any & every & naku

[Gerald Koenig <jlk@NETCOM.COM>]

Jorge said:
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.


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

GK> 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}.

GK> 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.

JL>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.


What we seem to disagree on is the meaning of the Lojban sentence 1'').

Jorge

-------------------------------------------------------------------
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,

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.
        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. I now suggest:

2''' ro kevna pu na se nerkla su'o bolci

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

  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 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. 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.

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.

I previously defined zeta-any to mean: (one, some, or all). Or use xe'e
if it works here. 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.
Do you agree with this post?

djer