paraphyly

[SKÁLA Zdeněk]

(I am splitting the answer into clades/classes and paraphyly messages since the two topics do not have much in common.)

zdenek and pierre (combined):
>Most of the discussion boiled down to a rather simple point:
>having a pectinate cladogram ((((A,B)C)D)E) and "significant gaps" B|C and 
>D|E, a cladist will probably name the taxa (((AB)CD)E), that is (ABCDE), 
>(ABCD), and AB.

The crucial point, I believe, is the following:

zdenek:
>>...there should be a criterion of
>>quantity of "gap significance" ... even cladistic taxa splitting will
>>deserve some measure of gap significance (say "S") - at least to decide at
>>which level will be the clades named

pierre:
>Yes, but to decide only that.
...
>For the strict
>cladist, "all significant gaps" will be worth naming the monophyletic group
>they support, while the eclecticist will need a supplementary criterion:
>among all significant gaps, what are the "more significant ones" ...

zdenek:
>>...the concept of having some measure of gap significance (S)
>>enables to make an ordering of gaps in the lines of
>>S(B|C)>S(D|E)>S(A|B)>...etc.

pierre:
>I simply don't think the sequence (hierarchy of gaps) is necessary for
>cladists. It's only "gap significant or not", .. Am I
>missing something here ?

I believe so. In the concept of *any* measure ("S" in our case) is implicit the ordering. For example, to measure the significance of gaps by number of apomorphies, % of bootstrap support or whatever it is implicit that 5>4>3>2 etc. Hence, once you have a measure (and even cladists need it for this purpose), you need no extra operation to have the hierarchy of gaps which is also sufficient for an eclecticist. Could it solve our discussion?
Best regards!
Zdenek