pc answers

["John E. Clifford" <pcliffje@CRL.COM>]

        To wander somewhat off the point, I have noted that in logic
quantifiers and descriptors have little to do with one another.  They are
grammatically quite distinct (in most systems) and they perform quite
different functions.  Descriptors *refer* to things, stand for them
directly or only moderately intermediated.  Quantifiers *range over*
things, make metalinguistic remarks about whatever refers to them but
refers to them not at all.  Descriptors are at most two linguistic levels
removed from the world, quantifiers are at least four levels out and rely
heavily (in most systems, essentially) on the directly referring
expressions. Descriptors are concrete, unique, precise;  quantifiers are
abstract, general, vague.  The nearest they come to contact one another is
that sometimes they systematically can be used to make claims that define
exactly the same logical situations.
        I have been trying to explore some cases in which the situation
described using some descriptor from Lojban could be expressed using the
quantifiers of logic.  I did not mean this to suggest that the descriptors
of Lojban *are* logical quantifiers.  But now I am told that it is built
into Lojban that each descriptor *means* some quantifier expression.  As a
logician, I hope that this is not true, since it would mean that the
"logical language" was ultimately not only illogical but unusable.  If all
descriptors are just quantifiers, then we have no way to refer to objects
in their absence.  When they are present we can point to them with the
deictors, _ti_ and _do_ and the like, and we can adress them, if they have
names, _coi_djan_.  But we cannot refer to them, only say some general
claim, which, if we are lucky, will happen to be true just in case those
ineffable things do so and so, but which will not mention those things at
all. Even the person I just called djan to his face becomes merely "there
is an x which I have in mind to call djan such that" when I try to talk
about him. Even fundamental logical operations, like instantiation or
generalization become rather transformations of gneralizations, since
there are no instances to get to or from.  Something seems seriously wrong
here.
        But the quantifier=descriptor system as it is laid out is also
incoherent.  We are told that _ci_gerku_ just is _ci_lo_gerku_, which just
is _ci_lo_so'u_gerku_.  From which we can infer that that just is
_ci_lo_so'u_lo_gerku_ which just is _ci_lo_so'u_lo_so'u_gerku_.  And so
on.  And, in the other direction, _ro_lo_ci_lo_nanmu_ just is ultimately
_ro_ci_nanmu_, which, if not ungrammatical, is at least not very sensible.
And if that is not wrong, what about _roda_poi_cide_poi_nanmu_ (or even
_cida_), which is also what the original expression is said to just be?
        I take it that those special cases where quantifiers and
descriptors can be used to describe the same situation in fairly obviously
related ways have been generalized to the claim that correspondingly
parallel sentences involving the two types of expressions will always
describe the same situations.  And this is now thought not to be a lucky
break but a part of the *meaning* of the expressions.  It is not even
obvious that it works at all (part of the reason for the investigation of
which this is a digression) and, if it does, it really is a lucky break,
since, as noted, it is not a part of meaning.  Of course, if it does work,
it will not be a lucky break at all but rather the result of a fiat by the
creators of the language and, hopefully, one that will be made with full
awareness of what is being done. pc>|83