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You commented:
<I see now a new difference in opinion here.  It's not cladistics or phylogenetic taxonomy you guys don't like, it's the assumption of parsimony in evolutionary theory.>
We were looking at 3 subjects, science and manipulation of reality, cladistic analysis, and nomenclature based on that analysis.  'Twas not I who mentioned parsimony (which is part of analysis).
Still, now that you've brought it up...
Let's say that in looking at available examples, you knew about 1 definite situation that violated parsimony and 99 that followed parsimony.  Then you could conclude that parsimony probably applies most often in situations similar to the 99.  You could even analyze the 99 situations in an attempt to find what was 'lacking' in the situation in which it did not.
Now, you can apply parsimony, believing it is probably applicable to a specific past situation.  You will never have a definitive answer (distant past evolution can be neither observed nor rerun), but you can come up with a most likely scenario.  That scenario is subject to change (being only most likely) and to question in a way that a direct observation or even a 'theory' like evolution is not.  The hypothesis remains the property of the person who made it and those who agree with it.
(I'm purposely leaving out what appear to be logical flaws in the methodology because I'd have to be a lot more knowledgeable to assert them with enough certainty to make them solid grounds for criticism.  Someday, I'd enjoy hearing the comments of a formal logician who has studied cladistics closely.)
In addition to the fact that the methodology a priori cannot guarantee accuracy, there are also errors/subjective elements to the data.  Human beings are making these decisions about which animals to include, what characters are present/absent, and how to code, particularly relative codings like ratios above or below a certain threshold.  I'm not criticizing the effort, but we know accuracy is a progressive process.
There are also the effects of missing data because fossils which would prove essential have not been and may never be found.
And then, after all that, the results of the computer program have to be interpreted.  Even with all the skills of the scientist looking at sheets of computer paper, the preference for a result with 17 reversals, say, compared to 18 is not what you would want to call an unarguable increase in credibility.
So, Pete, if by objective you mean unarguably accurate, cladistics isn't there.  If you mean without opinion, cladistics isn't there, either.
You concluded:
<So what if parsimony doesn't come up with the tree you constructed in your head?  What are you left with in the absence or parsimony?  Munificence makes science become impossible: there are so many infinitely more complicated schemes why bother testing any of them?>
Parsimony and the other problems all make the results of the analysis less than totally reliable.  You ask about alternatives.  I don't know how I'd go about finding one that didn't have the same flaws, though someone else might.  Should we stop trying to make sense of all these fossils (which are at the same time both many and far short of what we need)?  No.
But at the same time, I'd argue that we shouldn't be dismissive of alternatives.  We're not fending off inadequate challenges to perfect accuracy, we're making a continuing attempt to improve our understanding, with no guarantee of a successful result, and no certainty that we have made much progress so far.