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Classification is ultimately paradoxically contradictory, as Russell’s paradox shows. The reason is that classification is fundamentally orthogonal, ie, every class contains several (at least two) classes, by meaning that every single class is contradictory in number.
This fact leaves us with only two practical options:
1. to “acknowledge” the paradoxical contradiction, that is, to either accept an inconsistent (ie, contradictory) classification or to search in vain for a consistent classification (like cladistics does), or
2. to obtain consistency in numbers by using an orthogonal system of classification, like the Linnean systematics or evolutionary taxonomy, ie, treating every class consistently as single entity (either a finite class, ie, category, or an infinite class).
The option of finding a consistent classification, like the idea of a single True Tree of Life, is simply not given. Instead, this option is actually the opposite to a single entity, and since a single entity has two aspects: pattern and process, it instead IS two aspects AT THE SAME TIME, that is, an infinite recursion (ie, every particular solution pointing at another solution). The option is actually a conflation one and many, that is, of object and class, and as such a purely abstract construction.
Another contribution to understanding of conceptualization http://menvall.wordpress.com/
2012-08-10 03:22:52