Re: any & every & naku

[jorge@PHYAST.PITT.EDU]

> > >         1). No ball entered every pocket.
> > >         2). No ball entered any pocket.
>
> >         1'') no bolci pu nerkla ro kevna
> >              No ball entered every pocket.
> >
> >         2'') ro kevna pu se nerkla no bolci
> >              Every pocket was entered by zero balls.
>
> -------------------------------------------------------------------
> GK> (djer) continues:   I do continue to find the translation
>
> 1'' "no bolci pu nerkla ro kevna
>
> very questionable. But I think your alternative form that you believe
> equivalent,


(This equivalence is mentioned in one of the grammar papers, BTW)


> 1''' naku su'o bolci pu nerkla ro kevna
>
> is very, very good and does offer a valid short form alternative to the
> full logical expansion from predicate calculus without altering the
> meaning.

Notice that 1''' can also be written

        su'o bolci na pu nerkla ro kevna
        lo bolci na pu nerkla ro kevna
        It is false that: at least one ball entered every pocket.


>         When I tried to replace the "no" in your second translation,
>
> 2'' ro kevna pu se nerkla no bolci
>
> with what you say is equivalent I got:
>
>  ro kevna pu se nerkla naku su'o bolci
>
> which looks again very questionable.

Looks can deceive  :)

The sentence indeed means the same thing as 2''.

> I now suggest:
>
> 2''' ro kevna pu na se nerkla su'o bolci

This says:

        It is false that: For every pocket, at least one ball entered it.

This is NOT equivalent to 2) = 2'')


> Each pocket was not entered by one or more balls;

No, be careful. The negation applies to the whole claim, not only to the
part after the universal quantifier.

I think that what you want is:

2'''')   ro kevna naku pu se nerkla su'o bolci

which is equivalent to 2 and 2''.


> which carries the
> meaning of "no ball entered any pocket" in a short form. I hope I got
> that negation right. I just read the paper.

That explains your confusion. :)  That paper is not one of my favourites.


>   Your system of following the order of the predicate
> calculus formulation of 2.  and then converting the selbri gives a
> really compact expression.  So now we have:
>
> No ball entered every pocket.
> naku su'o bolci pu nerkla ro kevna
>
> No ball entered any pocket.
> ro kevna pu na se nerkla su'o bolci

The last one is wrong, but you can fix it by changing to {naku}.

> The neat symmetry of your "no" formulation is lost. But finally the
> meaning of"any" has been expressed in a compact form without actually
> using the word.

I still think the expressions with {no} mean what I said, but you are
welcome not to use them if you don't like them.

> Think about this:
>
> naku su'o bolci pu nerkla ro kevna
> It is not the case that at least one ball entered every  pocket.
> No ball entered every pocket.

Agreed.

> naku so'o bolci pu nerkla "zeta-any"  kevna
> It is not the case that at at least one ball  entered (one, some, or
> all) pockets.
> No ball entered any pocket.

(one, some, all) is su'o = "at least one".

And that's what you arrive at if you keep manipulating. Start with 2'''':

        ro kevna naku pu se nerkla su'o bolci

Now, if you pass a negation by a {ro} you change it to a {su'o}, so:

        naku su'o kevna pu se nerkla su'o bolci

And finally, existential quantifiers commute, so:

        naku su'o bolci pu nerkla su'o kevna

which is your "zeta-any" expression.

And you can even simplify it. {su'o bolci} is the same as {lo bolci}, and
a {naku} at the beginning of the sentence is the same as a {na} in front
of the selbri, so we end up with:

        lo bolci na pu nerkla lo kevna
        It is false that at least one ball entered at least one pocket.

Or more colloquially: No ball entered any pocket. We've come full circle.


> I previously defined zeta-any to mean: (one, some, or all). Or use xe'e
> if it works here.

No, it doesn't. {xe'e} is not a logical quantifier. Zeta-any is su'o.

> I'm not sure how you defined it. The use of a word for
> "any" requires a lot less mental gymnastics and maybe that's why it
> exists.

Yes, but "any" has many different meanings in English.

> Do you agree with this post?

With some parts. :)

Jorge