Subject: Re: [lojban] Re: [jboske] Quantifiers, Existential Import, and all that stuff

From: [email-masked]
Date: Thu, 7 Mar 2002 14:25:55 EST

In a message dated 3/7/2002 10:16:52 AM Central Standard Time, 
[email-masked] 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.