Subject: Re: [lojban] Re: importing ro

From: [email-masked]
Date: Thu, 7 Nov 2002 20:14:01 EST

In a message dated 11/7/2002 1:43:39 PM Central Standard Time, 
[email-masked] 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.