Re: pc answers

[jorge@phyast.pitt.edu]

pc:
>         Xorxes's Lojban versions are contentious.  The logical forms
> involve only quantifiers, his involve descriptors as well.

The descriptors only play the role of your preamble, limiting the
variables to the three relevant men and the three relevant dogs.
You can write them out more formally:

        ro da voi nanmu ku'o ro de voi gerku zo'u: da pencu de
        For each x out of the men I have in mind,
        for each y of the dogs I have in mind: x touches y.

Which is exactly equivalent to:

        le nanmu cu pencu le gerku
        Each of the men touches each of the dogs.

The same happens in all the other 5 cases. For example:

        su'o da voi nanmu ku'o ro de voi gerku zo'u: da pencu de
        For at least one of the men I have in mind,
        for each y of the dogs I have in mind: x touches y.

Which is equivalent to:

        su'o le nanmu cu pencu le gerku
        At least one of the men touches each of the dogs.


> His
> translations presuppose the answer to the question that is being
> investigated, what situations are covered by what descriptors, without
> discussing the plausibilities of the claimed translations other than
> appeal to a (logically unjustified, as I have noted) rule about
> quantifiers inherent in descriptors.

I didn't think there was still any doubt about how to handle {ro le nanmu}
or {su'o le nanmu}. The doubt comes with things like {re le nanmu},
and there are only two possibilities that I could identify for it.

> This is not to say that they are
> inaccurate, but, by calling them translations, xorxes appears to cut off
> the possibility that other expressions might also cover the same ground or
> that the lojban expressions might cover more ground than that it
> "translates."

I believe those six translations I gave are practically identical to
the six expressions you gave. I never intended that to curtail other
expressions from covering the same ground, but I don't see how those
six translations could cover more ground.

>         Xorxes call attention to a further problem also involved here, ci
> nanmu cu pencu ci gerku. The choices here are between one that involves
> three men and only three dogs and one that involves three men and as many
> as nine dogs, three for each man.

Right. Just so we all agree what we are talking about, {ci nanmu cu pencu
ci gerku} is by definition the same as {ci lo ro nanmu cu pencu ci
lo ro gerku}.

> The first starts like the _le_ case:
> for some six things, x,y,z,w,v,u, all distinct, x,y,z men, w,v,u dogs, and
> for all x1, if x1 is any of x, y, z then x1 touches w and x1 touches v and
> x1 touches u.  This has the charm of being convertible to ci gerku cu se
> pencu ci ranmu.

Yes, and that's why I originally thought this was the Right Thing.
But And convinced me that the other reading is more natural.

> But it plays havoc with the underlying quantifiers in the
> Lojban form.

I don't see why. Whichever way we choose to read it, it has to be
a rule on top of the rule for {ro} and {su'o}. {ci nanmu}, which
is {ci lo ro nanmu}, is not automatically expressed in terms of
{ro} and {su'o} alone. How to express it like that is the rule we
have to decide on.

> They seem better represented by for some x,y,z, distinct and
> men, for all w, if w is one of these, then there are v,u,x1, distinct and
> dogs, such that w touches each of them (as above). This is the natural
> generalization of something like la djan cu pencu ci gerku.

I agree that this would be the more natural generalization.

> As usual the
> first reading entails the second, so, if we decide that the Lojban means
> the second, we have a cover for the first as well. But the issue then is,
> how do we say the first explcitly (short of spelling out the quantifiers,
> of course).

One possibility is:

        ro lo ci lo nanmu cu pencu ro lo ci lo gerku
        Each of three of all men touch each of three of all dogs.

It is more wordy, but then it is probably in general a more
unlikely meaning.

Jorge