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Solve paraphyletic problem

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A reader of my blog found it using the search terms “solve paraphyletic problem”. This quest is extremely interesting.

The phenomenon which can be called “the paraphyletic problem” is namely actually a problem only for people that assume as an axiom that classes are real, and thereby also assume that there is a class of “natural groups”, and thus also assume that there is a single such “natural group” for all “natural groups” (ie, for everything), by showing that this axiom is inconsistent (ie, contradictory). Paraphyletic groups emerge in the moment we adopt this inconsistent (ie, contradictory) axiom (instead of the axiom that objects are real). Paraphyletic groups actually witness that this axiom is inconsistent (ie, contradictory).

“The paraphyletic problem” does thus not have a solution, but does actually instead falsify the inconsistent axiom that classes are real. The problem is thus actually not paraphyletic groups themselves, but the inconsistency of the axiom that classes are real they witness. Fact is, namely, that the assumption that classes are real is contradictory, which both can be understood by considering the fact that classification is orthogonal and also was demonstrated logically by Bertrand Russell in 1901 (called Russell’s paradox).

“The paraphyletic problem” can thus only be solved by discarding the inconsistent axiom that classes are real in favor for the consistent axiom that objects are real.  Logical reasoning based on the axiom that objects are real does not conflate monophyletic groups with holophyletic groups (in the form of “clades”), and does thus not distinguish paraphyletic groups at all. It simply doesn’t “see” this inconsistent class of phenomena.

“The paraphyletic problem” is fundamentally the problem that classes can’t be real, ie, Russell’s paradox. This problem does not have a solution within our discussion about reality (ie, within conceptualization). Whether it has a solution outside of it or not is a philosophical question, but the two facts that time is relative and that reality can’t stop changing indicate that it actually is a prerequisite for existence itself. It thus appears as the problem of existence itself.

The only thing we know for sure is that we can’t get rid of “the paraphyletic problem” by “denying” paraphyletic groups. Paraphyletic groups will remain monophyletic independently of whether we “deny” them or not. This “denial” is, instead, in practice, a vain attempt to either stop the world or channel our consistently changing opinion about it through typified canals (ie, the PhyloCode). Classification simply can’t be unambiguous; we can only choose between consistent classifications (using an orthogonal system like Linnean systematics and evolutionary taxonomy) or contradictory classifications (using cladistics). The option of unambiguity is simply not given, sorry to say.

I’m not offering an explanation of reality (ie, a solution of “the paraphyletic problem”), but only try to explain that cladistics is an irrational search for a contradiction (ie, a paradox). I’m saying that the fact that we can’t understand reality doesn’t mean that we have to go nuts. We can also admit that we can’t understand reality and that an unambiguous classification is a contradiction, ie, Russell’s paradox. The only alternative that remains then is to reach an agreement about a specific classification of biological organisms, which, unfortunately, appears even more impossible to solve practically than to solve “the paraphyletic problem” (ie, to find a solution to a paradox). The future for biological systematics thus appears to be a never-ending battle about the Pope’s beard, ie, about finding a solution of the paraphyletic problem, that is, about finding a way to bypass the fact that the axiom for the problem is inconsistent. The simple solution to discard the erroneous axiom is not even an option.

The solution of the paraphyletic problem thus appears unreachable by that the reason for it can’t be acknowledged, ie, the inconsistent axiom that causes it, since it would acknowledge Russell’s paradox and thus invalidate the approach that gave rise to it itself, that is, cladistics. The problem is nested in the approach, and the solution to it is thus unreachable by that it would falsify the approach.

Fact is that clades and paraphyletic groups can’t be distinguished consistently (ie, without contradiction), because both of them are monophyletic groups. The idea that there are “natural groups” of organisms is not wrong in itself (already Aristotle discussed genera with their species), but the assumption that they can form a class (like clades) is wrong, per definition, because classes are not “natural”. The cladistic idea of a single “true tree of life” is thus inconsistent (ie, contradictory) per definition (also shown by Russell’s paradox). This fact can’t, however, be acknowledged by cladists, since it would deny the fundament they arrived to when crossing Rubicon (ie, assuming as an axiom that classes are real). There is no way back for cladists.

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

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


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