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.
But that is 1) not obviously unfounded and 2) not
not obviously connect with the various things you
mentioned. They are all kinds, I suppose, and
have various subkinds. But they are also just
the sorts of things where the subkind relation is
founded on individuals (I am not sure there are
subkinds that are not so founded, outside of
mathematics perhaps).
> > > > > > 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.
Yes, but you want to make it say something about
the continuum and that takes looking at pairs of
things (between any two there is another, every
pair of sets contains at least one bound, and so
on).
> > 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.)
Well, that is not the apparent question you
raised at the beginning, but of course we do
treat it that way sometimes when we are doing
scientific things. But I doubt that there is a
use of {temci} or other temporal words outside of
specialized contexts that is clearly taking time
as continuous. We tend to measure time and that
gets us into units and definite fractions of
units. At best we take time as continuous when we
think about a thing called "time" rather than
what is happening.
> > > 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.
But they are not indefinitely divided. In any
given case, we stop with fixed fractions of
units. We could, of course, take a more precise
fraction of that unit, but that process cannot go
on indefinitely except in theory. That is, in
theory time is continuous in the mathematical
sense, but in ordinary language we treat it as
discrete, varying the units involved as is
convenient. And it was the latter issue that you
began by raising.
> And in Lojban it is even more clear, because a
> duration is
> {lo navysnidu be li 3.5} and not {3.5
> navysnidu}
Now, that is an interesting point (there was
bound to be one eventually). Lojban doesn't have
units, only measure functions which give raw
numbers. But would we ever say "its duration in
seconds is root 2" as we can say that its length
in inches is? If we can say it (outside of
examples), what does it mean?
> > 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.
We don't even take advantage of the putative
infinite divisibility of time intervals in the
way we do of space, for example. And, of course
(in both cases) scientific work, when striving
for accuracy, always gets down to units that are
not further divisible.
> > > 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.
I am just going — as I took you to be wanting --
on the linguistic evidence. How you conceive it
may well be influenced by all sorts of things,
but your speech always comes out in chunks, like
the dictionary says.
>
> > > 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!
The point is that you don't use all that
continuity stuff; you just use finitely divided
units (thus giving rise to smaller units: deci,
centi and so on). Now, there may be no
theoretical end to how much smaller the units
are, but we don't pursue that in language; we
take a convenient unit and stick with it (for a
sentence or so at least).
> > I am not quite sure how we got off on this
> > interesting 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.
How much more formal do you want than that every
bunch breaks down without remainder (or loss)
into individuals? I even wrote it out in
quasi-formal language and will — when I get a
symbolism I am comfortable with — do it again in
that formalism. What is obscure here?
> > 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).
Yes, that sounds about right. Didn't I say that.
It follows from foundation but could be listed
separately if I didn't before.