Bunches
> On 12/1/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > --- Jorge LlambÃas <jjllambias@gmail.com>
> wrote:
> >
> > > 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
>
> It's becoming hard for me to tell what the
> argument is
> about here. My claim is that kinds satisfy all
> the theses
> listed except the foundation one, because for
> the most
> part kinds always have proper subkinds.
>
> The individual dog "Fido", for example, would
> not normally
> be taken as a kind of dog. If someone asks
> "What kind of
> dog do you have?", answering "Fido" would be
> odd.
>
> Whether or not we use individuals in order to
> form our
> conception of kinds is, it seems to me, a
> separate issue.
> Even if it were true in all cases (which seems
> doubtful), it
> does not follow that a system of kinds must
> include
> the foundation thesis.
Well, the way I would do kinds — as collocations
of properties, the foundation thesis is, I think,
derivable, since there comes a point when all the
properties are dealt with one way or the other
and those kinds cannot have subkinds other than
themselves. But you may do kinds differently and
that may well give different results. Or you may
exclude transcendental kinds, which takes an
anti-foundation axiom, I think. I said that some
people did not like individuals as infima species
and took you as saying you were not one of those;
I stand corrected.
In any case, this argument is otiose: the issue
was whether ther was a useful system that did not
have the foundation thesis but otherwise was like
bunches and we have that, thank you, in union of
real line segments (well, I am not sure about
useful, but it is surely good enough for the
purpose at hand: showing that tha thesis is
indepndent of the others).
> > 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.
>
> I can only report that I think of the flow of
> events as
> something continuous. Even when watching a
> movie
> for example, even _knowing_ that what I'm
> seeing is really
> a discrete sequence of images, I can't help but
> seeing
> it as something continuous.
But the issue is not how you think of the flow of
events (loading the issue) or what you say in
English or anything other than what is the
linguistic nature of time in Lojban. And the
answer seems to be that time is always in
measurable intervals each immediately preceded
and immediately followed by another interval.
These intervals may be measured to any desired
degree of precision, that is a measure function
in terms of some unit may take a rational number
with any desired sized denominator (not reals
because you cannot measure irrationals nor even
compute them in one dimension). So, the systems
for measuring times are dense, but what they
measure are discrete.
All of which is again largely irrelevant. I did
not claim that time was discrete or even that
Lojban treats time as discrete — that was
attributed to me by xorxes to cover his
misreading of a Lojban word. However, as you
see, the claim that Lojban treats time as
discrete can be carried quite a ways. Whether it
is far enough to give a definitive answe, I am
not sure. And, as I have said before, I don't
really care, since nothing seems to hang on the
answer at the moment.
> > 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?
>
> I don't think one would normally say that the
> length
> of something in inches is root 2. I don't see
> much
> difference in the way we measure lengths and
> durations.
Well the length of a diagonal of a unit square is
root 2. That one comes up a lot.
> > We don't even take advantage of the putative
> > infinite divisibility of time intervals in
> the
> > way we do of space, for example.
>
> I see no significant difference in the way we
> treat space
> and time. In fact cross metaphores are very
> prevalent.
They are in English and that habit has been built
into Lojban, so I suppose that we havce to say
that Lojban treats them the same. But, of
course, Lojban taks space as coming in discrete
chunks, measured rationally (although in two or
more dimension you can compute irrationals so
they can come in as well).
>
> > > 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?
>
> It's not exactly obscure, I can intuitively
> understand
> pretty well what it means. But I see nothing
> close to
> a formalization (of that particular thesis)
> yet.
As you are fond of saying in similar situations,
what exactly do you want? I hope that, as I do,
you will give a fairly precise answer.
I gather that the point is that there is no
thesis that says directly "Every bunch breaks
down without remainder into individuals" although
(for finite bunches only, admittedly)the
foundation thesis (what I am calling ...) does
amount to that by induction. But even that
presupposes something to induce on and the
symbolism does not yet have that — the depth (or
cardinality) of a bunch. As noted, we could go
over to the corresponding sets and work it out
there but it would be nicer not to have to use
that apparatus. I have a few variant systems
which look promising for getting this point
across (and, if worse comes to worst, I can
always check out the various systems that batches
represent to see how they do it.)
> xod wrote:
> > That we generally refer to non-zero intervals
> of time does not
> > mean that we treat it as discrete. Those
> interval endpoints can be
> > situated anywhere in the timeline, and that
> means we treat it as
> > continuous.
>
> I agree.
No, by defintion thend points are always
immediately adjacent to another event — the
previous and the next. There is no timeline on
which they are laid out; the timeline is in
Lojban (if it can be done at all) an abstraction
from sequences of intervals — the rest is not in
the language but in what is said in the language.
> > Furthermore, people refer to instants and
> moments which have
> > no duration, like a point in space has no
> size. A pixel, however, does
> > have size. And there is no analogous
> time-pixel in English.
>
> I think "moments" are sometimes thought of as
> having duration
> ("wait a moment" for example) and sometimes as
> points.
> dictionary.com has:
>
> 1. A brief, indefinite interval of time.
> 2. A specific point in time, especially the
> present time: He is not
> here at the moment.
In any case, that ia bout English, not Lojban.
There are no time points in Lojban, only
intervals of time.