From pycyn@aol.com Thu Mar 07 12:24:37 2002 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: unknown); 7 Mar 2002 20:24:37 -0000 Received: (qmail 58904 invoked from network); 7 Mar 2002 19:25:58 -0000 Received: from unknown (216.115.97.167) by m3.grp.snv.yahoo.com with QMQP; 7 Mar 2002 19:25:58 -0000 Received: from unknown (HELO imo-d10.mx.aol.com) (205.188.157.42) by mta1.grp.snv.yahoo.com with SMTP; 7 Mar 2002 19:25:58 -0000 Received: from Pycyn@aol.com by imo-d10.mx.aol.com (mail_out_v32.5.) id r.102.119c6ff1 (17381) for ; Thu, 7 Mar 2002 14:25:55 -0500 (EST) Message-ID: <102.119c6ff1.29b918c3@aol.com> Date: Thu, 7 Mar 2002 14:25:55 EST Subject: Re: [lojban] Re: [jboske] Quantifiers, Existential Import, and all that stuff To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_102.119c6ff1.29b918c3_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_102.119c6ff1.29b918c3_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 3/7/2002 10:16:52 AM Central Standard Time, jjllambias@hotmail.com writes: > If {ro} can be {no}, then {ro lo ro broda} is not > the same as {ro lo su'o broda}. > I agree, but {ro} can't be {no}. <>{me'iro} and {da'a su'o} are quite right, since both seem to allow {no}. They do allow it. Does O+ entail I+ in your understanding? It doesn't in mine. In other words, does "some don't" entail "some do"?> No, nor does I+ entail O+, each is compatible with the corresponding universal, A+ and E+, espectively (in fact, entailed by). My worries about whether the existential import makes it through -- it is just a worry that the {no} which strictly applies to SP might carry over to S as well. I'll have to watch usage to see if that happens. <"Contradictories": >noda = naku su'oda >su'oda = naku noda >me'iroda = naku roda> > >Not perfectly clear what is going on here, combining + quantifier >expressions >with variables (intended for - quantification), and the negations seem >indifferent to import. They would still be valid if {da} is changed to {broda}:> No, the negation of a quantifer is a quantifer with opposite import, which this does not show in your examples (by the way, you have it "right" in your original list -- on the assumption that {lo ro broda} is different from {lo su'o broda} , which it is not in the relevant way.) Same problem (no change of import) remains. namely: The problem is that, if {ro} can be {no} then any claim at all can be made, since anything follows from a falsehood. Additionally, of course, this does not solve the import question, if {no} can have existential import -- be about S as well as SP. If you want to do empty-universe logic, the appropriate format is to replace every occurrence of {Q da} by {Qda poi zasti}. It would still be obnoxious to an empty-universe logician, but it would get all the theorems right. Outside of that weird case (and even in it in fact), {ro} entails {su'o}, A entails I, E entails O (with the same import). You sign on with logic, you get logic, not something else. --part1_102.119c6ff1.29b918c3_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 3/7/2002 10:16:52 AM Central Standard Time, jjllambias@hotmail.com writes:


If {ro} can be {no}, then {ro lo ro broda} is not
the same as {ro lo su'o broda}.


I agree, but {ro} can't be {no}.

<>{me'iro} and {da'a su'o} are quite right, since both seem to allow {no}.
They do allow it. Does O+ entail I+ in your understanding?
It doesn't in mine. In other words, does "some don't" entail
"some do"?>

No, nor does I+ entail O+, each is compatible with the corresponding universal, A+ and E+, espectively (in fact, entailed by).  My worries about whether the existential import makes it through  -- it is just a worry that the {no} which strictly applies to SP might carry over to S as well.  I'll have to watch usage to see if that happens.

<"Contradictories":

><roda = naku me'iroda
>noda = naku su'oda
>su'oda = naku noda
>me'iroda = naku roda>
>
>Not perfectly clear what is going on here, combining + quantifier
>expressions
>with variables (intended for - quantification), and the negations seem
>indifferent to import.

They would still be valid if {da} is changed to {broda}:>

No, the negation of a quantifer is a quantifer with opposite import, which this does not show in your examples (by the way, you have it "right" in your original list -- on the assumption that {lo ro broda} is different from {lo su'o broda} , which it is not in the relevant way.)

<the {da'a} notion is not classical.

{da'a} can also be changed to a postposed {naku} to make it more
classical:

ro broda = no broda naku
no broda = ro broda naku
su'o broda = me'iro broda naku
me'iro broda = su'o broda naku>

Same problem (no change of import) remains.

<I did put a warning saying that these hold only if {ro} can be {no}.> namely:
<and some of the relationships fail if {ro} is
taken to have existential import.)>

The problem is that, if {ro} can be {no} then any claim at all can be made, since anything follows from a falsehood. Additionally, of course, this does not solve the import question, if {no} can have existential import -- be about S as well as SP.

If you want to do empty-universe logic, the appropriate format is to replace every occurrence of {Q da} by {Qda poi zasti}.  It would still be obnoxious to an empty-universe logician, but it would get all the theorems right.  Outside of that weird case (and even in it in fact), {ro} entails {su'o}, A entails I, E entails O (with the same import).  You sign on with logic, you get logic, not something else.





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