An explanation of Russell’s paradox and its relation to Linnean systematics and cladistic classification
Russell’s paradox tells us that:
We can divide a particular kind of objects, like biological organisms, into finite sets, of for example definable or historically unified collections (like our notion of “biological species”), but every such division does ultimately encounter a paradoxical contradiction, ie, no such division breaks even.
This fact may seem ”unnatural” for us, but it is just because we do not realize that we implicitly divide reality from our conceptualization of reality by conceptualization itself. Russell’s paradox just tells us that this implicit division is artificial, ie, that reality actually is not divided from our conceptualization of it.
The only way to bypass this paradox, ie, to reach consistency and thereby become able to produce a conceptualization that breaks even, is by using an orthogonal system of classification classifying objects into categories of classes, like the Linnean system, because such system bypasses the paradox with its orthogonal relations between objects, categories and classes.
This solution does not, however, bridge our implicit (and thus artificial) division of reality from our conceptualization of it, but instead turns Russell’s paradox into an ambiguity between reality and our conceptualization of reality, at the same time as it makes all possible such conceptualizations consistent. It thus actually turns the orthogonal cube of interface that separates our conceptualization of reality from reality (which we call Russell’s paradox) into a consistent ambiguity.
The recently arisen (but actually pre-scientific) approach in biological systematics called “cladistics” instead boldly denies Russell’s paradox and moreover defines that there is no difference between reality and our conceptualization of reality (ie, that we do not implicitly divide reality from our conceptualization of it by our conceptualization). This “trick”, however, does neither eradicate Russell’s paradox, nor reverse our implicit artificial division of reality from our conceptualization of reality, but instead opens the door to an irrational search for Russell’s paradox, in the form of a typological idea of a single True Tree of Life. This idea is thus an inverted paradox, that is, an infinite recursion. Cladistics does thus actually turn the orthogonal cube of interface that separates our conceptualization of reality from reality (which we call Russell’s paradox) back from the Linnean consistent ambiguity to the paradox, but this time under the influence of a belief that the paradox is real, ie, that it can be found.
Russell’s paradox is thus actually an orthogonal cube of interface that separates our conceptualization of reality from reality, giving us two options for conceptualization: paradoxical contradiction (ie, subjectivity) and consistent ambiguity (ie, objectivity). Linnean systematics uses its consistently ambiguous option, thus being a consistent (but ambiguous) conceptualization of biological organisms, whereas cladistics uses its paradoxically contradictory option, thus being a vain search for an infinite recursion.
I welcome comments on and suggestions of corrections of this explanation.
Another contribution to understanding of conceptualization http://menvall.wordpress.com/
2012-09-06 05:58:51
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