I woke up towards the end, actually. (Again I seem to grasp this better based on concrete examples; I'm really lousy at theory.) From the cladist/echidna example you gave, it sounds like the cladist emphasizes the vertical relationships in the evolutionary tree, while the evolutionary systematist seems to look more at the horizontal. Am I on the right track at least?
(I realize this is overly simplified.)
Also, in your example, would the cladist say the echidna and the platypus are not similar, or only that they are not similar based only on the characteristic they both share of laying eggs?
"Cladists" are contrasted to "evolutionary systematists", who believe that key transitions in the history of life, such as the evolution of flight, should be recognized in classifications. Cladists argue that there are no objective criteria for defining key transitions and that so-called "key transitions" can evolve more than once.
This is part of a larger battle against received authority in biology. Fifty or more years ago, an expert in a group of organisms would propone a classification based on intuitive ideas of what features were most important. But one expert might introduce a classification based on structures of the nervous system and another on stuctures of the respiratory system. There was no way to decide between them.
This led to the reproducible methods of numerical taxonomy, in which the scientist produced a matrix of observation detailing the characteristics attributed to each taxon. Relationships were determined by overall similarity, not by key similarities. This method is called phenetics. Another school, cladistics, said that relationships should be determined only by derived similarity, not by overall similarity.
To a cladist, an echidna and a platypus are not similar because they both lay eggs; their ancestors also laid eggs, so there was no evolutionary change (in that regard). The change from laying eggs to having a placenta, on the other hand, is a derived similarity that can be used to determine relationships. The cladist tries to find the tree topology that uses the fewest number of steps (evolutionary changes) to explain the observations.
Well, I seem to be writing a textbook. I better stop there and see if anyone is still awake.
Mollusque, just read your post again (and again) to make sure I absorbed all of it into my tiny brain. It actually doesn't surprise me that people might agree on how the tree is organized but still disagree on particular animals. That seems like the heart of the debate, really, and the monophyletic/paraphyletic arguments stem from those debates over specific animals. "Here's this creature: how do we classify it?" would seem like the first question (to me, who doesn't know anything about this field of study really), and "no, no, we shouldn't classify it THAT way" seems like a second step.
Or maybe it's just because I can wrap my head around an argument about whether a given creature was a dinosaur or a bird, but not so much about an argument of how the tree of life should be laid out.
Is there a corresponding word to cladist, for someone who is not a cladist?
You've run into a conflict in theories of classification, c_b. Some biologists (cladists) think only monophyletic groups should be named (ones that contains the ancestor and all its descendants). Others think it's okay to name paraphyletic groups, which contain the ancestor and only some of its descendants.
If you cut the branch that contains dinosaurs out of the tree of life, birds come along with it. That branch is monophyletic. If you then cut off birds, the remaining group is paraphyletic. The strange thing about these debates is that the opponents might agree entirely on the description of the organism and on the topology of the tree, but disagree on whether the beast should be called a bird or a dinosaur.
Great. So I make six lists to classify these puppies, and then I find something like palaeopteryx:
"It was either a theropod dinosaur (a dromaeosaurid) or a bird; its classification is in dispute. Palaeopteryx was redescribed by Jensen and Padian in 1989 as belonging to Deinonychus. Fossils have been found in North America. Palaeopteryx named by Jensen in 1981. This is dubious genus."
Kudos, palaeopteryx. You're still controversial after all these years. :)