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logic; BCF (going gets tough)




Philidor,
In some ways I think you are unnecessarily self-inflicting a sort of mental pain by trying to logically analyze such questions and agonizing over each and every step. Especially over abstractions like circles and infinity. Using similar logic you could perhaps show that circles cannot exist, and therefore it is rather illogical to even debate measuring the area of something that doesn't exist.
In cladistically analyzing groups of organisms, I use the concept of sister groups. However, I do not think that sister groups actually exist. They are an abstraction that Hennig found to be methodologically useful (and pointing this out often helps students who otherwise find cladistic analysis illogical). I avoid ever getting into arguments of logic with those who insist that sister groups actually do exist (I figure it would be a waste of time), but I would think it would be much easier to argue against the reality of sister species than against the reality of circles (or even whether the areas they enclose can be determined, assuming they do "exist").
I use sister groups and calculus as useful methodologies, but I do not waste much time philosophically (especially logically) trying to justify it. Otherwise you really do risk miss seeing the forest for the trees (yes, I know I overuse such cliches).
Not that I think cladistic analysis is anywhere nearly as precise as calculus (for those who think my analogy is stretching it). On the contrary, cladistic analysis (however useful it may be when used properly) is quite vulnerable to subjective decisions, circular reasoning, and other inherent drawbacks.
I think it is still up in the air whether or not current dinosaur cladograms are flawed on the question of whether dinosaurs came first (still widely embraced) or birds came first (BCF). That is another reason I oppose using strictly cladistic classifications, but I also believe that cladistic analysis will ultimately decide the question once enough data is available. So I use "logic" in trying to detect possible circular reasoning, but pushing logic too far seems to be a sort of mental self-torture. All things in moderation.
-----Ken Kinman
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philidor11 wrote:
I've argued with a friend .... that the
area of a circle cannot be determined.  The formula assumes squares small
enough to fit the outline of a curved surface, and that can't happen until
the squares become points, in which case they can't measure...  And so many
functions don't work until you reach infinity, and by definition infinity
can never be reached....
but I break arguments into single
steps to worry each one.  For you and my grandfather calculus may be
enjoyably self-consistent and self-evident, but for me and a few other
people the inherent assumptions are downright painful.
Ok?
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