any & every

[Gerald Koenig <jlk@NETCOM.COM>]

Jorge quotes me (djer):
la djer cusku di'e

>         1). No ball entered every pocket.
>         2). No ball entered any pocket.
>
>         1') -E(x){ball(x) & All(y)[pocket(y) => entered(x,y)]}
>                                 -------------------------
>         2') All(y){pocket(y) => -E(x)[ball(x) & entered(x,y)]}
>                 -------------------------------------------
>
> Because lojban grammar is based on predicate calculus it is a fairly
> easy matter to translate these into lojban, but I am not going to do it
> here as I doubt that anyone would use these forms. It is like expressing
> the number 5. as s(s(s(s(s(0))))).

You can express both simple forms in Lojban:

        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.

The distinction every/any here allows you to reverse the order of quantifiers
in English, without having to reverse the order in which you say the
arguments. In Lojban you have no choice but to reverse the order of the
arguments (or use quantifiers in the prenex). {xe'e} doesn't help you here,
because it is not the right word to translate the "any" of (2).
-----------------------------------------------------

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. So we can say as above in 1.), except
for the negation:

        E(x)( ball(x) & All(y)( pocket(y) => entered(x,y)))

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.
Your sentence, 1'' says that "0 balls entered every pocket."  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.
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 havn't digested your other comments to my any & every post, I
hope others will comment.

djer