[lojban] Re: importing ro

[pycyn@aol.com]

In a message dated 11/7/2002 1:43:39 PM Central Standard Time, jjllambias@hotmail.com writes:
<<

-.  The quantifiers in your system do not
>carry
>over to the variable cases (except, of course, that work as long as the
>universe is non-empty).

They certainly do carry over to the variable cases, even in
the empty universe case. {ro da broda} is tautologically true
in an empty universe in my system, just like {me'iro da broda}
is tautologically true in your system, but false in mine.

>>
The fact that your {ro} gives truth in the empty universe shows that it is not the universal quantifier of standard logic, all of whose quantified sentences are false in the empty universe.  And, of course, {me'iro da broda} is not tautologically true, since it explicitly excludes the case of {ro da broda} -- or do you mean "in the empty universe", in which case, yes, it is true then (note, not "tautologically" which runs across universe size).  Both are vacuously true in the empty universe.  So far as I can recall, that is the only time that these two differ in this connection (well, some rules about instantiation and generalization that would only make sense in a proof), so the advantage of using your choice rather than the usual one, seems slight.  I gather that you do so as a reason for reading {ro broda cu brode} in a non-importing way. While it is nice to have someone concede that the same quantifier is involved in both places (but I suppose you have done this already), I still don't see the point of this, since you already have the non-importing (for broda) quantifier -- and in exactly the form it normally is in Logic.  Why not also have the importing one in the same way?

<<
I think (A-E-I+O+) is simpler, and I can get all cases as well,
of course.
>>
Well, let's see the "modern" version is simpler because you only need two basic quantifiers.  But that is true in this system as well; it's just clearer with four.  Q- DeMorgan goes through with your system but occasionally misleads as a result (correctable, of course).  As for the definitions, I don't remember any short ones for getting the +'s from the minuses or the minuses from the pluses, but I suppose there are some.  All the traditonal cases are just obversion: change the sign of the quantifier and the predicate, leaving  the generality the same: O+ is just {su'o broda naku brode} and so on.  Of course, there are the long forms as well: {ge me'i broda cu brode gi su'o broda cu broda}, to continue the example.






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