On lineages and cladistics

The smallest component of a lineage is in mathematical terms a projection. A projection, in turn, is a transformation from one matrix to another matrix via a transformation matrix. The projection is thus the operation (ie, the transformation) in itself. In this sense, the smallest component of a lineage does thus consist of three components: one situation before, one situation after and the transformation filter between them.

Now, it is consistent to view the situation before and the situation after as real, but it is inconsistent to view the transformation between them (ie, the lineage) as real (as cladistics does), because it (the lineage) is paradoxically contradictory between the situation before and the situation after. Ie, there’s no way to tell which of the situation before and the situation after that equals the lineage. The consistent handling of the transformation (ie, the lineage) is instead as a vector, that is,  as an element of the real coordinate space Rn, which thus also is consistent with the expression above of a lineage in mathematical terms as a projection (as in Linnean systematics).

In such consistent handling of a projection (transformation or lineage), every particular projection has at least one isomorphic projection that describes the same projection differently, meaning that the two isomorphic projections are indistinguishable if we inconsistently view the projection itself (instead of the situation before and the situation after) as real. This inconsistent view on the projection (eg, cladistics) does thus lead us into conflation of two isomorphic projections, which thus forms a paradox (ie, Russell’s paradox), which we in this view think we can find the solution of, although paradoxes actually lack solution. The inconsistent view on the projection (eg, cladistics) thus leads into a belief that we can find the solution of Russell’s paradox, although this paradox actually is a consequence of our own inconsistency.

The inconsistent view on projection (transformation or lineage), eg, cladistics, thus leads us into a belief that we can solve our own conceptual confusion by finding something that isn’t to be found, because it is a paradoxical contradiction. The view thus actually creates a problem that lacks a solution.

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