removing one set from another

Tom DiBenedetto tdib at UMICH.EDU
Tue Jun 17 10:10:25 CDT 1997


On Tue, 17 Jun 1997 12:30:25 -0400, Rodham E. Tulloss wrote:

>As a mathematician (in fact as a metamathematician who lived set theory in
>grad school), may I suggest that Maureen Kearney is confusing the
>membership of a set with the common properties of those members.  In fact,
>sets are defined by statements (all x, such that x is blue and has green
>stripes) including, but not restricted to, the statement that lists
>membership.

BUt of course, the problem for systematics is that taxa are only sets
to the extent that they are approximations to the real historical
lineages. Lineages are individuals, not classes. How do you carve up
nature at its joints, when in fact the history of life has flowed
uninterrupted in an outwardly diverging pattern, such that there are
contiguous links between everything at the terminals and the base? It
seems to me that the only "natural" way in which to divvy up this
hierarchy are at its branching points. And that is the cladistic
approach to naming groups,,,apply names to coherent branches and
their sub-branches.
        I think that many of the arguments, focusing on the
peripheral isolate example, are missing this vision. It is not the
number or size of the dispersal event, it is not the accumulation or
not of apomorphies in one or the other branch, it is the *fact* of a
branching event (obviously one that persists long enought to be
meaningful) which calls for the naming of a new, internested taxon.
All of the biological links between an ancestor and the large
unchanged remaining population (in the example we have all been
discussing) which cause everyone to insist that they be considered
the same, are present between the ancestor and the isolate as well.
So what is the basis of applying a new name to anything? Ultimately
it is not the new apomorphy *per se*, it is the fact of the branching
of the lineage. Of course we end up  using the new apomorphy as
evidence of the branching, so we all are comfortable with applying
names to things that look a bit different (and not to things which
look the same). Buf if we could know the history without character
evidence, wouldnt y'all want to represent that in classification?
Isnt that our bottom line?




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