Re: TECH: more thoughts on zi'o

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

mi'e .djan. .i la .art. protin. cusku di'e

> Though, I don't understand why the most useless and counterintuitive
> rules of precedence were chosen for combining the ellipsis and the
> negation.  I would have bound the negation tighter than the
> existential quantifying.  For example "not bluer-than" becomes
> "there exist a y such that it is false that x is bluer-than
> y".  If this is supposed to be the distinction between "scalar
> negation" and "logical negation", I believe that "scalar negation"
> is much more useful to me.  If that is the distinction between
> scalar & logicial negation, I believe that what I can say with
> logical negation is a proper subset of what I can say with scalar.
> If that is not the difference, then I am more comfortable with
> the use of logical negation but still fuzzy about the distinction.

No, it isn't.  Both those forms are logical negations, but as you correctly
say, the scope varies.  (Ey) ~bluer(a,y) is

                ko'a naku blanymau da
                It-1 ~not bluer-than some-x

which goes into prenex normal form as:

                da naku zo'u ko'a blanymau da
                (Ex) ~  :     it-1 bluer-than x

whereas the other case is:

                ko'a na blanymau da

which becomes

                naku da zo'u ko'a blanymau da
                ~    (Ex) :  it-1 bluer-than x

So by varying between "na" (which always negates the whole thing) and "naku"
(which negates only what is following it) you can capture the
anything/everything distinction in English.

But neither of these is scalar negation.  Contradictory negation expresses
what is false:  "ko'a na blanu" means "it is false that it-1 is blue".
Scalar negation says that something OTHER THAN what is expressed is true:
"ko'a na'e blanu" means "it-1 is other-than-blue/non-blue".  Scalar
negations cannot be manipulated logically, and are close-binding.

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