Re: TECH: Quantifiers (was: cukta)

[Logical Language Group <lojbab@ACCESS.DIGEX.NET>]

la i,n. cusku di'e

> > I don't understand the "For any given {DA}" here.  "ro DA" comes out "For
> > every {DA}", which (I think) is equivalent to your original interpretation.
>
> I think we've had essentially this disagreement/misunderstanding before.
> In my book, "For any [given] x" means exactly the same as "For all/every x",
> but is easier to interpret correctly (as a universal quantification)
> in complex situations.

You are right, of course; "for any" is a universal quantification, but I find
it harder, not easier, to interpret!

> > What you have here transcribes as "da de zo'u co'e da poi klama de".
>
> No, I disagree.  That would be "For _some_ {DA}".

Right you are.

> > That leads to a tangent.  One of my rules was in error.  A
> > variable appearing a second time with a quantifier doesn't cause rebinding,
> > as I earlier stated.  Instead, it has the normal behavior of a sumti
> > quantifier: it selects.  So "ro da poi broda cu klama pa da" means
> > "all thingummies go to one particular thingummy", because "pa da" means
> > "one of the {da}s" when "da" is already bound (analogously to "pa do" = "one
> > of you").
>
> And this is consistent with a subsequent restrictive clause selecting
> a subset.

It does and it doesn't, because in the context "da poi ... da" the second
use of "da" has been restricted by the "poi".  So "poi" really sets a
domain, rather than selecting a subset. "ro da poi" = "all-of those-things
in-domain".  Quirks like these are why a whole separate paper on "da" and
friends is needed in the reference grammar, and most of the other papers
just have brief notes saying "'da' is special; see elsewhere".

> > This may mean that a variable appearing in a "poi" clause attached to a
> > variable within a prenex is a >forward< reference to the same variable
> > appearing later in the prenex.
>
> I think this way lies madness.  The first occurence must define the
> principal quantification, and subsequent quantifications select.
>
> > As you say, this is potentially recursive:
>
> >         ro da poi broda de vau ro de poi brode de zo'u da brodi de
>                                                  ^
>                                                  da?

Yes.

>
> > meaning something like:
>
> >         All X's which foogle a Y (every Y?) snorgle all Y's which
> >                 zarkify an X (every X?)

But if forward reference is not possible, then the first occurrence of "de"
has scope forward from just after the first "poi", leading to the reading:

        All X's which foogle some Ys snorgle all of >those same< Y's which
                zarkify the X in question.

In order words, the "ro de" selects all of the {su'o} referents implicit
in the first appearance of "de".

This is a very different reading, which is not itself a problem, but I don't
see how to get back to the recursively-scoped reading (misreading) of my
previous message: i.e., how is that mess expressed in Lojban?

Overall conclusion: talking with pc is now a must.

--
John Cowan              sharing account <lojbab@access.digex.net> for now
                e'osai ko sarji la lojban.