Message-Id: <199602072336.BAA20514@xiron.pc.helsinki.fi>
Date:         Wed, 7 Feb 1996 15:11:43 -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: 9897
Lines: 202

lojbab:
The problem is that "ro" is defined as English "all" and hence is currently
ambiguous.
pc:
Actually, _ro_ is defined as the universal affirmative quantifier of
logic and has been since 1955 (through several changes of spelling),
"all" is just the keyword we use and we should use it with all the
caution we should by now have learned to apply to keywords.  So the
problem with English  (which has analogs, if not perfect parallels, in
all sorts of other languages) is not really a problem (but, yes, "every"
would have been a better keyword -- except that it would have
immediately sent folks off in quest of "any," which, as I keep
reminding any who read what I say, we already have covered).
Sanskrit and Chinese logics go down different paths, being much
more intensional from the beginning.  But a corresponding problem
arises and gets solved in about the same way (under translation).

Carter (on lojbab)
>having "ro" NOT have existential import (any?) and rosu'o
> be the version with existentiual import (every?)
Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes (10 yesses outweigh one no :-)
Definitely we need both.  To my mind, the more "logical" choice is to
have "ro"
mean "any" without existential import, while "rosu'o" clearly does explicitly
have the additional "at least one" meaning, for existential import.
pc:
Well, by the principle of parity, 10 yeses reduce to five noes which
reduce to a single -- and remarkably sensible, for Carter -- no.  We
have both and have had since slightly after Carter wandered on the
scene and both are _ro_.  Carter is, admittedly, about the only person
I know who really wants an importless _ro_, since he probably has a
language just for discussing an empty universe -- and, indeed, one
for the inhabitants of that universe to speak.

x:
> (0xSx)xPx is provably exactly equivalent to
>Ax:Sx => ~Px, _no da poi broda cu brode_ means  _ro da cu ganai
>broda gi naku brode_.
Yes, but that one is the same whichever of the two sets of imports
we choose.
pc:
Which one is the same whichever what we choose? The example is
of translation from one idiom to another within logic and within
Lojban, not a matter or choosing anything.

x:
With my choices for imports, these are the conversions:
  ro broda cu brode    =   ro da ganai broda gi brode
pc:
Again, I am not sure what the choice here is.  I guess it is what _ro
broda cu brode _ is an abbreviation for.  I do not know what the
official line is on that at the moment: is it as xorxes gives it or is it
_ro da poi broda cu brode_?  It has changed several times over the
last couple of years and Cowan recently flipped (and then, I think,
flopped back) but he may have been working on some other point
(scope?).  The same question arises for _ro lo broda cu brode_,
maybe independently.  I carefully have said nothing about either of
these two forms with _ro_ not directly attached to a bound
variable.
x:
  no broda cu brode    =   ro da ganai broda ginai brode
su'o broda cu brode    =   su'o da ge broda gi brode
da'a broda cu brode    =   su'o da ge broda ginai brode
(where {da'a} stands for the negative particular, in my case with
existential import).
pc:
These fit together with the abbreviation of  _ro broda_ alright.  By
definition, _da'a_ has existential import.
x:
With your choices of import, the conversions become:
  ro broda cu brode    =   ge su'o da broda gi ro de ganai broda gi brode
  no broda cu brode    =   ro da ganai broda ginai brode
su'o broda cu brode    =   su'o da ge broda gi brode
da'a broda cu brode    =   ganai su'o da broda gi su'o de ge broda ginai
brode
pc:
By parity, the alternative to the above should be that _ro broda cu
brode_ means _ro da poi broda cu brode_, but the chat here seems
to assume that it still means _ro da cu ganai broda gi brode_ (on
the right, at least).  It can't be both, so I am unsure what is going on
here.  What I THINK is going on here is that, if you translate the
four-quantifier system into the two quantifier system, the
translations are long and complex, a not very surprising result.
You get the same sort of change (the mirror images in fact), if you
translate the two-quantifier system into the four-.  Two-quantifier
_ro da ganai broda gi brode_ is four-quantifier _ga no da broda gi
ro da poi broda cu brode_ and so on (_no_ and _su'o_ are the least
different again).  Looks like a good reason to have both systems, as
we do.

x:
I find it especially
useful being able to convert from {naku ro broda cu brode} to
{su'o broda naku cu brode}, and similar things, which are not valid
in your system.
pc:
Again, I suppose this means that this will not work if _ro broda cu
brode_ means _ro da poi broda cu brode_ and so on.  Right, it is
not valid because the first _naku ro ..._ might be true because there
are no brodas, but the second, _su'o broda naku_ would then be
false.  However, with the _da poi_ reading of _Q broda_ , we get
the even simpler _naku ro broda cu brode_ = _xxx broda cu
brode_  (xxx being that missing quantifier, negative and without
import). To move on from there to the two quantifier system is, of
course, as messy as moving from the two quantifier system to this
one.

x:
Are you saying that we don't have to
make a choice because you, or someone else, have already decided that
{ro broda cu brode} has import in Lojban, and it is no longer open to
discussion, or because it is simply illogical to make another choice? If
the former, you may be right, although I certainly don't like it, if the
latter, I disagree. There is nothing in logic that requires that {ro broda
cu brode} --or {ro da poi broda cu brode}, I consider them equivalent--
have existential import. If I understood you correctly, any of the sixteen
choices for the import sets are internally self-consistent.
pc:
I suspect someone has decided whether _ro broda cu brode_  is _ro
da cu ganai broda gi brode_ or _ro da poi broda cu brode_.  It
wasn't me and I don't know what the decision is (this week).  For
all practical purposes I will admit that I did decide that _ro da poi
broda cu brode_ is true only when there are brodas (I do not
remember the details of the debate that introduced the form but I
was certainly on that side of the issue and there is no one else
around willing to admit being in on it).  In any case, the form was
introduced with that meaning and introduced for the purpose of
bearing that meaning.  It seems pointless at this time, after well
over a decade, to change all of that and reduce it to just another
(second?, third?, fourth?) version of  _ro da cu ganai broda gi
brode_.
As for the 16 interpretations of the square, they are all consistent
but most of them are incomplete in the sense that there are
possible states of affairs in which no sentence of that basic form
would be true (e.g., the first, "traditional,"  interpretation -- all
forms with import -- makes all basic sentences false when there are
no Ss, so all the rules about negations fall apart).   This makes
many of them too complicated to use for ordinary business.   There
are a couple of choices other than the two I discussed that will do
in a practical way but the strange arrangements of  imports are not
easy to remember. And, of course, we need to have a form with
_ro_ having import in the four-quantifier system, since we need to
have that for _ro_ in the two-quantifier system.

x:
> Use whichever you like or
>mix and match, just notice what you are doing.
By that do you mean that I can choose the set of imports to use, or are
you saying that I can always use the unrestricted quantifier versions,
over which we seem to have no disagreement?
pc:
Sure, you can always use _ro da ganai broda gi brode_ or whatever
abbreviates it.  Or you can always use _ro da poi broda cu brode_
or whatever abbreviates it.  Or you can use one sometimes (when
appropriate or important or just because you want to) and the other
other times. No surprise there.  But do be aware of which you are
using and what you are committed to.

x:
. Before
this discussion I would not even have thought possible that anyone
would prefer to use your set of choices, but then any of the sixteen
possible choices can be used. Some choices put more limits on the kind
of transformations that are allowed, that's all.
pc:
Before this discussion you did not even know there were 16
choices and did not even know what the question was about.  I will
take it as an article of faith (things hoped for, but yet unseen) that
you do now.

x:
> And don't say that
>something isn't true in one when you mean the other or are getting them
>totally mixed together.
Hear, hear!
pc:
Less cheering advice and more adhering to it, please.

I am getting tired of saying the same thing and answering the same
questions.  In addition I have some serious business to do for the
next couple of weeks.  So, I propose a recess on this thread to give
you all a chance to read what I have dsaid all the way through and
digest it, rather than shooting off a comment as soon as you think it
conflicts with some agenda item of yours.  Note: it does not
conflict with anyone's agenda unless that person has a commitment
either to empty universes or to not having any universals with
existential import, neither of which positions seems to me to have
much point.
A parting summary:
_ro_ commits to the non-emptiness of its domain
in _ro da poi broda cu brode_ that domain is the class of brodas, so
this says there are some
in _ro da ganai broda gi brode_ the domain of _ro_ is the whole
universe of discourse, which is, thus, nonempty, but -- because of
the conditional  and not the _ro_ -- no commitment is made about
brodas.
_ro broda cu brode_ and _ro lo broda cu brode_ each abbreivate one of the
above forms; it is unclear which one, each one abbreviates, whether both
the same or all different.  These forms have the commitments of their
unabbreviated forms.

pc>|83