Re: TECH: QUERY: quantifier scope & cumki

[John Cowan <snark!cowan@GVLS1.VFL.PARAMAX.COM>]

la kolin. cusku di'e

> And asks:
> ++++++>
>  How does one distinguish:
>    For every x, it is possible that x is ....
>    It is possible that every x is ....
> >++++++++
>
> I don't see a problem:
>
> ro da zo'u cumki fa le nu da broda
>
> cumki fa le nu ro da zo'u da broda

Correct.  The rules seem to say that the un-prenexed form

        cumki fa le nu da broda

means the latter, on the assumption that an undeclared logical variable is
effectively declared with the smallest possible scope.

> Until I noticed your subject I thought you were asking a different
> question - not about the predicative 'it is possible' but about
> the operators of modal logic - 'it is possible that' and
> 'it is necessary that'. Somehow the selbri 'cumki' and
> 'nibli' don't seem right for these.

Well, they are and they aren't.  Loglan, generally speaking, takes a Quinian
view of such things.  "nibli" is closer to the sentence operator Nec, which
in Quine takes a quoted sentence, than to the standard modal operator nec.
At least we know that Nec is logically tractable, which is not true of nec --
cf. the well-known paradox:

        nec 5 < 9
        9 = the number of planets
        nec 5 < the number of planets

which is fallacious.  Replacing "nec" with "Nec('...')" prevents us from
inferring things about the opaque argument, and so such bogosities are
Nec ~.  :-)

--
John Cowan      cowan@snark.thyrsus.com         ...!uunet!lock60!snark!cowan
                        e'osai ko sarji la lojban.