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logic; BCF (going gets tough)
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
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
but I break arguments into single
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....
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.
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