RE: [jboske] interpretation of LAhE (was: RE: Digest Number 136

["And Rosta" <a.rosta@lycos.co.uk>]

xorxes:
> la and cusku di'e
> 
> > > Would you give any meaning to {lu'o ko'a a ko'e a ko'i}?
> >
> >Yes. Sumti logical connectives are a syntactic abbreviation for
> >something else in logical form (either logically connected
> >bridi or else "su'o/ro cmima be X ce Y"). So the meaning would
> >be analogous to {broda ko'a a ko'e a ko'i} 
> 
> {broda ko'a a ko'e a ko'i} is just {broda ko'a ija broda ko'e
> ija broda ko'i} 
> 
> Would you have {lu'o ko'a a ko'e a ko'i} expanding to
> {lu'o ko'a lu'u a lu'o ko'e lu'u a lu'o ko'i}? If so, then
> {lu'o su'o da} should be {su'o da zo'u ... lu'o da}, 

yes

> but this is different from {lu'o ro da} 

no, on my current view, {lu'o ro da} would be {ro da zo'u
lu'o da}. "The mass of all" would have to be done as {lu'o
lo'i}.

> I'm not clear what analogous meaning you have in mind 

The analogy is that when predicates have quantified arguments,
the predicate cannot have scope over the argument.

> > > You're saying that {lu'o Q le broda} is always {lu'o ro le broda}
> > > no matter what Q is. Q becomes a cardinality indicator in this
> > > position, right?
> >
> >I think the consequence of my position is that {lu'o Q le broda}
> >must always be {Q le broda ku goi ko'a zo'u lu'o ko'a}, analagous
> >to {broda Q le broda} 
> 
> In that case, {lu'o le ci gerku} is not the mass of the three dogs,
> but each of the three masses of one dog. 

Yes. {lu'o le'i ci gerku} could do the mass of the three dogs.

> LAhEs lose much of their
> reason of being if they are transparent to quantifiers 

I agree. If you assume that LAhE is a tool well-designed for its
job, then it turns out to have less useful a job than if you
just think "here's a tool, what can it most usefully be used for?".

> > > The syntax of a brivla would be different than what I'm proposing,
> > > though. {LE se cmima be ro broda} is a set that contains every
> > > broda, but it may also contain other things. {lo'i ro broda} is
> > > the set that contains exactly every broda. The same would apply
> > > to masses
> >
> >Okay, but {lu'i} as a brivla would not mean "contains" but rather
> >"contains nothing but" 
> 
> How would you use such a brivla, what goes in x2? Suppose
> {rolvasru} means "x1 contains nothing but x2". Saying
> {le tanxe cu rolvasru re cukta} is nonsense, because it
> means that there are exactly two books such that each of
> them is the only thing contained in the box. The proper
> way of saying it would be {le tanxe cu rolvasru lei re cukta}
> if we refer to the two books specuifically. How do we do it
> nonspecifically? {le tanxe cu rolvasru lo'u re cukta}, the
> box contains nothing but two-books-as-a-whole. But if
> {lo'u re cukta} must be split into {re da poi cukta zo'u
> le tanxe cu rolvasru lo'u da}, we are making again a
> nonsensical claim 

The solution requires that there be some unquantified gadri 
like {lau'o re cukta} -- "a twosome such that each of its 
members is a cukta" -- or else "lo cukta re mei"

I have realized that this is what I used to think, without
having fully apprehended on a conscious level the rationale
for it, and I was dissuaded from my view by you.

> > > Our interpretations agree when there are no quantifiers
> > > inside the LAhE. Your interpretation changes the meaning of
> > > the outer quantifiers into something like the meaning of inner
> > > quantifiers
> >
> >My idea is that if Fxy always yields a unique y for a given x,
> >then y can be referred to by means of {Fx} rather than {gadri/PA
> >F be x}, since the gadri is redundant. The requisite syntax
> >for {Fx} referring to y would be that of LAhE 
> 
> That still works like that with my interpretation 
> 
> What we are disagreeing about is on how to handle the
> notationally odd F(Qx). You want it to be just a variation of
> Qx:...Fx... I want to give it a more complex but I think more
> useful meaning. But we are not disagreeing about the basic
> unquantified Fx 

That's right. But F(Qx) is odd whether F is a function or a
predicate. It's a notation allowed by Lojban as a convenience,
but it has to be translated into something logically sound.

I understand that your meaning is more useful, but you are in
effect changing the meaning of F when in F(Qx).

> How do you propose to say "a mass of two books (only)"?

{lo cukta re mei}, {lau'o re cukta}, {lu'o lau'i re cukta}.

There is no decent way in current Lojban, but I don't think
that justifies mungeing LAhE.

--And.