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la nitcion cusku di'e
The set of natural numbers has cardinality aleph-0 The set of real numbers has a cardinality, and it is aleph-1. That means that there are proper subsets of real numbers that are countable: N is a subset of R. It also means it is feasible to speak of 'all' over a transfinite set. It's just that the set is not countable.
But "real numbers" are not substance. A real number is a countable
thing, even if there are uncountably many of them.
_Bits_ of substance are uncountably many, just like real numbers,
but substance is not "many" in any sense.
There is the mathematical notion of "uncountably many", which can
only apply to semantic countables, like real numbers or bits of
substance, and there is the semantic notion of "uncountable" in
the sense of there being no individuals to count. {ro} indicates
semantic countability, not mathematical countability.
Since xod, we have been limiting the denotation of {ro} to countable
numbers, and tu'o to transinfinte numbers. This would mean we cannot
speak of ro namcu with respect to the set of Real numbers. This is
bogus.
I agree this is bogus. I disagree that this is what we have been doing, though.
There is a third reason to use tu'o: if there is no quantification going on at all. No quantification means no prenex. The kind divorces the quantificand from any prenex. So I contend tu'o lo mikce --- a non-counted, not an uncountable doctor --- is meaningful as an individual, not a substance: it is the intensional doctor, the doctor-kind.
I agree with that. I did define my use of {lo'e broda} as {tu'o
lo broda} at some point.
mu'o mi'e xorxes
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