> I think this identifies this entire discussion as a quiddity.  I'm not 
> interested in playing that game.  If I were, I could also go about saying

You call it a game, some of us call it mathematics. I agree it's fun
though, that's why we spend a lifetime doing it...


> There is no reason why what you consider an extrinsic property of sets, an 
> ordering, cannot also be considered an intrinsic property, especially if the 
> latter is more useful.

Except that set theory is the most formal of all mathematical
disciplines. Without precise definition it is nothing (and very easily
made inconsistent). You can take whatever useful construct you like and
choose to call it a set if it pleases you, but usually it's helpful to
use standard terms with standard meanings.

David

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