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John:
> In my earlier posting I had proposed, but not defended, the following
> (standard) assignment of existential import: A+E+I-O-. Jorge
> counter-proposed A-E+I-O+, but this would break Aristotelian logic, and
> reduce the very real distinction between it and modern logic to a nullity
> (Reminder: + means that if S, the subject term, is vacuous, the function
> is always false, whereas - means there is no such generalization available.)
>
> It is of the essence of the AEIO functions that they obey the laws
> of the Aristotelian square: A and O are contradictory, E and I are
> contradictory, A and I are contrary (can't be both true), E and O are
> subcontrary (can't be both false), A implies E, I implies O, and A and
> E can have their subject and predicate terms interchanged. These things
> are only true with the existential-import rules as I stated them
[...]
> And's point that lo'i ro broda is meaningful even if nothing broda's
> is a good one that I do not know how to address at present.
A pretty obvious way to address it is not to equate {ro} and A+.
Treat {ro} as the cardinality of the set being quantified over.
A+ can be done as {ro (fi'u) su'o}.
> I note
> however that for all such values of broda, the same set (viz. the empty
> one) is addressed. I reject all talk of "intensional sets": a set may be
> defined by extension or by intension, but set *identity* is defined
> by the following tautology:
>
> ro bu'a ro bu'e zo'u
> go lo'i bu'a cu du lo'i bu'e
> gi go ro da bu'a gi bu'e
>
> that is, sets are identical iff whatever is a member of one is a member
> of the other, and in particular there is only one null set
An "intensional set" is a Kind -- Mr Set of All Broda. Since SL
doesn't do Kinds, I accept what you say, but am endeavouring to
develop ways to do Kinds in AL.
--And.