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The problem cladistics tries to solve is to find a non-contradictory classification of a classification, ie, a classification of all biological organisms into a non-contradictory ”Tree of Life”.
The problem this search encounters is that any such classification consists of finite classes, ie, sets, per definition, because it means that any such solution is “the set of all sets”, which Bertrand Russell showed (1901) is paradoxically contradictory. The solution is thus an infinite recursion (ie, infinite loop) per definition. It means that cladistics was falsified already when it emerged.
Strangely enough, this fact does apparently not prevent cladists from continuing, and being paid to continue, this futile search.
Another contribution to understanding of conceptualization http://menvall.wordpress.com/
2012-12-06 22:40:39
Source: http://menvall.wordpress.com/2012/12/07/the-futile-cladistic-search/