> Here we need a rule, for example:
>
> The inside of the subset is the
> area that contains all that it is.
I've tried to figure out which of various possible meanings you intended,
but English is hopeless for this task. As you're good at formalisms,
could you try to make your argument more formally, and in particular,
indicate where you're using fuzzy sets and where 2-valued sets?
Needless to say, you should *expect* to arrive at contradictions and
paradoxes if you are reducing an argument expressed in fuzzy set theory
into another based on traditional logic --- Bertrand Russell showed
that very clearly. I worked a lot with higher-order functions and
typed objects while doing research on concurrent object-oriented purely
functional languages, and I used to come across this sort of problem
all the time. It's a good thing that people are beginning to show some
will to drop political correctness in maths at long last and look at more
powerful formalisms, as it's been an annoying bugbear for a long time.
Cheers,
Rich.
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