As for ONE kind of classification ...

[Ken Kinman]

Hi Christian,
     I agree with you up to a point.  But I will not concede that paraphyletic groups are inherently "bad" (polyphyletic groups are unnatural and bad, but paraphyletic groups are NOT).  The goal should be to eliminate ALL polyphyletic groups, but I see no reason to EVER abandon perfectly natural taxa like Nematocera, Prokaryota, Bryophyta, Pteridophyta, Sarcopterygii, Amphibia, Reptilia, and so on, just because they are paraphyletic (much less the even worse practice of converting them into clades, as has been done in the last three in that list, the Amphibia and Reptilia being shrunk down, and Sarcopterygii being massively enlarged to include all of its tetrapod descendants).

    Paraphyly is perfectly natural, and will always be useful if employed in moderation and is explicitly marked as being paraphyletic (as is being done with the subdivision of Diptera).  Why EVER abandon a taxon Nematocera just because it is paraphyletic?  And be forewarned if some nitwit ever tries to reduce Nematocera to a clade, I hope his colleagues burn him in effigy (or maybe tar and feather him, along with a few herpetologists who've hijacked paraphyletic taxon names and terribly destabilized them in the process).  For strict cladism (and its worst manifestation, PhyloCode), they destabilize in the name of stability, and now they've begun to bicker among themselves, and everyone else suffers the consequences.  What is working relatively well for the Diptera is a disaster applied to higher tetrapod systematics (and a lot of other taxa as well).
  ---Ken

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Christian Thompson wrote:
So, perhap we should follow their lead.  Yes, paraphyletic group are bad, but in some senses they may be useful.

So, as Ken well knows, at the Diptera WWW site, we use some paraphyletic and even polyphyletic groups, BUT they are clearly marked as such so users are warning that in some context they should  not be used (such as prediction, etc.). Take at look at:
http://www.sel.barc.usda.gov/Diptera/names/famlistt.htm