why are rodents and primates in separate orders?
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