On the consequence of Russell’s paradox (or the excluded middle) for biological systematics

The approach in biological systematics that is called “cladistics” rests on a sole acknowledgement of what it calls “clades”. The notion of “clades” is, however, difficult to straighten out for all of us (including cladists, although they don’t want to straighten it out, but rather the opposite) - it appears to be both a single entity, a group of entities and a class of entities at the same time.

This ambiguity is, however, totally understandable, since the notion actually is Russell’s paradox, or the excluded middle, and that it thus IS both a single entity, a group of entities and a class of entities at the same time. The problem with this combination is that it doubly contradictory, that is, if it is an entity, then it can’t be a group or a class, whereas if it is a group, then it can’t be an entity or a class, and if it is a class, then it can’t be an entity or a group. Instead, it is in practice neither an entity, a group nor a class, but an infinite recursion between the three.

The gate that leads into this infinite recursion (ie, to a sole acknowledgement of clades) is the fundamental assumption (ie, axiom) that classes are real (instead of that objects are real), because classes are ultimately contradictory (as Bertrand Russell demonstrated with Russell’s paradox in 1901). The notion (of clades) is actually fundamentally a class - The Class that conflates entities, groups of entities and classes, that is, Russell’s paradox per se, and is as such an infinite recursion under the assumption that it is real.

Instead assuming as an axiom that entities are real removes this gate to infinite recursion. In this approach, it is just possible to understand Russell’s paradox as Russell’s paradox. However, the worst problem for us is not understanding the inconsistency of cladistics, but understanding that there is nothing between the axiom that entities are real and the axiom that classes are real (ie, the excluded middle), that is, that there is no possibility to get rid of Russell’s paradox, but that it just can be avoided by using an orthogonal system of classification like Linnean systematics, including evolutionary taxonomy (which instead is ambiguous in relation to reality per definition).

The consistent understanding of this lack of a middle is that it represents change. It represents the face of reality that we can’t pinpoint per definition, because it is what we do when we do it. The reason we can’t pinpoint it is that it slips out of our pinpointing in the moment we try to pinpoint it. It eludes us backwards when we try to pinpoint it forwards. If we accept this factual lack of a middle, then we can classify reality consistently (although not unambiguously) using an orthogonal system like Linnean systematics, whereas if we don’t, then we enter a process of infinite recursion that today is called cladistics (but which actually is traditional in biological systematics).

These are thus the only two options biological systematics has:

1. to accept the fact that classification is ultimately contradictory and agree about a cerstain orthogonal system of classification and a specific classification using this system, or

2. to deny the fact that classification is ultimately contradictory and enter a process of infinite recursion, as cladistics.

I would appreciate your votes about which of these two options you prefer that biological systematics should choose, as comments to this post. It may not be the same clear win for cladistics as the voting back in the 80-ies was.

Another contribution to understanding of conceptualization http://menvall.wordpress.com/

Read more at Menvall’s Blog: change on different levels