On the relation between "entity", "class" and "category", and cladistics

There is a fundamental difference between entities (ie, objects) and classes in that every single class contains at least two entities. A single entity thus can't be a single class, just like a single class can't be a single entity. The reason is that if a single class indeed could be a single entity, then "infinite class" (what we traditionally call "class") would equal "finite class" (what we traditionally call "category"), and there would thus not be any difference between the concepts "entity", "class" and "category", which is contradicted by the fact that "class" can't equal "category", since it would mean that "infinity" equals "finity", which simply is a contradiction.

The relation between entity and class is thus orthogonal, which can be described mathematically by the formula X/Y=Y/X (read as that X (entity) relates to Y (class) like Y relates to X).

Cladistics conflates this orthogonal relation between entity and class by conflating the concepts "entity" and "class". This conflation does not equalize entities and classes, but just leaves consistency for consistent inconsistency.