Subject: Re: [lojban] Re: importing ro

From: [email-masked]
Date: Wed, 6 Nov 2002 13:12:04 EST

In a message dated 11/6/2002 9:45:31 AM Central Standard Time, 
[email-masked] writes:
<<
> "naku ro pavyseljirna cu blabi" is not a true statement, because
> it makes more claims than you are giving it credit for, and you
> only contradicted one of them. In fact, it's not even a true
> statement with a nonimporting universal quantifier, if we keep our
> negation boundary rules unchanged (more on this below).
>>
I think it is true, but it reduces down to {mei[ro] pavyseljirna cu blabi}, 
which is most likely not importing (not all questions are thoroughly worked 
out, after all). The "non-importing" version is certainly false, since, with 
a "non-importing" (of pavyseljirna) universal, the whjole is true if the 
antecedent is false.

> <<
> The reason is that you're constructing your original statement
> wrong. To work with an importing ro you have to do it by using a
> nonrestricted variable when you don't want to claim something exists;
> like this:
> 
> ro da zo'u ganai da pavyseljirna gi da blabi
> Ax(Ux -> Wx)
> 
> Which is true even in a universe of discourse where there are no
> unicorns. Though, it is false in the empty universe (not that we
> care much about that).
>>
This is right, but only distantly related to the original {ro pavyseljirna cu 
blabi}

<<> 
> It should be noted, btw, that:
> 
> no pavyseljirna cu blabi
> 
> is a false statement because no imports also, since it can be moved
> around.
>>
The status of restricted {no} is also in doubt, I think. Since it reduces 
back to {naku su'o} it seems to be non-importing (and was usually so 
historically).

<<
> Actually the more I think about this the more I like importing
> universals for lojban. Take a look at the generalization of what
> you were talking about:
> 
> naku ro da poi gerku cu broda
> 
> Now; imagine that ro *doesn't* import. The above sentence, then,
> can't have the negation boundary moved:
> 
> su'o da poi gerku naku broda
> 
> which claims there is at least one gerku.
> 
> So what's really going on is what AndR says here, I think: It is
> "da" that imports, not ro. Which is both consistent with book and
> makes sense (and i'm even starting to like it better than nonimporting
> foo).
>>
Well, {ro} imports the range of {da}, i.e., that variables always have 
something to stand in for. But, by that token, when the range of {da} is 
restricted -- or when there is not {da} at all -- the restricted set comes to 
be non-empty as well, according to one line of argument (the usual one, in 
fact).

adam:
<<
It sure is inconsistent on this point. According to the book, 'ro 
pavyseljirna xirma cu blabi' is false, since 'ro pavyseljirna' has 
existential import, and thus 'naku ro pavyseljirna xirma cu blabi' is 
true, since it is the negation of a false statement. According to ch. 16 
sec. 11, this is exactly equivalent to 'su'o pavyseljirna xirma naku 
blabi', which is false, since once again it claims existence of 
unicorns, and so either the book allows contradictions, and should be 
called 'the complete zenban language', or we can disregard that 
silliness about 'ro' having existential import, and use 'ro' as is 
standard in mathematics at least (whether or not that is the standard 
use in logic, as pc seems very certain that it is not).
Ther is a simpler explanation than either of these extreme forms -- and one 
with a lot of backup evidence. The book simply goofs badly at this point, 
jumping over a distinction and then back and forth between two ways of 
dealing with it. As noted above {naku ro pavyseljirna cu blabi} actually 
reduces to {me'iro pavyseljirna cu blabi} (it took a while to find the right 
quantifier here -- thanks, xorxes). Now, the modern logic of unrestricted 
variables treats this as {su'o da ge da pavyseljirna gi da na blabi} and then 
treats that as {su'o pavyseljirna na blabi} . The first of these shifts is 
at least questionable, although the second seems not to raise any problems by 
itself. At the least, each step here neds to be justified and that 
justification was left out of CLL (simply because no one noticed that it was 
needed -- or that it got things wrong). The alternative is to make 
non-emptiness a presupposition, which muddies the water much more.
Sorry, but you are just wrong about mathematics (where do you thing logic got 
its modern notion). To be sure, in unformalized presentations, the fact that 
the quantifier actually extends over everything (within reason) is not 
apparent, nor is the fact that the apparent subject term is actually 
antecedent in a conditional. But both these are the case in mathematics as 
well as in Logic. One of Lojban's virtues is that it separates these two 
expressions which get carelessly slopped together, to everyone's confusion.