Re: tech: logic matters

["Jorge J. Llambias" <jorge@INTERMEDIA.COM.AR>]

I see that the debate on {ro} has not died down during my absence.
That's nice... :)

>pc:
>     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_.

{nairo} can't work (morphologically speaking), because {nai} is always
absorbed by the word that precedes it. I think {da'asu'o} is the right
thing for this. The default for {da'a} is {da'apa}, but I think it
should be {da'asu'o}. This means "all but at least one", but I
understand that you don't like it if you want the quantifier in
question not to have existential import, which is surprising, although
consistent with {ro} getting the import.

> 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).

This works whether restricted {ro} has existential import or not.
Since we are not using restricted {ro} here at all, its import is
irrelevant there.

> 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.

Yes, but then you can't do contradiction! By giving existential import
to {ro}: if you want to be able to do contradiction you need the
weird lack of existential import for "not all". If you want to be
able to do obversion you need the weird existential import for "no".
And you can't do both contradiction and obversion and keep things
consistent! This seems to clearly indicate that lack of import for
{ro} is the simplest choice. Then we can do both contradiction and
obversion, and keep the intuitive import for "not all" and the
intuitive lack of import for "no".

> Importless _nairo_ has only fairly complicated
>translations to unrestricted quantifiers (ganai da broda gi de ge broda
>gi naku brode_).

Right, just as the complicated translation of {ro} with import. A strong
indication that importless {ro} and "nairo" with import are the better
choice.

> Of course, for unrestricted quantifiers, where
>existence is not an issue, obversion and the like go through
>smoothly.

Of course.

> 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 don't understand this last paragraph.

As far as I can tell, this is the situation (I use da'a instead
of {nairo}):

If {ro} and {no} don't have existential import, and {su'o} and {da'a} do,
then:

          ro broda cu brode
        = no broda naku cu brode
        = naku su'o broda naku cu brode
        = naku da'a broda cu brode

i.e. any of the four quantifiers can be obtained in terms of any of the
other three with appropriately placed negations.

On the other hand, if {ro} has existential import, that cannot be done.
In that case, we only have:

          ro broda cu brode
        = naku da'a broda cu brode

          su'o broda cu brode
        = naku no broda cu brode

if neither {no} nor {da'a} have existential import, or:

          ro broda cu brode
        = no broda naku cu brode

          su'o broda cu brode
        = da'a broda naku cu brode

if both {no} and {da'a} have existential import. In one case we can't
do obversions at the restricted quant. level, and in the other case
we can't do contradictions. (With importless {ro} we can do both.)

I'm amazed that you happily entertain having "not all" without import,
(or even "no" with import) and yet so strongly object to {ro} without
import. Why is it that we have the freedom to decide between giving
or not giving existential import to {no} and to "not all", and yet
there is no such possibility when it comes to {ro}?

Jorge