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

From: [email-masked]
Date: Thu, 7 Mar 2002 09:37:25 EST

In a message dated 3/7/2002 1:56:52 AM Central Standard Time, 
[email-masked] writes:

> I don't think he noted that at all. What I understood was that
> the fact that "not all Klingons are bad" is true in fiction
> should not be confused with a claim that Klingons exist in the
> real world. The existential import applies in the fictional
> world only, where the sentence is true. No conflict between
> logic and ordinary language.
> 
He said:
"The rule I have always seen is that ~A~ is equivalent to E, so "not 
all"/~(Ax)P is the same as "for some, not"/(Ex)~P, and therefore "not 
all" entails existence. But only in a strictly logical context, not 
in English generally. Certainly we can use "not all" in a purely 
fictional context, such as "Not all Klingons are bad," without 
suggesting that Klingons exist outside of ST. "
I can see your interpretation in there, too. In the further context -- as I 
understood it -- it was not the interpretation that came to mind.

<Let's see. In the fictional world:

"All Klingons are bad" is false.
"Not all Klingons are bad" is true.

Presumably we all agree about that, since in fiction the set
of Klingons is not empty, and we take it that Worf is not bad.

In non-fiction, since there are no Klingons:

"All Klingons are bad" is true or false according to your predilection.
"Not all Klingons are bad" is false or true respectively.

Now, which contradiction did he get into, and how does
importing universals gets you out of it?>

I understood him to hold that "Not all Klingons are bad" did not have 
existential import, from which it follows that "All Klingons are bad" does 
have existential import, contradictory to his claim that universal 
affirmatives do not have existential import.

<Besides, {na'e bo ro da} is "na'e bo (roda)", not "(na'e bo ro) da".>
If you say so, it's too hard to do by hand. I wonder what it means.

<Now, forgetting the nonsense that either {su'o lo ro broda}
or {su'o da poi broda} can be used for I- (and correspondingly
for O-) here is a system I can work with:

A+ ro lo su'o broda cu brode
E+ no lo su'o broda cu brode
I+ su'o lo broda cu brode
O+ me'iro lo broda cu brode = da'asu'o lo broda cu brode

A- ro lo broda cu brode
E- no lo broda cu brode
I- naku no lo su'o broda cu brode
O- naku ro lo su'o broda cu brode>

I agree that using {su'o} for either I- or O- is nonsense and that the best 
way to deal with them is probably to leave the negations unresolved (see 
below). The rest of your examples fail to indicate the difference between + 
and -, since the status of the two formulations, {lo ro broda} and {lo su'o 
broda} are, in that respect, exactly the same. So, I do worry about whether 
{me'iro} and {da'a su'o} are quite right, since both seem to allow {no}.

<I think {su'o no} is wrong. {su'o no broda cu brode} is true
when {no broda cu brode} is true, but I- should be false
if there are broda but none of them is brode, i.e. when E+ is true.>

By you {no broda cu broda} is E-, so its contradictory is I+. What happens 
with I- in this case? It is indeterminate: true if E- is true because there 
are no Ss, false if there are Ss but none of them is a P. If E+ is true, I- 
is false but, yes, {su'o no} would presumably be true. Well, it was a 
desperate move at best anyhow, so leaving it unreduced negations seems best.

<I don't think it's justified. The "inner quantifier" is the
cardinality of the set. Inner {su'o} says that the set in not empty.
Inner {ro} is tautological, because every set has cardinality {li ro}.>

I didn't say it was justified, I said it was as justified as your claim that 
{ro} does not imply {su'o}. So I agree that my claims was unjustified, since 
yours surely is. The empty set does not have ro members, only no. That's 
why we have to go into intensional contect to hunt unicorns. (It is true of 
everything that IF it is a member of the empty set, it is a broda -- but 
that is a property of IF, not of "everything".)

<"Contraries":
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.
Allowing for ambiguities of just that sort I suppose these work, but thay 
aren't very informative without the import notation (and with I- and O-, not 
even right then). What are here called "contraries" would (properly marked 
for import) be contradictories, I think.

<"Complementaries":
roda = da'anoda
noda = da'aroda
su'oda = da'ame'iroda
me'iroda = da'asu'oda>

Same problem. I'm not sure what to call these in traditional terms, so 
"complementaries" is as good as any -- the {da'a} notion is not classical. 

<"Duals":
roda = naku su'oda naku
noda = naku me'iroda naku
su'oda = naku roda naku
me'iroda = naku noda naku>

These are duals all right, but they have only a tenuous connection with the 
situation in hand, since they lack import notation, which makes all the 
difference. so, whether the identitis hold or not cannot be determined -- in 
the obvious readings, with the import the same on both sides, none of them 
do.