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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.
For example, in Jorge's scheme, A and E are not contraries, since if S
is vacuous, they are both true. Likewise, E and O are not subcontraries,
since if S is vacuous, they are both false. A does not imply E, since if
S is vacuous, A is true but E is false. In fact, the only relationships
that survive are the contradictory pairs. This is simply not Aristotelian
logic at all.
Fortunately, by applying modern logic with its unrestricted quantified
variables, where there are no subject terms, Jorge can get everything
he wants. The following paraphrases work perfectly:
A-: ro da zo'u ganai da S gi da P
E+: su'o da zo'u ge da S gi da P
I-: ro da zo'u ganai da S ginai da P
O+: su'o da zo'u ge da S ginai da P
The paraphrases break down only if the universe as a whole is vacuous,
which I consider to be an unimportant corner case.
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. 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.
--
Only do what only you can do. John Cowan <jcowan@hidden.email>
--Edsger W. Dijkstra, http://www.reutershealth.com
deceased 6 August 2002 http://www.ccil.org/~cowan