Bunches
On 12/1/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> --- Jorge LlambÃas <jjllambias@gmail.com> wrote:
> > On 11/30/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> > > Things we might really use that satisfy all the
> > > theses not tied with foundation.
> >
> > Dogs, unicorns, events of running, theories,
> > lies, all kinds of things.
> >
> I'm not sure whether you, the at least occasional
> champion of contextual relevance, have here
> brought in some totally irrelevant set of theses
No, just the ones you have listed.
> or whether you have some (unnamed) relation and
> operator for each of these sets that satisfies
> all the theses for "in" and "+" on the Bunches
> page, except those that rest on the foundation
> thesis.
No, not any unnamed relation, just the "subkind" relation
I named the first time I mentioned kinds.
> > > > > Well, {ru'i} doesn't seem to have anything to do
> > > > > with the continuum; it merely means "without
> > > > > significant interruption" "whenever there is an
> > > > > occasion" even.
>
> Nothing even linguistically. And if it did, it
> would say that time is not even dense, let alone
> analogous to the real line, since ti says that
> there is nothing between two occurrences of the
> event called continuous.
Why two occurrences? It says something about the one event
being continuous.
> As for other linguistic
> evidence, we note that we have concepts like
> "next," {lamji} which clearly apply to time and
> suggest a well-ordering, not even a dense one
> again.
I don't and never disputed that we often treat time discretely.
{<number> roi} is the clearest example in Lojban for that,
I think. The question at hand is whether or not we sometimes
treat it as if it were continuous (independently of its true
physical nature.)
> > So when you ask how long something took, you
> > expect
> > some number of indivisible chunks as an answer?
>
> Yup — and that is what I get: a day, a second,
> 3.5 nanoseconds, and so on.
You take 3.5 nanoseconds as counting half-nanoseconds?
Otherwise, if nanoseconds are treated as indefinitely divisible,
it sounds as a continuous measure.
And in Lojban it is even more clear, because a duration is
{lo navysnidu be li 3.5} and not {3.5 navysnidu}
> Always with a unit
> (by definition in Lojban's case) and always with
> a discrete total. I suppose it is conceivable
> that someone say "root 2 seconds" but I would
> take that to be some sort of scientific talk,
> since I don't see how he would have measured it.
You take the fact that we don't normally use irrational
numbers as measures as evidence that we consider
things to be discretely (and finitely) divisible? Very
interesting point of view, even if hard to understand.
> > I always thought x1 of temci was a continuous
> > interval
> > rather than a (very large?) number of (very
> > small?) chunks.
>
> That is about what it is scientifically, perhaps,
> but not linguistically, where the answer is
> always in terms of (variously sized) chunks.
No, I'm not talking about it scientifically, I mean in ordinary
contexts. I cannot normally conceive of durations as strings
of little time-chunks. It never occurred to me that others
would think of that as the natural point of view.
> > If you mean that the x1 is one chunk, then the
> > system of
> > time chunks seems to satisfy all the theses not
> > tied with
> > foundation.
>
> Well, the system of sizes of time chunks is
> probably dense (not a continuum. since the lower
> bound is outside the system, not being an
> interval). But on any given occasion the answer
> is linguistically in terms of some unit.
> Scientifically, this may be an approximation, but
> we were after the linguistic facts here, not the
> scientific.
There are many units that measure continuous quantities,
so I don't see how the answer being in terms of a unit
makes it a bunch measure. Especially if you allow fractional
measures!
> I am not quite sure how we got off on this
> intersting but so far rather useless discussion
> (nor do I care). So, back to the point: any
> additional theses that seemed to be required for
> bunches?
It would be nice to have the foundation theses expressed formally.
I'm not quite sure how that would go.
> Any surprising consequences of these
> theses — particularly ones that show the set
> inconsistent?
I can't see anything strange in them.
> Independence proofs for anything
> other than the foundation thesis?
None of the others seem especially noteworthy to me.
The "no empty bunches" is slightly ambiguous. What does
"empty" mean? I take it it does not mean that every bunch
has at least one bunch in it because that follows directly
from every bunch being in itself, so I suppose it means that
for every bunch there is at least one *individual* bunch in it.
I would say this thesis goes closely together with the
foundation one (and it is in fact stated in the same
parenthetical comment).
mu'o mi'e xorxes