WikiDiscuss

Posted by pycyn on Tue 09 of Nov, 2004 00:43 GMT posts: 2388

wrote:

>
> pc:
> > Umm, what does "outer quantifiers are always
> > distributive" mean?
>
> That they count the individuals that satisfy a
> given predication
> each by themself. So, for example:
>
> ci lo bidju poi cpana le jubme cu grake li
> panono
> Exactly three of the beads on the table weigh
> 100 grams.
>
> That says that for exactly three beads on the
> table, it can be said,
> of each individually, that it weighs 100 grams.
> It does not say that
> three beads together weigh 100 grams. That
> would be:
>
> lo ci bidju poi cpana le jubme cu grake li
> panono
> Three beads on the table weigh 100 grams.
I would read this last as saying first that there
are exactly three beads on the table and then
that each of them (because I take "distributive"
as the default) weighs 100 grams. That is, I
take the internal quantifier as being the
cardinal of the things described in the
surrounding description (I think this is
traditional Lojban)not as a more indefinite
expression. For the collective weight, I would
say {loi ci bidju poi cpana le jubme cu grake li
panono} — or {ci loi} depending upon whether it
was three out of (perhaps) larger number or the
three was all the beads on the table. This is not
official, but neither is your (rather strange)
suggestion. As I say, let's get this worked out.

> > Distribution is a feature of
> > predicate argument places.
>
> Many predicate argument places allow both
> distributive and
> non-distributive readings.

Yes, and that is why we need a way of marking
which is intended. I would do it first with the
difference between {lo} and {loi} etc., which is
built into Lojban, and then with some sort of
marker for cases where a differnt approach is
required. And also lexically for the predicates
with a unique distriibutivity (probably rather
few). This nicely allows me to talk about some
members of a larger totality in the way that
Lojban has always done — without thereby
committing myself to distributivity — I think
ten of the people surrounding the building can
wear green hats as well as all can.
>
> > Do you mean that the
> > sortal predicate place in which an outer
> > quantifer variable goes is always
> distributive?
> > That is clearly not right ("All those
> surrounding
> > the building wore green hats").
>
> ro lo sruri be le dinju cu dasni lo crino
> mapku
> Each of those surrounding the building wore a
> green hat.

But then there is nothing satisfying the sortal,
since no individual surrounds the building — or
are you covertly shifting to "is involved in
surrpounding the building"? I don't see what is
wrong with the usual Lojban {lo sruri be le dinju
cu dasni lo crino mapku}. But then, as noted,
conventions are needed now, so this may turn out
to be decided to be wrong.
>
> > That it is
> > individual rather than plural quantification?
>
>
> Yes, that's what I mean.
>
> PA sumti = PA da poi ke'a me sumti
>
> where {da} is an individual variable.
>
So, {lo broda} is a set or a group or some such
thing and we have to unpack all the predicates in
separate ways to interpret them. I'm not sure I
like that now that I see there is an alternative
well worked out. {me}, of course, as Lesniewski's
jest', deals indifferently with all of these
cases and the intensional ones as well, and
probably identity, too, when sumti has a
unique referent. Whether it works in conjunction
with the other definitions is not perfectly
clear, but I'll assume it does (not that that
helps any, given the deplorable state of the
other definitions).