Re: pc answers

["John E. Clifford" <pcliffje@crl.com>]

On Fri, 30 Jun 1995 jorge@PHYAST.PITT.EDU wrote:

> la djer cusku di'e
>
> > My predicate calculus formula:
> >
> > E^!3(x) (remna (x)  E^!9(y)(gerku(y)  & pencu(x,y)))
> >
> > declares that there are exactly 3 humans and exactly 9 dogs, for the
> > scope of the entire sentence.
>
> That's what I thought (and it seems that I convinced you) but now that
> I see it again, I think I was wrong. Assuming there is another "&"
> between "remna(x)" and "E^!9(y)", then you are not claiming that only
> three humans exist. Only that remna(x) and that other complicated
> claim about x are both true of only three objects. Each separately
> may be true of more.

Right.  The problem here is close to the problem with the absence of
referential expressions in Lojban: quantifiers pick up more than you
want, so miss the real point.

> In any case, the E^!9(y) is within the scope of the other, so it
> doesn't in any way say that the nine y's are the same for every x,
> only that for each x there are nine y's that fit that relationship.
> So your formula admits that up to 27 dogs are being touched in all.

No.  Although the dogs are in the scope of the men, they are not
interdependent; this form is equivalent (with the & as you note) to the
form with the dog and man quantifiers reversed, 9x(dog x & 3y (man y &
touch y x))  Think of the And form, "there is a cimei and there is a
somei..."

> Now I think that your formula (with an additional "&") is a good
> representation of {ci remna cu pencu so gerku}

No, for the reasons just given. That seems to require something like
3x(man x & Ay(man y => 9z (dog z & touch y z))) (the 3x man x can be
taken out of the parenthesis with the rest, since unrelated to it). I am
tentatively accepting  the xorxes-and reading here.

>
> > ro lo ci remna ku ro lo ci gerku zo'u ra pencu ri
>
> That would be, in your notation:
>
> ( E^!3(x) remna(x) ) & ( E^!9(x)(gerku(x) ) &
> (x)(y) ( (remna(x) & gerku(y)) -> pencu(x,y) )
>
> There are three and only three things that are human &
> there are nine and only nine things that are dogs &
> for every x that is human and every y that is a dog, x touches y.

That this is a symbolization of the Lojban is surely questionable, given
the now quite muddied relationship between quantifiers and descriptors in
Lojban and logic, but the logic at least does get the 3-men, 9-dogs
all-touch-all story right (at a small price in reality and efficiency  --
but it does pick out only one case in 512, so probably is about the right
size, such things being logarithmic, I think). I think there are shorter
forms.
pc>|83