After re-reading this thread it is clear to me that once again we have a disagreement that stems in semantics. I think Cking and I agree on the definitions of para and polyphyly, but he thinks paraphyly is a form of monophyly, where I equate the terms holophyly and monophyly. While I believe my use of these terms has historical precedence and is more widely accepted in the literature, I'd rather not argue semantics. If Cking were smarter he might have caught this before I did, but it looks like he instead resorted to claiming my example had "garbage" for data and never really took the time to examine the challenge. It is this type of dogma that prevents any progress from being made in these discussions.

I believe we still disagree on whether paraphyletic groups should be recognized in formal taxonomy, but that is a matter of opinion. I have shown that the distinction between para and polyphyly can be impossible sometimes even when the tree is fully resolved. This provided an excellent example of why non-monophyletic (or non-holophyletic if you please) is useful sometimes. It is also useful if you don't care whether the grouping is para or polyphyletic, only if the grouping is monophyletic (or holophyletic). So in the end much of the difference is opinion on two fronts (the meaning of the term monophyly and the acceptance of paraphyletic groups in formal taxonomy). But claiming that cladists are dishonest whenever they use the term non-monophyletic is clearly bull.

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