From pycyn@aol.com Thu Mar 14 07:42:04 2002 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: unknown); 14 Mar 2002 15:42:04 -0000 Received: (qmail 91180 invoked from network); 14 Mar 2002 15:42:04 -0000 Received: from unknown (216.115.97.171) by m12.grp.snv.yahoo.com with QMQP; 14 Mar 2002 15:42:04 -0000 Received: from unknown (HELO imo-m10.mx.aol.com) (64.12.136.165) by mta3.grp.snv.yahoo.com with SMTP; 14 Mar 2002 15:42:04 -0000 Received: from Pycyn@aol.com by imo-m10.mx.aol.com (mail_out_v32.5.) id r.17e.4ffcfff (4324) for ; Thu, 14 Mar 2002 10:41:58 -0500 (EST) Message-ID: <17e.4ffcfff.29c21ec6@aol.com> Date: Thu, 14 Mar 2002 10:41:58 EST Subject: Re: [lojban] More about quantifiers To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_17e.4ffcfff.29c21ec6_boundary" X-Mailer: AOL 7.0 for Windows US sub 118 From: pycyn@aol.com X-Yahoo-Group-Post: member; u=2455001 X-Yahoo-Profile: kaliputra --part1_17e.4ffcfff.29c21ec6_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 3/13/2002 5:29:15 PM Central Standard Time, jjllambias@hotmail.com writes: > So, in: > > ro broda su'o brode cu brodi > = no broda me'iro da poi brode cu brodi > > What is the "actual quantification" of broda and brode? > I can tell what the actual import is: - for broda and + for brode > in my system, ++ in yours. But what is the "actual > quantification"? I forget what my system is supposed by you to be. But in any case, I don't quite follow the identity you propose: Change {ro} into {no...naku}, change {su'o} into {me'iro ... naku} and then have the two {naku}s cancel out without also converting the {me'iro} back into a {su'o}? That doesn't look right. I assume that the {naku} goes directly in front of whatever is predicate to a given subject, so the one from getting {no} will be directly in front of {su'o}. Time to go back to ultimate forms and check how this does work, since I am pushing my intuitions a bit hard at the moment. In any case, {broda} is universal, negative, and importing and {brode} appears to be particular negative and free. But again I'm not sure that is right, as it seems to change what the original sentence says. <> > >All + with the assumption that all classes mentioned as subject are >non-null >(and maybe a few less certain things as well). That sounds exactly like (A-,E-,I+,O+) with the assumption that all classes mentioned as subject are non-null. Indeed, with that assumption we can drop the +/- distinction, as it becomes irrelevant.> It is any system with the +/- distinction dropped; that's what it has to recommend it. That, and the fact that it is the way to get all the conversions that one could desirte. And that it fits the needs of 99.9% cases of actual use (and the other per mill is cheaply gotten). As they do in his system, since it is just standard logic, where universal appear to be - and paticulars to be +. Or in the cases where non-nullity is assumed. Where I am at the moment, I diagree: the first is +, the second is - FOR {BRODA}, though + for {da}. <2. su'o da poi broda cu brode =||= su'o da zo'u ge da broda gi da brode> It just occurs to be to ask what "=||=" means; I have taken it as bi-entailment, but it might be nonidentity, which would change my answer. Continuing with my original assumption, though, I agree with this one. <>Every universal quantifier (in a non-empty universe) entails every instance >of its matrix, every matrix with a free term entails its particular >closure >on that term: >AxFx therefore Fa therefore ExFx. That is about as thorough a working out >as >I can think of. Assuming a non-empty universe (and you are assuming it by bringing up a), I have no problem with that.> Well, not assuming a non-empty universe makes problems for a language, since no only would there be nothing to talk about, there would be nothing to say and no one to say it. But, that being the case, "all" implies "some," which is all that I have claimed from the beginning. Of course not, and no one I know of has ever claimed that it did, so what is the point of bringing it up? Well, if they did hold, we could not say that, but, since they don't -- you left out the {ge de broda gi} clause on the first one (or the universal non-nullity of subject terms) -- we can. Every A entails its corresponding (same import) I -- this fails because you are shifting import or failing to take account of the fact that import has been neutralized because lo'i broda is non-null (as always in Lojban as now constituted, byt we can get rid of that problem by allowing {lo ro ni'u broda} and - quantifiers on things as well). I still need to read a bit more of this book, but it seems that he is using what I would call a non-standard definition of restricted quantification, using it only as a symtactic category, a different way of writing the usual system, without a different semantics attached. The equations you cite are strong evidence for this, as is the context in which all the examples I have seen so far occur. --part1_17e.4ffcfff.29c21ec6_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 3/13/2002 5:29:15 PM Central Standard Time, jjllambias@hotmail.com writes:


So, in:

    ro broda su'o brode cu brodi
=   no broda me'iro da poi brode cu brodi

What is the "actual quantification" of broda and brode?
I can tell what the actual import is: - for broda and + for brode
in my system, ++ in yours. But what is the "actual
quantification"?


I forget what my system is supposed by you to be.  But in any case, I don't quite follow the identity you propose: Change {ro} into {no...naku}, change {su'o} into {me'iro ... naku} and then have the two {naku}s cancel out without also converting the {me'iro} back into a {su'o}?  That doesn't look right.  I assume that the {naku} goes directly in front of whatever is predicate to a given subject, so the one from getting {no} will be directly in front of {su'o}.  Time to go back to ultimate forms and check how this does work, since I am pushing my intuitions a bit hard at the moment.  In any case, {broda} is universal, negative, and importing and {brode} appears to be particular negative and free.  But again I'm not sure that is right, as it seems to change what the original sentence says.

<><Which one is the traditional system?>
>
>All + with the  assumption that all classes mentioned as subject are
>non-null
>(and maybe a few less certain things as well).

That sounds exactly like (A-,E-,I+,O+) with the assumption
that all classes mentioned as subject are non-null. Indeed,
with that assumption we can drop the +/- distinction, as it
becomes irrelevant.>

It is any system with the +/- distinction dropped; that's what it has to recommend it.  That, and the fact that it is the way to get all the conversions that one could desirte.  And that it fits the needs of 99.9% cases of actual use (and the other per mill is cheaply gotten). 

<But for "not every" to be equivalent to "some not",
"every" and "some" must have opposite import.>

As they do in his system, since it is just standard logic, where universal appear to be - and paticulars to be +. 
Or in the cases where non-nullity is assumed.

<Do you agree or disagree that in Lojban these are equivalent:

1. ro da poi broda cu brode =||= ro da zo'u ganai da broda gi da brode>

Where I am at the moment, I diagree: the first is +, the second is - FOR {BRODA}, though + for {da}.

<2. su'o da poi broda cu brode =||= su'o da zo'u ge da broda gi da brode>

It just occurs to be to ask what "=||=" means; I have taken it as bi-entailment, but it might be nonidentity, which would change my answer.  Continuing with my original assumption, though, I agree with this one.

<>Every universal quantifier (in a non-empty universe) entails every instance
>of  its matrix, every matrix with a free term entails its particular
>closure
>on that term:
>AxFx therefore Fa therefore ExFx.  That is about as thorough a working out
>as
>I can think of.

Assuming a non-empty universe (and you are assuming it by bringing
up a), I have no problem with that.>

Well, not assuming a non-empty universe makes problems for a language, since no only would there be nothing to talk about, there would be nothing to say and no one to say it.
But, that being the case, "all" implies "some," which is all that I have claimed from the beginning.

<But of course that does not mean that
{ro da zo'u ganai da broda gi da brode} entails
{su'o da zo'u ge da broda gi da brode}. It does not.>

Of course not, and no one I know of has ever claimed that it did, so what is the point of bringing it up?

<So, if, as I believe, these hold:

1. ro da poi broda cu brode =||= ro da zo'u ganai da broda gi da brode

2. su'o da poi broda cu brode =||= su'o da zo'u ge da broda gi da brode

then we cannot say that {ro da poi broda cu brode} entails {su'o
da poi broda cu brode}. You may not like 1. and 2. as definitions,
but they seem to me fairly standard. At least they are presented
as valid in the page I found (from a random search I did for
"restricted quantification")..>

Well, if they did hold, we could not say that, but, since they don't -- you left out the {ge de broda gi} clause on the first one (or the universal non-nullity of subject terms) -- we can.  Every A entails its corresponding (same import) I -- this fails because you are shifting import or failing to take account of the fact that import has been neutralized because lo'i broda is non-null (as always in Lojban as now constituted, byt we can get rid of that problem by allowing {lo ro ni'u broda} and - quantifiers on things as well).
I still need to read a bit more of this book, but it seems that he is using what I would call a non-standard definition of restricted quantification, using it only as a symtactic category, a different way of writing the usual system, without a different semantics attached.  The equations you cite are strong evidence for this, as is the context in which all the examples I have seen so far occur.















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