BPFK Section: Inexact Numbers
A new set of eyes looked over my files and told
me that I had been oblivious to the fact that you
were talking about at least four different
things, taking them all to be about one — or at
most two. I confess that even with that
information — which does make sense of a few
things — I am often not sure just which of these
things you are talking about. I was also told
that I have been talking about at least as many
different things and not clearly distinguishing
them. Indeed, looking back over what I have said,
I am often not sure now — and probably was not
when I wrote them — which I am talking about.
The most important case pointed out to me was
that my attacks (at least the main one) on the
notion of plural constants was misguided, since
it was about a {lo} which was in collective
predication, a part of your ideal system, not a
distributive one, part of current Lojban or your
reconstruction of that in one of your proposals.
The logical objections to plural constants does
indeed not apply to collective cases (and I agree
that these are the basic cases), although there
are similar practical problems with particular
predicates (and the mirror image problems with
others). The problems with the distributive
cases disappear because these are now explicitly
quantified and so can be dealt with in that way.
You have also dealt with the "no broda" problem
of negated descriptions by moving to a gappy or
many-valued truth system (not clear which). The
problems with pluralities too large or too small
remain and I don't yet see how you will avoid
them, but they are relatively minor and apply
only to some predicates, not all.
As for your comments this time, I take it that
your claim to do without groups is more than a
bit disingenuous. I agree that you do not talk
about groups but you still seem to use them: if
{lo broda} is at any way related to {ro broda} or
{su'o broda} — or {ro da poi broda} and {su'o
da poi broda}, then the logic of the situation
still requires that it be a single thing, whether
it is called a group or a mass or a plurality or
whatever. And, as a collective, it is less open
to the easy confusion between group and members.
You have solved the core of that by getting down
to member only by quantifiers.
I didn't realize that I had said that {lo'i
broda} had a different referent from {da poi
selcmi be lo broda} (I assume that this has a
built in namely-rider so that it has a referent
at all), only different from {lo selcmi be lo
broda}, unless you are identifying them as well,
which seems against something you said elsewhere,
presumably on another topic altogether.
As for the rest of group theory, what can I add?
I have developed it far beyond what I thought I
would need, since my point was to get rid of
groups altogether and move to plural
quantification — explicitly so called.
wrote:
>
> pc:
> > what you say
> > fluctuates back and forth between plural
> > quantification and groups
>
> I use singular (i.e. distributive)
> quantification for
> outer quantifiers (ignoring piPA here, as I
> don't think they
> are properly quantifiers):
>
> PA sumti = PA da poi ke'a me sumti
>
> where {me sumti} means "x1 is/are among
> sumti",
> and PA are the ordinary quantifiers with
> singular variables.
>
> Inner quantifiers are similar in many respects
> to plural
> quantification, but I suspect not quite the
> same thing.
> Groups are very marginal in my system, they can
> be totally
> avoided by using the predicate {gunma} instead
> of the
> "mass" gadri. So I use neither plural
> quantification nor
> groups really.
>
> > > > Come on over!
> > >
> > > Where?
> >
> > To an intellecctually responsible theory that
> > gives you what your scattered wish list would
> > provide if it were feasible.
>
> Let me know when you have worked it out and
> I'll be more
> than happy to take a look.
>
> The bit you were presenting until recently,
> where {lo'i broda}
> and {lo pa selcmi be lo broda} have different
> referents, is
> not something I would want.
>
>
>
>