Message-Id: <199602010100.DAA27240@xiron.pc.helsinki.fi>
Date:         Wed, 31 Jan 1996 16:51:43 -0800
Reply-To: "John E. Clifford" <pcliffje@CRL.COM>
Sender: Lojban list <LOJBAN@CUVMB.BITNET>
From: "John E. Clifford" <pcliffje@CRL.COM>
Subject:      tech: logic matters
To: Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 4395
Lines: 95

i,n:
McCawley admits that in
this case, "all [his] bills" includes the possibility of
"no bills".
pc:
Sorry, I was reading this in the light of an earlier case.  Yes, English
"all" is the most uncertain of the universal forms, which is why
logicians, when they are careful, use "every" and "any."  But the
habit of using "all" in logic, even when "every" is meant, is fairly
firmly fixed (alas).

i,n
.  It tells you how to convert
{naku Q} to {naku Q'}, but it doesn't tell you how to interpret
{Q naku}.
pc:
Actually it is from _naku Q_ to _Q'_, since the quantifiers have
inherent negations or not, e.g. from _naku su'o_ to _no_
i,n:
> i,n:
> The other thing that needs to be worked out is how the
> existential-universal interacts with (bridi) negation.
> You may consider it to be a trivial exercise for the
> reader, but it's a significant part of the negation
> paper, and virtually part of the definition of what
> {na} and {naku} mean.
pc:
We have to distinguish cases -- the usual set -- here. For the
unrestricted quantifiers there are no problems, so long as the full
forms are used -- quantifier, variable, compound scope (conditional
or conjunction, usually).  Similarly, there are no problems with the
inward movement in the case of the restricted quantifiers from the
full four-membered set: drop _naku_ and replace the quantifier by its
diagonal opposite.  Outward movement is a little more complicated
in this case, since (my opinion notwithstanding) Lojban is not settled
on the reading of the negative quantifiers, _no_ and (say) _nairo_.  I
think that, as contradictories of quantifiers with existential import,
they lack same and so cannot be obverted into forms involving
restricted _ro_ and _su'o_.  On the other hand, this interpretation
does allow that restricted _no_ is readily interpreted as unrestricted
_ro_ with a negative consequent  _no da poi broda cu brode_ is then
exactly _roda ganai broda gi naku brode_ (and its variations).  If
_no_ (and more often _nairo_) has existential import, this does not
work as well, though obversion (from _no --_ to _ro- naku -_ etc.)
would hold.  Importless _nairo_ has only fairly complicated
translations to unrestricted quantifiers (ganai da broda gi de ge broda
gi naku brode_).  Of course, for unrestricted quantifiers, where
existence is not an issue, obversion and the like go through
smoothly.  The other problem is the exact way to deal with the
collapsed forms of unrestricted quantifiers (once we decide which
those are), since the nature of the implict connection between
subject and predicate changes with the passage of the quantifier.

i,n:
I'm talking about
numbers and you're talking about expressions.
pc:
Gee, it looks like expressions to me: how to say thus and so, with
various suggestions about how to do it, both old and new.  What
have I missed?

i,n:
I cannot quite see the relevance of the emptiness
or otherwise of the universe to any logical statement.
pc:
Well, if the universe could be empty, then a whole bunch of
theorems of standard logic would be false -- all those which started
off with an existential quantifier at least (and I would say the ones
that start with universals as well, but that is controversial, to put it
mildly) -- and many rules of inference would be invalid as they stand
(again, with some variations about which ones).

i,n:
I certainly can't claim
to be aware of _all_ the text, and I (no disrespect) doubt that
you are either, to the extent of spotting whether someone used
{ro} with the intention of allowing the zero option.
pc:
True.  But it has been my experience that anyone who is seriously
claiming -- or saying something that involves the claim -- that the
universe (of discourse, remember) even MIGHT be empty, makes a
big todo about, and I have not seen that todo nor has anyone else
mentioned it.  So, I suspect it hasn't happened.  And, again, it really
is a very unlikely (I am frequently tempted to say "contradictory")
position for anyone to want to take up and talk about.

i,n:
ro da poi te janta fi ro de nagi'a pleji pu li pamu po ro masti
cu jerna panoce'i me'ardi'a be ro lo vo'a selpapri
Is _that_ what you want us to say?
pc:
Beats the Hell outta me!  What might that be in English or symbols?  So, I
guess it is NOT what I want you to say, though I might wish you to espouse
some claim of the same content, said in one of my languages.
pc>|83