Message-Id: <m0pWmuY-0000PhC@xiron.pc.helsinki.fi>
Date:         Wed, 16 Feb 1994 13:55:28 GMT
Reply-To:     i.alexander.bra0125@oasis.icl.co.uk
Sender:       Lojban list <LOJBAN%CUVMB.bitnet@FINHUTC.hut.fi>
From:         i.alexander.bra0125@OASIS.ICL.CO.UK
Subject:      Re: TECH: Quantifiers (was: cukta)
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 2192
Lines: 56

la kau,n. tu'a mi spuda di'e
> >     For any given {DA}, we can choose a {de}, such that some predicate
> >     holds for those {DA}s which {klama de}.
> >
> > .oiro'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.

> 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}".

> 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.

> > I've already given the expansion I was originally assuming, with {de}
> > quantified inside the (virtual) restriction, and this looks to me like
> > a different claim.

> 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?

> meaning something like:

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

> I nominate this sentence for Most Confused Sentence Of The Year.

Certainly the most promising contender so far. :)

mi'e .i,n.