Clades are not classes

[SKÁLA Zdeněk]

>For monophyletic taxa to be classes of equivalence, the matrix above should
>be recoded :

    1   1'         2   3   4   5
A   +   +          +   +   +   +
B   +   -          +   +   +   +
C   +   -          +   +   -   -
D   +   -          -   -   -   -

>The recoding of columns 1 and 1'  makes sense only because the
>1' character state is considered a derived avatar of 1. The formal
>recoding above highlights the class nature of clades.

I do not believe that you can place a new property (that was not observable before) to the set of taxa *after* the analysis to make it class. Your definition "features interpreted as nested synapomorphies define classes" is in fact definition of clades, not of classes. In this respect, your argumentation is OK - as concern clades, but do not try to support it by a concept that does not know anything about unobservable properties. Funnily enough, from the point of view of the class theory, the only class in the above cladogram is the paraphyletic taxon BCD (supported by the +1). This can be a case also for other paraphyletic taxa, so it could be rather dangerous to operate with a class theory to support cladistic solutions ;-)

>Maybe this would give a handle for accepting some notion of "natural
>classification" after all:
>features interpreted as nested synapomorphies define classes... to the
>difference of phenetic clustering based overall and "face value"
>similarity, which would constitute a set of "natural similarity-based
>objects", not natural classes.

BTW, "to be in the euclidean distance less than 0.26 from the point (6;8)" is indeed "property", so even clusters can be considered classes if one really needs it. As you can see, the border between cladistics and phenetics will probably go in another direction :-)

Best!
Zdenek