Andreas Schueler Chokes Again- When "Groups Under Groups" Are NOT "Groups Within Groups"
Nested hierarchies are "groups within groups". For example with Linnean Classification the Animal Kingdom consists of and contains Phyla, which in turn consist of and contain Classes and so on. This scheme exhibits summativity. All nested hierachies exhibit summativity. If it doesn't exhibit summativity then it ain't a nested hierarchy. That is what is meant by "groups within groups".
Now it is true that this groups within groups scheme can be displayed as groups under groups. Phyla are under Kingdom. Classes are under Phyla and so on.
For some reason it appears that Andy thinks that this means all groups under groups are also a nested hierarchy. However it is obvious that ancestor populations do not consist of nor contain its descendent populations. That means that any and all schemes that depict ancestor-descendent relationships are non-nested hierarchies because a parent population does not consist of nor contain its descendent populations and it does not exhibit summativity.
Darwin's diagram in "On the Origins of Species..." is a non-nested hierarchy. Non-nested hierarchies are groups under groups (or groups sunordinate to groups) without being groups within groups.
And that brings us to another point- Andy's ignorance of summativity betray's his alleged knowledge of nested hierarchies.
Again for Andy- summary of the principles of hierarchy theory:
Nested and non-nested hierarchies: nested hierarchies involve levels which consist of, and contain, lower levels. Non-nested hierarchies are more general in that the requirement of containment of lower levels is relaxed. For example, an army consists of a collection of soldiers and is made up of them. Thus an army is a nested hierarchy. On the other hand, the general at the top of a military command does not consist of his soldiers and so the military command is a non-nested hierarchy with regard to the soldiers in the army. Pecking orders and a food chains are also non-nested hierarchies.THAT is why a family tree, with the parents at the top, is NOT a nested hierarchy. Parents do not consist of nor contain, their children.
Andy also seems to take issue with the fact that nested hierarchies require definitions for its sets and levels:
Level of organization: this type of level fits into its hierarchy by virtue of set of definitions that lock the level in question to those above and below. For example, a biological population level is an aggregate of entities from the organism level of organization, but it is only so by definition. There is no particular scale involved in the population level of organization, in that some organisms are larger than some populations, as in the case of skin parasites.Seriously- how does he thinks the entities occupy the space the are given? Does he think someone just puts them there because they want to?