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logical issues (lambda,ka, man-dogs, etc.)
Finally getting around to reading the last week's messages, I am
reminded again that Lo??an's claim to be a logical language in the sense of
being based upon the language of formal logic is under another series of
assaults. I have not been very effective at turning back the previous ones,
so the claim is pretty weak anyhow, but I would like to suggest that,
before we tinker some more, we do all stop to look where we are in this
respect, where we want to be, and -- rather importantly -- what logic has
to say about the matters at issue. Within that framework, we can then
discuss somewhat more clearly what to do. I do not want to limit the
discussion to those who do their homework, but I am not going to pay a lot
of attention -- at least until things get desperate -- to someone who shows
signs of not knowing what logic has done or not done in a given area. As
a sort of minimal entrance requirement, I would recommend the relevant
sections -- when there ae some (and there usually are) -- of McCawley's
"Everything that Linguists have Always Wanted to Know about Logic"
(U/Chicago Press -- I have the old, '81, edition to hand, but there is one
from a couple of years ago that updates matters slightly). After that, we
may have to go occasionally to Gamut or Kamp or the Handbook of
Philosophical Logic, but hopefully not often.
A few examples of what was already there to head off some of our
The talk of types, which is already beginning to appear in the
discussion of lambda, makes little sense in Lo??an, since the langugae is
basically reductive, taking all types as individuals -- the exception being
predicates predicating, but their characteristic functions and their senses
and other things that might count as their extensions are all
descriptors and bound by da variables.
We could do a number on the logician-linguists though, for they
are not too good on distinguishing sets and characteristic functions, for
example, and especially on sorting truth value functions and propositions
We could have saved a month or so by noting the forty-year-old
proof that no first-order linear device can represent independent
quantifiers in the scope of a more powerful one. That leaves the (not quite
so old) choice of using second order devices (which turn out to be
individuals in Lojban, in all probability) or devising non-linear structures
which can still be represented in a linear language (spoken, for example,
rather than spread out on paper). We have gotten to suggestions of that
sort now (excepting xorxes' use of _ce_, which is too deeply linear -- but
_joi_ might work) but it did take a while.
McCawley gives a nice test to demonstrate that restricted
quantifiers have existential import inherently, not just as a conversational
implicature, a matter that has been of some moment here from time to
time. That does, of course, go along with the situation for unrestricted
quantifiers but also leaves the best treatment of quantified descriptors up
in the air with, alas, most of the matters about plural objects (logic just
avoids these and linguists get mixed signals from their own work).
McCawley's mapping of lambdas onto English is not going to fit
perfectly with the hard cases in Lojban, because Lojban treats a number of
items in different clusterings from the way English does (events and
propositions apparently together, for example -- but, as noted, the
logicians are not too good on those anyhow).
So, let's take a break on all this deep stuff and come back with a
renewed sense. Or, let us spend some time figuring out where we are and
where we want to be, before we get back to arguing changes.