On the difference between Linnean systematics and cladistic classification

Both Linnean systematics and cladistic classification classify a bifurcating process in a generic aspect (ie, all specific aspects at the same time). The difference between them is that:

Linnean systematics is a consistent (ie, non-contradictory) orthogonal system, whereas cladistic classification is inconsistent (ie, contradictory).

It means that Linnean systematics can incorporate the generic aspect of a single bifurcating process, whereas cladistic classification can only produce specific (ie, contradictory) classifications.