Re: any & every

[jorge@PHYAST.PITT.EDU]

I translated this two sentences;

> >         1). No ball entered every pocket.
> >         2). No ball entered any pocket.

with result:

>         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.

This means that the effect of reversing the universal and negated existencial
quantifiers, that is achieved in English by changing from every to any, can
only be achieved in Lojban by actually reversing the arguments.

(This "any" is not {xe'e}.)

djer disagrees:

> GK>     Its not so easy as you think.  Consider this scenario: The white
> ball is marked with an X. During the course of a game it happens to get
> hit into pockets one through six.

Then you can say:  su'opa bolci pu nerkla ro kevna
                   At least one ball (to wit, the white one)
                   entered every pocket

> So we can say as above in 1.), except
> for the negation:
>
>         E(x)( ball(x) & All(y)( pocket(y) => entered(x,y)))

Yes.

> Notice that the other balls went into the pockets.  When this sentence
> is negated as in 1), it just denies the existence of the white ball
> with the X on it, or any that behaved similarly. It doesn't say all the
> pockets are empty.

Of course not.  1'') doesn't say that either.

2) = 2'') both say that all pockets are empty.

> Your sentence, 1'' says that "0 balls entered every pocket."

Maybe the English translation is confusing, but 1'') does not say that
every pocket is empty. It simply says that the number of balls that
entered all of the six pockets is zero. If each pocket was entered by
one different ball, it is still true that {no bolci pu nerkla ro kevna}.

If you say {pa bolci pu nerkla ro kevna} you claim that one ball entered
each and every pocket, the same ball. If each pocket has one ball, but
not the same one, then it is false that {pa bolci pu nerkla ro kevna},
but true that {ro kevna pu se nerkla pa bolci}.

> You can't
> translate the lojban word "no", which means the number 0, into the
> English word "no" which is a logical connective, and make sense.

Yes you can, in most cases. {noda} can always be replaced by {naku su'oda}.
If we do this in this case:

        no bolci pu nerkla ro kevna
        naku su'o bolci pu nerkla ro kevna
        It is false that at least one ball entered every single pocket.
        No ball entered every pocket.

> If you are inclined to argue about the meaning of the above sentence, I
> suggest you look at page 215 of the book Logic and Prolog, Cambridge
> University Press, which is where I learned about it.

I don't understand your comment. Sentences 1) and 2) mean two different
things. I don't see that we have any disagreement on what the English
sentences mean, so what can I check in that book? What we seem to disagree
on is the meaning of the Lojban sentence 1'').

Jorge