From pycyn@aol.com Wed Nov 06 10:12:09 2002 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_2_3_0); 6 Nov 2002 18:12:09 -0000 Received: (qmail 60354 invoked from network); 6 Nov 2002 18:12:08 -0000 Received: from unknown (66.218.66.216) by m13.grp.scd.yahoo.com with QMQP; 6 Nov 2002 18:12:08 -0000 Received: from unknown (HELO imo-d08.mx.aol.com) (205.188.157.40) by mta1.grp.scd.yahoo.com with SMTP; 6 Nov 2002 18:12:08 -0000 Received: from Pycyn@aol.com by imo-d08.mx.aol.com (mail_out_v34.13.) id r.9d.30a97809 (2612) for ; Wed, 6 Nov 2002 13:12:04 -0500 (EST) Message-ID: <9d.30a97809.2afab574@aol.com> Date: Wed, 6 Nov 2002 13:12:04 EST Subject: Re: [lojban] Re: importing ro To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_9d.30a97809.2afab574_boundary" X-Mailer: AOL 8.0 for Windows US sub 230 From: pycyn@aol.com X-Yahoo-Group-Post: member; u=2455001 X-Yahoo-Profile: kaliputra --part1_9d.30a97809.2afab574_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 11/6/2002 9:45:31 AM Central Standard Time, lojban-out@lojban.org 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. --part1_9d.30a97809.2afab574_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 11/6/2002 9:45:31 AM Central Standard Time, lojban-out@lojban.org 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.

 --part1_9d.30a97809.2afab574_boundary--