nominal characters

[Mr Fortuner connection modem]

I have the nagging suspicion that:

"A truly nominal character cannot be
present in a valid species in more than one state"

Is this true? The
proposition cannot be proven in the mathematical sense, but it could easily be
disproved if examples can be found to contradict it. Does anyone know of a
counter-example?

To make sure we all agree, a "nominal" character is one of
which the states cannot be ordered. Many (most?) qualitative characters are
ordinal, which means that their states can be arranged in a linear fashion
(state1 < state2 < state3, etc.), or in a bi-dimensional space (e.g., colors
arranged by wave length and grey level), or in a multi-dimensional space
(shapes - the form of the outline - can be represented by mathematical
expressions which can be subjected to a DFA for positioning each shape in a
multi-dimensional space). With nominal characters, the only thing that can be
said about states is that they are different, e.g., a cartilaginous fish is
different from a fish with an ossified skeleton or a monocotyledon is
different from a dicotyledon.

So, can you have a fish with an
ossified-cartilaginous skeleton or mono-dicotyledon plants?

To make things
more interesting, all presence/absence characters are disqualified.

Renaud
Fortuner
fortuner at math.u-bordeaux.fr