pc answers

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

        Xorxes has adequately dealt with djer's comments about quantifier
order.  djer's other comment, about the number of non-identities needed,
is correct in the real world, but logic does not know that relevant men
and relevant dogs are mutually exclusive groups, so we have to separate
them somehow.  Admittedly, it would be shorter to put in "not: for some
v1, both v1 is a relevant man and v1 is a relevant dog," but, as I said,
the translation was made without thinking too much.
        Xorxes's Lojban versions are contentious.  The logical forms
involve only quantifiers, his involve descriptors as well.  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.  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."
        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.  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. But it plays havoc with the underlying quantifiers in the
Lojban form.  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.  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).  Conversion will not help, since then we end up with three
dogs but possibly nine men. Prenexing does not obviously help, since it
does not seem likely that we can -- pace djer -- shift numerical
quantifiers around even in prenex.  I am tempted to propose another xV'V
to indicate non-subordinate quantifiers, but I think that, as always, we
need to try a few more formulations before we go to that point.  For
instance, if we make the first form be what the sentence means, how will
we say the second, using the material we already have? pc >|83