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Re: [lojban] "lo no"

Logic has a problem with referenceless nameoids.  If every (or, indeed, any) 
sentence containing one is true, then Particular Generalization is invalid; if 
all (any) are false, then Universal Instantiation fails. So, either they have no 
truth values (with all the problems that entails) or they have stange truth 
values (and that has problems, too).  Of, finally, we can deny that there are 
any referenceless nameoids. usually by forcing some randomly selected member  of 
the universe to be the default referent of such critters.  This last move is 
nice in formal semantics, but isn't much help languages, since the status of 
such sentences here-and-now, is undetermined (back to those problems again).  So 
the best solution is just not to use such terms.  The rule that use of a term 
guarantees its referent is in the domain does that pretty much.  But the extreme 
sort of contradictory terms, obvious ones as well as subtle, seem to foil even 
this attempt, and {lo no broda} is one of these. But Lojban ontology is said to 
embrace the impossible as well as the possible, So, there is a referent for {lo 
no broda} and, by other reasons, it is a broda, a medad and impossible.  Not a 
happy result, perhaps, but one of the joys of logical languages is that it keeps 
coming up with surprises.




----- Original Message ----
From: Jorge Llambías <jjllambias@gmail.com>
To: lojban@googlegroups.com
Sent: Sat, May 14, 2011 10:22:26 AM
Subject: Re: [lojban] "lo no"

I agree with the gist of tijlan's post, but I'd like to add some observations.

On Sat, May 14, 2011 at 7:56 AM, tijlan <jbotijlan@gmail.com> wrote:
>
> lo gerku = da poi gerku

I prefer: lo gerku = zo'e noi gerku

The reason is that "da" is meaningless until it is bound by a
quantifier, and assuming a default "su'o" has the problem that
quantifiers in Lojban are usually taken to bind singular variables
(i.e. they are distributive).

> ci lo gerku = ci da poi gerku
> no lo gerku = no da poi gerku

Here I prefer:

ci lo gerku = ci da poi me lo gerku
no lo gerku = no da poi me lo gerku

This is just an application of a more general rule: PA (sumti) = PA da
poi me (sumti)

Now, it is generally true that the selbri "me lo broda" can be reduced
to plain "broda" (as far as the x1 is concerned). But the exception is
precisely in the cases when there are no broda in the universe of
discourse. Since there are no broda in those cases, the sumti "lo
broda" can't refer to anything, but the selbri "broda" could perhaps
still have meaning. This won't affect tijlan's point though.

I would accept that:

ci gerku = ci da poi gerku
no gerku = no da poi gerku

since these follow a different paradigm, with no referring term being involved.

> lo ci gerku = da poi gerku je cimei
> lo no gerku = da poi gerku je nomei

lo ci gerku = zo'e noi gerku gi'e cimei
lo no gerku = zo'e noi gerku gi'e nomei

> Every sentence is syntactically valid, but the last one is logically
> questionable. You are yet to explain how exactly one could sensibly
> mean to refer to something which are both dogs and no dogs without a
> contradiction.

He is not referring to anything with "lo no gerku". "nomei" is not
true of anything, just as "su'omei" is true of anything at all.

He accepts terms that don't refer to anything, and arbitrarily assigns
a truth value of "True" to any predication involving those terms. But
those sentences don't really mean anything. He is extracting meaning
not from what the sentence states but from the fact that he is using a
non-referring term.

mu'o mi'e xorxes

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