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Let's say that in looking at available examples, you knew about 1 definite situation that violated parsimony and 99 that followed parsimony.
How could we know that?
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.
Most parsimonious, yes.
That scenario is subject to change (being only most likely) and to question
in a way that [...] a 'theory' like evolution is not.
No. Phlogiston was a theory according to http://www.dinosauria.com/jdp/law/evolfact.htm.
The hypothesis remains the property of the person who made it and those who agree with it.
How do you mean "remains the property"?
(I'm purposely leaving out what appear to be logical flaws in the methodology
such as algorithms that can find a local instead of the global minimum, the ability not to recognize long-branch attraction...
[...] Someday, I'd enjoy hearing the comments of a formal logician who has studied cladistics closely.)
So would I... good luck in finding any formal logician that has any interest in biology :-)
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.
Of course. Anyway, scientists are humans. Cladistic analysis is just the least subjective of all methods for finding out phylogeny invented so far. :-)
Relative codings are not so bad when there is a morphological gap (such as "less than 20 % (0), more than 60 % (1)").
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.
It is becoming more and more common (appears to me) to publish both the MPT and an interesting different tree that is slightly less parsimonious. The description of Rahona[vis] is an example: the MPT has
|   `--+--Archaeopteryx
|       `--Rahonavis
, while one tree that is one step longer has
-- the authors don't decide.
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.
But still more reliable than all other available methods (and the only one I can think of is using a lot of intuition, the sort of thing that HP Ken Kinman is currently accused of).
[...] with no guarantee of a successful result, and no certainty that we have made much progress so far.
That's because we can't compare our results to the truth and see how much progress we've made. I'm pretty sure that we have made quite some progress, though.